The Last Stoic

Expanding Consciousness in a Living Systems Universe

2011-10-01T10:25:00.000-07:00

EXPANDING CONSCIOUSNESS IN A LIVING SYSTEMS UNIVERSE
Ralph Metzner, Ph.D.

California Institute of Integral Studies

The word consciousness is derived from the Latin con-scire - “with-knowing”. We can ask “knowing-with” - what? A relational, or systems, view is implicit in this etymology: pointing to the relation between subject and object, between the knower and the known. Conscious knowing (con-scire) is knowing with knowing that you know. This can be contrasted to the unconscious knowing involved in my knowing how to grow hair, or skin cells over a wound; and my knowing how to tie my shoelaces, or ride a bicycle, which has become a kind of unconscious or automated knowing.

Historically there have been two main metaphors for consciousness, one spatial or topographical, and one temporal or developmental. The topographical metaphor is expressed in conceptions of consciousness as like a territory, a terrain, or a field, a “state” one can enter into or leave; or like empty space, as in Buddhist psychology. The spatial metaphor, can lead to a certain kind of fixity in one’s perception or worldview, a craving for stability and persistence, and anxiety about change. From this point of view, ordinary waking consciousness is the preferred state, and “altered states” are viewed with some anxiety and suspicion, -- as if an “altered” state is automatically abnormal. In many ways this is the attitude of mainstream Western thought toward alterations of consciousness—even the rich diversity of dreamlife and the changed awareness possible with introspection, psychotherapy or meditation is regarded with suspicion by the dominant extraverted worldview.

The temporal metaphor for consciousness is seen in conceptions such as William James’ “stream of thought”, or the stream of awareness, or the “flow experience”, as well as in developmental theories of consciousness going through various stages. Historically, we see the temporal metaphor emphasized in the thought of the pre-Socratic philosophers Thales and Heraclitus, in Buddhist teachings of impermanence (anicca) , and in the Taoist emphasis on the flows and eddies of water as the basic patterns of all life. From this point of view, wave-like fluctuations of consciousness are regarded as natural and inevitable, and health, well-being and creativity are linked to one’s ability to tune into and utilize the naturally occurring, and the “artificially” induced, modulations of consciousness.

According to Immanuel Kant, “space” and “time” are the a priori categories of all thinking. It seems appropriate that these are the two most common metaphors we have come up with in our reflections on consciousness. Perhaps the most balanced way to think about consciousness would be to keep both the spatial and the temporal metaphors in mind. We can recognize and identify the structural, persistent features of the perceived world we are “in” at any given moment, and we can be aware of the ever-changing, flowing stream of phenomena in which we are immersed. Heraclitus, in addition to the oft-quoted “you cannot step twice into the same river”, expanded on the metaphor by also saying that “when we step in the same river, the flowing water is always different and new.”

The definition of consciousness proposed by the Russian mathematician and physicist Victor Nalimov, in his book Realms of the Human Unconscious, is one that integrates both the topographical and the temporal aspect: he calls it a “semantic continuum”, i.e. a “continuum of meaning”. A continuum is defined as a “continuous extent, succession or whole”, which can be divided mentally into parts, but also considered as a whole. A continuum of meaning, like the sensorium of sense perception, conveys something of the elusive quality of consciousness, -- both stable and mobile, integrative and differentiated.

In contrast to cancient, Eastern and indigenous views, Western science in general and psychology in particular has never been comfortable with the study of the subjective side of life, with qualities of experience, purposes, intuitions, altered states or spiritual aspirations. Under the sway of the Newtonian-Cartesian mind-matter dichotomy, consciousness and experience were seen as belonging to the realm of religion, and science agreed to stay out of it. Later, as the ideological hold of the Church diminished and the materialist paradigm became paramount, consciousness and all subjective experience became even more firmly banished from scientific discourse.

In the 19th century, the German social philosopher Wilhelm Dilthey attempted to establish the “mental sciences” (Geisteswissenschaften), on an equivalent footing to the “natural sciences” (Naturwissenschaften). This idea never really took hold in the English-speaking world. Instead, the social sciences (psychology, sociology, anthropology, political science) adopted and imitated the empirical observational and quantitative analytical methods of the natural sciences. In psychology, the only observations that qualified as “scientific” were observations of behavior—to the extreme of B.F. Skinner’s behaviorism, in which mental states were said to be in an unknowable “black box”. Although the influence of strict behaviorism in psychology has waned in the latter half of the 20th century, the ideological commitment to a materialist worldview has not. In the leading paradigms of cognitive psychology or cognitive science (which includes brain sciences, computer modeling, information systems and the like) consciousenss is still treated as something to be explained (i.e. explained away) in the supposesdly more “real” terms of “neural nets”, “brain circuits” and the like.

In the latter half of the 19th century a European philosophical movement took a completely different and new approach to the study of consciousness. The German mathematician/philosopher Edmund Husserl (1859 - 1938) originally conceived of his phenomenology as an attempt to rescue philosophy and the quest for absolute knowledge from the “naturalism” and relativism of the newly arising experimental psychology. He criticized the psychophysical method of Wilhelm Wundt and G.T. Fechner as providing only correlations between subjective events and physical events, and ignoring the possibilities of “pre-understanding” of what consciousness was essentially. For Husserl, the abstract truths of mathematics are essences that are grasped by the mind directly, without relative or empirical observation. He proposed phenomenology as the method for directly arriving at essential and universal knowledge about the nature of consciousness and meaning, in part by clarifying the implicit pre-understandings that underlie other psychological approaches.

A core concept of Husserl’s phenomenology of consciousness is intentionality : consciousness is always intentional, always “of” or “about” something, always directed, like an arrow or a mathematical vector, toward some object of meaning. The objects that consciousness intends can be external, or they can be internal aspects of our own experience. Because intentional consciousness is always “constituting” the essential features of the various domains of existence, both external and internal, consciousness has a fundamental “ontological priority”—it is the “supporting ground of reality”. The focus on intention as the fundamental constituting attribute of consciousness is congruent with the emphasis on “set (and setting)” as the prime determinants of altered states, which I shall discuss further below. The ontological primacy of consciousness in Husserl’s phenomenology is consistent with the worldview of the mystics in Eastern and Western traditions as well as the insights coming from profound altered states.

A further innovative contribution to the phenomenology of consciousness was made by the French philosopher Maurice Merleau-Ponty (1908 - 1961). In his work, the focus of interest shifts from the subjective mind to the subjective body, or bodily experience (le corps propre). For Merleau-Ponty, perception is an inherently creative, participatory activity between the living body and its world. All subjectivity or consciousness presupposes our inherence in a corporeal world, a world that we perceive as the having depth, intimacy and horizon. The ecophilosopher David Abram has shown, in his work The Spell of the Sensuous, how in many ways Merleau-Ponty’s later thought anticipates the deep ecologists and others who are looking to develop a new conscious awareness of our embeddedness in the world of Nature.

The American philosopher William James (1842 - 1910) approached the psychology of consciousness in his characteristic multifarious manner. He may have been the first person to use the concept of “field” in talking about consciousness: human beings have “fields of consciousness”, which are always complex, -- containing body sensations, sense impressions, memories, thoughts, feelings, desires and “determinations of the will”, in fact “a teeming multiplicity of objects and relations.” He made it clear that his famous “stream of thought” image actually meant not just thoughts, but images, sensations, feelings, etc. He wrote that “the mind is, at every stage, a theater of simultaneous possibilities”. This idea is reminiscent of C. G. Jung’s conception of personality structure consisting of an aggregate of psychic entities or complexes: the persona, the shadow, the ego, the anima, the animus, with the Self forming the superordinate whole that includes all the parts, both conscious and unconscious.

William James explored the paranormal and mystical dimensions of consciousness, that usually lie outside the boundaries of scientific interest. He pursued a life-long interest in the phenomena of sub-liminal consciousness, what he called “exceptional mental states”, including those found in hypnotism, automatisms, such as sleep walking, hysteria, multiple personality, demoniacal possession, witchcraft, degeneration and genius. James’s interest in unusual states of consciousness led him to experiment with nitrous oxide, or “laughing gas” as it was then known, an experience that reinforced his understanding of transrational states of consciousness. He wrote that the conclusion he drew from these early “psychedelic” experiences was “that our normal waking consciousness, rational consciousness as we call it, is but one special type of consciousness, while all about it, parted from it by the filmiest of screens, there lie potential forms of consciousness entirely different.”

James wrote the above statement in his The Varieties of Religious Experience, probably his most influential book. In it he explored with great discernment and eloquence the nature and significance of mystical or “conversion” experiences, by which he meant not only a person’s change from one religion to another, but the process of attaining a sense of unity and the sacred dimension of life. In my book The Unfolding Self I adopted James’ empirical, comparative approach to the study of transformative experience — delineating the basic archetypal patterns of psychospiritual transformation.

It is only recently, in re-reading William James’ writings on his philosophy of radical empiricism that I came to realize that this philosophy actually provides the epistemology of choice for the study of altered states of consciousness. James started with the basic assumption of the empirical (which means “experience-based”) approach: all knowledge is derived from experience. Radical empiricism applies this principle inclusively, not exclusively: James writes:

To be radical an empiricism must neither admit into its construction any element that is not directly experienced, nor exclude from them any element that is directly experienced. For such a philosophy, the relations that connect experiences must themselves be experienced relations, and any kind of relation experienced must be accounted as ‘real’ as anything else in the system. (James, 1912/1996, p. 42)

Observations made in objective external reality perceived through our, aided and unaided senses, do not have an ontological priority and do not give “privileged access” to truth or validity. All knowledge must be based on observation, i.e. experience; so far this view coincides with the empiricism of the natural and social sciences. It’s the second statement that is truly radical and that explains why James included religious and paranormal experiences in his investigations. The experiences in modified states of consciousness are currently excluded from materialistic, reductionistic science, as are all kinds of anomalous experiences, such as UFO abductions, near-death experiences, and mystical or paranormal experiences. They need not and should not be excluded in a radical empiricism.

From the perspective of radical empiricism, it is not where or how observations are made that makes a field of study “scientific”, it is what is done with the observations afterwards. Repeated systematic observations from the same observer, and replicating observations from others, is what distinguishes the scientific method from casual or haphazard observations, or those made with intentions other than gathering knowledge. Whereas the ideology of fundamentalist scientism does not permit the objective investigation of subjective experience, the epistemology of radical empiricism posits that it is possible to be objective about subjective experience, using the accepted canons of the scientific method. The methodology of systematic introspection, and phenomenology, are the beginnings of such a more inclusive approach.

In Eastern systems of yoga and meditation, it has long been understood that reliable and replicable observations can be made in the interior landscapes of our experience. The meditative practice of “mindfulness” is exactly an attitude in which objectivity is added to the primary given (or “data”) of the experience. Religious texts describe the characteristic kinds of observations that a practicioner in a particular tradition may expect to make. This is, in essence, no different than a scientific text that describes the kinds of observations a student of biology can expect to make when looking through a microscope.

One of the most exciting consequences of adopting a worldview and epistemology in which no sources of new perceptions and observations will be ignored because of their provenance, leads to the opening up of vast new fields and possibilities of understanding, and a renewed bringing together of spiritual and scientific understandings into an integrated worldview, or sacred science.

In a systems view of humans and universe, a relational view of multi-level interconnectedness, things, objects and persons are temporary nodes, in ever-changing patterned relations with other nodes. All being is interbeing, in Thich Nhat Hanh’s felicitous phrase. Consciousness then is the experiential side, the knowing, feeling, sensing, imaging of relations, the “knowing-with”. It is the subjective, inner, concaveness of the transparent hollow sphere we call the space-time continuum; of which objective, outer, convexity is matter and energy, in their ceaseless transformations. According to Buddhist teachings, the inside of the sphere is empty, void, sunyata – hence no things, objects or persons actually exist. However, through the magic power of projection or maya, we seemingly perceive an objective universe, “out there”, of infinite differentiation and diversity.

The wise elder Thomas Berry, theologian turned evolutionary cosmologist, says that in the evolutionary transformation civilization is now going through, the transition from the cenozoic to the ecozoic era, our perspective on the world will change from seeing and measuring it as a “collection of objects”, to knowing and experiencing it as a “communion of subjects”. In other words, a living systems worldview, in which the conscious communion of living subjects is acknowledged as equally real and valid as the conscious perception of identifiable objects. We don’t need to stop utilizing the powerful methods science has developed for analyzing the complexities and details of our world; we add to them the inner, sensuous, feeling-based, aethestic appreciation of the essential oneness of the ever-transforming web of life.

Oneness and differentiation exist at every level of reality. The ecologists have made us aware of how the diversity of life, biodiversity and its preservation is the core requirement for sustainability. To this, the anthropologists and historians of culture have added the recognition of the importance of preserving cultural diversity – for the unique knowledge system or tradition that each culture has developed. As a psychologist, I would want to add to the celebration of diversity, an acknowledgement of the rich psychic multiplicity of our psychic inner life: we are all multiple personalities, each of us containing a “theater of simultaneous possibilities”. Learning from indigenous cosmologies as well as the spiritual traditions of ancient times, we may well want to return to a recognition of the animistic polytheism of our forebears, recognizing and celebrating the indwelling spiritual intelligences of all inorganic and organic life-forms, as well as of Earth and other planets, Sun and other stars, Milky Way and other galaxies, and Universe. As Buckminster Fuller said, wanting to include the metaphysical as well as physical in his definition, “Universe is everything that we can experience.”

The Centrality of Intention and Question

We have seen how in the phenomenological approach to the understanding of human consciousness, “intentionality” is the central organizing concept. Consciousness is said to always be “about” something; or, we are always “conscious of” something. The “mental status” examination in cases of shock or psychosis, asks whether the patient is oriented in time and space (do you know where you are? what day it is?). We have also noted how psychedelic and other altered states of consciousness can best be understood if one inquires into the “set” (= intention) that preceded or accompanied the catalyst that triggered the movement in consciousness. Carlos Castaneda, in his writings on the principles of Yaqui, or Toltec, sorcery, emphasizes repeatedly, that “intent” is the master key to sorcery; where sorcery may be defined as the intentional use of altered states, such as conscious dreaming, to acquire and exercise psychic power.

Following Michael Harner, I define shamanism as the intentional practice of altered states, called “shamanic journeys”, for healing, problem solving and guidance. In shamanic indigenous healing practices, as in ordinary medicine and psychotherapy, the intention is given by the problem or illness the patient brings to the practicioner. Indeed, it is perhaps too obvious to state, that in any situation, any state of consciousness, inquiring into the intention the person is holding, is a way of directing awareness to the experiencing subject or self, the starting point, the original orientation. In divination, which may be defined as the intentional use of the enhanced perception of altered states ( and sometimes divinatory tools such as cards or runes) to acquire knowledge and spiritual guidance from the divine of spirit world, conscious intention again provides the master key.

Intention, or “interest”, as William James phrased it, controls the selective function of attention, which in turn determines what it is we perceive or become aware of. We may express these relations as follows:

intention -> attention -> awareness

If our attention –perception is not guided by our conscious intention or interest, then it will be captured, or captivated, by whatever attractive, intense, insistent, prominent stimulus patterns present themselves to our sensorium.

Through my work with divination practices, both in the context of psychotherapy, and in the context of shamanic rituals using expanded states of consciousness, I have come to understand that the basic formula for divination is that of asking questions and receiving answers. Even when a mantic procedure, such as the I Ching, or casting runes, or laying out Tarot cards is used, inherent in the procedure is a question posed and an answer received (which may need to be interpreted). Divination in the context of healing aims at finding the origin or source of the illness – which in traditional societies may be attributed to sorcery in as many as 50% of illnesses. In Western medicine this process is called seeking a diagnosis, the origin and nature of the infection or injury. The primary difference between the indigenous shamanic approach in healing divination and the Western medical approach, is that traditional divination involves an induced altered state of consciousness, and asking questions of the practicioner’s tutelary spirits; whereas the Western approach involves highly focussed and detailed observations, supplemented by specialized instruments, in the ordinary waking state of conciousness.

The biologist Rupert Sheldrake has pointed out that the process of divination to obtain knowledge -- of the world, the environment, anything concealed or not understood, possible future outcomes – is a questioning process exactly analogous to the scientific experiment in Western science. The experiment is a precisely controlled situation, where detailed observations can be made to answer questions we are posing to Nature, the world, the environment, etc.

One can see then that intention and question are like two sides of the same coin, two equivalent ways of guiding our attention and perception, in both ordinary and non-ordinary states of consciousness. For example, if I am wanting to heal the effects of a childhood trauma, whether through shamanic soul retrieval work, or therapeutic regression, I can state my intention and say: “I want to (am interested, or aiming to) heal the effects of this trauma”; or, I can ask: “How can I heal (and integrate) the effects of this trauma?” There is a dynamic (yang) and receptive (yin) polarity here: the intention is focussed, directional, searching, seeking; the question (any question) is a basic gesture of receptivity and opening. If I ask a question of someone, I am placing myself in receptive mode to hear their answer. We can present the differences in these two ways of deploying attention by the following analogies:

Intention Question
psychic polarity dynamic receptive
process analogies hunting, tracking gathering, collecting
instrumental analogies arrow basket
mathematical analogies vector attractor

Levels of Consciousness in Shamanistic Cosmology and Living Systems Universe

Spiritual seekers and yogic meditators have described a universe of many levels of of reality and consciousness, to which we can gain access through various practices of consciousness expansion, though in ordinary life we are rarely, if ever, aware of these other “higher” dimensions. The Sufis say we are like a man who has a seven-story mansion, but who lives only on the ground floor, the most polluted, cluttered and unattractive parts of his mansion; to the point where he has completely forgotten that the other, grander rooms even exist, much less how to get there. The techniques of finding access again to these higher realms, is therefore a kind of memory exercise – often referred to in the literature as “recollection”, or “remembrance”.

We may formulate the relationship between states of consciousness and levels, planes, or worlds of consciousness as follows: in the ordinary waking state of consciousness, our awareness and identity is generally focussed on the level of ordinary, consensus reality. In meditative states, some dreams, expansive psychedelic states, mystical and visionary states, we may find ourselves seemingly in other kinds of reality altogether, other realms, other worlds. These other realms are then known to always exist, and we always to have potential access to them. Spiritual and shamanic practices are designed to intentionally allow us to move into and through these other realms, in which we can find sources of healing or spiritual knowledge, conveyed to us by spiritual teachers, elders, ancestors, angels, spirit animals or spirit guides. We call such practices of intentional access divination, as discussed above.

The level of “ordinary reality” is often called the physical or material plane, which implies the other planes are metaphysical or non-material (e.g. subtle, etheric). This ordinary, ground-floor level is also referred to as the time-space world, implying that in the other levels the laws of time and space as we know them don’t apply, or are different. This notion is readily verifiable when we recall that in dream states we can seemingly visit with, talk with, interact with, a person known to us, say a grandmother, who objectively lives thousands of miles away, or indeed may even be dead, and yet we traverse no space, and take no time, to get there. We also do not question the reality of a contact with a “dead” person. This malleability of the time-space framework is the reason why divination can reveal knowledge of probable futures, called “visions” (which are not “predictions”, as the dictionary definition of divination erroneously has it).

There have been numerous mappings of the different realms and levels of consciousness in the spiritual, meditative, and esoteric traditions of the world, and to compare and coordinate them all is a task far beyond my capability and the space limitations of this essay. I will briefly describe here, for illustrative purposes, (1) the traditional shamanistic cosmology; (2) a version of the seven-level map commonly found in the European and Asian esoteric, perennial and theosophical traditions; and (3) three of the many possible dimensional mappings that can be identified in a living systems worldview .

Those who have embarked on a serious psychospiritual practice of consciousness exploration using shamanic and yogic technologies, who are willing to trust their own experience more than the received views and concepts they have taken on faith, tend to find themselves gradually awakening to a vastly expanded and different worldview. I should point out however that many features of the traditional and newly revived shamanic-animistic worldview appear to be quite compatible with the most recent, growing edge theories of post-modern science. There is not the space here to enter into a discussion of these convergences in any detail. I will merely mention the particular relevance of ecology and living systems theory, as described for example in Fritjof Capra’s book The Web of Life; the Gaia theory of James Lovelock and Lynn Margulis; Rupert Sheldrake’s theories of morphogenesis; David Bohm’s “holomovement” interpretation of quantum theory; the integrative and synergetic cosmology of Buckminster Fuller; and the evolutionary cosmology articulated by Brian Swimme, Thomas Berry and others.

There is one fundamental commonality among the shamanic, Asian meditative, esoteric and living living systems worldview, and that is in their conception of the fundamental reality of the universe. The fundamental reality of the universe, according to the most ancient, and the most recent, post-modern formulations, is a continuum, a unitive field or fabric or process, of both energy and consciousness, that is beyond time, space and all forms, and yet somehow mysteriously within them; simultaneously transcendent and immanent. In traditional Asian religions, this unitive field is variously referred to as Tao, or Atman-Brahman, or Tantra (meaning “web” or “fabric”) or the “jewelled net of Indra.” Some Native North Americans refer to it as Wakan-Tanka, the all-pervading Creator Spirit. In the traditional Anglo-Saxon religion of the British Isles it was called the Wyrd, an invisible network of magical forces. In theistic religions like Christianity, this oneness corresponds to what is called the “Godhead”, a spiritual Beingness beyond the personal deity. In esoteric writings it is variously called The One, Absolute Beingness, the All That Is. In the systems language of post-modern science it is seen as an infinitely complex, multi-level system of interrelationships, or “web of life.”
(1) Shamanistic Cosmology. Worldwide, shamanic practicioners speak of a three-fold division of upper, middle and lower worlds. The names reflect the primary movement of the shamanic traveller, when engaged in divinatory practice. A journey to the Lower World, initiated by intention, and energized by psychoactive plants or rhythmic drumming, involves a downward movement in consciousness, into a cave, or opening, or tunnel – from which one emerges after a time to track the objects of one’s quest. Lower World journeys seem to be especially relevant for problems of healing, as if the traveller were actually “going down” into the material microcosm of the earth body. Upper World journeys involve ascent – through flying, soaring, climbing a World Tree or axis – and visiting light, airy worlds, with expansive vistas and luminous structures. These kinds of journeys may be involved when the shaman wishes to look ahead, “see” hidden realities, or envision future probabilities. In Middle World journeys, the movement is straight across, but may involve all kinds of strange, weird, magical, unusual places and beings – such as enchanted forests, magical castles, wastelands and wilderness. The characteristics of upper, middle and lower world journeys, as reflected in myths and fairy tales, as well as shamanic accounts, are described in more detail in the chapter on “Journeys to the Place of Vision and Power”, in my book The Unfolding Self.

Whereas the cosmography of three worlds is most often found, there are also mythic-shamanic traditions of five, or seven, nine or more worlds, often arrayed around a central World Tree or Axis Mundi. In the Nordic-Germanic mythic worldview, there are nine worlds arranged on the World Axis-Tree Yggdrasil. In the center is Midgard, the familiar ordinary world of humans, animals, and Earthly life; pathways go from this world to all the other worlds, which knowledge-seeking shamans can learn to find and travel. There are two worlds on the central axis above the Middle Earth realm: the World of Elves, who are light, airy spirits, and the World of the Aesir Sky Gods. Two worlds are vertically below Midgard: the World of Dwarves, or Dark Elves, the spirits of stones and minerals, and the world of Hel, the death goddess. Then there are four other worlds, in the same horizontal plane as Midgard, in the four directions: the World of Giants in the East and the World of Vanir Earth Deities in the West; in the North and South, two uninhabited worlds, of pure ice and pure fire respectively. I describe both ecological and mythic symbolic meanings associated with these nine worlds in my book on the Earth-Wisdom mythology of the Nordic-Germanic people, The Well of Remembrance. In myth and folklore of the European people, there is sometimes only one name for all the non-ordinary, nonmaterial realms that we humans may come across: they are called “Spirit World”, “Otherworld”, of “Faery World”.

(2) In esoteric and thesosophical traditions we usually hear of seven levels of consciousness, differing in vibratory rate or density, with the physical-material as the “lowest” or densest. We have a series of bodies, which are the bodies we occupy in the corresponding realm or world. Just as the physical body is the body we move around in while in the time-space physical world, the astral body is our body for functioning in the astral world or realm. Leaving aside for the moment the question of the different terms and names used for the different levels or realms, in the experiences of contemporary neo-shamanic practicioners, with or without mind-moving substances, experiences of visiting other worlds are quite common. Also, of course, they are accessible to us in dream states, and in meditative states. Alternatively, the person may feel that the veils, barriers or screens between worlds can become transparent or porous, so one can see and be in both the ordinary and the spirit world at the same time. In William Blake’s famous lines, “if the doors of perception were cleansed, everything would appear as it is – infinite”.

The mappings of different levels of consciousness or worlds, are based on accumulated observations by thousands of explorers and elders in the various spiritual traditions. In other words they are empirically based, just like maps of an unknown geographical area are based on accumulated observations; these maps then become available to be used by subsequent explorers. An individual explorer, using yogic, shamanic or meditative methods of journeying in consciousness, could, in theory, verify the accuracy of the mappings for him or her self. In practice, when we begin our explorations, we are not usually able to identify the particular worlds we are in. The dreamer, for example, may realize he is in a different world, an “otherworld”, but not be able to say whether it was the “astral” or some other realm. So, if we want to maintain a stance of radical empiricism, we can accept the maps given by the different traditions as provisional, to be verified by our others’ observations. The maps, as we know, are not the territory.

In that spirit, I present here a mapping of the seven major levels of consciousness, as I was taught them by my teachers, and as I continue to hold them, as a working hypothesis. The most useful analogy to help understand the differences between the levels, is, to my mind, the concept of frequency or vibratory rate, as in music theory. The different bodies or levels, differ in vibratory rate, like the tones of a scale or chord: that is why they can co-exist, co-incide, in the same place at the same time, without interference.

The seven/eight note structure of the octave, is also consistently found in mappings of the different levels of consciousness, including G. I. Gurdjieff’s formulation of the Law of Seven as one of the fundamental laws of the universe. It is not inconsistent with this principle that any given yogic or meditative practice may work primarily, or in the beginning stages, with two or three or five levels.

So, in ascending order of frequency rate, we have: the physical-material body and realm (in the Indian traditions this is called the “body/sheath of food” – annamayakosha); next, the perceptual or etheric body and realm; the emotional or astral body and realm (some combine the perceptual and emotional, calling it “psychic”); and the mental or noetic body and realm. These four together make up the personality-systems; they are subject to conditioning, and all the dualities and conflicts that we know at the physical body level. Above the mental, in vibratory rate, are the transpersonal, unobstructed dimensions, or “heavens”, in which there are individual differences, like different colors in a painting, or tones in a symphony, but no conflicts, dualities or antagonisms. The first transpersonal level is that of soul, called anandamayakosha, (“body/sheath of joy”), in the Indian tradition. In the writings of the esoteric teacher Rudolf Steiner, the intermediate personality levels are not called “bodies”, but levels of soul: in descending order, soul of understanding, soul of feeling, and soul of perception. If the physical is the DO of an ascending octave, the level of soul would be SOL, which is also the Latin word for “Sun”. Some alchemical texts describe the soul, when “seen” with clairvoyant vision, as a golden, sun-colored sphere.

Continuing with the upper part of the vibratory octave, we have, above the level of soul: the angelic or celestial realm, which corresponds in the Buddhist teachings to the mandala realm of the Dhyani Buddhas; the archetypal or cosmic, or realm of First Differentiation, or primordial Yin-Yang; and, as the upper DO of the octave, Formless Form, Spirit, Self or Atman, which is always in perfect union with the Macrocosmic Oneness (Atman=Brahman). The particular names used here for the inner and higher frequency dimensions, have no particular importance. Obviously, other languages have different names. What is important, is that once we accept the existence of these higher worlds, our participation in them, and our relationships with beings, usually called “spirits”, in these other worlds, a whole new focus on spiritual practices which provide us with access to these worlds, for greater knowledge, understanding, insight, creative inspiration, healing and problem-solving.

(3) Levels of consciousness in a living systems universe. Modern science is only slowly moving towards acceptance of an ecological or systems cosmology. Even in such a worldview, much less in conventional materialist science, the idea of subtle dimensions, differing in vibratory rate, has little credibility, mostly because there is no widely accepted way of measuring or quantifying such subtle levels of energy and matter. (Some mathematical-physical accounts of other dimensions have been written, for example in the work of William Tiller). In one important respect however, the sytems worldview is congruent with traditional esoteric or shamanistic traditions – and that is the notion of levels, or scales. A systems universe consists of a series of whole systems (also called holons) arranged in ordered series, in such a way that the parts of a whole at one level, become wholes at the scalar level “below” ; and are themselves parts of wholes at the scalar level “above”.

This layering of levels of complex ordering, has been called by some a hierarchical principle, since the holons at the higher levels include the holons at the lower level as parts. However, the word “hierarchy” refers to systems of social organization in human collectives, -- ecclesiastical, military and corporate – in which “command, control and communication” (the military’s favorite phraseology) flows from the top down, one way only. Systems of natural order, as found in nature, are quite different, and have for this reason been called “nested hierarchies” or “holarchies”. They are structural ordering principles of containment and interdependence. For example, the body or organism is a holarchy containing a dozen or so organ systems functioning as interdependent parts, each of which is itself a holarchy of cellular components. There is really no similarity, or even analogy, with a conventional hierarchy: the body does not issue commands to the organs, and does not control them; it contains them.

We may look then, to the holarchical levels of a living systems universe for means to map out inner journeys or explorations in consciousness. As stated above, consciousness is the experiential side, the knowing, feeling, sensing, imaging of relations, the “knowing-with”. It is the subjective, inner, concaveness of the space-time continuum; of which objective, outer, convexity is matter and energy, in their ceaseless transformations. Many different systemic ordering scales, in the physical universe, have been identified and named. I will select three for consideration, and use the octave principle here too to delineate the stages, although sometimes more and sometimes fewer levels have been identified by various writers. At each level, there is a characteristic aggregation of energy and matter; and consciousness is what Teilhard de Chardin called the “within” of things. Thus atoms, molecules, cells, stones, plants, animals, rivers, oceans, planets, galaxies… each have their “within”, their subjectivity, their spiritual essence, or even “gods”.

3.1 Humans-in-Universe. As the first example let us take the ascending holarchical octave series that goes from the individual human being to the whole Universe:

body-organism of the human animal;
the kingdom of all animal species;
the biosphere, which includes all five kingdoms of organic life;
the Earth, Gaia, which includes the biospher and all inorganic material systems, as well as oceans and athmosphere;
the solar system, including Sun and all the planets;
the Milky Way galaxy, with its ten billion stars;
the cluster of several thousand galaxies of which the Milky Way is one – a cluster quaintly referred to by astronomers as the “local group”; and
Universe – all galaxies and other cosmic formations.
One can note that within each step of the holarchy series, a further octave series of steps can be identified. For example, to get from the individual body-organism to all animals, evolutionary taxonomy tells us of the following seven stages: the species homo sapiens; the genus homo; the family hominidiae; the order primata; the class mammalia; the phylum chordata; and the kingdom animalia.

People in altered states using shamanic or entheogenic practices, have reported having thoughts, feelings and perceptions, i.e. consciousness contents, at any of those levels. Once the Gaia theory was put forward on purely scientific grounds, spokespersons from traditional societies as well as esotericists immediately pointed out the similarity to ancient notions of “Earth Mother” or Anima Mundi, a conscious, sentient, spiritual being that is the indwelling spirit of the Earth. Likewise, solar deities have been a part of many religious traditions, including early Christianity. “Cosmic Consciousness”, a field of consciousness expanded to the outer limits of the known universe, has often been identified and described in the writings of mystics. In their book The Universe Story, Brian Swimme and Thomas Berry have shown in detail how at each stage of the evolving universe, humans can not only know about that stage through external information, but can experience inwardly what it means to be a part of those evolving wholes; for example, what it means to be part of the story of star-formation.

3.2 The Microcosmic Descent. Here also, the physical and life sciences have identified and described in great detail the organization of matter and energy at each level. The primary difference of a systems view from the conventional physical science approach, is that in a systems view, there is no reductionism to the physics level as the privileged, “ultimate” science. So starting again with the body the descending octave series goes:
organism-body of the human animal;
organ systems of the body – a level to which it is relatively easy for anyone to expand awareness, as we do for example, in relaxation and healing meditation practices;
cells in their tissue clusters – cellular consciousness, perhaps because cells float in a fluid matrix, tends to be experienced as oceanic;
organelles, the sub-components of cells, which are probably the evolutionary descendants of monera (bacteria) that have been incorporated into cells by endosymbiosis, according to the microbiologist Lynn Margolis;
molecular level – an infinite web of interconnectedness, containing the DNA genetic code for all life forms, but extending into inorganic and elemental matter as well;
the atomic level;
the level of sub-atomic particles such as electrons, protons, quarks and the rest; and
the level of pure, photonic, mass-less energy or vibration.
Assuming that subjective, potentially conscious perception and knowledge is possible at each level, allows us to understand seemingly miraculous healings that have been reported as occuring without any physiological or pharmcological intervention: through healers laying on hands, transmitting energy through crystals and vibrational chants, through homeopathic dilutions in which no single molecule of the original substance is left, or through seeing, in expanded states of perception, into the interior energetic structure of the patient’s body. An example of how scientific understanding may be advanced and enhanced by conscious attunement to the cellular and molecular levels is given in the work of Jeremy Narby, author of The Cosmic Serpent, a book on serpent imagery in South American ayahuasca shamans. Narby brought geneticists and molecular biologists to take ayahuasca with traditional shamans; they would ask specific questions related to their field of research, and obtain useful answers (Narby, 2002). The ayahuasca apparently allowed these scientists to focus their perception and attention at the cellular and molecular levels, without resorting to electron microscope, or other instrumentation used in Western science.

3.3 Humans-in-Habitats. This is a holarchy series dealt with in the sciences of human ecology, anthropology and sociology. Starting here too, with the DO of the ascending octave :
the human body, in its immediate habitat of clothing; then,
the family, in its house/home habitat; then
the extended family or clan, in a cluster of houses; then
the community, perhaps of several hundred families, living in a village;
the tribe or population in a bioregion or urban environment;
the society, all speaking the same language, inhabiting a country or nation;
the multi-cultural, multi-lingual, multi-ethnic confederation or conglomeration inhabiting a whole continent ;
the whole of humanity on Earth, the “global village”, as the upper DO.
The notion that there exist collective forms of consciousness, beyond the individual self, is of course not new in psychology. In family systems therapy, for example, the focus of therapeutic attention is the relationship network of all the family members; the notion that certain beliefs, attitudes, characteristics may be shared by a whole clan or community, is also not new. C.G. Jung coined the concept of “collective unconscious”, meaning images, symbols and archetypes shared by all of humanity; later theoretical development by his students, identified a layer of “cultural unconscious” between the personal and the collective. This makes it clear that the “collective unconscious” is really the system of consciousness that includes all human beings – what Robert Lifton has called the “species self”. It also makes it clear that beyond the layer of collective human species consciousness (a term I prefer to “unconscious”, since many of these contents are not unconscious at all), are forms of consciousness shared by all primates, all mammals, all animals, all life on Earth, even the cosmos. Different series of holarchical systems branch off from every node point in the web of life.

Since we are part of the unified system of interdependence, just like every other being, we can never actually be outside of it, as a detached “objective” observer. But since the unified field is energy, we are energetically connected to every other form and being in the universe. And since the field is also consciousness, this enables us, as human beings, to attune with, identify with, and communicate with any and every other life-form, object or being in the universe, from the macrocosmic to the microscopic.
If, as shamanistic and spiritual teachings agree, we humans are multidimensional beings, living in a multidimensional universe, then there are profound implications for revolutionary changes in our perspectives on the world. The shamanistic animistic worldview, is although older historically, larger and more inclusive than mechanistic-materialistic worldview dominant in the modern world. In the modern worldview, only the material time-space world of measurable quantities is accorded reality status; intuitive, imagistic, spiritual impulses and needs are marginalized to lesser ontological status.

In the worldview of indigenous people everywhere, the worlds we know from dreams and visions, worlds inhabited by gods and spirits, including our own deceased ancestors, are accorded recognition of equal reality. Our disconnection from the recognition and honoring of the vastness of spiritual realms enclosing and permeating this physical world, amounts to a staggering gesture of self-crippling on the part of Western techno-industrial civilization. This opens up almost inconceivable possibilities of solving our problems and bringing about a truly sustainable civilization, infused with spiritual values.

References
Abram, David. The Spell of the Sensuous - Perception and Language in a More-than-Human World. New York: Pantheon Books, 1996.

Harner, Michael. The Way of the Shaman. San Francisco: Harper & Row, 1980.

James, William. 1890/1952. Principles of Psychology. Chicago: Great Books of the Western World. Encyclopedia Britannica.

James, William. 1901/1958. Varieties of Religious Experience. New York: New American Library.

James, William. 1912/1996. Essays in Radical Empiricism. Lincoln: University of Nebraska Press.

Metzner, Ralph. The Unfolding Self - Varieties of Transformative Experience. Novato, CA: Origin Press, 1998.

Metzner, Ralph . The Well of Remembrance – Rediscovering the Earth Wisdom Mythology of Northern Europe. Boston: Shambhala, 1994.

Metzner, Ralph. Green Psychology - Transforming Our Relationship to the Earth.
Rochester, VT: Park Street Press, 1999.

Narby, Jeremy. The Cosmic Serpent – DNA and the Origins of Knowledge. New York: Random House, 1998.

Narby, Jeremy. “Shamans and Scientists”. in Hallucinogens – A Reader. Ed. Charles Grob. New York: Jeremy P. Tarcher / Putnam. 2002.

Website: www.greenearthfound.org

A shorter version of this essay is to appear in a collection of essays on the “Primacy of Consciousness”, edited by Trish Pheiffer and John Mack.
http://greenearthfound.org/write/expanding.html

NASA Announces Results of Epic Space-Time Experiment

2011-06-02T10:17:00.000-07:00

May 4, 2011: Einstein was right again. There is a space-time vortex around Earth, and its shape precisely matches the predictions of Einstein's theory of gravity.
Researchers confirmed these points at a press conference today at NASA headquarters where they announced the long-awaited results of Gravity Probe B (GP-B).
"The space-time around Earth appears to be distorted just as general relativity predicts," says Stanford University physicist Francis Everitt, principal investigator of the Gravity Probe B mission.

An artist's concept of GP-B measuring the curved spacetime around Earth

"This is an epic result," adds Clifford Will of Washington University in St. Louis. An expert in Einstein's theories, Will chairs an independent panel of the National Research Council set up by NASA in 1998 to monitor and review the results of Gravity Probe B. "One day," he predicts, "this will be written up in textbooks as one of the classic experiments in the history of physics."
Time and space, according to Einstein's theories of relativity, are woven together, forming a four-dimensional fabric called "space-time." The mass of Earth dimples this fabric, much like a heavy person sitting in the middle of a trampoline. Gravity, says Einstein, is simply the motion of objects following the curvaceous lines of the dimple.
If Earth were stationary, that would be the end of the story. But Earth is not stationary. Our planet spins, and the spin should twist the dimple, slightly, pulling it around into a 4-dimensional swirl. This is what GP-B went to space in 2004 to check.
The idea behind the experiment is simple:
Put a spinning gyroscope into orbit around the Earth, with the spin axis pointed toward some distant star as a fixed reference point. Free from external forces, the gyroscope's axis should continue pointing at the star--forever. But if space is twisted, the direction of the gyroscope's axis should drift over time. By noting this change in direction relative to the star, the twists of space-time could be measured.
In practice, the experiment is tremendously difficult.

The four gyroscopes in GP-B are the most perfect spheres ever made by humans. These ping pong-sized balls of fused quartz and silicon are 1.5 inches across and never vary from a perfect sphere by more than 40 atomic layers. If the gyroscopes weren't so spherical, their spin axes would wobble even without the effects of relativity.
According to calculations, the twisted space-time around Earth should cause the axes of the gyros to drift merely 0.041 arcseconds over a year. An arcsecond is 1/3600th of a degree. To measure this angle reasonably well, GP-B needed a fantastic precision of 0.0005 arcseconds. It's like measuring the thickness of a sheet of paper held edge-on 100 miles away.
"GP-B researchers had to invent whole new technologies to make this possible," notes Will.
They developed a "drag free" satellite that could brush against the outer layers of Earth's atmosphere without disturbing the gyros. They figured out how to keep Earth's magnetic field from penetrating the spacecraft. And they created a device to measure the spin of a gyro--without touching the gyro. More information about these technologies may be found in the Science@NASA story "A Pocket of Near-Perfection."
Pulling off the experiment was an exceptional challenge. But after a year of data-taking and nearly five years of analysis, the GP-B scientists appear to have done it.
"We measured a geodetic precession of 6.600 plus or minus 0.017 arcseconds and a frame dragging effect of 0.039 plus or minus 0.007 arcseconds," says Everitt.
For readers who are not experts in relativity: Geodetic precession is the amount of wobble caused by the static mass of the Earth (the dimple in spacetime) and the frame dragging effect is the amount of wobble caused by the spin of the Earth (the twist in spacetime). Both values are in precise accord with Einstein's predictions.
"In the opinion of the committee that I chair, this effort was truly heroic. We were just blown away," says Will.

An artist's concept of twisted spacetime around a black hole. Credit: Joe Bergeron of Sky & Telescope magazine.
The results of Gravity Probe B give physicists renewed confidence that the strange predictions of Einstein's theory are indeed correct, and that these predictions may be applied elsewhere. The type of spacetime vortex that exists around Earth is duplicated and magnified elsewhere in the cosmos--around massive neutron stars, black holes, and active galactic nuclei.
"If you tried to spin a gyroscope in the severely twisted space-time around a black hole," says Will, "it wouldn't just gently precess by a fraction of a degree. It would wobble crazily and possibly even flip over."
In binary black hole systems--that is, where one black hole orbits another black hole--the black holes themselves are spinning and thus behave like gyroscopes. Imagine a system of orbiting, spinning, wobbling, flipping black holes! That's the sort of thing general relativity predicts and which GP-B tells us can really be true.
The scientific legacy of GP-B isn't limited to general relativity. The project also touched the lives of hundreds of young scientists:
"Because it was based at a university many students were able to work on the project," says Everitt. "More than 86 PhD theses at Stanford plus 14 more at other Universities were granted to students working on GP-B. Several hundred undergraduates and 55 high-school students also participated, including astronaut Sally Ride and eventual Nobel Laureate Eric Cornell."
NASA funding for Gravity Probe B began in the fall of 1963. That means Everitt and some colleagues have been planning, promoting, building, operating, and analyzing data from the experiment for more than 47 years—truly, an epic effort.
What's next?
Everitt recalls some advice given to him by his thesis advisor and Nobel Laureate Patrick M.S. Blackett: "If you can't think of what physics to do next, invent some new technology, and it will lead to new physics."
"Well," says Everitt, "we invented 13 new technologies for Gravity Probe B. Who knows where they will take us?"
This epic might just be getting started, after all….
Author: Dr. Tony Phillips Credit: Science@NASA

http://science.nasa.gov/science-news/science-at-nasa/2011/04may_epic/

Pi=4!

2011-05-07T04:17:00.001-07:00

"...I’ll place a straight ruler next to it and measure it and so I'll make a square out of a circle and place a marketplace in its centre where all the roads will be straight… It’ll be like a star which, though round, all its rays go off in all directions in straight lines."
~~Aristophanes, The Birds

We know π as the ratio of how many times the diameter of a circle fits in its circumference - somewhere in the region of 3.14159....ad infinitum. Because it is an infinite number, and therefore unknowable in its entirety, it means that in any situation where we use π, the answer we get is also incomplete. Everytime we use π, such as to determine the area of a circle, we only ever achieve an approximation - regardless of how accurate that approximation might be.

We imagine that in-order to increase the accuracy of π, we have to add more and more numbers to the millions and millions of digits that we already have. This might increase the accuracy of π, but it still only amounts to a more accurate approximation. If we want to know the exact answer, what we really need, is to KNOW pi.

Some argue that in certain situations, the infinite figure we have for pi is wrong, and that pi is really 4. This would mean that the number of times the diameter of a circle fits into its circumference is not three and a bit - but 4. Typically, we cannot draw a circle which has a circumference four times its diameter. We could try, but we would fail - and that failure would look a lot like a square.

If we were to roll-out the circumference of a circle, and compare it to the perimeter of a square with the same diameter, it would ably demonstrate that the length of the circle's circumference is roughly three-quarters that of the square. This being the case, how is it possible to produce a square from a circle which shares the same diameter?

In order to reach a length which is four times that of the diameter, it is necessary that the length of the circle's circumference is increased; that is, it is extended in some way. In effect, the line of the circumference has been stretched. Pi has mysteriously increased from the infinite figure of 3.14159... to the more finite figure of 4. What is more, if 4 can be produced by stretching π, it would further suggest that π is in some way, a compressed form of 4.

The number 4 is nowhere near as slippery as π to work with - it is neither transcendental, nor irrational. It is not weighed down by an infinite amount of digits after the decimal point. 4 is a nice whole number. In using 4, we no longer get approximate answers, we get THE answer. But how has the number 4 come into existence?

The new number of 4 for pi is not quite as bizarre, nor as impossible, as it at first might appear. The theory goes that a square can be manipulated in such a way that it effectively takes on the semblance of a circle. This circular shape is known as an infinite-sided concave polygon. Concave, as in the sides of the polygon are made to quite literally "cave-in."

"To remember what concave means it’s best to split the word up like this – “con” + “cave”. The important part is the “cave” part – the word concave is used to describe shapes that have something looking like a cave in them. When you talk about concave polygons, the cave is on the outside of the polygon. Another way of spotting concave polygons is to look out for any interior angles that are larger than 180°. Remember that angles larger than 180° are called reflex angles."

~~Image: The reflex angle of a concave polygon has an exterior angle which looks a bit like a "cave".

If a polygon has a reflex angle, then it is said to be a concave polygon. A reflex angle is greater than 180 degrees and less than 360 degrees. An infinite-sided concave polygon will have an infinite number of sides which "cave-in", producing an infinite number of reflex angles.

A simple concave polygon gives the impression of a shape which is awkward in nature. Increasing the number of "caves" (exterior angles) seems to make the polygon appear only more complex, and irregular. However, just as increasing the number of sides of a regular polygon will see it assume more and more of a circular shape - so too does a concave polygon whose reflex angles are increasing in number, and in uniform fashion. In other words, if we keep increasing the number of sides, ensuring that each side is the same length, and that they occur at regular intervals on the perimeter, then the concave polygon will begin to adopt a shape which is more circular. If you were to try and picture how this might look so far, then it is perhaps easier to imagine the perimeter as the blade of a circular saw.

~~Image: Circular saw blade on antique portable sawmill.

In order to cram as many sides into the perimeter as possible, it is imperative that every side has the same length. The sides act as the legs of the reflex angle, and the space formed between them, the "cave" as it were, must be infinitesimally small so that an infinite number of "caves" might occupy the circumference. These exterior angles are fundamental to the shape, as they serve to prevent the legs of the reflex angle from ever touching each other. In the case of an infinite-sided concave polygon the distance between each side is as infinitesimally small as can be imagined. If these "caves" or spaces did not exist, it would be impossible for a perimeter to shake its length, and dissolve into a circumference.

An infinite-sided concave polygon will have an infinite number of reflex angles. The sum of the reflex angles must surely provide some dazzling figure for the number of degrees inside the shape. Funny enough mind, regardless of the infinite figure in the interior, it can be argued that the sum of a concave polygon's exterior angles, infinite-sided or not, shall always remain at 360 degrees. This shares a remarkable symmetry with convex polygons, whose exterior angles undergo the exact same phenomena - they too always add up to 360 degrees.

If we observe each indivual reflex angle in the infinite-sided concave polygon, we find that it is imperative that the number of degrees inside the angle only ever approach 360 degrees. The reflex angle must maintain an angle which is as close to 360 degrees as permissable, so that the exterior angle remains as acute as possible. It is important that the reflex angle is never allowed to fully complete 360 degrees, otherwise the exterior angle would come to equal zero degrees, and the "cave" would simply "pop" out of existence.

If we were to return to our previous analogy, then I suppose we'd be looking at a circular saw blade with an infinite number of tiny teeth - each tooth seperated from the other by an infinitesimal gap. If we ourselves were infinitesimally small, we would be able to see that the circumference of the blade followed a distinct zig-zag pattern. If we were to increase the distance between us and the saw, then it would challenge our previous conception, as the blade now appears perfectly smooth. It's interesting to think that our judgement is made so bias by perspective.

The entire process described above, is brought to dramatic effect in the illustration below. Known to some as "π = 4! Problem Archimedes?", it's already gained some notoriety on various maths and physics forums, where some others have come to call it - undeservedly perhaps - "Troll Pi":

~~Image: "π = 4! Problem Archimedes?"

What the illustration shows, and rather well, is how the perimeter of a square might be reduced to occupy the circumference of an inscribed circle. Ordinarily, this would be deemed impossible because a square's perimeter is four times its diameter, while a circle's circumference is just over three times its diameter. To get a square to squeeze into a circle, the length of the square's perimeter will need to be shortened by as much as a quarter.

It begins with the square's corners being "removed" or inverted, so that it adopts the shape of a concave polygon. Accordingly, more corners are inverted, meaning that more sides are added, and the perimeter pretty much resembles a ziggurat made up of "Lego" blocks. More and more of the perimeter is encroached upon as the number of sides increase. As their numbers swell, we see the size of the blocks decrease - so much so - that by the time we arrive at numbers which are infinite, the perimeter is now a curve which possess a row of barely imperceptible jagged little teeth. Under its new guise, the perimeter seems able to fit perfectly inside the circumference of the circle.

One might imagine the square as having been panel-beaten, then concertinaed into the shape of a circle. The circle has been created by nothing short of square-mangling. If this is true, then we might also assume that the circle is just as easily taken and bent back into the shape of the square. Flipping between these shapes - from circle to square, and from square to circle - we can see that nowhere in the entire process is anything either added, or taken away. At no-time is the line cut or dismantled. The only thing which is observed is MOTION.

For a square to transform into a circle, its sides are allowed to crumble and fall into rubble around the circle's circumference. Those once imposing corners of the square have somehow been lost - buried - in the defining line of the circumference. The square can be rebuilt however, and it begins by sweeping the rubble back into piles - piles which grow bigger and bigger - until they are at last gathered into four mountainous heaps.

To summarise then, "π = 4! Problem Archimedes?" is a revelation in how the circumference can act as a perimeter, and how the perimeter can change into a circumference. This simple illustration explains very well how this transformation takes place, clearly showing how it is possible for the length to remain unchanged. The length of the square's perimeter is ALWAYS the same - and remains so - even when it is asked to assume the role of a circle's circumference.

All this is very good in theory, but if we were to examine a circle on a page - how do we go about peeling the circumference of a circle from the paper, so that we might use it to make a square of the same diameter? Surely, everytime we unravelled the circumference and measured it, the answer will always be π, not 4? To reach 4, something needs to be added to π. From where has the required extra bit materialised?

What is required is a reliable mathematical method to show how the extra length is gained legitimately. In a landmark paper, "The Extinction of π", Miles Mathis proposes that he has discovered one such method. Mathis appears to have resolved the problem of pi=4 by including time in his geometric analysis. It can be seen that his geometry is no longer describing some static abstraction, but something much more physical. Something real.

Much thanks:

http://en.wikipedia.org/wiki/Circle
http://betterexplained.com/articles/prehistoric-calculus-discovering-pi/
http://mathforum.org/~sanders/exploringandwritinggeometry/polygons.htm
http://paramanand.blogspot.com/2010/12/angle-sum-formula-for-polygons.html
http://www.jimloy.com/geometry/pi.htm
http://milesmathis.com/pi3.html
http://dyinglovegrape.wordpress.com/2010/11/17/homology-primer-2-triangulating-a-surface/
http://www.physicsinsights.org/pi_from_pythagoras-1.html
http://www.philosophynow.org/issue81/Mathematical_Knowledge_A_Dilemma
http://www.tutorvista.com/math/infinite-lines-of-symmetry
http://scienceblogs.com/goodmath/2008/10/infinity_is_not_a_number.php
http://www.mathopenref.com/polygoncentralangle.html
http://www.jimloy.com/geometry/pentagon.htm
http://forums.xkcd.com/viewtopic.php?f=3&t=67907
http://www.pi314.net/eng/aleatoire.php
http://jwilson.coe.uga.edu/emt668/EMAT6680.2000/Mylod/Math7200/Project/InscribedCircle.html
http://www.ugrad.math.ubc.ca/coursedoc/math101/notes/integration/archimedes.html
http://www.themathpage.com/atrig/measure-angles.htm

Circling The Square

2011-04-14T09:43:00.001-07:00

While looking at some facts about pi, there was one in particular that really engaged me. It is not a fact about pi as such, but more a statement about the nature of pi...

"Most people would say that a circle has no corners, but it is more accurate to say that it has an infinite number of corners."

I like this fact because it forces us to examine the nature of a circle. If a circle has corners, then surely, it must be related to the square in a fundamental way. The circle is proof that mere appearances can be deceptive. In a mathematical sense, a square and circle are not two entirely different shapes as such. Those severe bends that we see forming the four corners of a square, can surprisingly, be found to also exist in those soft curves which form a circle. The best way to get from a square to a circle is by increasing its number of corners.

~~Image: Red Square Painting (2009 Digital Remix) by Nigel Tomm

A square has its four sides and its four corners, and if we add another side to it, to create a five-sided polygon, then it also generates another corner. If everytime we keep adding more sides, and everytime we make all the sides the same length - then we can go on to form a fantastic array of regular polygons.

If we keep on increasing the polygon's number of sides, and keep on increasing them, then theoretically, the sides of the polygon will eventually reach numbers which are infinite. It shall produce a polygon with an infinite number of sides - and for all intents and purposes - a shape that looks convincingly like a circle. It is by creating polygons that the early pioneers of geometry, such as Archimedes, were able to gain more and more accurate approximations of pi. The following extract below comes from this site, which also offers some excellent working demos of how pi can be approximated - one by unravelling circles, and another by inscribing polygons:

"π is an irrational number, which means that we can never write the value of it completely accurately. So how do we calculate it? After all, it is difficult to measure round the edge of a circle. You could get an approximation by winding a piece of string round a tin, then measuring the string and across the tin, but this will not be very accurate. Another way is to fit a polygon (like a square or a hexagon) to the circle, either inside or outside. We can calculate the edge of a polygon. As we increase the number of sides in the polygon, it fits the circle better and better, so its edge becomes closer and closer to the circumference of the circle. What is more, the outer polygon will have a longer edge than the circle, and the inner one will be less. So we can get two approximations for for each polygon, one too big and one too small."

As you increase the number of sides of a polygon, you increase the sum of the interior angles of the polygon. Each time we increase the number of sides by one, the sum of the angles increase by 180 degrees. For example, a square (quadrilateral) has the interior sum of 360 degrees, while a five-sided polygon (pentagon) has a sum of 540 degrees. Going further, we see that the sum of the interior angles of a ten-sided polygon (decagon) are 1440 degrees. The sum of the interior angles of a polygon are calculated by inscribing triangles (triangulating). If we know that the sum of the interior angles of a triangle are ALWAYS 180 degrees, and we can count the number of triangles being used to form the shape of the polygon - then we have the perfect formula for calculating the sum of the polygon's interior angles (n being the polygon's number of sides):

(n-2) × 180° = sum of interior angles

Basically, everytime we add a side to a polygon, we generate a new triangle inside the polygon, and increase the sum of the interior angles by 180 degrees. A square, for example, can be made up by two triangles (hence 2 × 180° = 360°), while a pentagon can be made up by three triangles (3 × 180° = 540°).

~~Image: There are two triangles in a square.

~~Image: A pentagon has five sides, and can be made from three triangles.

If a circle can be described as a polygon with an infinite number of small sides, then we must assume that the sum of the interior angles of such a circle will too approach figures somewhere in the infinite. If we were to try and triangulate such a polygon to try and reach the sum of the interior angles, we would have to deduct two from the number of sides to give us the number of triangles. This means we would be left trying to tackle the rather troublesome sum of infinity minus 2 (n-2) to achieve the answer.

Trying to add or subtract to infinity is always a little awkward. After all, infinity is considered to be a concept rather than a number - you can't just go around ripping bits off it, or for that matter, slapping things on it. In order to deduct 2 from infinity to get a number, it means that we would have to ask infinity to be a little less infinite, and be a bit more finite, which is probably asking the impossible. Or is it?

Assuming that the sum of the interior angles will reach amounts which end somewhere in the infinite, it remains that the sum of the exterior angles of a such a polygon, a polygon with an infinite number of sides, if measured, will still be found to equal 360 degrees. This is because the sum of the exterior angles of any convex polygon will ALWAYS add upto 360 degrees. Essentially, all the exterior angles amount to one full revolution (360°). In other words, adding all the exterior angles together is the mathematical equivalent of taking the shape and rotating it one complete turn.

~~Image: In this diagram the exterior angles have been given different colours. You can see how they can be put together to make a full circle.

If we add up the interior angle and the exterior angle of a regular polygon, we get a straight line - 180 degrees. The interior and exterior angles are distinctly related. We can increase the polygon's number of sides to figures which are infinite, and with it, we will also see an increase in the sum of the interior angles. In theory, the number of degrees should become infinite - infinitely big. However, each interior angle cannot be seen to be equal to, or exceed, the boundary of 180 degrees, otherwise we will encroach upon the space of the exterior angle.

~~Image: Internal angle + external angle = 180°

Increasing the number of sides will see the sum of the interior angles grow,and grow, but this growth is wholly reliant on each exterior angle, the one at each vertex, becoming smaller, and smaller - infinitely smaller. In other words, the growth of the sum of the interior angles is severely restricted. The infinite sum of the interior angles are by no means boundless.

" The sum of the exterior angles of a polygon are 360 degrees regardless of the number of sides. That means that the measure of each exterior angle must get smaller as the number of sides increases. There is no "least possible measure" because even though the limiting value is 0 you can never achieve a 0 degree exterior angle and still have a polygon. You can get as close to zero as you like, but as close as you get, someone else can always come along and get closer. Another way to look at it is that a zero degree exterior angle measure implies that there are an infinite number of sides. And an infinite number of sides implies a circle, not a polygon."

Personally, I would argue that a circle, or infinite sided polygon, does not possess a zero degree exterior angle. That's because an infinite amount of nothing will still give you nothing. Nevermind how much nothing you get, you'll still be left holding nothing. The sum of the exterior angles, regardless of the fact that they are infinite in number, shall always add upto 360 degrees. Therefore each exterior angle must be seen to amount to something, even if it is something infinitesimally tiny, in order to reach the sum of 360 degrees. Coincidentally, this exact same restriction we find outside the circumference of any polygon, or circle, is also at work in the shape's centre.

One of the defining properties of a circle, and indeed, any regular polygon, is that its entire central angle ALWAYS measures 360 degrees. If we were to add a central vertex, or central point to a pentagon for example, and inscribe triangles in the same way that we might slice up a pizza, then our pentagon would produce 5 triangles - all sides would have the same length, and all the interior angles would be the exact same size. The central angle of each triangle will also be the same, and the sum of these shall ALWAYS add upto 360 degrees.

~~Image: The central angle of a regular pentagon (5 × 72° = 360°)

Using this same method, we can imagine inscribing triangles to an infinitely sided polygon, to create an infinite number of infinitesimal triangles. But if we add the sum of these infinitesimally tiny central angles together, they produce the sum of 360 degrees. It doesn't matter how many triangles we have, infinite number or not, they shall always add up to 360 degrees. An infinite sided polygon does not have a central angle whose sum reaches an infinite number of degrees - it produces only an infinite number of ways to percieve the finite sum of 360 degrees.

I have always imagined infinity as an entity which fulfils the very definition of freedom. But where is all the freedom that I was hoping to embrace? No, infinity offers only the illusion of freedom. Infinity can never escape the confines of the finite. The term infinite is not actually describing the phenomena of ever-expanding space - it only pretends to.

We imagine that in order to behold the infinite we have to travel to some far-flung, incomprehensible horizon - but the reality is, for us to comprehend the infinite, we don't so much as have to leave the spot. Infinity is always describing the exact same space - a space chopped up into an infinite number of ways, an infinite number of ways in-which to percieve it - but it is the exact same space nonetheless.

If the state of infinity were truly free, then surely, there should be no restrictions to its growth whatsoever. Here however, we can see that infinity is shackled to enormous constraints. We can try to develop a sense of the infinitely big - building a polygon with infinite sides - but we find that that growth is constricted by a number of finite limits.

Infinite growth is restricted by constraints imposed both inside and outside the circle. The sum of the central angle, and the sum of the exterior angle can never exceed 360 degrees. Also, the linear pair of the exterior and interior angles can never exceed 180 degrees. Infinity is dependent upon how big we make each interior angle, and at the same time, how small we make each exterior angle. Each interior angle can never extend to, or beyond 180 degrees, and at the same time, the exterior angle can never be allowed to fall to zero. If any of these restrictions are breached, well, then you no longer have a perfect circle.

A circle may well be a polygon with infinite sides, but at its heart, it is still very much a square - a square bent infinitely out of shape - but a square nonetheless. A square of finite proportions.

The sum of the interior angles, the angles which exist inside the circumference of the circle as it were, can reach figures which are infinite - but this stands only as an expression of how limited our understanding is. The sum of the interior angles could never truly, unrelentlessly expand into infinite space - there is a limit in place. A limit so vast that it is unknowable - but a limit nonetheless. We may not be able to know the number of that limit, but we can see it. We see it all the time. That's because the limit itself is a construct of a remarkably simple shape - the circle.

~~Image: The human eye - one of the most outstanding examples of a circle that we see everyday.

The state of infinity perhaps, might best be described as a place that exists somewhere between a square and a circle. If this were true, what exactly does it mean for the supposedly infinite ratio of pi?

Contemplating Infinity

2011-04-09T03:39:00.000-07:00

The word after "infinity" in my dictionary is "infirm," a definition of which is "weak of mind." This is how many of us who are not mathematically inclined feel upon contemplating infinity. (To see how mathematicians and similar thinkers regard infinity, see Working With Infinity: A Mathematical Perspective.)

We feel weak because our finite minds can only go so far with the concept, and because every time we think we're on the verge of securing even a shadowy understanding, we're tripped up by something. A friend of mine once told me that trying to hold her hyperactive toddler was like trying to hold a live salmon. Infinity is like that for us "infirm ones": slippery as a salmon, forever eluding our grasp.

Becoming numb

This is true no matter how you approach the concept. Many of us might consider numbers the most sure-footed way to come within sight of infinity, even if the mathematical notion of infinity is something we'll never even remotely comprehend.

We may think, for starters, that we're well on our way to getting a sense of infinity with the notion of no biggest number. There's always an ever larger number, right? Well, no and yes. Mathematicians tell us that any infinite set—anything with an infinite number of things in it—is defined as something that we can add to without increasing its size. The same holds true for subtraction, multiplication, or division. Infinity minus 25 is still infinity; infinity times infinity is—you got it—infinity. And yet, there is always an even larger number: infinity plus 1 is not larger than infinity, but 2infinity is.

Try another tack: huge numbers. When we play with mind-boggling figures we non-math types may think we're playing in infinity's neighborhood, if not in the same playground. When we're told that the decimals in certain significant numbers, like pi and the square root of two, go on forever, we can somehow accept that, especially when we learn that computers have calculated the value of pi, for one, to over a trillion places, with no final value for pi in sight. (For more on pi, see Approximating Pi.) When we're told that there are 43,252,003,274,489,856,000 possible ways to arrange the squares on the Rubik Cube's six sides, we may feel intuitively (if not rationally) that we must be on our way to the base of that loftiest of all peaks, Mt. Infinity.

One reason we may feel this way is that such numbers are as intellectually unapproachable to the mathematically challenged as infinity itself. Take a Googol. A Googol is 10100, or 1 followed by 100 zeroes, and is the largest named number in the West. The Buddhists have an even more robust number, 10140, which they know as asankhyeya. Just for fun, I'll name a larger number yet, 101000. I'll call it the "Olivian," after my daughter. Now, doesn't an Olivian get me a little closer to infinity than the Googolians or even the Buddhists can get? Nope. Infinity is just as far from an Olivian as it is from a Googol—or, for that matter, from 1.

For many of us uncomfortable with infinity, the word number can be defined as “that which makes numb.”

Perhaps we infirm ones would be wise to take a leaf from the lingual book of Madagascar. The word there for a million is tapitrisa, which means "the finishing of counting." For some tribal groups in other parts of the world, counting stops at three, in fact; anything above that is "many." In some ways this makes sense. How many of us can keep more than a few things in our minds at once? I remember playing a game with myself as a child in which I would think "I'm thinking that I'm thinking that I'm thinking that I'm thinking...." After the third or fourth "I'm thinking," I could no longer retain in my head all the degrees it implies. Such infirmity holds for simple counting as well, as Lewis Carroll reveals so tellingly in Through the Looking Glass:

"Can you do Addition?" the White Queen asks. "What's one and one and one and one and one and one and one and one and one and one?"

"I don't know," said Alice. "I lost count."

"She can't do Addition," the Red Queen interrupted. "Can you do Subtraction?"

For many of us uncomfortable with infinity, the word number can be defined as "that which makes numb," as Rudy Rucker wryly notes in his book Infinity and the Mind (Birkhäuser, 1982). This is especially true when a number is so outlandishly enormous that it smacks, however remotely, of the infinite. Galileo himself felt this way. "Infinities and indivisibles transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness," he wrote in his Dialogues of Two New Sciences of 1638. "Imagine what they are when combined." Rather not, thanks—makes me numb.

Incredible shrinking

Infinities do come in two sizes, of course—not only the infinitely large but also the infinitely small. As Jonathan Swift wrote, "So, naturalists observe, a flea/Has smaller fleas that on him prey/And these have smaller still to bite `em/And so proceed ad infinitum." We may not be able to conceive of Swift's infinitesimal fleas, because reason insists they don't exist, but we can imagine ever smaller numbers without much trouble. It's no hardship, for example, to grasp the notion of an infinity of numbers stretching between, say, the numerals 2 and 3. Take half of the 1 that separates them, we might tell ourselves, then half of that half, then half of that half, and so proceed ad infinitum.

Of course, just when we think we have infinity in the palm of our hands, we watch it evaporate in the harsh light of another of those confounding paradoxes: the numerals 2 and 3 are separated by both a finite number (1) and an infinity of numbers. This conundrum spawned one of the great paradoxes of history, known as Zeno's paradox. Zeno was a Greek philosopher of the fourth century B.C. who "proved" that motion was impossible. For a runner to move from one point to another, Zeno asserted, he must first cover half the distance, then half the remaining distance, then half the remaining distance again, and so on and so on. Since this would require an infinite number of strides, he could never reach his destination, even if it lay just a few strides away.

It wasn't for 2,000 years that Zeno's paradox finally got "solved," for all intents and purposes, by the calculus. Its inventors, Isaac Newton and Gottfried Leibniz, showed us how an infinite sum can add up to a finite amount, that it can converge to a limit. Thus, even though we can't count all the numbers between 2 and 3, we know they converge to 1.

No limits

As Zeno's paradox hints, considering infinity from the perspective of space has much correspondence with that of numbers. We can imagine, for instance, that space, like numbers, is infinitely divisible. We believe Hamlet when he says "I could be bounded in a nutshell/And count myself a king of infinite space." The shortest length physicists speak of is the Planck length, 10-33 centimeters. But might not there be an even shorter length, say, 10-333 centimeters, or 10-an infinite number of 3's centimeters?

Many of us are as queasy around eternity as we are around infinity.

As with numbers, we can also envision space as being infinitely large. After all, if the universe has a boundary, what's on the other side? We might flatter ourselves that we're somehow getting closer to infinity when we consider extremely large distances. On June 12, 1983, while traveling at over 30,000 mph, the Pioneer 10 spacecraft became the first human-made object to exit our solar system. Some 300,000 years from now, unless something interrupts its voyage, the craft is expected to pass near the star Ross 248, a red dwarf in the constellation Taurus. Ross 248 is about 10.1 light-years from Earth, or about 59,278,920,000,000 miles away. Pioneer 10 will still be in the early stages of its journey, though. When our sun bloats into a red giant about five billion years from now and incinerates our planet, our robotic ambassador will still be heading away, knocking off more than 250 million miles a year.

Are we making headway towards an infinite distance with such knowledge? Hardly. An infinite distance, as you've guessed, would be as far from where Pioneer 10 will be in five billion years as it is from the Earth now. If the universe is infinitely large, even the remotest stars we can detect, which are so far away that their light left them some 12 billion years ago, are as far from infinity as we are. (Things get tricky here: as one mathematician pointed out to me, infinity is an abstract concept, appearing only in our mental images of the universe. It is not actually in the universe.)

Forever and a day

Time is another way to contemplate infinity, though many of us are as queasy around eternity as we are around infinity. ("That's the trouble with eternity, there's no telling when it will end," Tom Stoppard writes in Rosencranz and Guildenstern Are Dead.) Yet isn't infinite time somehow easier to swallow than finite time? After all, what can stop time?

Many of us do indeed live our lives thinking that eternity is a given. And again, we may fool ourselves into thinking that we're on the way to eternity when we think of 12 billion years, or of any other frighteningly mind-bending length of time. One of the gamest attempts to define eternity appears in Hendrik Willem Van Loon's 1921 children's classic The Story of Mankind:

High up in the North in the land called Svithjod, there stands a rock. It is 100 miles high and 100 miles wide. Once every thousand years a little bird comes to the rock to sharpen its beak. When the rock has thus been worn away, then a single day of eternity will have gone by.

That passage gives you an inkling for just how gosh-darn long eternity is. But all the usual caveats apply: eternity doesn't have a length, that single "day" of eternity is as far in time from eternity itself as a normal day, etc., etc.

Fear of the infinite

If all this leaves you feeling numb, you're not alone. The Greeks, in fact, invented apeirophobia, fear of the infinite. (The term comes from the Greek word for infinity, apeiron, which means "without boundary.") Aristotle would only admit that the natural numbers (1, 2, 28, etc.) could be potentially infinite, because they have no greatest member. But they could not be actually infinite, because no one, he believed, could imagine the entire set of natural numbers as a finished thing. The Romans felt just as uncomfortable, with the emperor Marcus Aurelius dismissing infinity as "a fathomless gulf, into which all things vanish."

“Infinity is where things happen that don’t.”

The ancients' horror infiniti held sway through the Renaissance and right up to modern times. In 1600, the Inquisitors in Italy deemed the concept so heretical that when the philosopher Giordano Bruno insisted on promulgating his thoughts on infinity, they burned him at the stake for it. Later that century, the French mathematician Blaise Pascal deemed the concept truly disturbing: "When I consider the small span of my life absorbed in the eternity of all time, or the small part of space which I can touch or see engulfed by the infinite immensity of spaces that I know not and that know me not, I am frightened and astonished to see myself here instead of there ... now instead of then." Martin Buber, an Israeli philosopher who died in 1965, felt so undone by the concept of infinity that he "seriously thought of avoiding it by suicide."

Most of us will never feel so put out by infinity that we'll resort to contemplating such extreme measures. We may feel weak of mind, like the anonymous schoolboy who once declared that "infinity is where things happen that don't." But our uneasiness will never get much greater than the schoolboy's delightfully dismissive attitude suggests his got. We can live with that level of discomfort, contenting ourselves with the knowledge that all we can reasonably expect in musing on infinity is to get a feeling for it, like that engendered by this gem from another anonymous sufferer of our common infirmity: "Infinity is a floorless room without walls or ceiling."

~~Contemplating Infinity:
A Philosophical Perspective
by Peter Tyson
http://www.pbs.org/wgbh/nova/archimedes/contemplating.html

Give Me Some More Pi, Please

2011-04-07T05:02:00.000-07:00

~~Image: Pi Pie

I'm trying to wrap my head around pi. I mean, what is it exactly? We all know it's a ratio, and one that defines the relationship between the diameter of a circle to its circumference. That relationship is expressed as the number of times the diameter of a circle fits in around its circumference. That's essentially what pi is, but why is it that it is expressed as a seemingly infinite number of digits after the decimal point?

~~Image: Circle illustration showing a radius, a diameter, the centre and the circumference.

Plenty of sites all over the net offer lots of interesting facts about pi, but no matter how many of these you try to cram in, they all still seem to fail in satisfying the pangs for what it is that pi is exactly. For example, below are some facts about pi:

"The sequences of digits in Pi have so far passed all known tests for randomness.Here are the first 100 decimal places of Pi3.141592653589793238462643383279502884…

The fraction (22 / 7) is a well-used number for Pi. It is accurate to 0.04025%.

Another fraction used as an approximation to Pi is (355 / 113) which is accurate to 0.00000849%

A more accurate fraction of Pi is (104348 / 33215). This is accurate to 0.00000001056%.

Pi occurs in hundreds of equations in many sciences including those describing the DNA double helix, a rainbow, ripples spreading from where a raindrop fell into water, general relativity, geometry problems, waves, etc.

There is no zero in the first 31 digits of Pi.Pi is irrational. An irrational number is a number that cannot be expressed as a ratio of integers.

In 1991, the Chudnovsky brothers in New York, using their computer, m zero, calculated pi to two billion two hundred sixty million three hundred twenty one thousand three hundred sixty three digits (2, 260, 321, 363). They halted the program that summer.

The Pi memory champion is Hiroyoki Gotu, who memorized an amazing 42,000 digits.The old memory champion was Hideaki Tomoyori, born Sep. 30, 1932. In Yokohama, Japan, Hideaki recited pi from memory to 40,000 places in 17 hrs. 21 min. including breaks totaling 4 hrs. 15min. on 9-10 of March in 1987 at the Tsukuba University Club House.

Pi is of course the ratio of a circle's circumference to its diameter. If you bring everything up one dimension to get 3D value for Pi, the ratio of a sphere's surface area to the area of the circle seen if you cut the sphere in half is exactly 4."
Do you see what I mean? We can try and digest facts about pi all day long, just as we could try and consume the millions and millions of digits of pi over an entire lifetime, and we would still be left feeling ... empty. The reason as to why pi is an infinite number remains pervasively evasive. The mind, in its search for patterns and relationships, seems unable to relate to pi in any way whatsoever, other than drawing the one obvious conclusion that it is indeed a number. An apparently infinite number. But where do these numbers lead to?

I like the idea that it is a truly random collection of numbers, having been shown to exist without having being formed by any KNOWN pattern, but one that must be sub-ordinate to some higher order that we are as yet unaware of, simply because it is these exact same digits, innumerable as they are, appearing in the exact same order everytime we try to evoke pi. The post below is taken from The Sheila Variations, and offers a splendid insight into just how unrandom the random numbers of pi might be. Extracts used in the post are taken from a New Yorker article entitled The Mountains of Pi, written by Richard Preston, which reveal not only the lost world of homemade super-computers, but also something of man's obsession with identifying what is is that the empyreal pi is trying to convey:

"I knew I had read a profile in the New Yorker years ago about Pi, and then remembered that I have it in one of the New Yorker compilations that I own. It’s called “The Mountains of Pi”, and it’s from 1992, a profile of two brothers (the Chudnovsky brothers) on their quest for Pi. That makes it sound tame and intellectual. No. This is a profile of shared obsession.

I love having a library. “Wasn’t there something about Pi in one of those New Yorker books I have …?”

It’s also online – very fascinating profile of two men driven to extremes by their desire to understand pi. It’s also from a time when something like a “computer” in your house was something of a novelty, let alone a “supercomputer”, built to order. Built to serve Pi and Pi alone.

The Chudnovsky brothers claim that the digits of pi form the most nearly perfect random sequence of digits that has ever been discovered. They say that nothing known to humanity appears to be more deeply unpredictable than the succession of digits in pi, except, perhaps, the haphazard clicks of a Geiger counter as it detects the decay of radioactive nuclei. But pi is not random. The fact that pi can be produced by a relatively simple formula means that pi is orderly. Pi looks random only because the pattern in the digits is fantastically complex. The Ludolphian number is fixed in eternity – not a digit out of place, all characters in their proper order, an endless sentence written to the end of the world by the division of the circle’s diameter into its circumference. Various simple methods of approximation will always yield the same succession of digits in the same order. If a single digit in pi were to be changed anywhere between here and infinity, the resulting number would no longer be pi; it would be “garbage”, in David’s word, because to change a single digit in pi is to throw all the following digits out of whack and miles from pi.
“Pi is a damned good fake of a random number,” Gregory said. “I just wish it were not as good a fake. It would make our lives a lot easier.”

Around the three-hundred-millionth decimal place of pi, the digits go 88888888 – eight eights pop up in a row. Does this mean anything? It appears to be random noise. Later, ten sixes erupt: 6666666666. What does this mean? Apparently nothing, only more noise. Somewhere past the half-billion mark appears the string 123456789. It’s an accident, as it were. “We do not have a good, clear, crystallized idea of randomness,” Gregory said. “It cannot be that pi is truly random. Actually, truly random sequence of numbers has not yet been discovered.”

Our minds just don't seem capable of taking pi in. It is an infinite amount of digits, but ones that do not vanish over some distant horizon, stretched over an infinite distance, as the mind might imagine them doing. No, the infinite numbers of pi do not move further and further away from us, but can be seen to exist in a very finite distance, a space which recedes into nothing more than a point, an infinitesimal dot as it were. I wonder if it might be possible to create a form of pi which might be digested, and ultimately understood by the mind?

Mysterious Pi

2011-04-01T14:50:00.000-07:00

"Throughout the many centuries pi (π) has been examined and dissected in countless ways. The fascination with pi continues to the present. To this day no one has noticed anything unusual about pi.

When I was eighteen years I noticed the 3_4_5 right at the start of pi. I thought it odd that the Pythagorean triplet would begin right at the start of pi but gave it no more thought. Years later I noticed the 1_1_2 at the start of the square root of two and thought that this discovery was strange. These two oddities both at the same position fanned my curiosity. During the many years of examining pi (π), √2 and S I found that these three constants have an very odd interwoven relationship.

[..]Pi = 3.14159265358979323... It is very odd that a group of eight small different contiguous primes: 3, 14159, 2, 653, 5, 89, 7, 9323 are right at the start of pi. Many and possibly infinite small (numbers with five or fewer digits) and large (greater than five digits) different contiguous primes may exist after 9323. As it turns out right after the 9323 prime the next contiguous prime is: 846264338327........303906979207, it is 3057 digits long. So if pi started with 8462... the first prime would be 3057 digits long.

It will be interesting to see how many digits the average contiguous prime has. Perhaps more interesting may be to find how scarce are groups consisting of eight small contiguous primes of which none of the prime numbers are duplicated."

~~Extracts taken from "Proof of the Existence of God - The Ingenious Numeration of Three Constants" by Vasilios Gardiakos http://www.artmusicdance.com/vaspi/highlights.htm

Pi, Infinity and Zero

2011-03-31T07:44:00.000-07:00

If you visualize pi as the connection between a circumference and diameter, and you release the circumference from the diameter, you have just created reality (male and female, yin and yang, north and south). Pi, as a potential point, and diameter as connection between two real points, creates a mandatory circumference, even though the entire circumference may not show up in one place at one time. This is a mouthful and it takes some time to ponder. But this is how we end up with movement (any entity, process, system). Movement is nothing more, or less, than the connection of two points, a general X and Y. If we weren’t moving, we would not perceive (call) movement as movement. But, for now, this is a diversion.

We can begin with the idea of a point, and assume, from point, that point must assuredly be circle, since point, if it is real, must have a diameter (even if this diameter is too small to discern). Therefore, there are no points that are not also circles, or, another statement that goes with this one is, there are no points, just circles. So no matter how we start, we are at (with) a (the) circle (and also of, to, and from it). If we are the starting point, we are a circle that connects to many other circles (which we may view as points or units or entities, processes or systems). It becomes apparent, quickly, that many words are used to describe the same entity (similar entities). (Also, fortunately and unfortunately, there is no starting point, and there are only starting points.)

But back to pi. Pi, if it connects a circumference and diameter, also connects a half circumference and diameter. Half of the circumference might be showing, and the other hidden. Or, the diameter might be hidden with both halves of the circumference disconnected. If we eliminate any idea of time and-or space, and start out, instead, with pi, as a connector of diameter and half-circumference, we can notice pi is a necessary infinite movement that starts at zero. This allows for any movement anywhere with no limit, in no particular order, and with no particular direction, destination, and-or relationship to the original point. Pi, in this sense, is invisible. (Zero is an invisible circle.) How do we get there?

Imagine pi as a point on an invisible circle. Whatever point you pick is connected in a straight line (diameter) to another point, creating a mandatory circumference or set of circumferences. Assuming we collapse all the circumferences into one, and, further, assuming we divide the circumference in half at the point where the diameter connects one point to another on the same circle, we have created a mandatory second diameter (and third) which will act the same (be connected to another two half-circumferences which also function as diameter connected to another two half-circumferences ad infinitum. There is no limit to this expansion. This is how we get to infinity. It is also how we get velocity and acceleration, because even though the diameter and half-circumference connect the same two points, they are mandatorily different sizes, and this is the origination of time and space.

A constant connects two points via two routes which end up an infinite number of routes, and also a finite number of routes (either you stay on the sphere which is the total set of circumferences of one diameter or you escape it). Zero, in this view, then, would have to be pi. That is, pi is playing the role of both zero and infinity, as it connects a stationary spot to two moving spots, where the two moving spots are not moving at the same rate (or in the same direction, necessarily). This is a very simple analysis that ends up being quite complex, once we recognize, we are certainly NOT limited by our conventional ideas of dimension (sphere). That is, sphere is actually line, because they are both a connection of two circles.

Line means one circle has escaped from the other. Sphere means one circle has trapped the other. In this way, our idea of dimension is flawed. Dimension is more easily thought of in circles (since points must be circles, and thus eventually spheres). You can never say (know) how many circles are within a sphere. As long as you have one circle, you necessarily have two, which may, or may not, appear as a sphere (depending on where YOU are in time and-or space). You cannot disconnect a sphere from a circle or a circle from a sphere, but you must if you want to know what is really going on. One sphere interacts with another as if it were two circles. It is unaware it is a sphere.

We have confused the notions of point, circle, line, and sphere; we can also throw in disk, if we want to be clear. In actuality, we are stuck with circle (of circles) because of how a circle operates. That is, it always begins with pi, at any location, in either time or space, which mandates a diameter and circumference (line and circle) connection somewhere. These can appear in many shapes. All of the shapes, however, must reduce to line, and then circle. Line and circle can also be viewed as line and curve. This is how we get parabola and any open shape. And, also, any closed shape, trapezoid, for instance. What we see around us, as reality, and in our symbolic universes, is a wild set of lines and curves, in no particular order, except, if you look very closely, you will always find a one-two-three relationship (somewhere).

This one-two-three comes from pi-diameter-circumference, but does not necessarily end up in sphere (sometimes, but never always, because diameter and half-circumference are not equal). What it boils down to, though, is line is zero not equal to infinity. Circle is zero equal to infinity. Pi makes the decision, not zero or infinity. Pi is the observer that determines where things start and where they end. There are no starts and ends. Just pi on a continual circle connecting many things to many things. We see this as reality. We name it cosmos, universe, solar system, star, planet, cell, dna, particle, force, speed, acceleration, dimension, and, most important, gravity.

We experience it as ‘I,’ where I is an observer. Pi is the only observer, because observer, once he-she-it makes an observation, must make a circle (between observer and observation). Thus, observer is (always) circle. And what we ‘see’ is a snapshot of something that can never be ‘seen.’ Only a circle can create a circle. However, circle can be (and is) known by many different names. Movement, in this view, is an alternate word for observation (and thus an alternate word for circle). And movement, in physics, and also biology, is quite a convenient unifier. If we notice one entity observes another via relative movement (determines a size and speed) to determine whether or not and how to interact with it, and all entities do this, we can use movement as the entity and process that joins any two entities (or processes) together. (Movement is another word for line is another word for circle.) (Pi is doing the analysis and comparison, not either of the entities.)

Any entity and-or process produces the survival and reproduction of movement, as movement produces the survival and reproduction of any entity and-or process. Movement then, originates at pi (acting as zero) and can go to infinity (depending on the observer). We begin and end nowhere (via mind). Via matter, we have a beginning and end, and this is tied to the beginning and end of our surroundings which also have beginnings and ends. All of us, however, because of pi, have no true beginning, nor end. This is the beginning (and perhaps, in a sense an ending) of an understanding of the mind matter relationship in (via) physics (and biology). http://www.circular-theory.com/pi-infinity-and-zero/

Written by Ilexa Yardley, Conservation of the Circle, and The Circular Theory

The Way of the Tau

2011-03-19T06:42:00.000-07:00

The circumference of a circle is 2π times its radius. This is a bit confusing, having to stare at a factor TWO in an expression that is supposed to produce the circumference of ONE whole circle. Also, if you rotate the circle radius ONE full turn (360 degrees), your radian expression will contain an irrelevant factor TWO. Inelegant, clumsy, unnerving.

But these (and plenty more) annoyances can be resolved, if you care to define a different circle constant, τ (Greek letter tau):

τ= circumference/radius

Now, using this new circle constant τ , one full rotation (360 degrees) of a unit radius becomes simply 1 x τ = τ radians. Similarly, turning the radius 60 degrees means turning it one sixth (1/6) of a full turn and hence τ/6 radians, turning it 90 degrees is equivalent to ¼ of a full turn and hence τ/4 radians, and so on. Immensely more intuitive and straightforward, when there is no fooling around with an inexplicable factor 2, isn't it?

The inspiration of using the circumference/radius definition as the proper (and the one-and-only) circle constant first occurred to mathematician Bob Palais (in the article "Pi is wrong!"), but the idea of using the Greek letter τ (Tau) to denote it is due to physicist Michael Hartl. Hartl declared June 28 2010 "Tau Day", and he will probably celebrate the first Tau Day anniversary on June 28, 2011.

2π occurs in a large number of important mathematical expressions (Gaussian probability distribution, Fourier transform, Cauchy's integral formula, etc.), so replacing 2π by τ makes things easier and simpler.

The price of this simplicity is that the expression for the area of a circle becomes A = ½τr2, which contains an inconvenient factor ½. But Michael Hartl maintains that there are a lot of quadratic forms of this type in mathematics and physics (distance fallen: ½gt2, spring energy: ½kx2, kinetic energy: ½mv2, etc.), so the area formula for a circle will be easy to remember.

So τ = 6.283185 ... is the only circle constant worth remembering. Forget all others – there can only be one winner! But victory may take some time, I guess.

Reference:

http://tauday.com/

In The Beginning (and the bit that came before it.)

2011-01-15T05:40:00.000-08:00

"In the nineteenth century, scientists had thought that the cosmos was made up of ninety-two basic elements, such as hydrogen, oxygen and iron, which were indestructible. This implied that the universe had a diversity of independently existing materials. However, during this century research had revealed that all elements were in fact made up of a single energy. The cosmos was therefore intrinsically one, whether it appeared as a speck of dust, a tree, a Nobel Prize-winning genius or a black-hole beyond the galaxies. The differences were merely appearances. Our senses give us a knowledge of what is apparent, but not of the underlying one reality of the cosmos. This one energy which permeates the whole of creation was what Hinduism calls ‘brahma’. Long before physics discovered it, Shankara had argued that the world of sense experience, that is the world of matter, was a world of appearance (maya), because at the root of each individual existence is the same energy which forms the cosmos. The human self (atman) is ultimately not distinct from the universal self (brahma). Duality is illusion. Reality is not dual, but one. Science has yet to catch up with what the seers in India had already understood over 2500 years ago. While Greece is the country of my birth, India is the country of my soul."
~~Queen Frederika

What was there before the absolute beginning of creation? It is a question which has haunted humanity since ... well, for want of a better word, the beginning. We've always been curious as to where and what exactly it is that the Universe unfurled from. Modern theory holds to the idea that the fabric of the Universe - four dimensional space-time - was born from the Big Bang. But what was before the Big Bang? Because it is impossible to concieve of either space or time before the Big Bang, it makes the question terribly difficult to answer, except of course in terms of "nothing." In his paper, "What Happened Before the Big Bang?" Paul Davies sets about explaining some of the frustration in why it is that "nothing" (at least in terms of modern theory) is the only, though unsatisfactory, reply. An extract from the paper is given below:

"Well, what did happen before the big bang? Few schoolchildren have failed to frustrate their parents with questions of this sort. It often starts with puzzlement over whether space "goes on forever," or where humans came from, or how the planet Earth formed. In the end, the line of questioning always seems to get back to the ultimate origin of things: the big bang. "But what caused that?"

Children grow up with an intuitive sense of cause and effect. Events in the physical world aren't supposed to "just happen." Something makes them happen. Even when the rabbit appears convincingly from the hat, trickery is suspected. So could the entire universe simply pop into existence, magically, for no actual reason at all? This simple, schoolchild query has exercised the intellects of generations of philosophers, scientists, and theologians. Many have avoided it as an impenetrable mystery. Others have tried to define it away. Most have got themselves into an awful tangle just thinking about it.

The problem, at rock bottom, is this: If nothing happens without a cause, then something must have caused the universe to appear. But then we are faced with the inevitable question of what caused that something. And so on in an infinite regress. Some people simply proclaim that God created the universe, but children always want to know who created God, and that line of questioning gets uncomfortably difficult.

... Many people feel cheated. They want to ask why these weird things happened, why there is a universe, and why this universe. Perhaps science cannot answer such questions. Science is good at telling us how, but not so good on the why. Maybe there isn't a why. To wonder why is very human, but perhaps there is no answer in human terms to such deep questions of existence. Or perhaps there is, but we are looking at the problem in the wrong way.

Well, I didn't promise to provide the answers to life, the universe, and everything, but I have at least given a plausible answer to the question I started out with: What happened before the big bang? The answer is: Nothing.
http://www.fortunecity.com/emachines/e11/86/big-bang.html

~~Image: The 'ghost' of the Big Bang. A striking image showing the ghost of the Big Bang has been captured by a new space telescope. The Planck satellite was launched by the European Space Agency in May 2009 to study the early universe.
http://www.independent.co.uk/news/science/space-telescope-captures-images-of-big-bangs-afterglow-2018909.html

But I wonder, can it be possible for the human mind to concieve of something that does exist outside space and time, without leaning on something as unsubstantial as the term "nothing"? In terms of human history, is it possible to find any evidence of anyone ever having tried to point at the existence of such a thing? There is one source which comes to mind, and it's a place where the line between myth and metaphysics can get very fuzzy indeed - the Bible. Quite aptly, it is at the very beginning of the Bible, in the first words of the Book of Genesis, that we are introduced to a version of how things looked before the moment of creation:

"In the beginning God created the heaven and the earth."
~~Genesis 1:1

This would seem to suggest that God stands alone, and seperate from the heaven and earth which He created, forming a trinity as it were, of heaven, earth, and Himself. We think we know what heaven and earth are, but where exactly does that leave our understanding of God? The way in-which God enters the Bible from some unmentioned, hidden realm, guarantees His presence is virtually impossible to define. He has effectively been drawn from nothing, having appeared from nowhere, so that before creation, He is seen as being empty and invisible - a concept of meaningless proportions. This concept has been dragged over into our understanding of God in the time after creation too, having so far proved Himself impossible to substantiate in anyway, shape or form - either physically, or philosophically. All this has assured God a place in humanity's collective consciousness as someone, or something, whom is distant, and unapproachable, simply because He is unknowable. To some, God might be the Universe, but to others, He might as well not bother to exist at all.

Quite unexpectedly, what we find is that Big Bang theory seems to correspond with the creation story told in Genesis, in that the Universe was born from "nothing." The Universe might be here now, for whatever reason, but both the Bible and Big Bang theory seem to agree, you would not find anything which existed before it - that includes space-time, and apparently, that goes for God too.

However, our understanding of what was around previous to creation, at least in terms of Western religion, is based on but one interpretation of what amounts to a few choice words from the Bible. Is it at all possible to interpret them differently? Professor Van Wolde of Radboud Univerity in The Netherlands, claims to have done so, and her interpretation of the first sentence of the Book of Genesis, gives us the perfect opportunity to piece together an entirely new perception of God, the Universe, and lest we forget, ourselves:

...Prof Van Wolde, 54, who will present a thesis on the subject at Radboud University in The Netherlands where she studies, said she had re-analysed the original Hebrew text and placed it in the context of the Bible as a whole, and in the context of other creation stories from ancient Mesopotamia.

She said she eventually concluded the Hebrew verb "bara", which is used in the first sentence of the book of Genesis, does not mean "to create" but to "spatially separate".

The first sentence should now read "in the beginning God separated the Heaven and the Earth"
http://www.telegraph.co.uk/news/newstopics/religion/6274502/God-is-not-the-Creator-claims-academic.html

If you remember from previous posts, we've discussed how the doctrines of the alchemists acknowledged the materia prima as the uncreated substance of God. The materia prima, though never fully disclosed, was also known to them as "black earth." Taking the view that the black earth of the alchemists' is the same sort of stuff as the earth mentioned in Genesis, then it appears that our modern understanding of the creation story is not as cast-iron as we think. Apparently, God did not just happen to mysteriously materialise into existence at the point of creation, but rather, He'd been hanging out the entire time previous to it too, in the guise of something non-too-disimilar from common, everday dirt.

Maybe the Book of Genesis was not written quite so simply as we percieve it today. Perhaps there is more to it than it simply being a story of God's magical appearance, and how He pulled heaven and earth out of a hat. What Moses may have been trying to convey, was an explanation of how a rather impressive Being, whom having made some sort of decision to create the Universe, did so by separating into a duality containing both heaven and earth. This is not describing dualism in the sense of two opposing substances in conflict with one another, but more of a monoism, in-which just one substance creates the illusion of duality by opposing itself.

"The concept of duality seems to be an integral part of all life as we perceive it on this planet. To those who have become increasingly aware of a deeper place of being, it is still, at times, difficult to comprehend the connection or better said, oneness, between these “seemingly” two realms of relative reality. We have called it “heaven/earth”, spirit world/natural world, or material world/nirvana, but the same veiled reality exists within all these concepts. One world we would call “natural”, is a phenomenal world perceived by the natural senses of sight, hearing, touch, smell, and taste. The other world seems to be more a dimension of “spirit” and is “sensed” through a different set of senses which in most are hopelessly obscured behind an elusive veil. The subject of being able to reasonable discern the spirit realm to the extent that its peace, delightfulness and abundance may be experienced as a part of Life on earth has been the quest of people for millennia and has been woven into every form of religion, cult, or psychic group imaginable. Yet the premise that we are living in one realm “A” and needing to get to another realm “B” is foundation upon which all these formulae are based."
http://www.aplaceofbeing.com/Letters/articles/letters/on_duality.htm

If God is a substance of some description, it must mean that heaven is a substance too. Importantly, the substance of heaven is the exact same stuff, the exact same single element, from which God Himself is made. This one same substance, the materia prima, is the thing from which the Universe was created, and subsequently, it might be supposed that it is also the one thing which constitutes the entire Universe in this very moment too. It's exciting to imagine that if heaven is describing a substance, it means, at least theoretically, that we should be able to find it around here someplace. Maybe, just maybe, it's possible to enter heaven within the limits of our own lifetime.

If we choose to, God can now be seen, and fully understood, not as some errant dictator, but as an ever-present, all-pervading entity from which all of creation spilled forth. It's intruiging that this perception of God as Universe, now moves us much closer to the philosophy expounded by Eastern mystics. For them, God is not some separate entity to be worshipped, but One whom is very much entwined with our everyday lives.

" One of the main philosophical trends in Hinduism is known as the Vedanta. Several streams of thought emerge from Vedantism, of which one is referred to as non-dualistic. While God enters the soul for an intimate communion with the saint in Christianity, God is also a separate entity with an existence apart from the mystic, hence the dualistic nature associated with Christian mysticism. In the East, the world is a manifestation of God (pantheism); in the West, the world is the creation of God (theism). In theism the mystic never is or becomes identical with God; there is always a “great gulf” between God and man. When Meister Eckhart claimed that “God and I, we are one,” he was accused of heresy by the church. In Hindu mysticism and Plotinus, mysticism seeks to go beyond all dualism and rest in an absolute undifferentiated unity. To these mystics it appears that there is within their mystical consciousness no division whatsoever, there is no God outside the Self; God is the Self. The secret is realizing that the individual self, the pure unity of the finite ego, IS the Universal Self, the Absolute. Where there is consciousness of the Self, individuality is no more. It is not that the individual self Becomes the Universal Self. It always was the self. It comes to realize this truth in the moment of illumination."
http://www.soultrek.com/3%20eastern%20mys.html

If we were to accept that God, and heaven, and earth are all describing the same substance, then it seems only natural to want to know what this substance is precisely. The next line from the Book of Genesis does not tell us directly, but it does offer something of a clue to the nature of this biblical earth, the only thing to exist before creation and the supposed uncreated substance of God.

"And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters."
~~Genesis 1:2

Sure, it's not exactly brimming with adjectives, is it? We are told that the biblical earth is something without form - a void, or chasm or somesuch - to be found only in utter darkness. For all intents and purposes, these could be the same choice of words that a blind-folded person might use when asked to describe what they see. Despite knowing that the materia prima is a real, physical substance, we are resigned to a fate where it is never discovered, because it seems we are unable to elaborate further on its constitution, other than using words which seem only to add upto "nothing." However, Moses does appear to be trying to describe SOMETHING. Something moves. Something is there. It's not much to go on, but I wonder, might it be enough?

Many thanks:

http://www.theosociety.org/pasadena/sunrise/46-96-7/ev-prent.htm
http://apocryphile.org/jrm/articles/paradox.html
http://www.nonduality.com/whatis9.htm
http://www.kheper.net/topics/worldviews/dualism.htm
http://www.themystica.com/mystica/articles/d/dualism.html
http://www.booksie.com/religion_and_spirituality/article/juggernaut/collection-of-thoughts-from-hindu-mystics-partii
http://en.wikipedia.org/wiki/Buddhist_atomism
h http://www.suite101.com/content/hun-and-po-the-duality-of-the-taoist-soul-a253866
http://scripturetext.com/genesis/1-2.htm

First Matter

2010-11-27T04:35:00.001-08:00

"In the beginning God created the heaven and the earth."
~~Book of Genesis 1:1

~~The NASA Hubble Space Telescope photo of V838 Monocerotis (February 8, 2004)
http://www.wisdomportal.com/Ouroboros.html

Before physicists, the men of science, so to speak, were alchemists. Unlike modern theory today, the doctrine of the alchemists was very much centred around theology. To them, God was not some abstract philosphical concept, but rather, God was understood, and accepted as being something from which everything is made. In other words - God is everything - God is the Universe itself. In this sense, the alchemist was more closely related to the mystic than a scientist.

"Alchemists agree with chemists that there is unity in matter, but whereas chemistry teaches that atomic particles are the smallest units in matter, alchemists believe in an ultimate source they call Ether, or the universal fluid. Matter to the alchemist is therefore compact energy, which can be dissolved into free energy or force. For the alchemist energy and matter are the same thing, namely substance. The substance is the Absolute, the One that Hermes Trismegistus describes in the Emerald tablet. This One is divided into three parts: Intelligence or force, Energy and Matter."
~~The complete book of spells, ceremonies, and magic By Migene González-Wippler

~~The Alchymist by Joseph Wright of Derby (1734-97) 1771
http://www.alchemywebsite.com/wright.html

Alchemists hoped to move closer to God by developing a greater understanding of God, not only in the spiritual sense, but in a real, physical sense too. If God truly was everything, and everything owed its existence to God, then it must be possible to find the existence of God in any thing, in any place we care to look. What the alchemist was seeking in all material things, and that includes himself, was the very substance of God. There is a real possibility that some alchemists may have found it. Even the word "alchemy" seems to hint at something of the nature of this substance.

"The word alchemy is derived from the words Al and chemia.

Al is an ancient word meaning ‘God’ in the sense of the ‘All’, the ‘Absolute’. As part of the word alchemy it means ‘divine’ or ‘universal’. The word was used in many ancient languages and cultures, including the Egyptian, Mesopotamian, Hebrew and Celtic. Later, the Hebrew form of the word came to be written as El, which in the Christian bible is translated as ‘God’. In Islam the word appears as Allah.

Chemia is from the Greek word khemia, which itself is derived from the ancient Egyptian word kemit, meaning ‘black earth’."
http://www.zoence.co.uk/info_sheets/alchemical%20process.htm

In other words, the term "alchemy" could be interpreted as meaning "God is black earth." These choice of words to describe God may at first seem a bit off-key - one might have expected something a bit more poetic, more holy, more ethereal - such things as "God is mountain dew," or "God is sunshine." Instead, for those seeking the substance of God, the alchemist tells us to ignore all this fluffy idealism, and points only to the dirt at our feet. According to the Bible, this dirt, or dust is also the same foodstuff which the serpent of Eden is condemned to eat forever.

"And the LORD God said unto the serpent, Because thou hast done this, thou art cursed above all cattle, and above every beast of the field; upon thy belly shalt thou go, and dust shalt thou eat all the days of thy life."
~~Genesis 3:14

When God banishes Adam and Eve from the Garden of Eden, God makes a point of telling Adam that the dust of the ground served as the material from which he was created. This at first seems only slanderous, the final insult to be added to Adam's degradation - but this being the word of God, it is told only as a truth. It is intriguing that the only substance required by God to create intelligent life is little more than ordinary dust from the ground.

"By the sweat of your brow you will eat your food until you return to the ground, since from it you were taken; for dust you are and to dust you will return.”
~~Genesis 3:19

Thus, a significant clue to the nature of God, and the powers of creation, are all contained in nothing more than a speck of dust. In searching for the substance of God, it is likely that these same thoughts must have occured to the alchemist. If one could gain knowledge of this biblical dust, then one would know the form which God takes before creation. In other words, the dust mentioned in the Bible, woefully unflattering as it is, could be interpreted as being the definitive description for the uncreated substance of God.

"Uncreated Independent Substance: thing that is not dependent upon the causal power of any other thing in order to exist or to remain in existence, and is not a property of any other thing.(The only thing that satisfies this definition of "uncreated substance" is God.)"
http://home.wlu.edu/~mahonj/Descartes.Substance.htm

The alchemist believed that all material bodies are formed from only one substance, indeed, "the substance." The entire material of the Universe was said to consist of this one single element - the materia prima (first matter.) For some, the materia prima represented God in its most purest form. It represents the primordial matter from which all things, and especially living things, are made.

Using the Bible, Paracelsus and others, connected prima materia to God; "before Abraham was made, I am." (John 8:58) Since prima materia is supposedly the [philospher's] stone, also, this also demonstrated the stone is without beginning or end. Jung noted many Christians hearing this would not believe their ears, but it was plainly stated in the Liber Platonis quartorum, "That from which things arise is the invisible and immovable God."
http://www.themystica.com/mystica/articles/~alchemy/prima_materia.html

If the alchemist was able to gain mastery over this substance, then it should, at least in theory, be possible for them to take dominance over the will of God. The forces of God would be subjucated to the whim of the alchemist, giving him/her the power to fulfil all their earthly desires instantaneously. The alchemist would at last become master of their own fate, and the need for a God will have been entirely displaced.

The goal of Alchemy is the Great Opus or the Great Work which is the purification of the lesser or gross and its elevation to the greater or more refined, whether in plants, metals, or inconsciousness. The ultimate goal of the alchemist is to find the Prima Materia or the First Matter of nature as the dark, passive, unformed and raw virgin and universal stuff of creation. Through the alchemical process the alchemist transforms this Prima Materia into the Philosophers Stone. This accomplishment is most commonly known as the transformation of Lead into Gold, the heaviest, darkest, densest most earthbound, least valuable metal becoming Gold: Incarnated Light; the most glittering, luminous, valuable metal; symbol of the sun and of spiritual attainment and consciousness, spiritual illumination as cosmic consciousness which is the ultimate goal of the human evolution.
http://www.scribd.com/doc/3466745/What-is-Alchemy

Certainly, one of the goals of alchemy was to achieve great wealth (after all, regardless of how close they moved towards God, there was always the danger of getting deeper into debt!). Possessing the philospher's stone would allow the alchemist to turn lead into gold, which quite literally, would give them the power to print their own currency. This remarkable prize however, pales in significance when compared to the true treasure which awaits the seeker. It is the one thing which is universally prized by humans, and desired above all other things, though seldom believed possible - the gift of immortality. The alchemist would finally be allowed to lift the veil, and to enter the world hidden from view, and recieve the key which will give him/her the power, and ultimately freedom, to choose the day they die. To become immortal would signify the alchemist's completion of the Great Work.

This philosopher’s stone is a metaphor – which means that it has both an inner and outer reality, neither of which can be taken for granted or understood exclusively. The development of the philosopher’s stone could only occur through a refinement of the initially untransformed base material of the world – the “prima materia” or black earth, which is simultaneously the alchemist’s own psyche, both conscious and unconscious (Jung, 1967, 1978, 1993) 4, as well as the actual underlying physicality of all the world’s substances.
http://www.spiritalchemy.com/t1-Ch1.html

Descriptions of how the philospher's stone appears physically, are understandably evasive, but that does not mean that the stone, "a stone which is not a stone," is necessarily hidden from view. Quite the contrary, it was sometimes said to be a common substance, found everywhere but unrecognized and unappreciated.

As you can see, the importance of identifying the substance of the materia prima is essential to the creation of the philosopher's stone. So, what exactly is the materia prima? Which one of the elements from the periodic table is meant to be the hidden substance of God?

Many thanks:

http://etext.lib.virginia.edu/journals/abraham/sjsr/issues/volume2/number1/sjsr02-01-e05.html
http://www.authorama.com/god-idea-of-the-ancients-13.html
http://www.spirasolaris.ca/sbb4f.html
http://www.radicalacademy.com/adiphilnaturalism2.htm
http://www.spiritsound.com/aum.html
http://www.zoence.co.uk/info_sheets/alchemical%20process.htm
http://hem.bredband.net/arenamontanus/Mage/alchemy.html
http://www.unhinderedliving.com/energyGod.html
http://www.alchemylab.com/christian.htm
http://www.iep.utm.edu/spinoza/
http://www.awakeninthedream.com/artis/SacredArtOfAlchemy.html
http://www.unexplainedstuff.com/Magic-and-Sorcery/Alchemy.html
http://www.thelemapedia.org/index.php/Alchemy
http://www.soul-guidance.com/houseofthesun/alchemy%202.htm
Alchemy: an introduction to the symbolism and the psychology By Marie-Luise von Franz
http://www.annebaring.com/anbar08_seminarl1.htm
http://forums.skadi.net/showthread.php?p=456245
http://www.stichtingargus.nl/vrijmetselarij/sria_r3.html
http://www.angelfire.com/journal/cathbodua/EsodictS.html
http://www.aether-is-one.com/intro.html
http://wapedia.mobi/en/Stoicism
http://basyevortex.com/index.php?option=com_content&task=view&id=40&Itemid=59
http://fusionanomaly.net/philosophersstone.html

Anaxagoras

2010-11-06T08:58:00.000-07:00

Who appointed their path to sun and stars?
Who but Thou is it through whom the moon waxes and wanes?
Who set the earth in its place below and the cloudy sky
that it shall not fall?
Who established the waters and the plants?
Who yoked the steeds to wind and clouds?
Who, O Wise One, is the creator of Good Mind?
What artificer made light and darkness?
What artificer sleeping and waking?
Who made morning, midday and night,
to remind the wise man of his task?
Is it as Good Mind that thou hast founded thy Dominion?
Who created Devotion, sacred with Dominion?

ZARATHUSHTRA

All other things have a portion of everything, but Mind is infinite and self-ruled. . . . For it is the finest of all things and the purest; it has all knowledge about everything and the greatest power. And Mind controls all things, both the greater and the smaller, that have life.

ANAXAGORAS

European history began with the emergence of Athens as the classical cosmopolis of the northern Mediterranean. Athena won a dispute with Poseidon for protective sovereignty over Attica by giving the area the sacred and nourishing olive tree, and her sacred bird, the owl, became the city's symbol. Doubly blest, Athens became the focus of the converging forces that would in a brief time initiate a culture of such creativity and splendour that subsequent generations in Europe would look to her as the source of science, ethics and knowledge of the soul. Athens first drew ideas to herself, and later attracted thinkers, until she housed the schools and traditions that provided the foundation of European thought. Perhaps even before the time of Homer, an incipient anthropomorphic decadence began to undermine the spiritual appeal of Mycenaean and Minoan mythology. The gods as personifications of intelligent forces in Man and Nature were degraded into beings that reflected only the most superficial human traits. As the Mysteries withdrew increasingly from the desecrating gaze of the public eye, though not from public knowledge, thinkers sought for new ways to vivify the deeper meanings of human existence. Early philosophers emphasized either an understanding of nature shorn of its anthropocentric excesses or the ethical dimension in the structure of the cosmos. Pythagoras and Plato brought this latter concern to sublime fruition, and Anaxagoras laid the foundation for experimental method and theoretical science.

Anaxagoras was born in the port city of Clazomenae in Ionia around 500 B.C., though almost nothing is known about his life or the order of happenings. His father, Hegesibulus, was extremely wealthy, and Anaxagoras apparently devoted the early years of his life to leisurely study. Though a Greek city, Clazomenae had fallen to the Persians, and it is likely that the thoughtful Anaxagoras would have learnt the rudiments of the religion taught by Zarathushtra, whom the Greeks called Zoroaster. Ahura Mazda, the Lord of Light, cannot be described in crude human terms, though Vohu Manah, Good Mind, the first aspect of manifest deity, is seen as that which orders and moves all things. Rather than a human form, Ahura Mazda and its seven aspects are best represented by an eternal fire and the seven-branched candelabrum. From the beginning of his active life, Anaxagoras made fire a central theme in his thought. When he was about twenty years of age, he journeyed to Athens, where his wealth (and perhaps his father's connections) gained him immediate entrance into the highest circles where he became good friends with Themistocles and Pericles. Though Pericles was probably never a student of Anaxagoras in a formal sense, he often acknowledged his debt to Anaxagoras for many of his ideas and policies, and eventually their relationship became famous.

Anaxagoras taught in Athens throughout his adult life. Sometime during that period he became the focus of opponents of Periclean political reform. Satyrus wrote that Thucydides, a long-standing enemy of Pericles, found it impossible to confront his opponent successfully, and so attacked him indirectly by bringing charges of asebeia (impiety) against Anaxagoras. Since the Athenians officially held the sun to be a deity, the view held by Anaxagoras that the sun is like a molten stone was construed by some as impiety. But Thucydides also charged him with treason in the Persian wars. Anaxagoras fled Athens and only later returned with full pardon after Pericles had more firmly secured his own position. Sotion, however, wrote that Anaxagoras had been charged with impiety late in life for his teachings about the sun and that he was forced into exile. Whatever the literal truth, Anaxagoras lived in tumultuous as well as glorious times, and it would not have been impossible for him to be exiled twice. Though vulnerable because of his acquaintances, Anaxagoras neither took part in the political life of the city nor paid any attention to the opinion of others. Much to the dismay of friends and relatives, he allowed his extensive inheritance to waste away, either permitting his farmland to return to pasture or giving it to relatives. His concern lay wholly in the contemplation of heaven and earth.

Anaxagoras was not the first Greek to observe nature studiously, though he was an exceptionally careful scrutinizer of phenomena. For example, painstaking observation led him to the discovery that the image reflected in the dark pupil of the eye constitutes the exact field of vision. Whilst others were teaching that the whole eye saw, he correctly identified the pupil as the active window of perception. Observation alone, however, was insufficient to discover the causes of things. Anaxagoras developed the method of experimentation as a means of confirming explanations of natural processes. His observations of wind blowing through trees convinced him that gases exert pressure, but to convince a sceptical Athenian audience, he filled a bladder with air and sealed it shut, and then invited challengers to crush the bag. Since air was trapped inside, he surmised that the air exerted pressure which manifested as resistance to anyone attempting to flatten the bag. Besides observation and experimentation, Anaxagoras recognized the need for a unity of explanation, a coherence of theory, to account for nature. Though he did not emphasize the mathematical nature of the world as did Pythagoras, Anaxagoras drew together the other elements of scientific endeavour, laying down the broad foundations of scientific method used even to this day.

His concern with explaining the occurrence of natural phenomena in terms of invariable laws and not special circumstances – such as the whimsy of capricious deities – along with his reticent form of life resulted in the status of prophet being attributed to him. On the basis of his theory of the stars and planets, he argued that it was possible for rocky material to fall from them to earth. When a meteorite fell to earth at Aegospotami, perhaps during his lifetime, the legend arose that he had predicted it in detail. His grasp of the nature of eclipses enabled him to inform Pericles of the time of a total solar obscuration, and the statesman used that advance knowledge to reassure the Athenians when it occurred. Ammianus Marcellinus wrote that Anaxagoras had gained such knowledge in Egypt. Plutarch asserted that he had mastered geometry and had successfully squared the circle. Satyrus reported that Euripides greatly admired him and might even have been his student. Theodoretus supported the less likely possibility that Socrates as a youth studied with Anaxagoras.

Anaxagoras followed the tradition of his day and taught students who came to hear him discourse, but he did not establish a permanent school. Nevertheless, like Parmenides, he wrote one book outlining his methodology and explanations of nature. Since Parmenides had taught that change was logically impossible, the work of Anaxagoras, taking change as fundamental to nature, became the standard text for nascent Athenian science. Socrates is made to refer to this work in Plato's Apology and to criticize its approaches in the Phaedo, where he does not say Anaxagoras is wrong but rather that his explanations of behaviour are inadequate when applied to human action. The strong motivation to understand nature so profoundly moved Anaxagoras that he renounced concern for his own welfare, exemplified in his abandonment of his large inheritance, withdrew from the exciting public affairs of the day, and remained aloof from personal involvements of every kind. His detachment from worldly involvements became legendary when he responded to a report of his son's death by saying that he knew that his son was mortal from the moment of his birth. When asked why one should be pleased to have been born rather than not, he answered, "In order to contemplate the heavens and the structure of the world-order as a whole." This constitutes the truly happy life, Anaxagoras said, though most people would not think so.

Anaxagoras lived in Athens for about thirty years, a time spanning the golden age of classical Greek culture. He represented the rational approach to understanding events and things, advocating a calm and detached perception supported by an alert mind, freed from the obscuring clouds of unrestrained emotion and self-seeking bias. Near the end of his life he left Athens, perhaps because he was again charged with impiety, and retired around 433 B.C. to the Hellespontine city of Lampsacus. There he was welcomed, surrounded by students and honoured by the citizens. When he died in about 428 B.C., he was given a public funeral, and the citizenry inscribed a tribute on his tomb:

Here lies Anaxagoras, whose picture
of the order of the universe
came closest to the truth.

Shortly before his death his followers asked him what he would consider an appropriate way to honour his memory. He replied that students should be given the month in which he died as a vacation each year. Anaxagoras was so highly respected in Lampsacus that his death was observed as he wished for well over a century.

The scientific philosophy developed by Anaxagoras rested upon two fundamental convictions: that nature and all its operations are rational, i.e., accessible to understanding through reason, and every account of nature must be consistent with and explain observed phenomena. Affirming that "visible things are a sight of the unseen", he did not think that universal order is limited to the empirical realm, but only that any explanation of Nature must take visible nature into account. His physics began with the theoretical assumption that matter is eternal, for without it one has to explain wholly unobserved processes of matter coming into existence from immateriality. Anaxagoras also recognized that the fundamental feature of every aspect of the universe is change. Whilst Parmenides argued from the fact of ceaseless change in nature to a metaphysical conception of the world in which neither change nor plurality is real, Anaxagoras left aside metaphysics and attempted to explain the principles of change and the maintenance of multiplicity. He did accept the sheer logic of the Parmenidean demonstration that nothing comes into being nor passes away and taught that change is due to separation and combination.

Matter for Anaxagoras is eternal and changeless in its essential nature. Since whatever is cannot cease to be, material substances cannot be reduced to fundamentally different elements. Therefore, matter must be infinitely varied in its irreducible parts to account for the vast variety of things that exist. The doctrine of homoiomeria is simply that the parts have the same nature as the whole, and the ultimate parts are eternal. Since living forms must be composed of parts of the same nature, and since they are nourished by food, every object must contain particles of an infinite variety and life must be part of everything that exists. Just as bone is called bone because of a predominance of bone particles, and rock is so named because of a predominance of mineral particles, so living things are recognized as such when the arrangement of particles allows for the expression of life. Given that "in everything there is a portion of everything", if material particles are of any size and of infinite variety, each thing, for example, a loaf of bread, would be infinite in size. If particles are of no size, however, even an infinite number would constitute no size at all. Therefore, Anaxagoras reasoned, particles are infinitesimal.

For of the small there is no smallest, but there is always a smaller; for it is not possible for what is not to be. But of the great there is always a greater also. And it is equal in number to the small, each thing being in respect to itself both great and small.

This ingenious view explains nutrition, for each part of the body extracts from ingested food that which is like itself, and it requires an infinitely large universe to accommodate an infinitude of particles. There is nothing in the nature of particles, though, that accounts for change. Particles are eternal, but structures composed of them come into existence and pass away. All change is the result of motion, and any rational theory of dynamics must aim to isolate one force or principle of motion which can account for every kind of change. Since the rational order of the universe includes change, the only rational entity which meets the required criteria is Nous or Mind. Materially, the macrocosm and microcosm reflect one another exactly; dynamically, the obvious operation of Nous in man, animals and even plants must reflect the universal operation of cosmic Mind. Mind as a rational principle of change manifests throughout nature as Law. Thus the universe consists of eternal, unchanging particulate matter and eternal, unchanging dynamic Mind. Subsequent philosophers criticized Anaxagoras for describing mechanical processes to explain natural phenomena and for not invoking Mind, but Anaxagoras saw clearly that calling on Mind as the direct cause of everything explained nothing, and that the universality of Mind implies that all mechanical processes are expressions of dynamic Nous. Mind, being as vast as the infinite cosmos, cannot be described in the language of secondary and derivative laws; nevertheless, being rational, it makes possible those describable laws whilst remaining an impenetrable yet undeniable mystery hidden behind them.

Whilst mechanistic explanations are sufficient for many natural phenomena, the laws involved cannot be thought of as simply mechanical. Law is the intelligent activity of Nous. Anaxagoras thought that this was shown by a study of perception. When two fluids of the same temperature are brought together, no alteration in temperature is observed. Only when qualitative opposites are conjoined does change occur. Perception involves change, and it too must follow the general principle that observable changes take place only between bodies whose states differ in some way. Universal Mind pervades every area of nature and is responsible for all change. Therefore Nous is qualitatively different from every material substance, and so is incorporeal yet substantial. This utter difference from everything else allows Mind to perceive and know everything. Nothing is hidden from Mind, which thus operates intelligently.

Armed with these principles of physics, Anaxagoras boldly set forth a theory of origins. Since everything contains everything else, differing only in preponderance of types of particles, Anaxagoras imagined that prior to the activity of Mind, matter abided in a state of chaos in which all particles were evenly distributed. Since nothing would differ from anything in this primordial condition, neither existence nor perception was possible, though matter and Mind were in a kind of timeless Be-Ness. For reasons now impossible to ascertain, Mind began to move matter in an initial rotational motion that tended to gather more dense particles at the centre and lighter particles in the extremes. The vestiges of this initial rotation can be seen in the movements of planets and the turning of the celestial vault. Once the rudimentary separation of material masses had occurred, a second motion, rising and falling, became dominant, as can be seen, Anaxagoras thought, in the convection currents which cause many meteorological phenomena. These motions produced the gross arrangement of the world as presently experienced, and Mind uses numerous more focalized processes to refine the world-order. Mind, being eternal as matter is, cannot perish. Whilst sleep is like death within a lifetime, there is one critical difference between the two.

Sleep comes from weariness of the body. It is a thing undergone by the body, not the soul. And death is the separation of the soul from the body.

Mind is immortal, but observation does not reveal its post-mortem destiny. For Anaxagoras, there is no reason to doubt that Mind continues to experience after the death of the body, remains involved in the ordering of the world, and ever reincarnates.

Since Anaxagoras refused to use Mind as a blanket explanation for every phenomenon, he had to construct explanations of diverse natural processes on the basis of observation and experimentation. Whilst some of his conclusions might appear to be absurd in comparison with contemporary explanations, his fidelity to his rigorous method led him to many remarkable insights. He held that all planets and stars are composed of the same substances of which the earth consists, and that they all follow the same laws. He recognized that thunder and lightning were effects of the same cause, which had to do with fiery etheric forces. He taught that light must travel in straight lines, that lunar eclipses are due to the earth's shadow falling on the moon, and that, unlike the sun which is incandescent, the moon shines by reflected sunlight. Long before Galileo dared to report his telescopic observation, Anaxagoras recognized that the moon is covered with mountains and ravines but is devoid of water. He taught that the Milky Way consists of innumerable stars and that the Nile floods in summer owing to far distant snows melting in the spring. Observation taught him that plants as well as animals breathe. He noted that in humans the father determines the sex of the child. So complete was his commitment to the unity of all life that he could not say the human being differs from animals because he possesses mind: all things are pervaded by Mind. Man is distinguished by his ability to express Nous more fully than other creatures, and this shows up in the human frame. When asked what the human hallmark is, Anaxagoras replied that "Men are the wisest of the animals because they have hands."

Anaxagoras not only exemplified the spirit of the Periclean age; he stood in the forefront of its creators. His faith in reason, reverence for Nature, rigour in method and refinement of experimental techniques earned him a permanent place as one of the early founders of modern science. Because Nous suffused everything, for Anaxagoras the ethical dimension of life is inherent in it, and so he gave no special attention to the subject. Plato saw that ethics had to be made explicit in a society rapidly losing its nearness to Nature, and that Mind in Man, psychology, is also a central study. In refraining from focussing on these critical areas of human understanding, Anaxagoras also adopted an attitude of true scepticism, neither pronouncing upon nor claiming to know anything about them other than that rational enquiry of the loftiest and most precise kind would lead to knowledge here as everywhere else. Whereupon he did focus his gaze, he influenced all subsequent generations of seekers, both in his theoretical methodology and in the experimental practices he laid down. Perhaps it is fitting that historians and philosophers nicknamed him 'Mind'.

Copyright©2010 Theosophy Trust
http://theosophytrust.org/tlodocs/articlesTeacher.php?d=Anaxagoras.htm&p=7

Prime time

2010-11-06T06:11:00.000-07:00

Fame and fortune await the person who cracks the greatest problem in mathematics.
And that could be any day now, says Erica Klarreich

WHEN G. H. Hardy faced a stormy sea passage from Scandinavia to England, he took out an unusual insurance policy. Hardy scribbled a postcard to a friend with the words: "Have proved the Riemann hypothesis". God, Hardy reasoned, would not let him die in a shipwreck, because he would then be feted for solving the most famous problem in mathematics. He survived the trip.

Almost a century later, the Riemann hypothesis is still unsolved. Its glamour is unequalled because it holds the key to the primes, those mysterious numbers that underpin so much of math-ematics. And now whoever cracks it will find not only glory in posterity, but a tidy reward in this life: a $1 million prize announced this April by the Clay Mathematics Institute in Cambridge, Massachusetts.

There are signs that the great prize might soon be claimed, and the most promising approaches come not from pure mathematics, but from physics. Researchers have discovered a deep connection between the Riemann hypothesis and the physical world—a connection that could not only prove the hypothesis, but also tell us something profound about the behaviour of atoms, molecules and even concert halls. One mathematician has followed this lead into a very strange place, seeking a solution in an intricately twisted space with infinitely many dimensions.

Yet the primes seem simple enough at first glance. They are those numbers, like 2, 3, 5 and 7, that are only divisible by 1 and themselves, although 1 isn't included among them. Primes are the atoms of the number system, because every other number can be built by multiplying primes together. Unfortunately there is no periodic table for the primes—they are maddeningly unpredictable, and finding new primes is mostly a matter of trial and error.

In the 19th century, mathematicians found a little order in this apparent chaos. Even though individual primes pop up unexpectedly, their distribution follows a trend. It's like tossing a coin. The result is unpredictable, but after many coin tosses we expect roughly half heads and half tails. The primes get rarer as you look at larger and larger numbers (see Diagram), and mathematicians found that this thinning out is predictable. Below a given number x, the proportion of primes is about 1/ln(x), where ln(x) is the natural logarithm of x. So, for example, about 4 per cent of numbers smaller than ten billion are prime.

So far so good. But that "about" is very vague. Numbers are products of pure logic, and so surely they ought to behave in a precise, regular way. Mathematicians would at least like to know how far the prime numbers stray from the distribution.

Georg Riemann found a vital clue. In 1859, he discovered that the secrets of the primes are locked inside something called the zeta function. The zeta function is simply a particular way of turning one number into another number, like the function "multiply by 5". Riemann decided to see what would happen if he fed the zeta function complex numbers—numbers made from a real part (an ordinary number) and a so-called imaginary part (a multiple of i, the square root of -1). Complex numbers can be visualised as arrayed on the complex plane, with real numbers on the horizontal axis and imaginary numbers on the vertical axis.

Riemann found that certain complex numbers, when plugged into the zeta function, produce the result zero. The few zeros he could calculate lay on a vertical line in the complex plane, and he guessed that, except for a few well-understood cases, all the infinity of zeros should lie exactly on this line.

What does this have to do with the primes? If you plot how many primes exist below a given number (see Diagram above), what you get is a smooth curve with small wiggles added—that is, the 1/ln(x) rule, plus deviations.

According to Michael Berry of Bristol University, you can think of that pattern of deviations as a wave. Just like a sound wave, it is made up of many frequencies. "And what are the frequencies?" asks Berry. "They're the Riemann zeros. The zeros are harmonies in the music of the primes."

Berry isn't speaking in metaphors. "I've tried to play this music by putting a few thousand primes into my computer," he says "but it's just a horrible cacophony. You'd actually need billions or trillions—someone with a more powerful machine should do it."

Riemann worked out that if the zeros really do lie on the critical line, then the primes stray from the 1/ln(x) distribution exactly as much as a bunch of coin tosses stray from the 50:50 distribution law. This is a startling conclusion. The primes aren't just unpredictable, they really do behave as if each prime number is picked at random, with the probability 1/ln(x)--almost as if they were chosen with a weighted coin. So to some extent the primes are tamed, because we can make statistical predictions about them, just as we can about coin tosses.

But only if Riemann's guess was right. If the zeros don't line up, then the prime numbers are much more unruly. As Enrico Bombieri of the Institute for Advanced Study in Princeton writes on the Clay Institute website (www.claymath.org/prize_problems/riemann.htm): "The failure of the Riemann hypothesis would create havoc in the distribution of prime numbers." And the havoc would spread further. Hundreds of results in number theory begin, "If the Riemann hypothesis is true, then . . ."

This is why mathematicians long to prove the hypothesis. But how do you prove something about an infinity of numbers?

Researchers have used supercomputers to calculate the first 1,500,000,001 zeros above the x-axis, and millions of other zeros higher up, and so far all of them lie on the critical line. If just one of them did not, the Riemann hypothesis would be killed.

This is heartening, but no amount of computer hacking can prove the hypothesis. There are always more zeros to check. And, cautions Andrew Odlyzko of AT&T Labs, who has spearheaded the effort to calculate zeros, "number theory has many examples of conjectures that are plausible, are supported by seemingly overwhelming numerical evidence, and yet are false."

Some deeper insight is needed. Early in the 20th century, mathematicians made a daring conjecture: that the Riemann zeros could correspond to the energy levels of a quantum mechanical system.

Quantum mechanics deals with the behaviour of tiny particles such as electrons. Crucially, its equations work with complex numbers, but the energy of a physical system is always measured by a real number. So energy levels form an infinite set of numbers lying along the real axis of the complex plane--a straight line.

This sounds like Riemann's zeros. The line of zeros is vertical, rather than horizontal, but it is a simple bit of maths to rotate it and put it on top of the real line. If the zeros then match up with the energy levels of a quantum system, the Riemann hypothesis is proved.

For decades, this idea was only wishful thinking. Then in 1972 came a hint that it could work. Hugh Montgomery, at the University of Michigan, had found a formula for the spacings between Riemann zeros. Visiting the Institute for Advanced Study at Princeton, he ran into physicist Freeman Dyson at afternoon tea, and mentioned his formula. Dyson recognised it immediately. It was identical to a formula that gives the spacings between energy levels in a category of quantum systems—quantum chaotic systems, to be precise.

Chaos theory applies to physical systems so sensitive to their starting conditions that they are impossible to predict. In the Earth's chaotic atmosphere, for example, the tiny draught caused by the flap of a butterfly's wings can eventually lead to a tremendous storm. Almost all complicated systems are chaotic.

The quantum versions of these systems have a jumble of energy levels, scattered apparently at random but in fact spaced according to Montgomery's formula. Quantum chaotic systems include atoms bigger than hydrogen, large atomic nuclei, all molecules, and electrons trapped in the microscopic arenas called quantum dots. Could the Riemann zeros fit one of these quantum chaotic systems?

In the late 1980s, Odlyzko picked an assortment of systems, and compared their energy levels with the Riemann zeros. In a discovery that electrified mathematicians and physicists, Odlyzko found that when he averaged out over many different chaotic systems, the energy level spacings fitted the Riemann spacings with stunning precision.

That's still not enough. To prove the Riemann hypothesis, researchers must pinpoint a specific quantum system whose energy levels correspond exactly to the zeros, and prove that they do so all the way to infinity. Which, of all the different systems, is the right one?

Berry and his colleague Jonathan Keating have made one suggestion. In a chaotic system, an object usually moves unpredictably, but sometimes its path will cycle back on itself in a "periodic orbit". Berry and Keating think that the right quantum system will have an infinite collection of periodic orbits, one for each prime number. And last year, Nicholas Katz and Peter Sarnak predicted that the system should have a special kind of symmetry called symplectic symmetry.

Both of these clues should help quantum chaologists zero in on the one system that will prove the Riemann hypothesis. "I have a feeling that the hypothesis will be cracked in the next few years," says Berry. "I see the strands coming together. Someone will soon get the million dollars."

The winner could well be Alain Connes, a mathematician based at the Institute of Advanced Scientific Study in Bures-sur-Yvette, France. Connes has a startlingly direct approach to the problem: create a system that already includes the prime numbers. To understand how, you have to imagine a quantum system not as a particle bouncing around an atom, say, but as a geometrical space. It sounds odd, but it represents one of the weird things about quantum systems: they can be two or more things at once.

Like Schrödinger's cat, which is a peculiar mixture of dead and alive, any quantum object can find itself in a "superposition" of different states. To characterise this messy existence, physicists use what they call a state space. For each kind of possibility (say "alive" and "dead"), you draw a new axis and add a dimension to the space. If there are just two possible states, as is the case for Schrödinger's cat, the space is two dimensional, with three states it is three dimensional, and so on.

Then in the Schrödinger's cat space, you would mark a cross one unit along the x-axis to represent a fully alive cat. Similarly, a stone dead cat would be one unit up the y-axis, and a part-alive, part-dead cat would appear somewhere along an arc between these points.

The "shape" of the space affects how the state moves around in it, and therefore how the system works, including the way its energy levels are arrayed. This depends not just on the number of dimensions, but also on the geometry of how they are stuck together.

Connes decided to build a quantum state space out of the prime numbers. Of course, the primes are a bunch of isolated numbers, nothing like the smooth expanses of space in which we can measure things like angles and lengths. But mathematicians have invented some bizarrely twisted geometries that are based on the primes. In "5-adic" geometry, for example, numbers far apart (in the ordinary way) are pulled close together if they differ by 5, or 15, or 250—any multiple of 5. In the same way, 2-adic geometry pulls together all the even numbers.

To put all the primes in the mix, Connes constructed an infinite-dimensional space called the Adeles. In the first dimension, measurements are made with 2-adic geometry, in the second dimension with 3-adic geometry, in the third dimension with 5-adic geometry, and so on, to include all the prime numbers.

Last year Connes proved that his prime-based quantum system has energy levels corresponding to all the Riemann zeros that lie on the critical line. He will win the fame and the million-dollar prize if he can make one last step: prove that there aren't any extra zeros hanging around, unaccounted for by his energy levels.

That last step is a formidable one. Has Connes simply replaced the Riemann hypothesis with an equally difficult question? Some experts advise caution. "I still think that some major new idea is needed here," says Bombieri.

Berry, for his part, doesn't flinch at the mathematical peculiarity of Connes's system. "I'm absolutely sure that if he's right, someone will find a clever way to make it in the lab. Then you'll get the Riemann zeros out just by observing its spectrum."

Berry and Keating are now turning around this connection with physics, using mathematics based on the Riemann zeta function to predict the behaviour of chaotic systems. Most models of quantum chaos are complicated and difficult to calculate. The Riemann zeros, by comparison, are easy to compute. "We always test our formulae on the Riemann zeta function to see if they work," says Keating.

If Connes or one of the physicists proves the Riemann hypothesis using a quantum system, the link will be firmly established. Then, Berry predicts, the field will blossom. Using the mathematics of the zeta function, scientists will be able to predict the scattering of very high energy levels in atoms, molecules and nuclei, and the fluctuations in the resistance of quantum dots in a magnetic field.

And it turns out that the same mathematics applies to any situation where waves bounce around chaotically, including light waves and sound. So the performance of microwave cavities and fibre optics could be improved, and the acoustics of real concert halls might profit from the music of the primes.

Even so, it is mathematics that will gain the most. "Right now, when we tackle problems without knowing the truth of the Riemann hypothesis, it's as if we have a screwdriver," says Sarnak. "But when we have it, it'll be more like a bulldozer." For example, it should lead to an efficient way of deciding whether a given large number is prime. No existing algorithms designed to do this are guaranteed to terminate in a finite number of steps.

Proving the Riemann hypothesis won't be the end of the story. It will prompt a sequence of even harder, more penetrating questions. Why do the primes achieve such a delicate balance between randomness and order? And if their patterns do encode the behaviour of quantum chaotic systems, what other jewels will we uncover when we dig deeper?

Those who believe that mathematics holds the key to the Universe might do well to ponder a question that goes back to the ancients: What secrets are locked within the primes?
http://www.timetoeternity.com/time_space_light/prime_time.htm

Sri Nisargadatta Maharaj

2010-11-05T07:33:00.000-07:00

In the following passages, you will find the unparalleled words of Nisargadatta Maharaj as seen in the book I Am That, translated by Maurice Frydman from Acorn Press.

Only the dead can die, not the living. That which is alive in you is immortal.

In reality there is only the source, dark in itself, making everything shine. Unperceived, it causes perception. Unfelt, it causes feeling. Unthinkable, it causes thought. Non-being, it gives birth to being. It is the immovable background of motion. Once you are there, you are at home everywhere.

In reality there are no others, and by helping yourself you help
everybody else.

That which you are, your true self, you love it, and whatever you do, you do for your own happiness. To find it, to know it, to cherish it is your basic urge. Since time immemorial you loved yourself, but never wisely. Use your body and mind wisely in the service of the self, that is all. Be true to your own self, love yourself absolutely. Do not pretend that you love others as yourself. Unless you have realized them as one with yourself, you cannot love them. Don't pretend to be what you are not, don't refuse to be what you are. Your love of others is the result of self- knowledge, not its cause. Without self-realization, no virtue is genuine. When you know beyond all doubting that the same life flows through all that is and you are that life, you will love all naturally and spontaneously. When you realize the depth and fullness of yourself, you know that every living being and the entire universe are included in your affection. But when you look at anything as separate from you, you cannot love it for you are afraid of it. Alienation causes fear and fear deepens alienation. It is a vicious circle. Only self-realization can break it. Go for it resolutely.

I see what you too could see, here and now, but for the wrong focus of your attention. You give no attention to your self. Your mind is all with things, people and ideas, never with your self. Bring your self into focus, become aware of your own existence. See how you function, watch the motives and results of your actions. Study the prison you have built around yourself, by inadvertence.

The seeker is he who is in search of himself. Give up all questions except one: 'Who am I?' After all, the only fact you are sure of is that you are. The 'I am' is certain. The 'I am this' is not. Struggle to find out what you are in reality. To know what you are, you must first investigate and know what you are not. Discover all that you are not - body, feelings, thoughts, time, space, this or that - nothing, concrete or abstract, which you perceive can be you. The very act of perceiving shows that you are not what you perceive. The clearer you understand that on the level of mind you can be described in negative terms only, the quicker will you come to the end of your search and realize that you are the limitless being.

Nothing is wrong with you, but the ideas you have of yourself are altogether wrong. It is not you who desires, fears and suffers, it is the person built on the foundation of your body by circumstances and influences. You are not that person. This must be clearly established in your mind and never lost sight of.

What is really your own, you are not conscious of. What you are conscious of is neither you nor yours. Yours is the power of perception, not what you perceive. It is a mistake to take the conscious to be the whole of man. Man is the unconscious, the conscious and the superconscious, but you are not the man.Yours is the cinema screen, the light as well as the seeing power, but the picture is not you.

The source of all has all. Whatever flows from it must be there already in seed form. And as a seed is the last of innumerable seeds, and contains the experience and the promise of numberless forests, so does the Unknown contain all that was, or could have been and all that shall or would be. The entire field of becoming is open and accessible; past and future co-exist in the eternal now.

Only when you realize the true peace, the peace you have never lost, that peace will remain with you, for it was never away. Instead of searching for what you do not have, find out what is it that you have never lost? That which is there before the beginning and after the ending of everything; that to which there is no birth, nor death. That immoveable state, which is not affected by birth and death of a body or a mind, that state you must perceive.

Back To Words Of Wisdom

If you seek reality you must set yourself free of all backgrounds, of all cultures, of all patterns of thinking and feeling. Even the idea of being man or woman, or even human should be discarded. The ocean of life contains all, not only humans. So, first of all abandon all self-identification, stop thinking of yourself as such-and-such or so-and-so, this or that. Abandon all self-concern, worry not about your welfare, material or spiritual, abandon every desire, gross or subtle, stop thinking of achievement of any kind. You are complete here and now, you need absolutely nothing.

I find that somehow, by shifting the focus of attention, I become the very thing I look at, and experience the kind of consciousness it has; I become the inner witness of the thing. I call this capacity of entering other focal points of consciousness, love; you may give it any name you like. Love says "I am everything". Wisdom says "I am nothing". Between the two, my life flows. Since at any point of time and space I can be both the subject and the object of experience, I express it by saying that I am both, and neither, and beyond both.

Giving up desire after desire is a lengthy process with the end never in sight. Leave alone your desires and fears, give your entire attention to the subject, to him who is behind the experience of desire and fear. Ask: who desires? Let each desire bring you back to yourself.

Questioner: It will take much time if I just wait for self-realization.
Maharaj: What have you to wait for when it is already here and now? You have only to look and see. Look at your self, at your own being. You know that you are and you like it. Abandon all imagining, that is all. Do not rely on time. Time is death. Who waits--dies. Life is now only. Do not talk to me about past and future--they exist only in your mind.
Questioner: You too will die.
Maharaj: I am dead already. Physical death will make no difference in my case. I am timeless being. I am free of desire or fear, because I do not remember the past or imagine the future. Where there are no names and shapes, how can there be desire and fear? With desirelessness comes timelessness. I am safe, because what is not, cannot touch what is. You feel unsafe, because you imagine danger. Of course, your body as such is complex and vulnerable and needs protection. But not you. Once you realize your own unassailable being, you will be at peace.
Questioner: How can I find peace when the world suffers?
Maharaj: The world suffers for very valid reasons. If you want to help the world, you must be beyond the need of help. Then all your doing as well as not doing will help the world most effectively.
http://peacefulrivers.homestead.com/NisargadattaMaharaj.html

Are We Ready?

2010-11-04T05:07:00.000-07:00

"It's a waste of energy to be angry with a man who behaves badly, just as it is to be angry with a car that won't go."
~~Bertrand Russell

Nowadays, the idea that energy could be a substance is actively discouraged, and very often ridiculed. However, reducing the term "energy" to what amounts to nothing more than an abstract concept, is really only a recent development in terms of human history. Before the advent of modern theory, our knowledge was based on traditions, stemming back to ancient times, which percieved energy as a substance. Indeed, it was supposed that the entire Universe is immersed in it. In an enlightening article taken from Centerpointe's newsletter "Mind Chatter" - "What is Reality (and why should you care?)" - Bill Harris, writes a fascinating account of how the mystics came to interpret "reality." As Harris explains, what the mystics percieved as energy, also had a lot to do with what they saw as the Divine. Below, is an extract taken from the article:

"For thousands of years, mystics have said that there is one energy in the Universe, that the Universe and everything in it is the play, the dance, the vibration, of that one energy. Underneath the seeming multiplicity, they say, everything is made of the same substance. This energy, they say, is everywhere and "everywhen." This principle is sometimes described as Omnipresence or God. The Hindus and Buddhists call this principle, Sat-one energy, everywhere, making up everything, always, past, present, and future.

Quantum mechanical physicists, for several decades, have been saying the same thing. They notice that on the sub-atomic level, particles come into being, seemingly out of nothing, and dissolve, and disappear back into nothing, that two or more particles collide, and one, two, three or more particles, of a different kind, appear from the collision, or all the particles cease to exist. There is a "something" that everything comes out of, and returns to, and which makes up, or is the background of, everything.

The mystics, however, went one step further. In adddition to noting that this one energy is Omnipresent, they also said something else that I think is rather startling. They said that this one energy is aware of itself being everything and everywhere and everywhen: that it is conscious, that it has consciousness. The mystics called this second characteristic of reality Chit."
http://www.centerpointe.com/about/article_downloads/whatisreality.pdf

I suspect that one of the reasons as to why modern theory is so reluctant to imagine energy as a substance, is because admission immediately arouses unwelcome religious fervour. Science wants only to deal with the stuff in the Universe that it can quantify, and substantiate - it's not overly concerned with an invisible, intangible God, nor for that matter, any unseen, immaterial, imponderable substances which might, or might not be energy, or consciousness, or whatever. To science, the questions and answers to these concepts are irrelevant - mere distractions from the job at hand. Entering philosophical and theological discourse will quite often do nothing to enhance their sums.

If science were ever tempted to admit energy as a substance, conceding to the idea that it can be quantified in someway, it would fling the door wide open to suggestions that the stuff of energy, which it is weighing, measuring, and collecting, comes very close to being the pure substance of God. It would allow practically every person on the planet to point out to scientists, that the substance of energy, which they are pouring from their flasks into test tubes, also amounts to unequivocal proof in the existence of God. Now, it is not simply energy which we can reach out and touch, all with our very own fingers, but God's personal Being.

I suspect that there are some physicists who are more than familiar with the God-energy conundrum, but are hesitant to openly discuss it - not because they are wilfully obstructive, or even particularly dispassionate - but because they are aware of the chain of events such an admission will unleash. The question which rises to the forefront most is not: is science willing to admit to the existence of God? The question we should really be asking is: is humanity ready to recieve all that power?

Searching After Truth

2010-10-27T13:31:00.000-07:00

Searching After Truth
~~By Aja

Being More Spiritual

Often we hear from someone how they wish to be more spiritual. It usually sounds something like, "I really want to be more spiritual. I should meditate more, or chant more, or read more, or do more service or worship more, or do more yoga, or I should quit watching TV, or quit smoking, or quit drinking, or...." There is always the idea that by adding something to oneself it will make them more spiritual. Or it will make them feel more spiritual. Or, it will make others see them as more spiritual. And generally this is a very sincere desire. People feel that there is something lacking in their lives. They know that there is more to life than making a living, eating, sleeping, and getting little temporary pleasures from this or that. They want real substance, and they know that substance comes from something greater than themselves - love, community, God, spirituality, meaning. But how do you get this? How do you become more spiritual?
The difficulty is in thinking that one can become more spiritual! It is like a man saying I want to be more manly or a woman saying I want to be more womanly, or a human saying they want to be more human. Being a man is intrinsic to men. Being a woman is intrinsic to women. Being a human is intrinsic to a human. Being spiritual is intrinsic to everyone. Who and what you are is spiritual. What are you going to add to yourself to be more a man, more a woman, more a human, or more spiritual. Anything that you add will simply make you less of, or detract from the intrinsic nature. It is like adding red paint and artificial rose perfume to a rose to make it more rose-like. These will only cover what is already perfect. If you wish to fully appreciate the beauty of a rose, don¹t try to add to the rose. Remove that which obscures the pure vision of the rose and keeps you from experiencing it in its perfect roseness. Similarly, if you want to purely experience your own spiritual nature, you must subtract, not add. How can you add to what is already perfect? It is simply a matter of recognition, of stopping the search for something to add to make you more, better, greater.
But this, in itself, can be the most difficult task for it means letting go in every way. Say you have an old chair you have found, and it has layers of old and chipping paint. You can just add something, paint over the old paint, in an effort to make it perfect. But the real beauty comes from stripping away all the old paint until you have only the pure wooden chair and you can appreciate the perfect symmetry and simplicity of the wood. What we see as imperfect in ourselves is not our intrinsic nature. It is what we ourselves have added or layered on to our pure being. By adding more beliefs in the name of religiosity or spirituality, we are only furthering ourselves from the pure, simple, symmetry of our inherent Being. So the key is not in adding, but in subtracting. It is easy to add. It is also easy to continue on exactly as we are. It is more difficult to subtract, because for most people subtracting feels very much like dying. We are maintained by our belief systems. They make up who and what we are, or rather what we think we are. We have built our own reality based on our principles of what is good and bad and right and wrong, and have factored out our real spiritual nature in the equation. The world then is made up of dualities a whole universe created as a means to give one some standing in what would otherwise be empty space. Because if you subtract all your beliefs, all your ideas of good and bad, all of your dualities, everything you hold on to as what you are and what the world is, what are you left with? Nothing. You, as who you thought you were, is dead. If you are no longer a man or a woman, a spiritual person, a doctor, car mechanic, a loner, a people person, an intellectual, or slower learner, a Canadian, a music buff, a mother or father, a sister or brother, a human, an angel, a child of the universe, a... any possible definition you can apply, then what is left. Only "I", without definition, without location, without any parameters, or limits. Suddenly there is nothing to strive for, nothing to fear, nothing to be joyful about and nothing to grieve. And then you recognize that this is your True Self. This is your spiritual Self. This is being more spiritual. It is beyond material, which means outside of all concepts bound by time and space. There is no longer even a past or a future, but only an eternal Now and an unlimited Here.

Bliss of Non-Being

You are the Bliss of Non-Being You do not exist as you. This is the truth. You have a conception of who and what you are that is an imagination or dream. The truth of who you are is infinitely more profound, yet is only accessed by letting go of all ideas of who you are now - ALL of them. And the conceptions and ideas themselves are nearly infinite in their number and subtlety. This is what makes Awakening so difficult. As long as you have any idea or mental conception of who you are, you are yourself holding the pattern in the field of consciousness that maintains that belief existence. And if you try to let go of the beliefs one by one, you will first find that they are infinite, and secondly that the very idea of someone letting go of their beliefs becomes a very strong new identification that oversees all of the other beliefs. You have superimposed layers of personal beliefs over what is in fact consciousness alone. It has nothing to do with a personal entity. And yet, we literally fight to maintain the very individual existence which is the cause of our bondage and suffering. But the truth is that we do not exist as an individual any more than a mirage in the desert has water. It is due to a combination of circumstances only. Apparently objective experiences arise and we create a subjective entity to whom they are arising. Then we build a whole set of ideologies and conceptions around that apparent subjectivity, based on this primordial misconception, create a universe of duality which is especially attracted to the concepts of right and wrong, and our suffering is confirmed and assured. We must be able to see that the very root cause of suffering and pain are our insistence on maintaining ideologies centered on an individuality that doesn¹t exist. We are exactly like a ball of twine. If you unravel the twine to get to whatever is inside, you only end up with a pile of twine and empty space. When you unravel the ideas and beliefs that hold "you" together, all that remains is empty space. There is no "you" in the way that you think. So the preeminent question arises, "Who are you?" Until you can seriously begin to ask this question of yourself and delve into the depths of consciousness, honestly and courageously abandoning all that is not you, there will continue to be an apparent entity suffering the "slings and arrows of outrageous misfortune".
You are the Bliss of Non-Being However, you immerse yourself in your desires of selfishness. You identify with the river of thoughts and desires that arise in the ocean of consciousness. All desires are selfish. Your actions are based on desires that you think will make You happy. They are selfish. Even if you are trying to save the world, you do so out of selfishness. Even if you are feeding the hungry, clothing the poor, or worshipping God, you are doing it because you think that it is "right" to do so and it makes you happy to think that you are "right". Even those seeking enlightenment, freedom, salvation, liberation, are doing so because it is "right". They seek to end suffering, to attain eternal bliss, to be free from death and bondage. Surely these are noble causes, honorable beliefs, but they are still based on a person desiring something. They are the apparent effect of an apparent ego, struggling in an apparent world, attempting to gain apparent happiness, to counteract apparent suffering. Guess What? It¹s all an illusion - the ego, the world, the suffering, the happiness. It is all a dream state, being dreamed in a cosmic dream. When you abandon the body/mind, what is left? When you give up all identification, what remains? It is only I Am, without any identification. It is the I Am that becomes identified. So first revert to the I Am without identification. Dwell in that and see where it comes from. From what does I Am arise. Even the I Am has no location. It is not located within space and time. You cannot find it¹s beginning or end. It is only consciousness without objects. It is the infinite subjective state without a sense of other. Remove all else and dwell in that. Do not think about it, but simply reside in that absolute consciousness. As one sinks deeper (surrenders) into that pure awareness, even the sense of I Am begins to dissolve, for even it is a part of the dream. There is only empty awareness of non-being. It is pure existence, awareness and, yes, bliss. This is the state which you actually are, always have been and always will be.
You are the bliss of non-being. But if all of this is non-being, from what does it arise? There is no answer in words to that question for all questions and answers arise from duality. But rest for a moment in non-duality and what occurs? There is a spontaneous arising to experience. The bliss of non-being is the spontaneous arising of "That" to experience "Itself". In Sanskrit, the Absolute is termed Sat-Chit-Ananda or Existence-Awareness-Bliss. These are non dual expressions of a singularity. Just as heat and light are non dual aspects of fire - you cannot separate heat and light from fire - so existence, awareness and bliss cannot be separated from the Absolute. They are three aspects of the same singularity. They are not linear or causal in any way, but a simultaneous expression. For the Absolute is existence eternal. It is Being-ness or That which Is. And in its Beingness, awareness Is, for awareness is a symptom of existence. But awareness alone is pure subjectivity only and must by its nature be aware of an object, so expresses Itself as multiplicity in order to experience Ananda or Bliss. So what Is, all that is, for no other reason than the necessity to Be and expand, is Bliss. It is what Is. It is Awareness. It is Bliss. Every moment, every day, every thing, from the most "Holy" to the most "wretched" is the Bliss of the Absolute, expressing Itself infinitely as you, me, the universe, and all of this one thing. But when you create personhood when you make a someone separate, create "a" being separate from the One Beingness, conjure up a someone to try and experience that bliss, you separate yourself from the very Bliss that you already are. Like a spark leaving the fire to experience the heat of the flames, you lose your innate bliss in a vain journey away from your Self.
You are the Bliss of Non-Being And when you are ready to give up your separateness, to abandon the vain and continuous searching for happiness, to free yourself from the limitation of personhood that appear to bind you, then you can again experience the bliss of non-being.

All Is God

When one dives deep into consciousness, what do you find? At first, all seems dark and empty. We are so used to putting our attention on and faith in the mind, our thoughts, our senses and the world, that we would not know what to do if they no longer existed. And yet, how are we assured of the reality of this world in which we put so much faith? What makes it real. How do we know that it is the concrete, tangible thing that we make it out to be?
The truth is that it may not be as certain as we think. Many scientists and the new quantum physics are exploring realms that were once only found in the mystical writings of the East. They are considering the possibility that all this is but vibration. They have recognized that atoms are vast universes of empty space, and that the only tangible parts, the electrons, protons, and neutrons, are really nothing but vibrational nodes, in an ocean of similar material. And that these atoms, dancing around the universe, are all sharing atomic particles with each other, so that the boundaries of one to another, and thus with each "individual" thing in the universe becomes extremely blurred - blurred to the point of extinction. So what the universe tells us through the scientists, and through the ancient mystics, is that there is only One thing. That one thing is doing it all. It is the background, foreground, and the dance itself. So what is this one thing? I like to call it God.
Now the difficulty with names is that they are immediately inaccurate. The moment you name something, you have taken away any reality it had and put a label upon it which makes it a concept. We allow ourselves to define the entire universe with names, and thus lose our ability to directly experience it. This is especially true with all of the experiences which we have within ourselves. We have stopped feeling anything that arises, and have instead replaced the initial signs of something with a name that allows us to stop it in its tracks. Emotions are a perfect example of this. Try to describe fear, what it really is, and you¹ll get more labels like afraid, excited, goose bumps, etc. The moment any particular energy arises within us, we have a box that we put that feeling into that has a label - fear, anger, guilt, sadness, happiness, hunger, and so on. Almost no one stops to actually experience the physical feelings, the thought patterns, energetic pulses, and other signs that arises throughout the day. The moment they come up, they go into a box called fear, happy, pain, and sorrow. In the end all we get is a box called "I¹m fine."
What has happened is that we have developed a duality based judgement of good and bad. We assume, because of our belief systems, most of which have been foisted upon us, that certain things are good and others are bad. And we have this gigantic spectrum which goes from really, really good, and includes things like God, saints, heaven, bliss, love and enlightenment, to really, really bad like Satan, demons, hell, agony, hate and delusion. But all this is the knowledge of good and evil.
Remember the Bible story. What was it that forced Adam and Eve from the Paradise of the Garden of Eden? It was that they tasted from the fruit of the tree of knowledge of good and evil. It was not the tree of good and evil, but the tree of knowledge of good and evil. Prior to tasting that fruit, they had no concepts of some things being good and others being evil. Everything was of Paradise. Everything was of God. They had no reason to doubt the serpent. He was also one of God¹s creatures. But they ate of this fruit, and began to distinguish duality.
When you distinguish duality, you are forced to make judgements that this is good, and this is bad. We do it every day, practically every moment. Even now you may be evaluating what you are reading as being good or bad. But when you stop distinguishing any duality - when you see everything and experience everything, including yourself as Divine, then their ceases to be judgement. Life becomes a great dance. There is only the Absolute. All is One. All is Truth. All is God.
But we must not think of God as that great white-bearded man sitting on His throne in Heaven, judging your every action as good and bad. This is our own projection of God. This is our own judgement of ourselves creating a picture of God as a Being of ultimate love and ultimate anger, rewarding us when we are good and punishing us when we are bad. We must let go of our concepts that hold us to our own ideal of what Reality is.
As long as we have concepts, ideas, belief systems, we are boxed into our own existence. We have allowed our beliefs to create who we are. We have allowed words and language to define us. You must fully experience that you are not a man or woman. You are not a human being. You are life itself. And life is God. You are the awareness which sees all, and yet makes no judgement. The mind makes judgements. The mind compartmentalizes everything, putting it in boxes. The mind separates Reality into pieces, and then decides which are right and wrong, good and bad. When the mind of another seems to have developed different beliefs and concepts than yours, they become wrong. They become the enemy. You see it as your duty to correct them or punish them, or avoid them. If you think you are liberal and open minded, then you decide you will listen with an open mind. But still you are evaluating according to your own beliefs. Or some people accept everything that anyone says, immediately reforming their own beliefs to whatever is the new fashion, the new trend, the new age fad. But you should accept or reject nothing. It is the accepting and rejecting of things which makes you unhappy. It is the accepting and rejection of ideas that makes you bound. If you truly wish to be free, you must stop this judgemental accepting and rejecting. Just stop! You must do it right now, in the moment.
The truth is, if you are seeing some things as good and others as bad, or accepting some while rejecting others, you are accepting, and simultaneously, rejecting God, the Absolute. Because as we have already said, there is only one thing. What is happening is all the Absolute. It is all God. Even if you take a very anthropomorphic view of God as an individual person, scriptures say that in the beginning there was only God, and God created the universes. So from what did He create them? From Himself. Some say the universes are the energies of God, like the sunlight from the sun. But that is also non-different. The energy and energetic are one. They cannot be separated. You cannot take heat or light from fire. Fire IS heat and light. All that arises from God IS God. So abandon all conceptions, all that you hold, and recognize the divinity that is all around you. Deeply experience that there is nothing outside of God, including yourself. Whatever you see, whatever you hear, whatever you smell, taste, or feel, whatever thoughts arise, even the concepts themselves, are God. You are God. Saturate yourself with that reality that there is absolutely nothing except God (or Brahman, the Absolute, Beingness, Divine Subjectivity, etc. etc.) and you will find that you yourself are that Divine Ocean of Bliss!

Doorway to Heaven

What is our definition of Heaven, the Absolute, or Enlightenment? What does that look like for you? What is it according to the saints of the world who have realized Truth? Everyone assumes that they know the truth that it automatically corresponds to what they believe it to be, as if the fact that they believe it makes it a certainty. Obviously, this has been the cause of religious wars throughout the centuries.
Now, of course, we are in a more enlightened state and we recognize that all of the worlds religions hold some portion of truth. It would be politically incorrect to suggest that one belief system was more true than any other. And since we are broad minded and open to all of them, certainly we are more fully conversant with the ultimate truth. Now we are enlightened in the great mysteries of spirit. We see that truth is like a great diamond with many facets. We understand and accept that there is one truth with many paths to reach it, and we honor each path and the people who choose to accept it.
But the path is not the goal, and while there are many paths that lead to that enlightened state, what does it look like once you get there? And if we don¹t know what it looks like when we get there, how do we even know that the path we are on will ultimately arrive at where we want to go? The difficulty is compounded by the fact that the enlightened state has been characterized as beyond definition, unspeakable, un-nameable, unknowable and beyond thought, beyond concepts and beyond mind. So any definition or name that we attribute to it is simply that - a name, not "It". This leads the aspirant, almost by necessity, to explore what is not "It" in hopes of finding "It". Since we are, to a great extent, motivated by, influenced by, and limited by our own conceptions of the Absolute, we will study and aspire for those things which match our conception of what "It" is, too often in a vain search, waiting for an experience which will prove to us that we have reached the "unknowable", "indescribable" "It".
The situation is very much like an analogy that was recently shared with me. If you had two doorways, a doorway to heaven and a doorway to a lecture about heaven, you would find the vast majority of people lined up before the doorway to the lecture about heaven. Often we aren¹t as interested in experiencing the divine as we are in being able to Œknow¹ about it, talk about it, and impress people with our astounding depth of information about it. And what if you could actually open the doors and look in? In the doorway to the lecture about heaven, you would find a room full of beautiful people, drinking organic tea, talking about Gods & Goddesses, doing energy work, singing songs, meditating together, discussing the pros and cons of various paths and spiritual techniques generally having a great time. On the other hand, when you opened the door to heaven, standing outside and peering in, you would see nothing. It would appear empty, dark, unattractive - because through that door there is nothing for the mind to know, nothing for the body to experience, no concepts or beliefs to grasp and certainly nothing that would "attract" our mind, unless annihilation was attractive. For to enter into the absolute is to be totally beyond the mind and ego.
But the good news is that there is nowhere to go, no doorway to step through, in fact, no pathway to follow. You, who you really are, is already That. For you are pure awareness, being-ness. You are what precedes mind, beliefs, concepts, ideas, hopes, struggles, body and ego. You do not need to find heaven. You are heaven.

Seeking a Spiritual Path

Seeking a Path In this day and age, knowledge of spiritual practices has become common, so much so that by simply plugging into the internet, one can access some of the most secret, ancient, and esoteric spiritual practices. Often these are practices, mantras, and rituals that were handed from teacher to disciple in strictest confidence, preceded by preparatory rites and given only with understanding and agreement to never reveal them. Now you can find them in about 2 minutes on the world wide web.
This has been both a great boon, and a curse. It has been a boon, because it reveals for the first time the depth of commonality between the world¹s religions and philosophies. It allows us to explore in greater detail the richness of spiritual teachings that were unavailable to a world without airplanes or internet. And in a time and culture when the village priest, guru or shaman is not quite as readily available, we can still find the teachings we seek. But there is a down side. One of the primary things that has been taken from us with this wealth of knowledge is the simplicity of knowingness. Our life has been turned topsy turvy with choice. Where we once knew where our destiny lay, what our path was, and what was required of us to gain the graces of the divine and enter into our conceived heaven, now we flounder in an ocean of choices. We painstakingly search through the plethora of spiritual options, dabbling in a little of this, trying a little of that. Our desperate hope being that we will find the perfect path, a saving grace that will fulfill all our material and spiritual desires, and conform with our own conceptions of the Truth.
But this too reveals to us that there must be something wrong if we need to choose one religion or path over another, assuming the correctness of one and the imperfections of another. Perhaps all of them fall short of the mark, the glory of God, the unnameable absolute. Perhaps it is our very search for an answer outside of ourselves that must be questioned. Perhaps not knowing is a blessing after all. For what is it that we can fully rely on? What can we know for certain? Any opinion that we maintain can always be refuted by someone else. Any set of rules, ideas, techniques, philosophies, theories, vows, ethics, will always clash with that of another. Our existence in the world is always accompanied by polarities of opposites, especially when it comes to beliefs.
But again, what can we know for sure? Even the existence of anything outside of ourselves can not be ascertained. God, heaven, hell, truth - are not provable to oneself from an outside source. In fact, the existence of the world itself, as a tangible reality, is unprovable. For instance, you could be dreaming at this moment. Few people are able to distinquish dream from reality while in a dream. Or perhaps your whole worldly existence is some kind of a projection as if a movie, like if you were merely a brain in a bell jar somewhere. Even many scientists suggest that this so-called reality may be much more spacial illusion than hard fact, and that we may be more floating in an ocean of nothingness, including our own bodies, than a concrete realm.
But the world is filled with such ideas, many ancient and many new, but the truth, such as it is, can only be found in one place. It is the only thing that can be taken as a certainty. It is the one thing that everyone shares in common. That is the fact of their own existence as awareness. Each person knows that they are. They have always known that they are. Each persons experience of themselves as existing has remained constant for as long as they can remember. Certainly the ideas they hold, the goals they strive for, even the complexity of their thoughts has changed, but the fact of their very existence is a constant that is never questioned. It is the questioning of this existence that must take place. It is the only thing that we can really be sure of, and it must be investigated thoroughly and continuously.
What is the method for this inquiry? One must investigate as to what is this "I". Prior to everything is the simple sense of existing as "I". But what is it? Where is it? When and where does it begin and end. Remember here, you¹re not seeking your ideas and thoughts, but that I-ness which witnesses all thoughts. What some might call "I Am" the simple, pure awareness which witnesses and perceives all. Delve into this! Rest in this! And you will find the only true path which means anything your Self!

Truth Beyond Belief
A Subjective Inquiry into Life

Belief. Everything we do is based on it. In fact, everything we say, think, or feel is centered around our own belief system. But what is belief? The first definition given in Webster¹s is: " a state or habit of mind in which trust or confidence is placed in some person or thing." Okay, it¹s a state of mind, or worse yet, a habit of the mind. I believe it¹s a nice day. I believe in the inherent goodness of people. I believe in God. I believe that people should be kind to each other. I believe that chocolate is better than vanilla. I believe that early to bed and early to rise make a man healthy, wealthy, and wise. I believe that hush puppies are ugly shoes. I believe that the movie Gandhi is more spiritual than Ferris Beuller¹s Day Off. I believe that for every drop of rain that falls a flower grows. Big deal. Every single one of these and the literally millions of other beliefs I hold as a habit in my mind can be directly refuted by someone, probably many people. Their logic, reasoning or emotional appeal regarding their beliefs may or may not be better than mine. However, their beliefs are also nothing more than a state, or habit of mind.
Now what about religion? (You may substitute faith, philosophy, ideal life-style, etc.) All great religions (etc.) are based in Truth. However, they are practiced as a belief. Let me say that again. All great religions are based in Truth but are practiced from belief. Truth and belief are not the same thing. The Truth is absolutely beyond beliefs. Even if the beliefs correspond to the Truth, the belief is but a dim reflection of the Truth. For instance, the Tao Te Ching says (more or less) "The Tao that can be named is not the eternal Tao." The Bhagavad Gita tells us that, "There is a banyan tree with its roots up and branches down. The real form of this tree cannot be perceived in this world." In other words, this is the world of misperception, and as long as we exist within this world we are bound to persist, as a habit of mind, in the realm of misperceptions and concepts. The mind is like a lens through which the light of Truth may shine. The more colored gels and filters there are over that lens, the more tainted is the light that shines through. Now what happens in the mind is similar. It is filled with concept gels and belief filters that obstruct the direct flow of light. Worse yet, the mind itself is an obstruction to direct experience of Truth as it must perceive Truth as an objective thing. I¹m told God is in Heaven. Sounds good to me, and I take it as a belief. However, each word is a concept to me, not Truth. I have a concept about God. God is the creator, therefore He must be real old. God is everywhere. Everything is God. God is in your heart.. Even more concepts about God. Now where is Heaven? It¹s up there. It¹s everywhere. It¹s where you make it. It¹s where dreams come true. Heaven is within. More concepts. Where is within? What is in? For that matter, what is "is"? Every word is a concept. It is a symbol or representation for what, in fact, is. There is a very distinct differentiation between an object, its name, and our mental image of that. And the mind, by nature, is objective. That is, it sees and describes objects apart from itself and therefore cannot in actuality, in Truth, experience that object as it is, in a subjective way. An objective experience is indirect. A subjective experience is direct. Let¹s give an analogy. I can describe to you what it is like to ride in a sports car. I can describe it in such detail that you can practically feel the wind in your hair, smell the upholstery, experience the vibration of the tires against the road. All concept. Thought patterns in your mind simulating Truth. Objective experience. Or I could put you in a sports car, give you the keys and say, "have at it," and let you directly experience those things. Subjective experience. In Truth, that so called subjective experience is also an objective experience, because it is taken in through our senses and mind which are themselves barriers to the direct experience, and thus we perceive ourselves driving the car objectively. But this is just an analogy. How about another? This is more along the lines of a direct experience. I can either hand you an orange and say, "smell it, feel it, eat it," which is an indirect experience, objective, or I can say, "be this orange. Directly experience it." Now this is a subjective experience, if you can do it. Actually, even the word experience throws us off because it implies a subject/object relationship. Someone or something is experiencing someone or something else. So - be an orange.
Truth is the same way. I can tell you what I believe Truth is, what God is, what the world is. I can quote from great authorities and from scriptures around the world. I can present evidence with startling logic and reasoning, until you too are absolutely convinced and ready to give your life for my cause, but it will only be a belief, a concept, an objective perception or misperception of the Truth. I may or may not have experienced the Truth, but no matter how many people I convince through non direct means, they will be experiencing beliefs, not truths.
Now what has generally happened in the past is that someone has experienced the Truth. The Truth, being outside of the confining world of language, is self evident to that individual, however it must be communicated, and for the most part is communicated in words. Occasionally, someone will communicate in a different way, such as Buddha holding up a flower or Jesus feeding the multitude. But for the most part what we get is words. We grab onto those words and hold on for dear life. Like trying to grab the reflection of the moon in a pond, it "ain¹t" the real thing.
Truth, however, is available to us. It is as close to us as our breath or our heart beat. It is the very fabric of life. But, unless you directly experience this (be the orange) it is just another concept, a belief. There are methods for directly experiencing Truth, and many of the better religions and philosophies have those methods built within them, although they are often lost within the dogmas, concepts and personality cultism. The problem is that many of these methods are themselves indirect, unclear, and often very, very slow, taking maybe years, decades or lifetimes to achieve the goal. There actually is a method by which one can directly experience the Truth, Self, Enlightenment, God, the Kingdom of Heaven within, the Christ Consciousness, whatever you want to term it, in a very short time, in fact, instantly, in this moment. It¹s called Self Inquiry and is really no method at all, but really a stopping of all methods, all techniques, all searching after Truth, and inquirying into the source of "I", awareness itself beyond concepts and misperceptions. It is a quantum shift in consciousness to a direct, subjective experience of Truth. Truth beyond belief!
http://www.atmainstitute.org/searching.htm

The Mother of God

2010-10-19T10:04:00.000-07:00

~~An extract

On the question "Who created the Universe and who created God?" Return of the Aryans quotes Sindhu Putra, the spiritual leader of 5,000 BC, to reply, "God created the Universe, but before Him was She -- the Mother!" This reply conforms to the Hymn of Creation as it was then known in Bharat Varsha, which Return of the Aryans quotes as follows:

Hymn of Creation

Then nothingness was not, nor existence then,
Nor air nor depths nor heavens beyond their ken
What covered it? Where was it? In whose Keeping ?
In unfathomed folds, was it cosmic water seeping ?
Then there was no life, no birth nor death,
Neither night nor day nor wind nor breath,
At last One sighed " a self sustained Mother,
There was that One then, and none other,
Then there was darkness wrapped in darkness;
Was this unlit water, unseen, dry, wetless ?
That one which came to be, enclosed in naught,
Arose, who knows, how, from the power of what !
"But after all who knows and who can say
Who, how, why, whence began creation's day ?

"Gods came after creation did they not ?
So who knows truly, whence it was wrought!_.
"Does that first Mother Herself know, now?
Did She create or was Herself created somehow;
She, who surveys form the heavens, above us all,
She knows " or maybe She knows not at all.

"Did She Herself create the one god !
And gladly gave Him the Creator's rod !
But so re- fashioned Time and Space
That He was more, and She was less ?
"Did She turn future into past ?
So He came first and She was last!
"But surely, She told Him all, all!
Then how could He not know at all?
"Or perhaps He knows it not, and cannot tell
Oh! He knows, He knows, but will not tell...

(Return of the Aryans, p.124-125)
http://www.indiastar.com/Trivedi.html

The Circle of Nature

2010-10-12T08:57:00.000-07:00

~~An extract

"The ancients had a striking mythical image called the Ourobouros that represented the totality of the alchemical process—a dragon or snake swallowing its own tail. It is a symbol of the great circulation of Nature: what was above as the very subtle spirit descends and becomes—by adaptation through a process of heat and digestion—the below, or earthy and fixed. Then by reversing the process, what is below—fixed, heavy and earthy—ascends and gradually becomes volatile and subtle as the above. By this great circulation of Nature, from above to below and from below to above, the circle is closed. Homer, the Greek philosopher, called it the golden chain because Nature is in reality a chain, in itself like a circle, where each link supports the other, thus making a chain from Heaven to Earth.

In alchemy, this chain is the series of substances and chemical states that appear in the course of the alchemical process. It also refers to the chain of alchemical adepts, who link Heaven with Earth, beginning with the great Egyptian alchemist Hermes Trismegistus, who wrote on his Emerald Tablet, “Make that what is above become like what is below, then what is below returns to what is above, thus creating the miracles of one thing.” In these few simple words he concealed and summarized all of the knowledge, practice and mysteries of the Hermetic (alchemical) science."
http://www.tonicgold.com/alchemy.htm

OM, baby!

2010-10-11T10:06:00.000-07:00

Transcendental and Krishna consciousness: experiencing the eternal self: Bhagavad Gita truths
excerpted from OM, baby! a pilgrimage to the eternal self, by Jack Haas

I suppose it was this immense intent and determination of mine, as well as Krishna's benevolent descent upon my consciousness, which soon took me out and away farther than I could ever have imagined- for such a distance cannot be imagined, because it goes far beyond everything, including imagination.

This transcendent exodus began on the train as my soror and I departed Calcutta, while I was tearing myself away from the energetic constraints of the dark Mother, heading south towards a mountain renowned for its cosmic communion with the ever-free Father- Mt. Arunachala.

On that train ride I slowly but undeniably became untangled from the Mother's clutches, and therefore became assimilated into absolute, liberation consciousness. At least this is what I called it at first, for I had never experienced such a tremendous release from all that is.

I had floated out of this paradigm, out of humanity, out of the world, and had entered a subtle consciousness which goes far beyond anything that exists. Anything. For there is nothing which exists which is as subtle as this non-existent, liberated consciousness. It is pure awareness, nothing more, and it is not bound by anything within this realm or any other.

I had been taken across the great divide by Krishna himself. I had received the benediction of transcendental consciousness. I was now outside of all that is, was, or will be. I was free.

It was an incredible experience to receive this initiation while humming southward on a crammed and noisy Indian train. It was truly incredible to be a part of such a profane, involved, manifested milieu which existed on that train, and yet to be totally apart from it as well. I had entered the subtle realm of eternal, transcendental awareness, and suddenly all the words that I had read years earlier in the Bhagavad Gita, and the Uddhava Gita- in which Krishna expounds the actuality of this transcendent realm, which is beyond everything that exists, no matter what- made sense, and I realized that I had arrived in the unbound place of which he was talking.

I knew then that in order to get there you have to take all things that exist in any realm, visible or invisible, physical or metaphysical, obvious or obscure, material or mental, and, enclosing them into a singular event, step outside of that event altogether; in doing so you become the subtle, transcendent consciousness which lies outside of the one event of all that is. You have to let go of everything to go beyond everything. This is detached peace.

Nothing but conscious clear space and peace lies beyond all realms, beyond all ideas and understandings, beyond self and source, beyond being and non-being, for beyond everything is the realm of eternal, transcendent consciousness.

To enter transcendental consciousness is to become the tranquil, reactionless space. To get to that liberated space you cannot associate yourself with the plane of manifestation, nor with the mind, nor with any spirit of force, no matter what, for liberation consciousness is not in any way related to worldly or even otherworldly actions or non-actions; it is absolutely independent of all realms.

Whereas this plane embodies all dualities that are yet one- the invisible and visible, male and female, good and evil, etcetera- transcendental consciousness is beyond all duality, and cannot be compared, or related to anything, however sacred or profane.

Neither can transcendental consciousness be apprehended by the senses nor the mind, for it is absolute, inviolable, effortless, identitiless awareness.

In order to get there, as I have said, you have to let go of everything. You have to let all of manifestation be, and you have to penetrate through and beyond it, for transcendental consciousness is far more subtle than any form of manifestation or thought. Beyond self and source lies this liberated, eternal awareness.

This liberation is different than enlightenment, because enlightenment is caught up in the idea of wisdom, of understanding; but with the attainment of liberating, transcendental consciousness you don't necessarily understand anything, and yet you are free.

Transcendental consciousness is peace, and is a peace unlike any peace in the relative field, for it is not associated with nor mirrored by unpeace. Transcendental peace is absent of all qualities; it is a nothingness that yet is.
This is the realm of unity, of oneness, which is beyond anything that is composed of definition, duality, or opposition.

The mind and the eyes inherently divide and fragment the world which lies before us, and therefore cannot be used as tools to realize the One. The One, subtle, eternal, transcendental consciousness lies neither within nor without. It is apprehended only when anything that can be thought of or experienced is released.

As the self emerges out of form, out of the duality of existence and non-existence, of life and death, it enters the timeless space of eternity.

I look back now on earlier years along my path, and see how this transcendental consciousness was attempting to come through to my awareness by penetrating the thick cloud of my unwitting dilemmas.

In fact, as a young man I would often 'liberate' my paradigmatic consciousness by inwardly acknowledging to myself a de-affirmation of this human paradigm; I would do this through a subtle method, by consciously perceiving that reality is "not-I, and, not-this".

Although I never experienced anything, at that time, like I was experiencing now, somewhere in the dark recesses of my eternity I knew that I had to go beyond everything in order to be aware of my true, subtle, immortal nature.

Krishna had granted me an immense boon by assisting my attainment of transcendental consciousness. And yet, perhaps I was destined to arrive at this liberating awareness at some point anyway, because I had often categorically stated many times in the past that I did not want to come back to this plane nor this paradigm, ever again. I had become incredibly discontented and bored with the whole mad show, and I wanted to be done with it once and for all. I wanted to leap off of the cyclic wheel of becoming, only I did not know how. But now it had happened. I had become liberated through my blind ambition not to be sucked back into the dark Mother's great gravity. Krishna had heard my call, and had carried me into the vast reaches of the eternal void of awareness. I had attained eternal, omnipresent, transcendental consciousness.[1]

To become eternal is to awaken to that which is beyond anything bound to time. To go beyond time is to go beyond becoming. To go beyond becoming is to be, but not in the sense of anything that has a being, for this eternity is a subtle awareness which ought never be compared nor confused with any partiality, any thing, or any event. Only the negation of all that is will offer a glimpse of that which cannot be negated.

[1] In fact, I had unconsciously documented the growing seed of this subtle, transcendental consciousness in some of the art pieces I had produced over the years. My mandala The Tree of Life, shown at the beginning of this book, is a perfect example; I now know that the two eyes present in behind the main design represent the subtle, eternal, unbound awareness of which I am speaking. Many of my earlier drawings contained such eyes, though I had no clue that these were subconsciously representing the subtle awareness that is beyond all form and thought.
http://www.spiritandflesh.com/bookOMTranscendentalKrishnaconsciousnesseternalBhagavadGita_religion_spirituality.htm

Is There Such A "Thing" As Energy?

2010-10-05T08:58:00.000-07:00

"There is a theory which states that if ever anybody discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another theory which states that this has already happened."
~~Douglas Adams

~~Image
http://uncyclopedia.wikia.com/wiki/File:Hot_crumpet.jpg

Previously, we've discussed force as an "interaction energy." The use of the word "interaction" suggests that this energy is found BETWEEN two objects. The implications of this are twofold: there is such a "thing" as energy - a real physical thing - and that it is possible for this thing to exist outside matter. Under modern theory mind, all sorts of complications arise when you start saying this kind of stuff. It seems to break every convention that physics has. That's mainly because energy is not seen as a substance, or indeed, anything in particular. It is observed strictly as an abstract concept.

With perhaps the exception of energy in the form of light, energy is not a thing per se. Rather, energy refers to a condition or state of a thing.
http://www.nmsea.org/Curriculum/Primer/what_is_energy.htm

Getting to the core concept of energy is no mean feat, because we are now messing with fundamental laws of physics. These dictate that energy cannot exist outside matter because it is solely a property of matter. Properly defined, matter has energy, but in itself, is not energy per se. Matter needs energy, for without it, matter cannot exist.Described in this way, it suggests that energy is a different "thing" from matter.

A kind of cyclic argument ensues, which says that even if it was possible for energy to exist outside matter, it cannot physically exist as a thing, because energy only refers to the condition or state of an object. Consistently treating energy as only describing the energetic state of a material object, ensures that it remains indescribable as an independent substance. Once you do decide to try and seperate energy from matter, then out pops a big, wrestling squid in the shape of the laws of conservation. Basically, the laws all subscribe to the idea that energy has to belong to an object or body, and because of this, it is impossible for energy to simply enter, or exit a system, without it belonging to another object or body. This concept is known as the conservation of energy.

The conservation of energy is a fundamental concept of physics along with the conservation of mass and the conservation of momentum. Within some problem domain, the amount of energy remains constant and energy is neither created nor destroyed. Energy can be converted from one form to another (potential energy can be converted to kinetic energy) but the total energy within the domain remains fixed.
http://www.grc.nasa.gov/WWW/K-12/airplane/thermo1f.html

The law behind the conservation of energy refuses to admit that energy can exist outside matter. This means that the space around matter is strictly space - with nothing in it - nada, zip, donut, etc. However, something is still needed to explain how energy is transferred from one body to another. Because the energy is moving from one body to the other, regardless of how small that distance is, there must come a moment where energy is seen to exist by itself. This should give us the perfect opportunity to finally get a glimpse of "energy." What we find though is not energy in the buff - but energy dressed-up in a new outfit. To help explain energy transfer, modern theory devised a vehicle to carry the energy - the photon. Happily for modern theory, the photon is still maintained to be a particle of matter, even though this particle has no mass whatsoever.

Physics experiments over the past hundred years or so have demonstrated that light has a dual nature. In many instances, it is convenient to represent light as a "particle" phenomenon, thinking of light as discrete "packets" of energy that we call photons. Now in this way of thinking, not all photons are created equal, at least in terms of how much energy they contain. Each photon of X-ray light contains a lot of energy in comparison with, say, an optical or radio photon.
http://fuse.pha.jhu.edu/~wpb/spectroscopy/basics.html

Conveniently, because the photon has no mass, it means that it does not have to obey the confines of space-time, and therefore does not experience our idea of "time." This allows the photon to quite literally arrive at its destination before it has even departed from its source - including distances which span the entire Universe!Because the photon can cross the divide between bodies instantaneously, modern theory is not obligated to explain how the photon might appear in the void. Modern theory persists in refusing to define energy, and maintains that the photon is only an energy carrier and not energy per se. Fortunately for us, this presents something of a crack for us to try and pry open.

Now that the photon has been emitted and begins its flight, we are purely in a relativistic mode. Einsteins equations for space distortion and time dilation tell us that the path in front of the photon shrinks to zero and the time of flight shrinks to zero as well. Now that the photon has been emitted and begins its flight, we are purely in a relativistic mode. Einsteins equations for space distortion and time dilation tell us that the path in front of the photon shrinks to zero and the time of flight shrinks to zero as well. This has always raised a troubling problem because we know that some photons take billions of years to fly across the universe and move about 1 nanosecond a foot of travel.
http://quantumweird.wordpress.com/category/quantum-mechanics/

As the author of "Quantumweird" points out, how is it possible for instantaneous energy transfer to take place if the photon is physically restricted by a maximum speed limit? If the photon cannot physically travel faster than light, how is it possible for energy to do so? The only thing which makes any sense is to admit that it is only energy, and not the photon, which is capable of instantaneous transfer. Quite what this means is very open to debate, but I like the idea of a surrounding medium, a medium of surrounding energy, being responsible for the transfer of energy between bodies.

"As far as a photon is concerned the passage from point A to point B is instantaneous – and it always has been. It was instantaneous around 13.7 billion years ago when the entire universe was much smaller than a breadbox – and it still is now.

But once you decide that the speed of light is variable, this whole schema unravels. Without an absolute and intrinsic speed for relatively instantaneous information transfer, the actions of fundamental forces must be intimately linked to the particular point of evolution that the universe happens to be at.

For this to work, information about the evolutionary status of the universe must be constantly relayed to all the constituents of the universe – or otherwise those constituents must have their own internal clock that refers to some absolute cosmic time – or those constituents must be influenced by a change in state of an all-pervading luminiferous ether."
http://www.universetoday.com/74426/astronomy-without-a-telescope-dark-denial-2/

Science has long been able to avoid confronting the question of what energy is exactly, by using a formula which allows it to inter-change energy for mass. The formula, probably the most famous equation of all time, is unequivocal proof that energy and mass are equivalent. I am of course referring to E = mc2.

Einstein correctly described the equivalence of mass and energy as “the most important upshot of the special theory of relativity” (Einstein, 1919), for this result lies at the core of modern physics. According to Einstein's famous equation E = mc2, the energy E of a physical system is numerically equal to the product of its mass m and the speed of light c squared. It is customary to refer to this result as “the equivalence of mass and energy,” or simply “mass-energy equivalence,” because one can choose units in which c = 1, and hence E = m.
http://plato.stanford.edu/entries/equivME/

If science ever needs to draw upon a physical represention of energy, then it does so in the form of matter. What this does though, is screw around with our previous statement where we said "without energy, matter cannot exist." Because energy and matter are inter-changeable, the statement must also be able to read "without matter, energy cannot exist." Which is not what we agreed on at all. We know that matter cannot exist without energy, but nowhere have we said that energy cannot exist without matter. The problem with E=mc2 is that it can be manipulated in such a way, it forces us to accept the notion that energy cannot exist without matter, when in-fact, there is no direct proof that this is true.

If you remember, we agreed that "matter has energy, but in itself, is not energy per se." In this way, energy and matter can be seen as two different entities. If they are different, then it must be possible to seperate them. On one hand, we have matter which we know needs energy to exist, but on the other, we might find that energy, pure unadulterated energy, is more than able to exist as an entity in its' own right. Detractors will say that trying to seperate energy from matter, is a bit like trying to seperate butter from hot crumpets. I mean, why would you want to? Crumpets taste lovely with butter. To seperate the two is simply pointless. But of course it's not. Mankind's final understanding of what energy is, could represent our greatest adventure yet.

Many thanks:
http://newscenter.lbl.gov/feature-stories/2010/05/10/untangling-quantum-entanglement/
http://www.smartplanet.com/business/blog/smart-takes/physicist-proves-that-teleportation-of-energy-is-possible/3967/

Zeno and the Buddha

2010-09-25T01:21:00.000-07:00

ZENO AND THE BUDDHA
September 29, 2007, 9:05 pm
Filed under: Buddhism, Philosophy

“Man conquers the world by conquering himself.”
-Zeno

“Greater in combat
Than a person who conquers
A thousand times a thousand people
Is the person who conquers oneself.”
(Dhammapada 8:103)

“Get rid of the judgement, get rid of the ‘I am hurt,’ you are rid of the hurt itself.”
-Marcus Aurelius

“All things are not-self”
Seeing this with insight,
One becomes disenchanted with suffering.
This is the path to purity.
-Dhammapada 20: 279

“Where is the good? In the will. Where is the evil? In the will. Where is neither of them? In those things which are independent of the will.”
-Epictetus

“All the suffering of this world arises from a wrong attitude.
The world is neither good or bad.
It is only the relation to our ego that makes it seem the one or the other. “
-Lama Anagorika Govinda

While stoic has come to mean unemotional or indifferent to worldly things, it was a lively and popular philosophy to the ancient Greeks and Romans, influential to it’s many adherents. It appealed to many people of different swaths of life, from the slave Epictetus, to the Roman emperor Marcus Aurelius. And as we’ve seen, it shares some similarities and perhaps even connections with Buddhism. So what is Stoicism and how similar is it to Buddhism? Of course, one person’s definition of Stoicism and Buddhism will differ from another’s so you will have to bear with me as I try to make the connections.

Stoicism was founded by Zeno of Citium in 301 B.C.E. He was a merchant who studied under the Cynics and carried with him some of their thoughts. He spoke from his porch (the stoa), and taught his students to ease their suffering by becoming indifferent or “apathetic” to the rising and falling of emotions and desires, our passions. Interestingly, passion is also equivalent to suffering in Christianity, although the meaning and use of the word may be different. While Christians are to live in line with God, Stoics were to live in line with the rational Universe, which to them was virtuous. Zeno taught that by becoming indifferent to the passions that arise in us, we learn wisdom and learn to live in line with the Universe. Ignorance of this leads to suffering.

By becoming less moved by our emotions, it seems, we learn to be restrained without emotion instead of restrained by emotions. This has translated to the modern definition of stoic. For the Stoics, living stoicly was not just to become a stubborn rock, unmoved by anything. Living in such a way means to live peacefully, with a sense of inner tranquility. This is similar to the Buddhist arahats who become awakened through renunciation and letting go of attachments and desires. Both claim to achieve a state of inner peace from suffering, which are the two traditions’ common goal. The Stoics as well as the Buddha and his disciples sought to free people of suffering. The difference however is that Zeno taught the suppression of the passions whereas the Buddha spoke of becoming open and free from passions.

Apparently, the Stoics also used meditation to practice. The Stoics used “contemplation of death, training attention to remain in the present moment” to gain that indifference that they are now so famous for. Contemplation of death is also a practice used by wandering forest monks in Buddhism. They would settle into cemeteries and contemplate the similarities of their own aging bodies with that of the corpses, the only difference being that of time. And the practice of training attention to remain in the present moment is common to all of Buddhism. Known as dhyana, practitioners begin by focusing on the in and out of the breath, eventually extending their attention to other sensations in their body and mind. It is said that a peaceful state of bliss arises during dhyana, and is emphasized in the tradition of Zen (chan, seon, thien, etc).

Stoics had one major difference in their beliefs with Buddhism. Stoics upheld, paradoxically, both determinism and free will. They believed that the Universe was rational and that it carried people along with it. While people had the free will to act in whatever way they saw fit, voluntarily conforming to the Universe led to the freedom of suffering.

It has been said that Marcus Aurelius was the last Stoic philosopher. Stoicism has since then kept itself in the background, but it’s ideas have re-emerged or taken a different representation. Examples include the French expression, “C’est La Vie”, or the Christian serenity prayer: “God grant me the serenity to accept the things I cannot change; courage to change the things I can; and wisdom to know the difference….”

P.S. After a little search on the Interwebs, it seems some have already beat me to the punch. There’s even a Japanese Zen monks who wrote a blogpost noting the similarities (though I wish he had a greater command of the paragraphical indentation). There are even some class notes for a philosophy class comparing the two.
http://scubasocal.wordpress.com/2007/09/29/zeno-and-the-buddha/

The Quantum Theory of Life and Buddhism

2010-09-24T08:18:00.000-07:00

The quantum theory of life and Buddhism

By Dr. Senaka Ranasinghe

According to Buddhism, the whole universe is a single, dynamic web of energy which can exist in three forms. These three forms of energy that exist in the universe also exist in the human body.

Energy in the universe can exist are: 1. Free Energy, 2. Forces, 3. Matter.

Free energy is pure, undifferentiated energy. Therefore, this form cannot be perceived directly or indirectly. Free, undifferentiated energy exists in the human body as consciousness. In Buddhism, consciousness is described as Vinnana.

Forces are a type of differentiated energy produced by moving matter, which in turn causes movement of matter. The forces that exist in the universe are: 1. Electricity, 2. Magnetism, 3. Gravity.

These forces do not exist in the material form. (i.e. particles or waves). Their existence is in the form of an energy field which can be detected indirectly.

By these forces, the movements that occur in all matter in the universe are inter-connected.

Though these forces are studied separately, in reality they exist in union, giving rise to a unified field which can be called the thought force. This is the force that moves the whole universe. The moving matter produces thought forces which in turn cause similar movement in matter.

The thought force exists in association with the living human body as the subconscious force of the individual. By this force, the individual is connected to all human beings and events in the universe.

The subconscious force determines the future events of the individual. In Buddhism, the subconscious force is described as Bhavanga.

Matter

Matter is a manifestation of differentiated energy. This form of energy can be perceived directly.

In an individual, matter is represented by the physical body. The fundamental unit of matter that exists in the universe and in the human body has four inseparable but interchangeable qualities. They are Solidity, Liquidity, Motion and Heat.

Depending on the predominant element, the quality of matter may differ.

Eg: Solidity is predominant in the earth, mountains, bones, liver muscles, kidney etc.

Liquidity is predominant in water, saliva, gastric secretions etc.

Motion is predominant in the wind, breathing, blood circulation etc.

Heat is predominant in fire, the sun, bile etc.

The material body contains the following six sensory organs, by which the individual perceives the universe:

1. Eye _ Visual perception

2. Nose _ Olfactory perception

3. Ear _ Sound perception

4. Tongue _ Perception of taste

5. Skin _ Perception of touch

6. Mind _ Perception of thoughts.

Mind is simply an area in the brain (known as the Limbic system) by which the individual perceives thoughts that exist outside.

A musician trains his ears to a particular note. Similarly, the mind can be trained and developed by concentration.

Consciousness

Consciousness is awareness. It is pure undifferentiated energy. For the consciousness (awareness) to manifest, it has to come in contact with one of the six sensory stimuli.

Eg. eye consciousness is awareness of vision. Thought consciousness is awareness of thought.

The cycle of events during a particular consciousness is analysed in great detail in Buddhism.

The process of eye consciousness can be analysed the following way:

* When a visual object comes into contact with the eye, the image is conducted to the brain.

* This image in the brain causes differentiation of free energy (consciousness) to eye consciousness. When an eye consciousness is born, this is the SELF that will perceive the image.

* Then the eye consciousness receives the visual image.

* The self inside the eye consciousness scans through the memory (which is in the brain) and identifies the object.

* According to the identification, a feeling is experienced by the SELF in the eye consciousness. It may be pleasant, unpleasant or neutral.

* Depending on the feeling, a volition is experienced by the SELF in the eye consciousness. During this stage the SELF will gather more energy and also it will divert body energy to act. Then at this stage VOLITION IS ACTION.

* Then the SELF in the eye consciousness will register the event in the memory.

* When the registration is done, the eye consciousness which is the SELF leaves the body. Then it exists in association with the body as a thought force. These accumulated thought forces of the individual will form its subconscious force.

This is the last event of the cycle. The moment the eye consciousness leaves the body, the concept of SELF dies off because it cannot exist without a body.

During this cycle of events, the material body also undergoes changes; i.e. Respiration, movements of blood in the circulation, movement of food in the stomach etc.

Then at the end of the cycle there is a different, new body which will replenish its free energy (consciousness) from the environment and is ready for the next cycle.

This cycle of events can be called a unit of eye consciousness or a QUANTUM of eye consciousness. (QUANTUM = a packet). The cycle of events is the same with all six types of sensory modalities. This is the fundamental unit of LIFE. After one sensory quantum wanes, another sensory quantum comes up like the waves in the seashore. Life is a pulsatile interrupted flow of these cycles (sensory quantums).

The time duration of one quantum may be about 1/20th of a second (=50 milliseconds). Then per every one second there is an interrupted flow of about 20 quantums of life, with each and every quantum there arises a NEW SELF, with new perception, new volition and a new body lasting only for about 1/20th of a second and dies off.

Selflessness

In the analysis of a quantum of life, it is very clear that there is no permanent, unchangeable self inside the body who can perceive, think and act. Instead there are different SELVES coming up with each consciousness and passes away with the same consciousness which lives only for about 1/20th of a second (=50 milliseconds).

When the next cycle of events are in progress, the self image of the previous cycle of events (quantum) is still present in the memory. (Because a nerve impulse lasts for about 50 milliseconds). So the Memory interprets and projects as if there is a permanent, unchangeable self, who feels and acts.

When an individual starts living with the memory projection of the illusion of a permanent, unchangeable self, they become in it. They become actors of this so-called permanent self which is actually a memory projection. When an individual becomes an actor of the SELF, he himself cannot watch the drama as an outsider; i.e. he cannot perceive the impermanence of self.

But if an individual can come out from the illusion of a permanent self and watch the drama of life as an outsider, then he could see the flow of quantums (life packets) which lasts for about 1/20th of a second and dying off.

At that stage there is no person who observes the process; Only the observation exists.

Then there will be no person to perceive; Only the perception exists.

There is no person inside the body to act; Only the action exists.

There is no person inside the body to think; Only the THINKING exists.

Action and Effect

When a thought comes in contact with the mind, the consciousness will differentiate into thought consciousness. The SELF inside this thought consciousness will identify and fell the thought. Depending on the feeling, there will be volition, which will manifest immediately as the act (Volition is Action). Then the particular SELF inside this thought consciousness will register the event and leaves the body as a thought force and exists in the individual's subconsciousness. Since the individual is connected to the whole universe by its subconscious force, the registered event will manifest as REALITY in the individual's life.

Then, by repetitive thoughts, the individual CREATES its own social environment. This social environment inturn will CONDITION all its activities, emotions, thinking and activities.

Since the social environment will only CONDITION the individual but will NOT CREATE the individual, there is no place for absolute predeterminism of future events. Though the social conditioning is present, there exists a certain element of free will.

The Buddha mentioned that by being conscious at the present and by consciously altering the thought forces, the previously accumulated undesirable thought forces can be neutralised or abolished before being manifested. It is similar to the potential energy of a seed. Only when the conditions are favourable, it will grow up as a plant. If the conditions are not favourable, the seed dies off.

In the same way, evil deeds will manifest similarly in the individual's life giving rise to unpleasant feelings as the result of the action. Virtuous deeds will manifest similarly giving rise to pleasant feelings as a result of the action. Also, the previously accumulated undesirable thought forces can be altered or neutralised by doing virtuous deeds at present.

Life after death

At the time of death, a thought comes up from the individual's subconscious field and it will be perceived by the mind.

The last thought may:

* Related to a habit the individual would have practised during life.

* Related to a strong volitional activity performed by the individual during life.

* Indicate the next birthplace.

This last thought is perceived by the thought consciousness. At the stage of volition, it will divert body energy to act and also gather more energy. After this stage the LAST THOUGHT CONSCIOUSNESS leaves the body with the remaining subconscious force. This last thought consciousness can exist in the environment as a force. During this period it consumes some of the subconscious forces which it had gathered during life. This is also another form of life (life in fine material world Rupa Loka). Also depending on the development of the mind, of the individual and according to the last thought consciousness, the subconscious forces can exist in the form of free energy till the energy in the subconscious forces wane. This form of life is described as Arupa Loka in Buddhism.

The disadvantage in this form of life is that it cannot collect NEW thought forces because of the lack of a physical body. (Since thought forces are produced by moving MATTER).

After some time when most of the subconscious forces are consumed by this form of life, the last consciousness will be attracted to an embryo with a similar potential energy. (Similar to a radio-signal being attracted by a radio tuned to the particular FREQUENCY).

Then the last thought consciousness of the previous life will become the first thought consciousness of the present life, and the cycle of change proceeds. (Samsara).

So it is clear that there is no transfer of matter from one life to another life but only a transfer of energy as thought force. Then again the process of change begins. In reality there is nothing to change but only the process of change exists.

Conclusion

Life is made up of an interrupted flow of life-packets (quantums of life). Each life packet contains a self which feels and acts and dies off within about 1/20th of a second. That is, about 20 different `selves,' feelings, acts come up within about 1 second - with a definite gap between each self.

Since the critical fusion frequency (the rate at which stimuli can be presented and still be perceived as separate stimuli) of the human memory is also about 20 per second, the memory projects and interprets as if there is a permanent self inside the body which acts and feels. Because of this ignorance of selflessness, emptiness and unsatisfactoriness, various volitional activities are done by the individuals. The root of volitional activity may be due to the illusion of a permanent self, greed or hatred.

When volitional activities are performed, it will gather more thought forces, which will again give rise to another new material body. So the life cycle goes on forever (Samsara).

Due to ignorance, there will be greed and hatred which will produce more thought forces and the cycle goes on.

If a person has completely eradicated the illusion of self, greed and hatred, such an individual will not accumulate more thought forces. The past collected thought forces will manifest in present life. Since there will be no further collection of thought forces to be manifested in a next life, there will not be a continuation of the process. Such an individual has stopped the process. The process of change has come to an end.

At this stage, the person has attained Nirvana. There all the sensory perceptions are interpreted as selflessness, impermanence, and emptiness by the memory.

Then at this stage, the person has completely eradicated the illusion of self. Then there is no person to achieve Nirvana. There exists only the greatest achievement. The ultimate truth of nothingness. The truth of impermanence.

@ WWW Virtual Library - Sri Lanka -
http://www.lankalibrary.com/Bud/energy.htm

Repulsion Force

2010-09-21T08:35:00.000-07:00

ZetaTalk: Repulsion Force
Note: written on Sep 15, 1995.

Scientists are acutely aware of the attraction force inherent in gravity, as are folks in general. The babe learns about this early, while taking his first few steps. Oops. Ouch! It is assumed that gravity has only an attractive force, and that the planets, in orbit around the Sun, are held in place by their momentum. Does this make sense? What caused the momentum in the first place? Children play with a ball on the end of a string, swinging it around and around their head. As long as the arm is tugging, the ball maintains its orbit, else stops. Why would the planets not drift into the Sun? Are the orbits all that swift so that centrifugal force is extreme?

The reason Mankind is Unaware of a repulsive force, also inherent in gravity, is that for this to become evident there must be a semblance of equality in size and weight, i.e. the mass of the objects, and freedom of movement such as exists in space, and lack of undue influence from other nearby objects. Objects on the surface of the Earth have none of these. They are infinitesimal in proportion to the Earth itself, and thus any repulsion the Earth may have toward a tiny speck on its surface is also infinitesimal. Proportionally, its all gravity, a one way trip. The object on the surface, pushing away, is overwhelmed by the Earth's gravitational pull, the attraction. The repulsion force is generated as a result of two bodies exerting a gravitational force on each other. In the case of a tiny object on the surface of the Earth, its gravitational pull on the Earth is scarcely noticed by the Earth. A gnat or mite. A nothing. Where the repulsion force has not been invoked within the Earth by any objects placed on the surface of the Earth, this is in play between the Earth and her Moon. The repulsion force is invoked between objects on the surface of the Earth, incessantly, but this is masked by the intense force of gravity the Earth presents and other factors such as surface tension or friction or chemical bonding so that the repulsion force cannot be recognized.

The gravitational force exists first. It is the static condition. The repulsion phenomena only manifests when, as we said, the objects are of equal size, are free to move, and dominate the immediate environment. Where the repulsion force comes to equal the force of gravity by the time the objects in play would make contact, it builds at a rate that differs from gravity. Humans have calculated the force of gravity, which at first they assumed was equal for all objects but lately have come to understand is stronger for larger objects. They have formulas for the force of gravity which have proved accurate on the face of their home planet. These formulas are incomplete, and would not work as expected elsewhere, however. The repulsion force is infinitesimally smaller than the force of gravity, but has a sharper curve so that it equals the force of gravity at the point of contact. For experimental purposes, one would have to be almost at the point of contact for it to come into play at all, and this in an environment where other factors are eliminated or negated. To examine the phenomena, Earth scientists would have to set up a lab in space, far enough away from any planetary body so that free movement is possible. Place two balls in a cage. Put one in motion toward another. Microscopically examine the interchange. They do not touch. They do not bounce off one another. They do not touch.

All rights reserved: ZetaTalk@ZetaTalk.com
http://www.zetatalk.com/science/s34.htm

Don't Fight Forces, Use Them! : Don't Fight Forces, Use Them! :The Integrity of Tension in Science and Architecture

2010-09-18T07:05:00.000-07:00

Renee Verdier

What do Buckminster Fuller's geodesic domes and the human body have in common?

In 1932 R. Buckminster Fuller famously philosophized: "Don't fight forces. Use them!" (Fuller, Shelter). A man of many trades -- architect, author, designer, futurist, inventor, and the second president of Mensa -- he applied this mantra throughout many aspects of his work. In particular, it is more or less the backbone of his studies of and theories on synergetics, an interdisciplinary science that explores the formation and self-organization of patterns in systems. Fuller believed that all experience could be communicated using geometric concepts, and further claimed that the natural analytic geometry of the universe is based on tetrahedra, or triangular pyramids. He explored these ideas through studies of the close-packing of spheres and tensile and compressive stabilization models, noting that tension and compression are not opposites, but rather complements that can be found together; when the two forces are harmonious, continuous pull is balanced by equally discontinuous pushing forces. This synergy between compression and tension is what Fuller calls tensegrity, "a system that stabilizes itself mechanically because of the way in which tensional and compressive forces are distributed and balanced within the structure (Ingber 48-9). It is the underlying principle behind what is perhaps his most well-known invention, the geodesic dome -- a nearly spherical shell structure based on a network of triangular elements lying approximately on the surface of a sphere. On a grander scale, it is also a fundamental property of several self-assembled systems within the body, from the anatomical to the cellular to the molecular level.

Fuller originally coined the term tensegrity, a portmanteau of tensional integrity, while studying "energetic-synergetic geometry" during World War II. He provides a comprehensive definition of the term in his book Synergetics:

Tensegrity describes a structural-relationship principle in which structural shape is guaranteed by the finitely closed, comprehensively continuous, tensional behaviors of the system and not by the discontinuous and exclusively local compressional member behaviors. Tensegrity provides the ability to yield increasingly without ultimately breaking or coming asunder (Fuller, Synergetics 372).

Tensegrity structures fall into two main categories -- prestressed and geodesic. Both types rely on continuous transmission of tensional forces in order to maintain their shape, and stabilize themselves through decentralized tension and local compression; an increase in tension on one part of the structure causes increased tension on other parts of the structure - even those on the opposite side -- which is then balanced out by increased compression within other parts of the structure. The former encompass structural members which are already in tension or compression before they are exposed to any external force, stabilizing themselves through a phenomenon called prestress; within these structures, "the compression-bearing rigid struts stretch, or tense, the flexible, tension-bearing members, while those tension bearing members compress the rigid struts. These counteracting forces, which equilibrate throughout the structure, are what enable it to stabilize itself" (Ingber 49).

Geodesic tensegrity structures are "frameworks made up of rigid struts, each of which can bear tension or compression" (Ingber 49). These struts are positioned to hold the joints that make up the framework into fixed places, so as to stabilize the entire structure. Perhaps the most familiar example of these structures is the geodesic dome, immortalized by Fuller's golf-ball-esque Spaceship Earth building at Disney's Epcot. Influenced by the notion that the strongest possible homogenous truss is cyclically tetrahedral, a conclusion he reached from his studies of synergy, Fuller developed geodesic domes in the late 1940s to demonstrate the ways in which these ideas can be applied to housing and architecture.1 A geodesic dome is a sphere -- or ball-shaped structure comprised of a complex network of rigid rods connected into triangles, or tetrahedral, which form a roughly spherical surface. These triangular elements have local rigidity as well as distribute tension across the entire structure; each rod can withstand both tension and compression depending on where and how much pressure is applied, and the omnitriangulated surface provides an inherently stable structure. Moreover, the spherical shape of the structure encloses the maximal volume for the least amount of surface area. The geodesic dome's durability, minimization and efficient use of building materials, and mobile flexibility -- its modular structure makes it easy to transport and build -- were the source of its appeal to Fuller, who hoped it would provide a solution to the post-war housing crisis (Bowers).

The presence of tensegrity structures is not limited to avant-garde architecture, however. Nor are the principles of tensegrity merely the product of the human mind; rather, they manifest themselves within countless patterns in nature. Both prestressed and geodesic tensegrity structures are found in a variety of natural self-assembled systems, including carbon atoms, water molecules, proteins, viruses, cells, tissues, and animals (Ingber 48). Of particular interest is their prevalence in the human body, on an anatomical, cellular, and molecular level.

On an anatomical level, the human body provides a good example of a prestressed tensegrity structure. Bones act as struts resisting the pull of tensile muscles, tendons and ligaments. Moreover, the stability of the shape of the body, or its stiffness, of the body is a function of the tone, or prestress, of its muscles (Ingber Lab). As Ingber puts it, "We are 206 compression-resistant bones that are pulled up against the force of gravity and stabilized through a connection with a continuous series of tensile tendons, muscles, and ligaments" (Ingber Lab).

The principles of prestressed tensegrity are similarly applicable on the cellular level; although, as we shall see later on, geodesic structures are also found in the cell on a smaller scale. The cell possesses a molecular framework called the cytoskeleton enclosed within the surface membrane that mechanically stabilizes the cell. The cytoskeleton is comprised of three different types of molecular protein polymers, called microfilaments, intermediate filaments and microtubules. The microfilaments, which are the thinnest proteins in the cytoskeleton, comprise a network that extends throughout the cell, exerting tension by pulling the cell's external membrane and everything in between towards the nucleus at its center (Ingber, The Bridge). To counterbalance the tensional forces, the microtubules -- the thickest protein chains of the three -- act as struts that bear compression. The adhesions of the extracellular matrix, or the "anchoring scaffolding to which cells are naturally secured in the body," create an external interconnected compression force (Ingber 51). The contractile actomyosin apparatus -- rigid actin filament bundles which bear compression by pushing the cell membrane and its internal components outwards - generates the tensional prestress that stabilizes the entire cell (Ingber, The Bridge). The intermediate filaments connect the microfilaments, microtubules, the cell membrane, and the cell nucleus to one another and "act as guy wires, stiffening the central nucleus and securing it in place" (Ingber 51). Some individual filaments have dual functions and therefore "bear either tension or compression in different structural contexts or at different size scales (e.g. contractile microfilaments generate tension, whereas actin microfilament bundles that are rigified by cross links bear compression)" (Ingber Lab).

This network of molecular struts and cables allows the cell to alter the balance of tension and compression throughout its structure in order to maintain its shape, even when external forces are imposed upon it. When cells are stretched or face other increases in prestress, they do not lose their original shape but rather stiffen themselves by varying the prestress within the cytoskeleton. Prodding the outside of a cell, for instance, affects the tension felt throughout the interlinked proteins of the cell (Ingber 53). Like Fuller's geodesic domes, the cell's durability is derived from its capacity to distribute tension throughout its structure as well as respond to and neutralize tensional forces with specialized compression. Though the cellular tensegrity model is a prestressed tensegirty configuration, recent work by mathematician Robert Connelly proves that there is a common structural basis for prestressed and geodesic structures; the same fundamental mathematical rules describe the closest packing of cells within the extracellular matrix as they do the different geodesic forms (Ingber, Tensegrity 2).

Several geodesic tensegrity structures naturally occur on the molecular level. Basement membrane proteins, polyhedral enzyme complexes, clatrin-coated transport vehicles, viral capsides, lipid micelles, individual proteins, and RNA and DNA molecules all employ hexagonal arrangements (Vondrejs). The cell's microfilament network itself is a geodesic tensegrity structure. Contractile microfilaments within the cytoskeleton form lattices that naturally assemble themselves locally into different forms, including geodesic networks of triangles (Ingber 53).

Geodesic forms are also found in human red blood cells. A recent study conducted by scientists at the Jacobs School of Engineering determined that the red blood cell's membrane skeleton is comprised of a network of over 30,000 protein hexagons which look similar to a microscopic geodesic dome. At the center of each hexagon, an elongated protein complex, called a proto-filament, acts as a rigid rod that moves and compresses in response to pulling forces. These proto-filaments stabilize red blood cells in the same manner as the rods of a geodesic dome; according to the UCSD researchers, "the more a red blood cell is mechanically deformed, the more likely its individual proto-filaments will rotate left and right" in order to maintain the cell's shape and stability (ScienceDaily).

It is clear that tensegrity structures, both prestressed and geodesic, are prevalent in many natural and man-made systems, from the architecture of Buckminster Fuller to the architecture of the body on an anatomical, cellular, and molecular level. What is particularly fascinating about these congruities is that their discoveries had no direct influence on one another; Buckminster Fuller did not fashion his tensegrity models after cellular structure, nor did Ingber or other scientists set out to hunt for geodesic domes within the cell. However, Fuller's geodesic dome initiated a common language and reference point for scientists to use when navigating their studies of cellular tensegrity; The Ingber Laboratory notes on the Buckminster Fuller Institute's website:

We introduced the concept that living cells stabilize their internal cytoskeleton, and control their shape and mechanics, using an architectural system first described by Buckminster Fuller, known as tensegrity (The Ingber Lab).

Indeed, the convergence of these two tensegrity theories is no coincidence. Just as Buckminster Fuller sought to design a maximally efficient and resilient structure, so too did Ingber seek to understand the efficiency and resilience of various structures and systems of the human body. Both speak to a fundamental understanding of the ingenuity of self-assembling structures and their methods of maintaining stability; when you use forces, you don't need to fight them.

Sources

Bowers. Robert T. "Geodesic Domes," The R. Buckminster Fuller FAQ 26 Nov 2002. 24
Nov 2008 http://www.cjfearnley.com/fuller-faq-4.html

Fuller, Buckminster. Shelter: A correlating medium for the forces of Architecture. 2nd.
1932.

Fuller, Richard Buckminster. Synergetics. 1982. New York, NY: Macmillan Pub Co,
1982.

Ingber , Donald E. . "The Architecture of Life ." Scientific American Jan 1998: 48-57.

Ingber, Donald E.. "Mechanochemical Basis of Cell and Tissue Regulation." The Bridge
Vol 4 No 3Fall 2004 24 Nov 2008
.

Ingber, Donald E.. "Tensegrity I. Cell Structure and Hierarchical Systems Biology."
Journal of Cell Science (2003): 1157-1173.

"Scientists Discover Secret Behind Human Red Blood Cell's Amazing Flexibility,"
ScienceDaily 25 Oct 2005. ScienceDaily LLC. 24 Nov 2008

"Tensegrity and Complex Systems Biology," Ingber Lab: Children's Hospital
Boston/Harvard Medical School 2004. The Ingber Lab. 24 Nov 2008

Vondrejs. Vladimir. "Tensegrity Structures in Science, Technique, and Art," 24 Nov
2008

This article originally appeared on Evolver.net.
http://www.realitysandwich.com/dont_fight_forces_use_them

Learning Maxwell's Rope

2010-09-14T04:08:00.000-07:00

"A person needs a little madness, or else they never dare cut the rope and be free."
~~Nikos Kazantzakis

In his 1861 paper, "On Lines of Physical Force," Maxwell elaborates on his desire to investigate "the mechanical results of certain states of tension and motion in a medium," so that they might be compared with "the observed phenomena of magnetism and electricity." A copy of the paper, and fascinating it is too, can be seen here, thanks to Wikisource:
http://en.wikisource.org/wiki/On_Physical_Lines_of_Force

Maxwell, just as Faraday had done before him, treated the lines of magnetic force (as revealed by iron filings spilled over paper held above a magnet,) as being real entities. Maxwell describes each filing as being "magnetized by induction," and that they unite to form "fibres," and that these fibres will then "indicate the direction of the lines of force." Maxwell considers the lines of magnetic force as "existing in the form of some kind of pressure or tension, or, more generally, of stress in the medium." He imagines the stress evoked by the lines of magnetic force as representative of tension, "like that of a rope." Rope? I wonder what exactly was Maxwell getting at?

If you look at a piece of string under a magnifying glass as you pull on the ends more and more strongly, you will see the fibers straightening and becoming taut. Different parts of the string are apparently exerting forces on each other. For instance, if we think of the two halves of the string as two objects, then each half is exerting a force on the other half. If we imagine the string as consisting of many small parts, then each segment is transmitting a force to the next segment, and if the string has very little mass, then all the forces are equal in magnitude. We refer to the magnitude of the forces as the tension in the string, T.
http://www.vias.org/physics/bk1_07_04.html

Tension usually arises in the use of ropes or cables to transmit a force. It is the opposite of compression. Tension is the force with which a rope or line pulls. If we hang a length of rope from the ceiling, and add a weight to the end of it, the pull force created by the weight is called the tension force. The tension force on the rope is equal to the weight of the object.

In general, low-mass objects can be treated approximately as if they simply transmitted forces from one object to another. This can be true for strings, ropes, and cords, and also for rigid objects such as rods and sticks.
http://www.lightandmatter.com/html_books/1np/ch05/ch05.html#Section5.4

Tension force, or tensile force, is an example of a pulling force, and is typically measured in pounds (Ibs) or newtons (N.) Tension force will act on opposite ends of the rope and pull it tight. The force is applied in the direction of the rope. Objects on both ends of the rope will experience a pulling force equal to the tension force. Tension force in the rope is of equal magnitude throughout the rope.

If you think about it, a rope without tension is remarkably useless when you need to get something moved (unless of course, you use it as a whip and order someone else to move it!) For example, a length of rope is not much use in pushing an object across a flat surface - it can't be used like a rod or stick. However, if the rope is tied round said object, and I pull on it, then I stand a chance of shifting the thing. Tension generated in the rope thus allows me to transmit force. Strings, ropes, cables and chains can only be used in instances where there is pull force. Essentially, somebody, or something has to pull the rope.

If we translate these ideas back to lines of magnetic force, and imagine them as ropes or chains that are fashioned in a series of continous loops, then something must be pulling at them. What is required is a mechanism of some description, one that resides in the material of the magnet, and acts upon these "ropes" by pulling on them. What emerges is something that is highly reminiscent of a pulley system.

A pulley is a simple machine consisting of a string (or rope) wrapped around a wheel (sometimes with a groove) with one end of the string attached to an object and the other end attached to a person or a motor. Pulleys may seem simple, but they can provide a powerful mechanical advantage so lifting tasks may be done easily.
http://www.teachengineering.org/view_lesson.php?url=http://www.teachengineering.org/collection/cub_/lessons/cub_simple/cub_simple_lesson05.xml

Rope-pulley systems are used when there is a need to transmit rotary motion. The advantage of ropes and chains is that they can transmit force without their performance being affected by length. A common misconception holds that simple machines, such as levers and pulleys, increase forces - but this is not quite correct; levers and pulleys transmit forces, and if the masses of the levers or pulleys are negligible, the input and output forces are equal. In other words, simple machines make it possible to lift heavy objects because they reduce the magnitude of the required input force, but it shall be seen that regardless of whether we use a pulley system or not, the amount of over-all effort needed to move an object always remains the same. A box that weighs 100 Newtons is always going to need an upward force greater than 100 Newtons to lift it.

The effect of a pulley is analogous to the gears of a bicycle; a lower gear makes it easier to turn the pedals, but they must be turned more often for the bicycle to travel the same distance. Likewise, a pulley system makes it easier to lift a load, but the length of cable used to lift the load is greater than the distance the load is lifted. The more pulleys that are used, the easier it is to lift the load, but the longer the length of cable needed to lift the the same distance.
http://wiki.answers.com/Q/Where_is_a_pulley_used

In practise, rope-pulley systems are generally regarded as inefficient due to the force of friction. Ropes tend to slip and stick along pulley wheels, meaning that energy is lost from the system. Another disadvantage with the system is that rope can permanently stretch under tension, robbing the rope of its elasticity and strength. This is why in some installations it is better to use a chain system, whose rigid design allows it to retain tension, and prevents stretching. Chains can also be made to fit on gears so that slipping is not a problem. For these reasons, if I were to try and imagine how lines of force might physically appear, then I would come up with a chain system. I then picture these chains as being pushed and pulled by a multitude of sprockets and gears, all whizzing frantically away inside the magnetic material.

A sprocket is a profiled wheel with teeth that meshes with a chain, track or other perforated or indented material. It is distinguished from a gear in that sprockets are never meshed together directly, and differs from a pulley in that sprockets have teeth and pulleys are smooth.

Sprockets are used in bicycles, motorcycles, cars, tanks, and other machinery either to transmit rotary motion between two shafts where gears are unsuitable or to impart linear motion to a track, tape etc.
http://en.wikipedia.org/wiki/Sprocket

Effectively, what a chain or rope-pulley system allows us to do is "trade" force for distance - which is the exact same principle by which a simple lever works. Pulleys lengthen the distance of the rope, thereby increasing the distance over which the force acts. By increasing distance, the system is able to increase the amount of energy that it stores. I tend to imagine it somewhat as the total force that is required to lift an object, as being broken down into smaller, more manageable units, and then spread over a greater distance.

With four wheels and four ropes, a pulley cuts the lifting force you need to one quarter. But you have to pull the end of the rope four times as far.
http://www.explainthatstuff.com/pulleys.html

It is interesting that as a direct consequence of the increase in distance, we are now seeing that action takes place over a longer time. This is in compliance with the "golden rule" of mechanics, in that the mechanical advantage derived will always be accompanied by a loss in displacement, or in other words, time. This further suggests that force, regardless of the amount, always seems to be transmitted at the same speed. It means that Archimedes claim to be able to lift the world, given a lever that was long enough, is theoretically possible - just as long as we're prepared to wait a few million years!

Archimedes knew that by applying a lever, one could lift the heaviest of weights by applying even the weakest of forces. One had only to apply this force to the levers longer arm and cause the shorter one to act on the load. He therefore thought that by pressing with his hand on the extremely long arm of a lever he would be able to lift a weight, the mass of which would be equivalent to that of the earth.

Let us imagine for a moment that Archimedes had at his disposal "another earth" and also the point of support he sought. Further imagine that he was even able to manufacture a lever of the required length. I wonder if you can guess the amount of time he would need to lift a load equivalent in mass to that of the earth, by at least a centimeter? Thirty million million years- and no less!!
http://www.buzzle.com/editorials/7-30-2004-57259.asp

When you push down on a lever, the force you push with is multiplied by the length of the lever to produce a torque. The torque of a force is the turning effect of the force about a point. Torque is, by definition, the product of a force applied in a rotational motion or twisting force. It is a turning force. It is the force that produces rotation. Because pulley systems use rotational forces, they too use the principle of torque.

Torque, also called moment or moment of force, is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist.
http://en.wikipedia.org/wiki/Torque

Whenever I think of torque, I'm always reminded of the cordless screwdriver I would wield at work. You may have noticed that most cordless screwdrivers have a torque setting. To remove a screw from the wall, one that was wedged in especially tight, it is necessary for the torque to be switched over to a high setting. If the torque is not high enough, the screw will not budge, because the drill is simply not strong enough. It is torque which is defining the drill's strength. If the screw is especially tight, and the torque setting is strong enough, you might find that the screw will still not move, but now it is your arm that the drill wants to spin round!

Both levers and the inclined plane lower the force required for a task at the price of having to apply that force over a longer distance. With wheels and axles the same is true: a poweful force and movement of the axle is converted to a greater movement, but less force, at the circumference of the wheel. In a circular geometry, torque is a more useful concept than force and distance. The wheel and axle can be thought of as simply a circular lever, as shown in Figure 5 [below]. Many common items rely on the wheel and axle such as the screwdriver, the steering wheel, the wrench, and the faucet.
http://cnx.org/content/m13594/latest/

If you want to increase the load that a pulley system may carry, then it is necessary to increase torque. The greater the torque, the more energy stored. Torque units contain a distance and a force. Torque is, in effect, the product of the force and the length of the lever arm. Understood in this way, it is clear that there are two ways of increasing torque; either increase the force or increase the length of the lever arm. As torque is a product of force and distance, one may be "traded" for the other.

Torque, like work is measured in pound-feet (lb-ft) However, torque, unlike work, may exist even though no movement occurs. A good example of this is the torque exerted when you try and loosen a very tight nut. As you are pulling on the wrench you are exerting a force, but not until the the nut moves has this torque resulted in work.

Work is done when we use a force (a push or pull) to move something over a distance. Energy is needed to move a force through distance. In calculating work done, two things need to be measured: the amount of force and the distance that it moves. Thus, it is important to make the distinction that work is a measure of what is done, not the effort applied in trying to move it. Where energy is the capacity for doing work, it means that both these quantities are measured by the same unit - in a sense the two are equivalent. Work and energy are merely different ways of looking at the same thing.

Because of the way it is defined, there will be plenty of times in my life (some might say the story of my life!) where I will spend energy, but no work is done. That's because it's possible to for me to exert a force where we see nothing move. If I remain still, holding a dumbell above my head, a physics textbook will tell me that I have done no work because my actions do not involve motion - no distance, no work. A physicist might be cheeky enough to tell me that I'm not doing any work - but given a few minutes, it won't stop my arms from feeling like they want to fall off! The fact is, I am still spending energy even though there is no evidence of "work done."

People often confuse energy, power, and force. Force is a push or a pull on an object or body. The strength of the force used and the distance through which it moves determine the amount of work done. Two factors determine the amount of work done. One factor is the amount of force applied. The other is the distance the object moves. In physics, work occurs only when the force is sufficient to move the object. In other words, work is a measure of what is done, not the effort applied in attempting to move the object. People do work when lifting, pushing, or sliding an object from one place to another. They do no work when holding an object without moving it, even though they may become tired.
http://www.sci-ctr.edu.sg/ssc/detailed.jsp?artid=4875&type=6&root=5&parent=5&cat=57

If work and energy are both a measure of force times distance, what does this mean if we extract distance from the equation? Of course we don't even have to go as far as removing it, but simply reduce its quantity to zero. Thus, energy now becomes equal to force times zero distance, surely meaning that force is only describing energy in some way? Looking at this equation again, it is also interesting that distance too emerges as being another means of describing energy.

Returning to the idea that a lever, or pulley system are able to reduce the magnitude of the necessary force by applying force over a longer distance, it seems that this "trade" of force for distance would suggest that the system is storing force in some way. Indeed, if we were to expand on this a little further, it might be said that distance itself is responsible for storing this force.

Now, I must tread carefully in how I explain the idea of how a system might "store force." As any physics textbook will tell you, it is not possible to "store force" as such - rather, it is energy which is stored, and not force. This is because force, at least in terms of how some physicists describe it, is not energy. Energy and force are treated as being something of different concepts, but this does not mean they are incompatible. I think it's possible to argue that energy and forces are merely different guises of the same entity.

Now there may well be some who are more familiar with physics, whose sensibilities are more delicate than others, and whom after reading that last sentence, might just have sprayed the wall with coffee. To these persons I apologise profusely for any mess caused, but I believe that there are good grounds for such a theory, and I'm going to discuss them in my next post (those that are consuming drinks have been warned!)

Many thanks to:

http://www.bearsoft.co.uk/Magf.html
http://en.wikipedia.org/wiki/Ferromagnetism
http://gksingla.tripod.com/Research/Domain.html
http://www.daviddarling.info/encyclopedia/M/magnet.ht ml
http://my.opera.com/nielsol/blog/?id=1730460
http://www.energeticforum.com/renewable-energy/3781-physics-primary-state-matter-2.html
http://en.wikipedia.org/wiki/Electromagnetic_shielding
http://newscenter.lbl.gov/news-releases/2009/01/28/domain-walls-that-conduct-electricity/
http://www.viewsfromscience.com/documents/webpages/chaos_p8.html
http://www.labyrinthos.net/nepalese.html
http://sci-toys.com/scitoys/scitoys/magnets/calculating/calculating.html
http://farside.ph.utexas.edu/teaching/316/lectures/node77.html
http://education.online.sr/
http://www.ndt-ed.org/EducationResources/CommunityCollege/Materials/Structure/solidification.htm
http://www.ndt-ed.org/EducationResources/CommunityCollege/Materials/Structure/point_defects.htm
http://www.chemguide.co.uk/atoms/structures/metals.html
http://www.sciencedaily.com/releases/2007/06/070606113438.htm
http://quest.nasa.gov/space/teachers/microgravity/emat.html
http://incolor.inebraska.com/bill_r/fun_with_molten_metal.htm
http://www.matter.org.uk/matscicdrom/manual/di.html
http://www.answers.com/topic/elasticity
http://www.daviddarling.info/encyclopedia/E/elasticity.html
http://science.jrank.org/pages/2293/Elasticity.html
http://equalrightsforall.net/mechanical_waves/009_waves.htm
http://physics.bu.edu/~duffy/py105/Resonance.html
http://sofisworld.com/course/category.php?id=10
http://www.explainthatstuff.com/piezoelectricity.html
http://www.rockhoundingar.com/quartz/experiments.html
http://humanise.org/demining/phenomenons
Physicists look back: studies in the history of physics By John Roche
What is electricity? By John Trowbridge, I. Bernard Cohen
http://qhxb.lib.tsinghua.edu.cn/myweb/english/98n1/980101.html
http://science.jrank.org/pages/49241/magnetism.html
http://www.tpub.com/neets/book1/chapter1/1g.htm
http://www.1stardrive.com/solar/mag.htm
http://www.lassp.cornell.edu/sethna/hysteresis/WhatIsHysteresis.html
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/hyst.html
http://openbookproject.net/electricCircuits/DC/DC_14.html
http://www.school-for-champions.com/science/magnetism_lorentz.htm
http://mysite.du.edu/~jcalvert/tech/fluids/vortex.htm
http://www.desktop.aero/appliedaero/potential3d/3dtheory.html
http://electron9.phys.utk.edu/phys135d/modules/m4/3rdLaw.htm
http://en.wikisource.org/wiki/On_Physical_Lines_of_Force
http://en.wikipedia.org/wiki/Reaction_(physics)
http://quest.nasa.gov/space/teachers/rockets/principles.html
http://www.lhup.edu/~dsimanek/cutting/3rdlaw.htm
http://ffden-2.phys.uaf.edu/211_fall2002.web.dir/ben_townsend/staticandkineticfriction.htm
http://www.madsci.org/posts/archives/2002-03/1015259194.Ph.r.html
http://answers.yahoo.com/question/index?qid=20080805020633AAurlxP
http://cnx.org/content/m13594/latest/
http://www.sparknotes.com/physics/dynamics/newtonapplications/section3.rhtml
http://www.wisegeek.com/what-is-tension-force.htm
http://chain-guide.com/basics/2-2-1-chordal-action.html
http://www.vias.org/physics/bk1_07_04.html
http://www.physicsforums.com/archive/index.php/t-160355.html
http://www.lightandmatter.com/html_books/1np/ch05/ch05.html
http://www.vixra.org/pdf/0910.0066v1.pdf
http://nov55.com/lev.html
http://www.buzzle.com/editorials/7-30-2004-57259.asp
http://en.wikipedia.org/wiki/Torque
http://www.bikeland.org/bridges/Torque-The-question-you-didn-t-ask.html
http://www.lightandmatter.com/html_books/1np/ch04/ch04.html
http://www.cleavebooks.co.uk/dictunit/notes3.htm
http://www.physicsclassroom.com/class/newtlaws/u2l2a.cfm
http://ezinearticles.com/?Force-and-Motion&id=4175015
http://www.vicphysics.org/documents/students/Unit%203%20Materials%20notes.doc.

Forces, Energies, and Consciouness

2010-09-04T07:20:00.000-07:00

Forces, Energies, and Consciouness

By G. de Purucker

The universe and all in it, great and small, is built in and upon consciousness, which includes in its qualities those other phases of cosmic being which we call life, mind, substance. Yet that consciousness, when applied to the universe, is an abstraction, and it is equally proper, and to many minds more accurate, to speak of the kosmic universe as being infilled with consciousnesses, infinite in number. These consciousnesses are in virtually innumerable stages of evolutionary development and are structurally arranged according to hierarchical families. Thus everything in the universe, considered as an individual expression of an indwelling and self-expressing monad, is not only an individualized atom of the Boundless, but in its inmost essence is philosophically to be considered as identic with the universe itself.

All space, infinitesimal and cosmic, is filled full of forces and substances in all-various grades of substantiality, ethereality, and spirituality. Such relatively physical force-substances as electricity and light may be cited as instances. For what are electricity and light, and indeed any other force-substance? They are, without exception, emanations from entities of cosmic magnitude. In other words, the Boundless is full of cosmic entities, each of which has its own universe acting as its own individual "bearer" or "carrier"; and the vital forces or energies in any such entity are the identical forces, energies, substances, which infill that universe, and therefore, because substantially of the nature of consciousness, direct it, guide it, control it, and are in fact that inner and eternal urge behind all the outer phenomenal appearances.

In the atom as in the cosmos, the same principles, the same energies, substances, and structural operations prevail, because both atom and cosmos are forever inseparable parts of the boundless All, and therefore reflect, each according to its power and capacity, the spiritual primordials which the Boundless contains. Hence cosmos and atoms -- inner and invisible, outer and visible, worlds and planes and spheres, considered as a cosmic composite -- are what we call not only the veils and garments of the cosmic life, but the expressions of that cosmic life itself.

Is consciousness then different from force or energy? No, consciousness or mind is both the root and focus of force or energy, their very soul, and being such, it is substantial, although not matter as we understand it. Our grossest physical matter is but the concretion of dormant monads, a vast aggregate of psychomagnetic consciousness centers. When they awake to kinetic movement or individual activity, these "sleeping" monads forming the matter around us begin their respective individual evolutionary journeys upwards again towards that freedom of spirit, of pure consciousness-force, from which in the beginnings of things they originally "fell" into matter, which is thus their own collective concretion.

This last thought gives the key to a clear understanding of what the forces of nature really are in themselves. They are essentially cosmic entities manifesting themselves in an energic fluidic form; and this fluidic form or activity is what we sense as nature's forces. They are the emanations or outpourings of the aggregative cosmic consciousness.

We may take gravitation, electricity, magnetism, heat, chemical affinity, light, as instances, because these are the cosmic forces that most usually come under the observation of human beings. They are all forces, i.e., outpourings from an individual source, this source being one of the cosmic entities with which space is filled; and these entities in their turn are ultimately to be traced back to their origins as emanations from the universal cosmic consciousness. Being forces they are likewise substantial, because matter and force are essentially one. Likewise, spirit (or consciousness) and essential substance are intrinsically one. So whenever there is force or energy, or its manifestations --gravitation, magnetism, heat, whatever it may be -- it is likewise as substantial as it is energic; therefore it is likewise essentially consciousness expressing itself as consciousnesses.

In the esoteric philosophy heat and light are substantial just because they are forces. Being forces manifesting as energies, they have in them the same essential qualities that the human entity has, although not expressing themselves as these do in us. These aggregative factors are to be grouped as consciousness. Nevertheless these various forces of nature -- gravitation, as an illustration -- are not in themselves each one a consciousness, but each such force is rather the manifestation or self-expression of a cosmic consciousness: the emanation or vital fluid, expressing itself as gravitation, of some living, conscious, cosmic entity behind.

The forces of nature, then, are the vital fluids, working in the cosmos, of spiritual beings from whom this nervous energy flows, in whom this vital electricity inheres, and working and operating in their circuits around the vehicular being of the spiritual entity which thus emanationally gives them birth; or to put it in another way, each such cosmic force is the outflowing from some cosmic entity of its characteristic vital fluid of the particular grade belonging to this entity's lowest cosmic body.

This vital force or cosmic electric energy is inherently and throughout guided, automatically to us humans, by the mind and will of the cosmic entities from which it flows in emanational series -- each unit in such series being what we call this, that, or some other force of nature. These cosmic entities in themselves form an interlocking and interwoven hierarchy of lofty spiritual intelligences; and because their individual characters are nearly akin, they cooperate in producing the entirety of the cosmic phenomena or operations which commonly are grouped under the term nature.

Human magnetism will perhaps illustrate this point in the small, as working in even such derivative phenomena as the circulation of the blood or the digestive functions. None of these functions of the human body, considered alone, is physical man. In their aggregate, combined with the framework of the body, they form physical man, but in themselves they are functions brought about by the interplay of the emanations of man's vital essence, and thus form the operative economy of his body, and are ultimately derived from the real man of consciousness and thought. These operations, which eventuate in producing and running the physical body, emanate from the man himself by and through the medium of his permeant consciousness and through the instrumentality of his will, acting in him partly consciously and partly unconsciously, precisely as the forces of nature act on the macrocosmic scale in the universe surrounding us. -- Condensed from The Esoteric Tradition, ch. 14

(From Sunrise magazine, April/May 2003; copyright © 2003 Theosophical University Press)

Science Menu

We have today to learn to get back into accord with the wisdom of nature and realize again our brotherhood with the animals and with the water and the sea. To say that the divinity informs all things is condemned as pantheism. But pantheism is a misleading word. It suggests that a personal god is supposed to inhabit the world, but that is not the idea at all. The idea is . . . of an undefinable, inconceivable mystery, thought of as a power, that is the source and end and supporting ground of all life and being. -- Joseph Campbell

Speculations: nature of matter: lines of force

2010-07-29T14:26:00.000-07:00

~~An extract~~

The lines of force have their roots in the magnet, and though they may expand into infinite space, they eventually return to the magnet. Now these lines may be intersected close to the magnet or at a distance from it. Faraday finds distance to be perfectly immaterial so long as the number of lines intersected is the same. For example, when the loop connecting the equator and the pole of his barmagnet performs one complete revolution round the magnet, it is manifest that all the lines of force issuing from the magnet are once intersected. Now it matters not whether the loop be ten feet or ten inches in length, it matters not how it may be twisted and contorted, it matters not how near to the magnet or how distant from it the loop may be, one revolution always produces the same amount of current electricity, because in all these cases all the lines of force issuing from the magnet are once intersected and no more.

From the external portion of the circuit he passes in idea to the internal, and follows the lines of force into the body of the magnet itself. His conclusion is that there exist lines of force within the magnet of the same nature as those without. What is more, they are exactly equal in amount to those without. They have a relation in direction to those without; and in fact are continuations of them.... 'Every line of force, therefore, at whatever distance it may be taken from the magnet, must be considered as a closed circuit, passing in some part of its course through the magnet, and having an equal amount of force in every part of its course.'
http://worldebooklibrary.org/eBooks/WorldeBookLibrary.com/fdayd.htm

Discovery of diamagnetism--researches on magne-crystallic action.

2010-07-29T09:52:00.000-07:00

~~An extract~~

Faraday's thoughts ran intuitively into experimental combinations, so that subjects whose capacity for experimental treatment would, to ordinary minds, seem to be exhausted in a moment, were shown by him to be all but inexhaustible. He has now an object in view, the first step towards which is the proof that the principle of Archimedes is true of magnetism. He forms magnetic solutions of various degrees of strength, places them between the poles of his magnet, and suspends in the solutions various magnetic bodies. He proves that when the solution is stronger than the body plunged in it, the body, though magnetic, is repelled; and when an elongated piece of it is surrounded by the solution, it sets, like a diamagnetic body, equatorially between the excited poles. The same body when suspended in a solution of weaker magnetic power than itself, is attracted as a whole, while an elongated portion of it sets axially.

...After the description of the general character of this new force, Faraday states with the emphasis here reproduced its mode of action: 'The law of action appears to be that the line or axis of MAGNE-CRYSTALLIC force (being the resultant of the action of all the molecules) tends to place itself parallel, or as a tangent, to the magnetic curve, or line of magnetic force, passing through the place where the crystal is situated.' The magne-crystallic force, moreover, appears to him 'to be clearly distinguished from the magnetic or diamagnetic forces, in that it causes neither approach nor recession, consisting not in attraction or repulsion, but in giving a certain determinate position to the mass under its influence.' And then he goes on 'very carefully to examine and prove the conclusion that there was no connection of the force with attractive or repulsive influences.' With the most refined ingenuity he shows that, under certain circumstances, the magne-crystallic force can cause the centre of gravity of a highly magnetic body to retreat from the poles, and the centre of gravity of a highly diamagnetic body to approach them. His experiments root his mind more and more firmly in the conclusion that 'neither attraction nor repulsion causes the set, or governs the final position' of the crystal in the magnetic field. That the force which does so is therefore 'distinct in its character and effects from the magnetic and diamagnetic forms of force. On the other hand,' he continues, 'it has a most manifest relation to the crystalline structure of bismuth and other bodies, and therefore to the power by which their molecules are able to build up the crystalline masses.'

And here follows one of those expressions which characterize the conceptions of Faraday in regard to force generally:--'It appears to me impossible to conceive of the results in any other way than by a mutual reaction of the magnetic force, and the force of the particles of the crystals upon each other.' He proves that the action of the force, though thus molecular, is an action at a distance; he shows that a bismuth crystal can cause a freely suspended magnetic needle to set parallel to its magne-crystallic axis. Few living men are aware of the difficulty of obtaining results like this, or of the delicacy necessary to their attainment. 'But though it thus takes up the character of a force acting at a distance, still it is due to that power of the particles which makes them cohere in regular order and gives the mass its crystalline aggregation, which we call at other times the attraction of aggregation, and so often speak of as acting at insensible distances.' Thus he broods over this new force, and looks at it from all possible points of inspection. Experiment follows experiment, as thought follows thought. He will not relinquish the subject as long as a hope exists of throwing more light upon it. He knows full well the anomalous nature of the conclusion to which his experiments lead him. But experiment to him is final, and he will not shrink from the conclusion. 'This force,' he says, 'appears to me to be very strange and striking in its character. It is not polar, for there is no attraction or repulsion.' And then, as if startled by his own utterance, he asks--'What is the nature of the mechanical force which turns the crystal round, and makes it affect a magnet?'... 'I do not remember,' he continues 'heretofore such a case of force as the present one, where a body is brought into position only, without attraction or repulsion.'

Plucker, the celebrated geometer already mentioned, who pursued experimental physics for many years of his life with singular devotion and success, visited Faraday in those days, and repeated before him his beautiful experiments on magneto-optic action. Faraday repeated and verified Plucker's observations, and concluded, what he at first seemed to doubt, that Plucker's results and magne-crystallic action had the same origin.

At the end of his papers, when he takes a last look along the line of research, and then turns his eyes to the future, utterances quite as much emotional as scientific escape from Faraday. 'I cannot,' he says, at the end of his first paper on magne-crystallic action, 'conclude this series of researches without remarking how rapidly the knowledge of molecular forces grows upon us, and how strikingly every investigation tends to develop more and more their importance, and their extreme attraction as an object of study. A few years ago magnetism was to us an occult power, affecting only a few bodies, now it is found to influence all bodies, and to possess the most intimate relations with electricity, heat, chemical action, light, crystallization, and through it, with the forces concerned in cohesion; and we may, in the present state of things, well feel urged to continue in our labours, encouraged by the hope of bringing it into a bond of union with gravity itself.'

The law of action in relation to this point is, that in diamagnetic crystals, the line along which the repulsion is a maximum, sets equatorially in the magnetic field; while in magnetic crystals the line along which the attraction is a maximum sets from pole to pole. Faraday had said that the magne-crystallic force was neither attraction nor repulsion. Thus far he was right. It was neither taken singly, but it was both. By the combination of the doctrine of diamagnetic polarity with these differential attractions and repulsions, and by paying due regard to the character of the magnetic field, every fact brought to light in the domain of magne-crystallic action received complete explanation. The most perplexing of those facts were shown to result from the action of mechanical couples, which the proved polarity both of magnetism and diamagnetism brought into play. Indeed the thoroughness with which the experiments of Faraday were thus explained, is the most striking possible demonstration of the marvellous precision with which they were executed.
~~Author: John Tyndall
http://worldebooklibrary.org/eBooks/WorldeBookLibrary.com/fdayd.htm

Faraday As A Discoverer

2010-07-29T05:07:00.000-07:00

~~An extract~~

Discovery of Magneto-electricity: Explanation of Argo's magnetism of rotation: Terrestrial magneto-electric induction: The extra current.

The work thus referred to, though sufficient of itself to secure no mean scientific reputation, forms but the vestibule of Faraday's achievements. He had been engaged within these walls for eighteen years. During part of the time he had drunk in knowledge from Davy, and during the remainder he continually exercised his capacity for independent inquiry. In 1831 we have him at the climax of his intellectual strength, forty years of age, stored with knowledge and full of original power. Through reading, lecturing, and experimenting, he had become thoroughly familiar with electrical science: he saw where light was needed and expansion possible. The phenomena of ordinary electric induction belonged, as it were, to the alphabet of his knowledge: he knew that under ordinary circumstances the presence of an electrified body was sufficient to excite, by induction, an unelectrified body. He knew that the wire which carried an electric current was an electrified body, and still that all attempts had failed to make it excite in other wires a state similar to its own.

What was the reason of this failure? Faraday never could work from the experiments of others, however clearly described. He knew well that from every experiment issues a kind of radiation, luminous in different degrees to different minds, and he hardly trusted himself to reason upon an experiment that he had not seen. In the autumn of 1831 he began to repeat the experiments with electric currents, which, up to that time, had produced no positive result. And here, for the sake of younger inquirers, if not for the sake of us all, it is worth while to dwell for a moment on a power which Faraday possessed in an extraordinary degree. He united vast strength with perfect flexibility. His momentum was that of a river, which combines weight and directness with the ability to yield to the flexures of its bed. The intentness of his vision in any direction did not apparently diminish his power of perception in other directions; and when he attacked a subject, expecting results he had the faculty of keeping his mind alert, so that results different from those which he expected should not escape him through preoccupation.

He began his experiments 'on the induction of electric currents' by composing a helix of two insulated wires which were wound side by side round the same wooden cylinder. One of these wires he connected with a voltaic battery of ten cells, and the other with a sensitive galvanometer. When connection with the battery was made, and while the current flowed, no effect whatever was observed at the galvanometer. But he never accepted an experimental result, until he had applied to it the utmost power at his command. He raised his battery from 10 cells to 120 cells, but without avail. The current flowed calmly through the battery wire without producing, during its flow, any sensible result upon the galvanometer.

'During its flow,' and this was the time when an effect was expected-- but here Faraday's power of lateral vision, separating, as it were, from the line of expectation, came into play--he noticed that a feeble movement of the needle always occurred at the moment when he made contact with the battery; that the needle would afterwards return to its former position and remain quietly there unaffected by the flowing current. At the moment, however, when the circuit was interrupted the needle again moved, and in a direction opposed to that observed on the completion of the circuit.

This result, and others of a similar kind, led him to the conclusion 'that the battery current through the one wire did in reality induce a similar current through the other; but that it continued for an instant only, and partook more of the nature of the electric wave from a common Leyden jar than of the current from a voltaic battery.' The momentary currents thus generated were called induced currents, while the current which generated them was called the inducing current. It was immediately proved that the current generated at making the circuit was always opposed in direction to its generator, while that developed on the rupture of the circuit coincided in direction with the inducing current. It appeared as if the current on its first rush through the primary wire sought a purchase in the secondary one, and, by a kind of kick, impelled backward through the latter an electric wave, which subsided as soon as the primary current was fully established.

Faraday, for a time, believed that the secondary wire, though quiescent when the primary current had been once established, was not in its natural condition, its return to that condition being declared by the current observed at breaking the circuit. He called this hypothetical state of the wire the electro-tonic state: he afterwards abandoned this hypothesis, but seemed to return to it in later life. The term electro-tonic is also preserved by Professor Du Bois Reymond to express a certain electric condition of the nerves, and Professor Clerk Maxwell has ably defined and illustrated the hypothesis in the Tenth Volume of the 'Transactions of the Cambridge Philosophical Society.'

The mere approach of a wire forming a closed curve to a second wire through which a voltaic current flowed was then shown by Faraday to be sufficient to arouse in the neutral wire an induced current, opposed in direction to the inducing current; the withdrawal of the wire also generated a current having the same direction as the inducing current; those currents existed only during the time of approach or withdrawal, and when neither the primary nor the secondary wire was in motion, no matter how close their proximity might be, no induced current was generated.

Faraday has been called a purely inductive philosopher. A great deal of nonsense is, I fear, uttered in this land of England about induction and deduction. Some profess to befriend the one, some the other, while the real vocation of an investigator, like Faraday, consists in the incessant marriage of both. He was at this time full of the theory of Ampere, and it cannot be doubted that numbers of his experiments were executed merely to test his deductions from that theory. Starting from the discovery of Oersted, the illustrious French philosopher had shown that all the phenomena of magnetism then known might be reduced to the mutual attractions and repulsions of electric currents. Magnetism had been produced from electricity, and Faraday, who all his life long entertained a strong belief in such reciprocal actions, now attempted to effect the evolution of electricity from magnetism. Round a welded iron ring he placed two distinct coils of covered wire, causing the coils to occupy opposite halves of the ring. Connecting the ends of one of the coils with a galvanometer, he found that the moment the ring was magnetised, by sending a current through the other coil, the galvanometer needle whirled round four or five times in succession. The action, as before, was that of a pulse, which vanished immediately. On interrupting the circuit, a whirl of the needle in the opposite direction occurred. It was only during the time of magnetization or demagnetization that these effects were produced. The induced currents declared a change of condition only, and they vanished the moment the act of magnetization or demagnetization was complete.

The effects obtained with the welded ring were also obtained with straight bars of iron. Whether the bars were magnetised by the electric current, or were excited by the contact of permanent steel magnets, induced currents were always generated during the rise, and during the subsidence of the magnetism. The use of iron was then abandoned, and the same effects were obtained by merely thrusting a permanent steel magnet into a coil of wire. A rush of electricity through the coil accompanied the insertion of the magnet; an equal rush in the opposite direction accompanied its withdrawal. The precision with which Faraday describes these results, and the completeness with which he defines the boundaries of his facts, are wonderful. The magnet, for example, must not be passed quite through the coil, but only half through; for if passed wholly through, the needle is stopped as by a blow, and then he shows how this blow results from a reversal of the electric wave in the helix. He next operated with the powerful permanent magnet of the Royal Society, and obtained with it, in an exalted degree, all the foregoing phenomena.

And now he turned the light of these discoveries upon the darkest physical phenomenon of that day. Arago had discovered, in 1824, that a disk of non-magnetic metal had the power of bringing a vibrating magnetic needle suspended over it rapidly to rest; and that on causing the disk to rotate the magnetic needle rotated along with it. When both were quiescent, there was not the slightest measurable attraction or repulsion exerted between the needle and the disk; still when in motion the disk was competent to drag after it, not only a light needle, but a heavy magnet. The question had been probed and investigated with admirable skill both by Arago and Ampere, and Poisson had published a theoretic memoir on the subject; but no cause could be assigned for so extraordinary an action. It had also been examined in this country by two celebrated men, Mr. Babbage and Sir John Herschel; but it still remained a mystery. Faraday always recommended the suspension of judgment in cases of doubt. 'I have always admired,' he says, 'the prudence and philosophical reserve shown by M. Arago in resisting the temptation to give a theory of the effect he had discovered, so long as he could not devise one which was perfect in its application, and in refusing to assent to the imperfect theories of others.' Now, however, the time for theory had come. Faraday saw mentally the rotating disk, under the operation of the magnet, flooded with his induced currents, and from the known laws of interaction between currents and magnets he hoped to deduce the motion observed by Arago. That hope he realised, showing by actual experiment that when his disk rotated currents passed through it, their position and direction being such as must, in accordance with the established laws of electro-magnetic action, produce the observed rotation.

Introducing the edge of his disk between the poles of the large horseshoe magnet of the Royal Society, and connecting the axis and the edge of the disk, each by a wire with a galvanometer, he obtained, when the disk was turned round, a constant flow of electricity. The direction of the current was determined by the direction of the motion, the current being reversed when the rotation was reversed. He now states the law which rules the production of currents in both disks and wires, and in so doing uses, for the first time, a phrase which has since become famous. When iron filings are scattered over a magnet, the particles of iron arrange themselves in certain determinate lines called magnetic curves. In 1831, Faraday for the first time called these curves 'lines of magnetic force'; and he showed that to produce induced currents neither approach to nor withdrawal from a magnetic source, or centre, or pole, was essential, but that it was only necessary to cut appropriately the lines of magnetic force. Faraday's first paper on Magneto-electric Induction, which I have here endeavoured to condense, was read before the Royal Society on the 24th of November, 1831.

On January 12, 1832, he communicated to the Royal Society a second paper on Terrestrial Magneto-electric Induction, which was chosen as the Bakerian Lecture for the year. He placed a bar of iron in a coil of wire, and lifting the bar into the direction of the dipping needle, he excited by this action a current in the coil. On reversing the bar, a current in the opposite direction rushed through the wire. The same effect was produced when, on holding the helix in the line of dip, a bar of iron was thrust into it. Here, however, the earth acted on the coil through the intermediation of the bar of iron. He abandoned the bar and simply set a copper plate spinning in a horizontal plane; he knew that the earth's lines of magnetic force then crossed the plate at an angle of about 70degrees. When the plate spun round, the lines of force were intersected and induced currents generated, which produced their proper effect when carried from the plate to the galvanometer. 'When the plate was in the magnetic meridian, or in any other plane coinciding with the magnetic dip, then its rotation produced no effect upon the galvanometer.'

At the suggestion of a mind fruitful in suggestions of a profound and philosophic character--I mean that of Sir John Herschel-- Mr. Barlow, of Woolwich, had experimented with a rotating iron shell. Mr. Christie had also performed an elaborate series of experiments on a rotating iron disk. Both of them had found that when in rotation the body exercised a peculiar action upon the magnetic needle, deflecting it in a manner which was not observed during quiescence; but neither of them was aware at the time of the agent which produced this extraordinary deflection. They ascribed it to some change in the magnetism of the iron shell and disk.

But Faraday at once saw that his induced currents must come into play here, and he immediately obtained them from an iron disk. With a hollow brass ball, moreover, he produced the effects obtained by Mr. Barlow. Iron was in no way necessary: the only condition of success was that the rotating body should be of a character to admit of the formation of currents in its substance: it must, in other words, be a conductor of electricity. The higher the conducting power the more copious were the currents. He now passes from his little brass globe to the globe of the earth. He plays like a magician with the earth's magnetism. He sees the invisible lines along which its magnetic action is exerted, and sweeping his wand across these lines evokes this new power. Placing a simple loop of wire round a magnetic needle he bends its upper portion to the west: the north pole of the needle immediately swerves to the east: he bends his loop to the east, and the north pole moves to the west. Suspending a common bar magnet in a vertical position, he causes it to spin round its own axis. Its pole being connected with one end of a galvanometer wire, and its equator with the other end, electricity rushes round the galvanometer from the rotating magnet. He remarks upon the 'singular independence' of the magnetism and the body of the magnet which carries it. The steel behaves as if it were isolated from its own magnetism.

And then his thoughts suddenly widen, and he asks himself whether the rotating earth does not generate induced currents as it turns round its axis from west to east. In his experiment with the twirling magnet the galvanometer wire remained at rest; one portion of the circuit was in motion relatively to another portion. But in the case of the twirling planet the galvanometer wire would necessarily be carried along with the earth; there would be no relative motion. What must be the consequence? Take the case of a telegraph wire with its two terminal plates dipped into the earth, and suppose the wire to lie in the magnetic meridian. The ground underneath the wire is influenced like the wire itself by the earth's rotation; if a current from south to north be generated in the wire, a similar current from south to north would be generated in the earth under the wire; these currents would run against the same terminal plate, and thus neutralise each other.

This inference appears inevitable, but his profound vision perceived its possible invalidity. He saw that it was at least possible that the difference of conducting power between the earth and the wire might give one an advantage over the other, and that thus a residual or differential current might be obtained. He combined wires of different materials, and caused them to act in opposition to each other, but found the combination ineffectual. The more copious flow in the better conductor was exactly counterbalanced by the resistance of the worse. Still, though experiment was thus emphatic, he would clear his mind of all discomfort by operating on the earth itself. He went to the round lake near Kensington Palace, and stretched 480 feet of copper wire, north and south, over the lake, causing plates soldered to the wire at its ends to dip into the water. The copper wire was severed at the middle, and the severed ends connected with a galvanometer. No effect whatever was observed. But though quiescent water gave no effect, moving water might. He therefore worked at London Bridge for three days during the ebb and flow of the tide, but without any satisfactory result. Still he urges, 'Theoretically it seems a necessary consequence, that where water is flowing there electric currents should be formed. If a line be imagined passing from Dover to Calais through the sea, and returning through the land, beneath the water, to Dover, it traces out a circuit of conducting matter one part of which, when the water moves up or down the channel, is cutting the magnetic curves of the earth, whilst the other is relatively at rest.... There is every reason to believe that currents do run in the general direction of the circuit described, either one way or the other, according as the passage of the waters is up or down the channel.' This was written before the submarine cable was thought of, and he once informed me that actual observation upon that cable had been found to be in accordance with his theoretic deduction.[1]

Three years subsequent to the publication of these researches-- that is to say, on January 29, 1835--Faraday read before the Royal Society a paper 'On the influence by induction of an electric current upon itself.' A shock and spark of a peculiar character had been observed by a young man named William Jenkin, who must have been a youth of some scientific promise, but who, as Faraday once informed me, was dissuaded by his own father from having anything to do with science. The investigation of the fact noticed by Mr. Jenkin led Faraday to the discovery of the extra current, or the current induced in the primary wire itself at the moments of making and breaking contact, the phenomena of which he described and illustrated in the beautiful and exhaustive paper referred to.

Seven-and-thirty years have passed since the discovery of magneto-electricity; but, if we except the extra current, until quite recently nothing of moment was added to the subject. Faraday entertained the opinion that the discoverer of a great law or principle had a right to the 'spoils'--this was his term--arising from its illustration; and guided by the principle he had discovered, his wonderful mind, aided by his wonderful ten fingers, overran in a single autumn this vast domain, and hardly left behind him the shred of a fact to be gathered by his successors.

And here the question may arise in some minds, What is the use of it all? The answer is, that if man's intellectual nature thirsts for knowledge, then knowledge is useful because it satisfies this thirst. If you demand practical ends, you must, I think, expand your definition of the term practical, and make it include all that elevates and enlightens the intellect, as well as all that ministers to the bodily health and comfort of men. Still, if needed, an answer of another kind might be given to the question 'What is its use?' As far as electricity has been applied for medical purposes, it has been almost exclusively Faraday's electricity. You have noticed those lines of wire which cross the streets of London. It is Faraday's currents that speed from place to place through these wires. Approaching the point of Dungeness, the mariner sees an unusually brilliant light, and from the noble phares of La Heve the same light flashes across the sea. These are Faraday's sparks exalted by suitable machinery to sunlike splendour. At the present moment the Board of Trade and the Brethren of the Trinity House, as well as the Commissioners of Northern Lights, are contemplating the introduction of the Magneto-electric Light at numerous points upon our coasts; and future generations will be able to refer to those guiding stars in answer to the question. What has been the practical use of the labours of Faraday? But I would again emphatically say, that his work needs no such justification, and that if he had allowed his vision to be disturbed by considerations regarding the practical use of his discoveries, those discoveries would never have been made by him. 'I have rather,' he writes in 1831, 'been desirous of discovering new facts and new relations dependent on magneto-electric induction, than of exalting the force of those already obtained; being assured that the latter would find their full development hereafter.'

In 1817, when lecturing before a private society in London on the element chlorine, Faraday thus expressed himself with reference to this question of utility. 'Before leaving this subject, I will point out the history of this substance, as an answer to those who are in the habit of saying to every new fact. "What is its use?" Dr. Franklin says to such, "What is the use of an infant?" The answer of the experimentalist is, "Endeavour to make it useful." When Scheele discovered this substance, it appeared to have no use; it was in its infancy and useless state, but having grown up to maturity, witness its powers, and see what endeavours to make it useful have done.'

Footnote to Chapter 3

[1] I am indebted to a friend for the following exquisite morsel:--

'A short time after the publication of Faraday's first researches in magneto-electricity, he attended the meeting of the British Association at Oxford, in 1832. On this occasion he was requested by some of the authorities to repeat the celebrated experiment of eliciting a spark from a magnet, employing for this purpose the large magnet in the Ashmolean Museum. To this he consented, and a large party assembled to witness the experiments, which, I need not say, were perfectly successful. Whilst he was repeating them a dignitary of the University entered the room, and addressing himself to Professor Daniell, who was standing near Faraday, inquired what was going on. The Professor explained to him as popularly as possible this striking result of Faraday's great discovery. The Dean listened with attention and looked earnestly at the brilliant spark, but a moment after he assumed a serious countenance and shook his head; "I am sorry for it," said he, as he walked away; in the middle of the room he stopped for a moment and repeated, "I am sorry for it:" then walking towards the door, when the handle was in his hand he turned round and said, "Indeed I am sorry for it; it is putting new arms into the hands of the incendiary." This occurred a short time after the papers had been filled with the doings of the hayrick burners. An erroneous statement of what fell from the Dean's mouth was printed at the time in one of the Oxford papers. He is there wrongly stated to have said, "It is putting new arms into the hands of the infidel."'
~~Author: John Tyndall
http://worldebooklibrary.org/eBooks/WorldeBookLibrary.com/fdayd.htm

James Prescott Joule

2010-07-27T05:11:00.000-07:00

James Prescott Joule was born at Salford, England on Christmas Eve of the year 1818. His father and his grandfather before him were brewers, and the business, in due course, descended to Mr. Joule and his elder brother, and by them was carried on with success till it was sold, in 1854. Mr. Joule's grandfather came from Elton, in Derbyshire, settled near Manchester, where he founded the business, and died at the age of fifty-four, in 1799. His father, one of a numerous family, married a daughter of John Prescott of Wigan. They had five children, of whom James Prescott Joule was the second, and of whom three were sons--Benjamin, the eldest, James, and John--and two daughters--Alice and Mary. Mr. Joule's mother died in 1836 at the age of forty-eight; and his father, who was an invalid for many years before his death, died at the age of seventy-four, in the year 1858.

Young Joule was a delicate child, and was not sent to school. His early education was commenced by his mother's half sister, and was carried on at his father's house, Broomhill, Pendlebury, by tutors till he was about fifteen years of age. At fifteen he commenced working in the brewery, which, as his father's health declined, fell entirely into the hands of his brother Benjamin and himself.

Mr. Joule obtained his first instruction in physical science from Dalton, to whom his father sent the two brothers to learn chemistry. Dalton, one of the most distinguished chemists of any age or country, was then President of the Manchester Literary and Philosophical Society, and lived and received pupils in the rooms of the Society's house. Many of his most important memoirs were communicated to the Society, whose "Transactions" are likewise enriched by a large number of communications from his distinguished pupil. Dalton's instruction to the two young men commenced with arithmetic, algebra, and geometry. He then taught them natural philosophy out of Cavallo's text-book, and afterward, but only for a short time before his health gave way, in 1837, chemistry from his own "New System of Chemical Philosophy." "Profound, patient, intuitive," his teaching must have had great influence on his pupils. We find Mr. Joule early at work on the molecular constitution of gases, following in the footsteps of his illustrious master, whose own investigations on the constitution of mixed gases, and on the behavior of vapors and gases under heat, were among the most important of his day, and whose brilliant discovery of the atomic theory revolutionized the science of chemistry and placed him at the head of the philosophical chemists of Europe.

Under Dalton, Mr. Joule first became acquainted with physical apparatus; and the interest excited in his mind very soon began to produce fruit. Almost immediately he commenced experimenting on his own account. Obtaining a room in his father's house for the purpose, he began by constructing a cylinder electric machine in a very primitive way. A glass tube served for the cylinder; a poker hung up by silk threads, as in the very oldest forms of electric machine, was the prime conductor; and for a Leyden jar he went back to the old historical jar of Cunaeus, and used a bottle half filled with water, standing in an outer vessel, which contained water also.
Enlarging his stock of apparatus, chiefly by the work of his own hands, he soon entered the ranks as an investigator, and original papers followed each other in quick succession. The Royal Society list now contains, the titles of ninety-seven papers due to Joule, exclusive of over twenty very important papers detailing researches undertaken by him conjointly with Thomson, with Lyon Playfair, and with Scoresby.

Mr. Joule's first investigations were in the field of magnetism. In 1838, at the age of nineteen, he constructed an electro-magnetic engine, which he described in Sturgeon's "Annals of Electricity" for January of that year. In the same year, and in the three years following, he constructed other electro-magnetic machines and electro-magnets of novel forms; and experimenting with the new apparatus, he obtained results of great importance in the theory of electro-magnetism. In 1840 he discovered and determined the value of the limit to the magnetization communicable to soft iron by the electric current; showing for the case of an electro-magnet supporting weight, that when the exciting current is made stronger and stronger, the sustaining power tends to a certain definite limit, which, according to his estimate, amounts to about 140 lb. per square inch of either of the attracting surfaces. He investigated the relative values of solid iron cores for the electro-magnetic machine, as compared with bundles of iron wire; and, applying the principles which he had discovered, he proceeded to the construction of electro-magnets of much greater lifting power than any previously made, while he studied also the methods of modifying the distribution of the force in the magnetic field.

In commencing these investigations he was met at the very outset, as he tells us, with "the difficulty, if not impossibility, of understanding experiments and comparing them with one another, which arises in general from incomplete descriptions of apparatus, and from the arbitrary and vague numbers which are used to characterize electric currents. Such a practice," he says, "might be tolerated in the infancy of science; but in its present state of advancement greater precision and propriety are imperatively demanded. I have therefore determined," he continues, "for my own part to abandon my old quantity numbers, and to express my results on the basis of a unit which shall be at once scientific and convenient."

The discovery by Faraday of the law of electro-chemical equivalents had induced him to propose the voltameter as a measurer of electric currents, but the system proposed had not been used in the researches of any electrician, not excepting those of Faraday himself. Joule, realizing for the first time the importance of having a system of electric measurement which would make experimental results obtained at different times and under various circumstances comparable among themselves, and perceiving at the same time the advantages of a system of electric measurement dependent on, or at any rate comparable with, the chemical action producing the electric current, adopted as unit quantity of electricity the quantity required to decompose nine grains of water, 9 being the atomic weight of water, according to the chemical nomenclature then in use.

He had already made and described very important improvements in the construction of galvanometers, and he graduated his tangent galvanometer to correspond with the system of electric measurement he had adopted. The electric currents used in his experiments were thenceforth measured on the new system; and the numbers given in Joule's papers from 1840 downward are easily reducible to the modern absolute system of electric measurements, in the construction and general introduction of which he himself took so prominent a part. It was in 1840, also, that after experimenting on improvements in voltaic apparatus, he turned his attention to "the heat evolved by metallic conductors of electricity and in the cells of a battery during electrolysis." In this paper, and those following it in 1841 and 1842, he laid the foundation of a new province in physical science-electric and chemical thermodynamics-then totally unknown, but now wonderfully familiar, even to the roughest common sense practical electrician. With regard to the heat evolved by a metallic conductor carrying an electric current, he established what was already supposed to be the law, namely, that "the quantity of heat evolved by it [in a given time] is always proportional to the resistance which it presents, whatever may be the length, thickness, shape, or kind of the metallic conductor," while he obtained the law, then unknown, that the heat evolved is proportional to the "square" of the quantity of electricity passing in a given time. Corresponding laws were established for the heat evolved by the current passing in the electrolytic cell, and likewise for the heat developed in the cells of the battery itself.

In the year 1840 he was already speculating on the transformation of chemical energy into heat. In the paper last referred to and in a short abstract in the "Proceedings of the Royal Society", December, 1840, he points out that the heat generated in a wire conveying a current of electricity is a part of the heat of chemical combination of the materials used in the voltaic cell, and that the remainder, not the whole heat of combination, is evolved within the cell in which the chemical action takes place. In papers given in 1841 and 1842, he pushes his investigations further, and shows that the sum of the heat produced in all parts of the circuit during voltaic action is proportional to the chemical action that goes on in the voltaic pile, and again, that the quantities of heat which are evolved by the combustion of equivalents of bodies are proportional to the intensities of their affinities for oxygen. Having proceeded thus far, he carried on the same train of reasoning and experiment till he was able to announce in January, 1843, that the magneto-electric machine enables us to "convert mechanical power into heat". Most of his spare time in the early part of the year 1843 was devoted to making experiments necessary for the discovery of the laws of the development of heat by magneto-electricity, and for the definite determination of the mechanical value of heat.

At the meeting of the British Association at Cork, on August 21, 1843, he read his paper "On the Calorific Effects of Magneto-Electricity, and on the Mechanical Value of Heat." The paper gives an account of an admirable series of experiments, proving that "heat is generated" (not merely "transferred" from some source) by the magneto-electric machine. The investigation was pushed on for the purpose of finding whether a "constant ratio exists between the heat generated and the mechanical power" used in its production. As the result of one set of magneto-electric experiments, he finds 838 foot pounds to be the mechanical equivalent of the quantity of heat capable of increasing the temperature of one pound of water by one degree of Fahrenheit's scale. The paper is dated Broomhill, July, 1843, but a postscript, dated August, 1843, contains the following sentences:

"We shall be obliged to admit that Count Rumford was right in attributing the heat evolved by boring cannon to friction, and not (in any considerable degree) to any change in the capacity of the metal. I have lately proved experimentally that "heat is evolved by the passage of water through narrow tubes". My apparatus consisted of a piston perforated by a number of small holes, working in a cylindrical glass jar containing about 7 lb. of water. I thus obtained one degree of heat per pound of water from a mechanical force capable of raising about 770 lb. to the height of one foot, a result which will be allowed to be very strongly confirmatory of our previous deductions. I shall lose no time in repeating and extending these experiments, being satisfied that the grand agents of nature are, by the Creator's fiat, "indestructible", and that wherever mechanical force is expended, an exact equivalent of heat is "always" obtained."

This was the first determination of the dynamical equivalent of heat. Other naturalists and experimenters about the same time were attempting to compare the quantity of heat produced under certain circumstances with the quantity of work expended in producing it; and results and deductions (some of them very remarkable) were given by Séguin (1839), Mayer (1842), Colding (1843), founded partly on experiment, and partly on a kind of metaphysical reasoning. It was Joule, however, who first definitely proposed the problem of determining the relation between heat produced and work done in any mechanical action, and solved the problem directly.

It is not to be supposed that Joule's discovery and the results of his investigation met with immediate attention or with ready acquiescence. The problem occupied him almost continuously for many years; and in 1878 he gives in the "Philosophical Transactions" the results of a fresh determination, according to which the quantity of work required to be expended in order to raise the temperature of one pound of water weighed in vacuum from 60° to 61° Fahr., is 772.55 foot pounds of work at the sea level and in the latitude of Greenwich. His results of 1849 and 1878 agree in a striking manner with those obtained by Hirn and with those derived from an elaborate series of experiments carried out by Prof. Rowland, at the expense of the Government of the United States.

His experiments subsequent to 1843 on the dynamical equivalent of heat must be mentioned briefly. In that year his father removed from Pendlebury to Oak Field, Whalley Range, on the south side of Manchester, and built for his son a convenient laboratory near to the house. It was at this time that he felt the pressing need of accurate thermometers; and while Regnault was doing the same thing in France, Mr. Joule produced, with the assistance of Mr. Dancer, instrument maker, of Manchester, the first English thermometers possessing such accuracy as the mercury-in-glass thermometer is capable of. Some of them were forwarded to Prof. Graham and to Prof. Lyon Playfair; and the production of these instruments was in itself a most important contribution to scientific equipment.
As the direct experiment of friction of a fluid is dependent on no hypothesis, and appears to be wholly unexceptionable, it was used by Mr. Joule repeatedly in modified forms. The stirring of mercury, of oil, and of water with a paddle, which was turned by a falling weight, was compared, and solid friction, the friction of iron on iron under mercury, was tried; but the simple stirring of water seemed preferable to any, and was employed in all his later determinations.

In 1847 Mr. Joule was married to Amelia, daughter of Mr. John Grimes, Comptroller of Customs, Liverpool. His wife died early (1854), leaving him one son and one daughter.

The meeting of the British Association at Oxford, in this year, proved an interesting and important one. Here Joule read a fresh paper "On the Mechanical Equivalent of Heat." Of this meeting Sir William Thomson writes as follows to the author of this notice:

"I made Joule's acquaintance at the Oxford meeting, and it quickly ripened into a lifelong friendship.

"I heard his paper read in the section, and felt strongly impelled at first to rise and say that it must be wrong, because the true mechanical value of heat given, suppose in warm water, must, for small differences of temperature, be proportional to the square of its quantity. I knew from Carnot that this "must" be true (and it "is" true; only now I call it 'motivity,' to avoid clashing with Joule's 'mechanical value'). But as I listened on and on, I saw that (though Carnot had vitally important truth, not to be abandoned) Joule had certainly a great truth and a great discovery, and a most important measurement to bring forward. So, instead of rising, with my objection, to the meeting, I waited till it was over, and said my say to Joule himself, at the end of the meeting. This made my first introduction to him. After that I had a long talk over the whole matter at one of the "conversaziones" of the Association, and we became fast friends from thenceforward. However, he did not tell me he was to be married in a week or so; but about a fortnight later I was walking down from Chamounix to commence the tour of Mont Blanc, and whom should I meet walking up but Joule, with a long thermometer in his hand, and a carriage with a lady in it not far off. He told me he had been married since we had parted at Oxford! and he was going to try for elevation of temperature in waterfalls. We trysted to meet a few days later at Martigny, and look at the Cascade de Sallanches, to see if it might answer. We found it too much broken into spray. His young wife, as long as she lived, took complete interest in his scientific work, and both she and he showed me the greatest kindness during my visits to them in Manchester for our experiments on the thermal effects of fluid in motion, which we commenced a few years later"

"Joule's paper at the Oxford meeting made a great sensation. Faraday was there and was much struck with it, but did not enter fully into the new views. It was many years after that before any of the scientific chiefs began to give their adhesion. It was not long after, when Stokes told me he was inclined to be a Joulite."

"Miller, or Graham, or both, were for years quite incredulous as to Joule's results, because they all depended on fractions of a degree of temperature--sometimes very small fractions. His boldness in making such large conclusions from such very small observational effects is almost as noteworthy and admirable as his skill in extorting accuracy from them. I remember distinctly at the Royal Society, I think it was either Graham or Miller, saying simply he did not believe Joule, because he had nothing but hundredths of a degree to prove his case by."

The friendship formed between Joule and Thomson in 1847 grew rapidly. A voluminous correspondence was kept up between them, and several important researches were undertaken by the two friends in common. Their first joint research was on the thermal effects experienced by air rushing through small apertures The results of this investigation give for the first time an experimental basis for the hypothesis assumed without proof by Mayer as the foundation for an estimate of the numerical relation between quantities of heat and mechanical work, and they show that for permanent gases the hypothesis is very approximately true. Subsequently, Joule and Thomson undertook more comprehensive investigations on the thermal effects of fluids in motion, and on the heat acquired by bodies moving rapidly through the air. They found the heat generated by a body moving at one mile per second through the air sufficient to account for its ignition. The phenomena of "shooting stars" were explained by Mr. Joule in 1847 by the heat developed by bodies rushing into our atmosphere.

It is impossible within the limits to which this sketch is necessarily confined to speak in detail of the many researches undertaken by Mr. Joule on various physical subjects. Even of the most interesting of these a very brief notice must suffice for the present.

Molecular physics, as I have already remarked, early claimed his attention. Various papers on electrolysis of liquids, and on the constitution of gases, have been the result. A very interesting paper on "Heat and the Constitution of Elastic Fluids" was read before the Manchester Literary and Philosophical Society in 1848. In it he developed Daniel Bernoulli's explanation of air pressure by the impact of the molecules of the gas on the sides of the vessel which contains it, and from very simple considerations he calculated the average velocity of the particles requisite to produce ordinary atmospheric pressure at different temperatures. The average velocity of the particles of hydrogen at 32° F. he found to be 6,055 feet per second, the velocities at various temperatures being proportional to the square roots of the numbers which express those temperatures on the absolute thermodynamic scale.

His contribution to the theory of the velocity of sound in air was likewise of great importance, and is distinguished alike for the acuteness of his explanations of the existing causes of error in the work of previous experimenters, and for the accuracy, so far as was required for the purpose in hand, of his own experiments. His determination of the specific heat of air, pressure constant, and the specific heat of air, volume constant, furnished the data necessary for making Laplace's theoretical velocity agree with the velocity of sound experimentally determined. On the other hand, he was able to account for most puzzling discrepancies, which appeared in attempted direct determinations of the differences between the two specific heats by careful experimenters. He pointed out that in experiments in which air was allowed to rush violently or "explode" into a vacuum, there was a source of loss of energy that no one had taken account of, namely, in the sound produced by the explosion. Hence in the most careful experiments, where the vacuum was made as perfect as possible, and the explosion correspondingly the more violent, the results were actually the worst. With his explanations, the theory of the subject was rendered quite complete.

Space fails, or I should mention in detail Mr. Joule's experiments on magnetism and electro-magnets, referred to at the commencement of this sketch. He discovered the now celebrated change of dimensions produced by the magnetization of soft iron by the current. The peculiar noise which accompanies the magnetization of an iron bar by the current, sometimes called the "magnetic tick," was thus explained.

Mr. Joule's improvements in galvanometers have already been incidentally mentioned, and the construction by him of accurate thermometers has been referred to. It should never be forgotten that "he first" used small enough needles in tangent galvanometers to practically annul error from want of uniformity of the magnetic field. Of other improvements and additions to philosophical instruments may be mentioned a thermometer, unaffected by radiation, for measuring the temperature of the atmosphere, an improved barometer, a mercurial vacuum pump, one of the very first of the species which is now doing such valuable work, not only in scientific laboratories, but in the manufacture of incandescent electric lamps, and an apparatus for determining the earth's horizontal magnetic force in absolute measure.

Here this imperfect sketch must close. My limits are already passed. Mr. Joule has never been in any sense a public man; and, of those who know his name as that of the discoverer who has given the experimental basis for the grandest generalization in the whole of physical science, very few have ever seen his face. Of his private character this is scarcely the place to speak. Mr. Joule is still among us. May he long be spared to work for that cause to which he has given his life with heart-whole devotion that has never been excelled.

In June, 1878, he received a letter from the Earl of Beaconsfield announcing to him that Her Majesty the Queen had been pleased to grant him a pension of £200 per annum. This recognition of his labors by his country was a subject of much gratification to Mr. Joule.

Mr. Joule received the Gold Royal Medal of the Royal Society in 1852, the Copley Gold Medal of the Royal Society in 1870, and the Albert Medal of the Society of Arts from the hand of the Prince of Wales in 1880.

Source: Scientific American Supplement. Vol. XIV, No. 363

http://all-biographies.com/scientists/james_prescott_joule.htm

Arguments On Reincarnation

2010-07-26T05:15:00.000-07:00

III: IS THERE A "SOUL"?

IF readers have erroneously thought the preceding arguments merely metaphysical, of no personal importance, they may now see that they lead to the most important issue possible for each one of us.

Reverting to Argument II. If thought, will, and feeling are part of the same source from which substance springs, and thus interconnected with substance, time, space, energy, then there is the possibility of consciousness being connected with substance and yet not necessarily dependent for continuity upon the maintenance of the physical form.

If consciousness is inherent in space, time, matter, energy, then there are as many grades of evolution in it as there are in matter. There must be electronic consciousness, atomic consciousness, energic consciousness, etheric consciousness; as well as the varied and comprehensive consciousness of organized beings, which must be compounds of the consciousnesses of all their component elements.

There is an organizing will and force in our involuntary processes; in the birth and growth of our bodies; in our so-called "subconscious mind" which has such powerful influence on our fates. These consciousnesses are part of our man-consciousness and yet partly separable from it, since they act largely without its knowledge.

These conscious organizing factors are not only necessary to maintain life, but organic evolution could not have taken place without them, as Prof. Seba Eldridge has shown. Eldridge shows that they have to be independent of the vital processes in order to regulate them; therefore, they must inhere in other forms of substance than those of which the organs are composed. They must be forms so far evolved that material means can know them only by their effects. And how about the ruling consciousness and will of man, which presides over all the organs, and can modify and direct their action?

The contradictory qualities ascribed to the "ether" indicate clearly the probability that instead of one "ether" as usually thought, science has to deal with a whole series of substances of a non-physical nature, lumped as yet under the one term. So taught the ancients, who approached the problem from the conscious side of things instead of the unconscious, unlike modern science.

If there be such a range of substances, each carrying its own shade or degree of consciousness, there is the possibility of the physical body being merely the visible aspect of a compound organism of vastly greater scope, not all parts of which need go to pieces with the visible part, any more than taking an organ from the body involves necessarily the death of the body.

There is an obvious difference in the quality and capacity of the consciousness of a rock, a plant, an animal, and a man. These differences must have come about by evolution, from the simple to the complex. Does such consciousness lie entirely in the visible substance of each of these forms, which go to pieces for good at death? Hardly, since in each living form the visible substance is drawn from lower forms, even from the mineral. If one claims that increasing complexity of organism creates a fuller consciousness, then a locomotive is more conscious than a rock, and a printing press more conscious than a locomotive.

This is the reductio ad absurdum, to which materialistic reasoning leads. Moreover, to control body and brain, often against their own impulses, involves a power superior to them. The simplest possible solution is the existence of a form or forms of highly evolved substance, interpenetrating and affecting the physical body, though invisible, as the magnetic field interpenetrates and affects iron. That is, a form coherent enough, old enough, to contain and carry past experience, and also able to act as a biological magnet to draw together and hold a new form from time to time through the processes of birth.

Is there any scientific obstacle to the idea of consciousness as existing within the limits of the body, but wedded to invisible forms of substance? Certainly not. Dr. Mathews shows this:

That we have aspirations and strivings for better things, for self-mastery, which are present in some degree in all human beings, is self evident. That is the kernel of the religion of every man in whatever philosophical system he may enshroud it. Do these aspirations spring from our atoms, or from something between them? Do they come from the ether which penetrates us and is, at times at least, gripped by our electrons, as it at other times grips them? Or since that ether flows through our electrons, are they inherent in the very atoms of which our bodies are made? Here is the whole question of the nature of man; the common puzzle for theologian and scientist; the common ground on which science and religion meet.
At the close of his volume he evidently leans toward the hypothesis of the invisible as containing greater possibilities.
... But the greater part of the volume of the body is the present, the uncreated, the immortal. It is part of the great universe; part of "I am."
Which of these two things are we: the gossamer, spider web of mortal; or the dense, unknown, immaterial, immortal ether which forms its background?

But whichever we are, we are part of the One, for the ether, the One, is streaming through our electrons either in time or space. While the distortion of these electrons may be but temporary and they be mortal, that essence of which they are made, the real essence, is the immortal. Perhaps this essence is the "élan vital" of Bergson; the driving force of evolution; the source of the unconquerable soul of man, and of its age and aeon-long struggle for freedom.

If evolution through reincarnation is not implied in this thought when logically carried out, what is?
The mental difference, therefore, between the different orders of life is due to the past nature and scope of the evolution of the respective controlling forms. In the mineral, for instance, such a form is hardly even incipient, its functioning confined solely to cohesion. Nothing but the preservation and transmission of acquired function and intelligence will explain the "ladder of life," with its closely-knit gradations of form and intelligence.

To science at the present date the forces behind evolution -- and we can give quote after quote -- are such an insoluble mystery that many have given up even discussing it. We have set forth above the true "missing link" without which no solution is possible.

The materialistically-inclined refuse to accept it -- as they say openly -- because it "would close the door to further knowledge." There is no logic in this -- the idea ought to be a stimulus instead of a discouragement. If there is a permanent form in man, it has been evolved under natural law and can become as much an object of study as anything else, if the proper means are found.

It happens that the ancients found that means.

COMPILER'S NOTE: The following is a separate item which followed the above article but was on the same page. I felt it was useful to include it here:
THE "MISSING LINK"

If the doctrine of Metempsychosis(1) had been properly understood in its application to the indestructibility of matter and the immortality of spirit, it would have been perceived that it is a sublime conception. If the Pythagorean metempsychosis should be thoroughly explained and compared with the modern theory of evolution, it would be found to supply every "missing link" in the chain of the latter.

--H.P.B.
Next article:
Arguments on Reincarnation
IV: Nature of Memory

ONE (1) FOOTNOTE LISTED BELOW:
COMPILER'S NOTE: I added this footnote; it was not in the article. If it doesn't paint an accurate enough picture, or is incorrect, I hope the Editors of THEOSOPHY magazine will spot it and point it out to me, so that I can make the necessary corrections.

(1) "Metempsychosis" is the progress of the soul from one stage of existence to another.
Back to text.
http://www.blavatsky.net/magazine/theosophy/ww/setting/soul.html

The Benefits of Blue Blood

2010-07-22T04:57:00.000-07:00

It fuels the journeys of shorebirds along the Eastern Seaboard and feeds some loggerhead sea turtles and sharks. The horseshoe crab is intricately woven into the web of life. Yet this harmless and primitive sea creature not only plays a key role in nature, it occupies a crucial place in the human world as well.

Over three decades ago, medicine claimed this ancient animal as a new life-saving tool. In 1971 researchers discovered that when they exposed the horseshoe crab to E. coli bacteria, the crab’s blood clotted. The clotting indicated the presence of endotoxins, toxic substances released by E. coli and other gram-negative bacteria that could produce severe symptoms in exposed humans such as fever or hemorrhagic stroke.

The simplicity of its immune system is actually what makes the crab’s blood useful to our biomedical industry. Horseshoe crabs live under the constant threat of infection in a habitat that can easily contain billions of bacteria per milliliter. To fight off infection, the horseshoe crab has a compound in its blood — LAL, or Limulus Amebocyte Lysate — which immediately binds and clots around fungi, viruses, and bacterial endotoxins.

LAL’s endotoxin binding and clotting ability is what makes it so invaluable to our own pharmaceutical industry. Once the LAL test was recognized by the Food and Drug Administration (FDA) as an alternative to then current methods of testing for endotoxins, the pharmaceutical industry tapped in. Horseshoe crabs were abundant, their blood easy to harvest and the test took only one hour.

Today, LAL has become the worldwide standard screening test for bacterial contamination. Every drug certified by the FDA must be tested using LAL, as do surgical implants such as pacemakers and prosthetic devices.

Horseshoe crab blood has not only become a key weapon in our medical arsenal, it has also become big business. On the world market, a quart of horseshoe crab blood has a price tag of an estimated $15,000, leading to overall revenues from the LAL industry estimated at U.S. $50 million per year. But that pales in comparison to its value to the pharmaceutical industry.

Of course, to obtain LAL you need horseshoe crabs — and lots of them. According to the Atlantic States Marine Fisheries Commission, that $50 million dollar industry requires the blood of approximately 250,000 horseshoe crabs.

While the blood of a horseshoe crab can be extracted without killing the animal, there is some question of how harmful bleeding is to the animals. The LAL industry says the bleeding causes no long-term injury.

Adult horseshoe crabs are collected by trawlers and transported to the LAL lab, where they are washed to remove sand and other marine debris from their exoskeletons. Those crabs without visible injuries are placed on a rack and bled with a large-gauge needle. Up to 30% of the crab’s blood is removed. Within 72 hours, the bled horseshoe crabs are returned to the water, where their blood volume rebounds in about a week.

LAL manufacturers have measured mortality rates of less then 3%. Yet two recent studies estimate that between 10% and 15% of crabs do not survive the bleeding procedure, which accounts for the mortality of 20,000 to 37,500 horseshoe crabs per year. Another concern is that it takes the crab a few months to rebuild its blood cell count level back up after a bleeding. Horseshoe crabs could be bled up to three or four times a year, which would take a toll on the health of the animals. But LAL manufacturers claim they only bleed them once a year.

Whether we can or will protect the health of horseshoe crabs for their own benefit, for the good of other creatures, or for our own use remains to be seen. Despite supporting the fishing industry for over 100 years, the condition of horseshoe crab populations has largely been ignored by fishery managers until recently. With growing concern over declining populations, regulations on the harvest of Horseshoe Crabs have just recently been imposed, though some states are already loosening restrictions.

Perhaps science can step in and “give back” to the animal for all of the good it has done us. Researchers are focusing their attention on producing LAL without the horseshoe crab, exploring the potential to cultivate and produce LAL from other sources.
http://www.pbs.org/wnet/nature/episodes/crash-a-tale-of-two-species/the-benefits-of-blue-blood/595/

On Faraday's Lines of Force

2010-07-17T06:09:00.000-07:00

The present state of electrical science seems peculiarly unfavourable to speculation. The laws of the distribution of electricity on the surface of conductors have been analytically deduced from experiment ; some parts of the mathematical theory of magnetism are established, while in other parts the experimental data are wanting ; the theory of the conduction of galvanism and that of the mutual attraction of conductors have been reduced to mathematical formulae, but have not fallen into relation with the other parts of the science. No electrical theory can now be put forth, unless it shews the connexion not only between electricity at rest and current electricity, but between the attractions and inductive effects of electricity in both states. Such a theory must accurately satisfy those laws, the mathematical form of which is known, and must afford the means of calculating the effects in the limiting cases where the known formulae are inapplicable. In order therefore to appreciate the requirements of the science, the student must make himself familiar with a considerable body of most intricate mathematics, the mere retention of which in the memory materially interferes with further progress. The first process therefore in the effectual study of the science, must be one of simplification and reduction of the results of previous investigation to a form in which the mind can grasp them. The results of this simplification may take the form of a purely mathematical formula or of a physical hypothesis. In the first case we entirely lose sight of the phenomena to be explained ; and though we may trace out the consequences of given laws, we can never obtain more extended views of the connexions of the subject. If, on the other hand, we adopt a physical hypothesis, we see the phenomena only through a medium, and are liable to that blindness to facts and rashness in assumption which a partial explanation encourages. We must therefore discover some method of investigation which allows the mind at every step to lay hold of a clear physical conception, without being committed to any theory founded on the physical science from which that conception is borrowed, so that it is neither drawn aside from the subject in pursuit of analytical subtleties, nor carried beyond the truth by a favourite hypothesis.

In order to obtain physical ideas without adopting a physical theory we must make ourselves familiar with the existence of physical analogies. By a physical analogy I mean that partial similarity between the laws of one science and those of another which makes each of them illustrate the other. Thus all the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers. Passing from the most universal of all analogies to a very partial one, we find the same resemblance in mathematical form between two different phenomena giving rise to a physical theory of light.

The changes of direction which light undergoes in passing from one medium to another, are identical with the deviations of the patli of a particle in moving through a narrow space in which intense forces act. This analogy, which extends only to the direction, and not to the velocity of motion, was long believed to be the true explanation of the refraction of light ; and we still find it useful in the solution of certain problems, in which we employ it without danger, as an artificial method. The other analogy, between light and the vibrations of an elastic medium, extends much farther, but, though its importance and fruitfulness cannot be over-estimated, we must recollect that it is founded only on a resemblance in form between the laws of light and those of vibrations. By stripping it of its physical dress and reducing it to a theory of " transverse alternations," we might obtain a system of truth strictly founded on observation, but probably deficient both in the vividness of its conceptions and the fertility of its method. I have said thus much on the disputed questions of Optics, as a preparation for the discussion of the almost universally admitted theory of attraction at a distance.

We have all acquired the mathematical conception of these attractions. We can reason about them and determine their appropriate forms or formulae. These formulae have a distinct mathematical significance, and their results are found to be in accordance with natural phenomena. There is no formula in applied mathematics more consistent with nature than the formula of attractions, and no theory better established in the minds of men than that of the action of bodies on one another at a distance. The laws of the conduction of heat in uniform media appear at first sight among the most different in their physical relations from those relating to attractions. The quantities which enter into them are temperature, heat, conductivity. The word force is foreign to the subject. Yet we find that the mathematical laws of the uniform motion of heat in homogeneous media are identical in form with those of attractions varying inversely as the square of the distance. We have only to substitute source of heat for centre of attraction, flow of heat for accelerating effect of attraction at any point, and temperature for potential, and the solution of a problem in attractions is transformed into that of a problem in heat.

Now the conduction of heat is supposed to proceed by an action between contiguous parts of a medium, while the force of attraction is a relation between distant bodies, and yet, if we knew nothing more than is expressed in the mathematical formulae, there would be nothing to distinguish between the one set of phenomena and the other.

It is true, that if we introduce other considerations and observe additional facts, the two subjects will assume very different aspects, but the mathematical resemblance of some of their laws will remain, and may still be made useful in exciting appropriate mathematical ideas.

It is by the use of analogies of this kind that I have attempted to bring before the mind, in a convenient and manageable form, those mathematical ideas which are necessary to the study of the phenomena of electricity. The methods are generally those suggested by the processes of reasoning which are found in the researches of Faraday, and which, though they have been interpreted mathematically by Prof. Thomson and others, are very generally supposed to be of an indefinite and unmathematical character, when compared with those employed by the professed mathematicians. By the method which I adopt, I hope to render it evident that I am not attempting to establish any physical theory of a science in which I have hardly made a single experiment, and that the limit of my design is to shew how, by a strict application of the ideas and methods of Faraday, the connexion of the very different orders of phenomena which he has discovered may be clearly placed before the mathematical mind. I shall therefore avoid as much as I can the introduction of anything which does not serve as a direct illustration of Faraday's methods, or of the mathe matical deductions which may be made from them. In treating the simpler parts of the subject I shall use Faraday's mathematical methods as well as his ideas. When the complexity of the subject requires it, I shall use analytical notation, still confining myself to the development of ideas originated by the same philosopher.

I have in the first place to explain and illustrate the idea of " lines of force."

When a body is electrified in any manner, a small body charged with positive electricity, and placed in any given position, will experience a force urging it in a certain direction. If the small body be now negatively electrified, it will be urged by an equal force in a direction exactly opposite.

The same relations hold between a magnetic body and the north or south poles of a small magnet. If the north pole is urged in one direction, the south pole is urged in the opposite direction.

In this way we might find a line passing through any point of space, such that it represents the direction of the force acting on a positively electrified particle, or on an elementary north pole, and the reverse direction of the force on a negatively electrified particle or an elementary south pole. Since at every point of space such a direction may be found, if we commeilce at any point and draw a line so that, as we go along it, its direction at any point shall always coincide with that of the resultant force at that point, this curve will indicate the direction of that force for every point through which it passes, and might be called on that account a line of force. We might in the same way draw other lines of force, till we had filled all space with curves indicating by their direction that of the force at any assigned point.

We should thus obtain a geometrical model of the physical phenomena, which would tell us the direction of the force, but we should still require some method of indicating the intensity of the force at any point. If we consider these curves not as mere lines, but as fine tubes of variable section carrying an incompressible fluid, then, since the velocity of the fluid is inversely as the section of the tube, we may make the velocity vary according to any given law, by regulating the section of the tube, and in this way we might represent the intensity of the force as well as its direction by the motion of the fluid in these tubes. This method of representing the intensity of a force by the velocity of an imaginary fluid in a tube is applicable to any conceivable system of forces, but it is capable of great simplification in the case in which the forces are such as can be explained by the hypothesis of attractions varying inversely as the square of the distance, such as those observed in electrical and magnetic phenomena. In the case of a perfectly arbitrary system of forces, there will generally be interstices between the tubes; but in the case of electric and magnetic forces it is possible to arrange the tubes so as to leave no interstices. The tubes will then be mere surfaces, directing the motion of a fluid filling up the whole space. It has been usual to commence the investigation of the laws of these forces by at once assuming that the phenomena are due to attractive or repulsive forces acting between certain points. We may however obtain a different view of the subject, and one more suited to our more difficult inquiries, by adopting for the definition of the forces of which we treat, that they may be represented in magnitude and direction by the uniform motion of an incompressible fluid.

I propose, then, first to describe a method by which the motion of such a fluid can be clearly conceived ; secondly to trace the consequences of assuming certain conditions of motion, and to point out the application of the method to some of the less complicated phenomena of electricity, magnetism, and galvanism ; and lastly to shew how by an extension of these methods, and the introduction of another idea due to Faraday, the laws of the attractions and inductive actions of magnets and currents may be clearly conceived, without making any assump- tions as to the physical nature of electricity, or adding anything to that which has been already proved by experiment.

By referring everything to the purely geometrical idea of the motion of an imaginary fluid, I hope to attain generality and precision, and to avoid the dangers arising from a premature theory professing to explain the cause of the phenomena. If the results of mere speculation which I have collected are found to be of any use to experimental philosophers, in arranging and interpreting their results, they will have served their purpose, and a mature theory, in which physical facts will be physically explained, will be formed by those who by interrogating Nature herself can obtain the only true solution of the questions which the mathematical theory suggests.

~~James Clerk Maxwell
http://www.listentogenius.com/author.php/383

A new theory of Magnetic Fields

2010-07-17T04:15:00.000-07:00

The tip of the iceberg

When man first discovered that a piece of loadstone hanging on a thread would always point in the same direction; when Oersted discovered that an electric current in wire affected a compass needle; when Faraday discovered that electricity can be generated by moving a magnet inside a wire coil; they perceived only the tip of the iceberg. The phenomena which we observe and have used to construct wonderful technologies are just the by products of the true nature of magnetism.

What I will show is that magnetism is as fundamental to the structure of matter as the electric force which binds the negative electrons to their positive nuclei. As we delve into the inner mechanisms of nature, magnetism becomes ever more significant. It is the regulator of processes. The phenomena we observe in the macro world are bye products of the inner workings of matter.

Without this insight, Oersted, Ampere, Faraday, Gauss, Biot, Savart and Michelson were working in the dark. The laws they developed are not fundamental laws of nature, but mathematical models designed to mimic the observed phenomena. As a result, they are not wholly self consistent and do not make complete sense. I remember sitting in a lecture trying to follow the mathematics. I am dyslexic and so was unable to take meaningful notes. The other students were writing everything down without understanding. I was more concerned with the way a term of seemed to come and go from equations. This was before the days of S.I. Units and there were four or five systems of units in operation. I plucked up courage and interrupted the lecture. It was easy with only 20 students in the cosy little physics department of Royal Holloway College.

"Excuse me Doctor F..... , but ......"

My memory is not good enough to recount the exact details, but it transpired under cross examination that the good doctor had compiled his notes from two text books. What he had not realised was that the two books were based on two different sets of units. In one set, an equation would need a term of , while in the other it would be absent. You will not be surprised by the good doctor's reply.

"I did that to keep you on your toes"

I tell this tale because it is symptomatic of the way in which knowledge is passed from one generation to the next. All too often, teachers do not understand what they are teaching. They have learnt it, not understood it. The students blindly copy down the notes and they in turn learn it without understanding.

Being dyslexic, I am a stranger to this process. It has taken me 40 years to acquire the technology and learn how to use it to overcome this disability. I could not record information in writing and recover it. My disability meant that any notes I made were not comprehensible to me. I never had the luxury of being able to learn. I had to understand. I have to understand. If I cannot understand something, I cannot capture it in my mind. If it has a structure which I can comprehend, its in for good.

In the enforced leisure of my early retirement, I have been revising my physics. I found that I could not understand the principles of electricity and magnetism. So I did what I should have done 30 years ago and worked out the theory for myself. Searching out and wrestling with the paradoxes, I hope I now comprehend the subject. In the film "The man went up a hill and came down a mountain" there are two Welsh farmers. Brothers, they are and know locally as Thomas Tupp and Thomas Tupp Too. The word tupp means "thick" or stupid, or educationally disadvantaged. One of the brothers introduces them.

"I'm Thomas Tupp and this is my brother Thomas Tupp Too.
"Folk say we are tupp, but we are not so tupp that we do not know that we are tupp."

And therein lies the dilemma of the scientific community. When people do not realise their own intellectual limits, they do not enter into the struggle to understand that which they have failed to comprehend. Learning is no substitute for understanding. It is in admitting a lack of understanding and in wrestling with the problem that the mistakes of the past are rectified. I came across a paper by TFG Searle, a colleague of JJ Thompson. He was looking at the magnetic field which should in theory surround a moving charge. This was just a few years after the discovery of the electron. JJ Thompson devoted a vast amount of energy to trying to explain the existence of matter in terms of vortices in the aether. Searle's paper tried to show that a moving spherical charge would posses the property of inertia. It does not manage to do that but ends in hope that he might be able to do so one day. A second paper on the subject nearly ten years latter is a load of rubbish.

This is the basic concept. A moving charge generates a magnetic field. Magnetic fields contain energy. To accelerate a charge, you must do work in order to create the magnetic field. So the charge resists being accelerated with a kind of inertial force. The concept is correct, but existing electromagnetic theory makes the task of calculating this impossible. The law of Biot-Savart tells us the magnetic field must be

When we accelerate the charge, increases. Magnetic flux moves outwards from the surface of the charge. Faraday's law says that this movement generates an electric field. This electric field can then act on the surface of the charge and produce a force. But there is a problem. When we try to calculate the number of lines of force which surround the charge, this is the integral of over a half plane extending to infinity from the line of motion of the charge, we get infinity. If Faraday is right, then nothing in the universe could move.

What I have done is to work out how magnetic flux must behave in order to overcome this paradox. It turns out that magnetism gives charges the property of inertia. We find that what we had called mass can be accounted for entirely in terms of energy in magnetic fields. The phenomena observed in the study of electricity and magnetism are but the tip of the iceberg.

Invisible fingers

When Oersted discovered that an electric current in wire affected a compass needle, he missed the point. The magnetic effect is a clue to something far more fundamental to our understanding. The pertinent question is "how is it that the movement of an electric current within a wire can generate an effect outside the wire". The accepted answer that it generates a magnetic field which flows out into the surrounding space is in a sense wrong. What is actually happening is that the electric fields which surround the individual electrons extend out into the surrounding space and move with their electrons. This gives the electric current the ability to generate a magnetic field beyond the wire.
When an electron and a proton form an atom of hydrogen, we find that we cannot measure an electric field of either from a distance. We have a theoretical method of measurement of an electric field by measuring the force on a small test charge. In practice this is impossible, but we can still perform a thought experiment. If we have one proton, it is surrounded by an electric field pointing outward. If we have one electron, it is surrounded by an electric field pointing inwards. When we put the two together, the result is that our test charge no longer shows any signs of experiencing a force. There are two possible reasons for this. Either the test charge experiences two equal and opposite forces, or it experiences no force. Either the two electric fields coexist in space, or they combine to eliminate each other. The accepted view is that they combine to eliminate each other.
The accepted view has its good points. It explains how the energy in the electric fields of the two charges in the atom is less than it would be if they were separate. Thus it provides a storage mechanism for the potential energy which must be given to the two charges in order to free the electron from the proton. But we might well ask if potential energy has to be physically stored. Might it be equally valid to say that potential energy exists by virtue of the geometry of the situation. What I would like to suggest is that the magnetic field generated in the region surrounding a current carrying wire is prima facie evidence for the fact the electric fields of individual charges coexist. They are like invisible fingers reaching out into space from every single charge. When the charge moves, the electric field moves with it. When an electric current flows in a wire, there is an imbalance in the random thermal velocities of the conduction band electrons. This is felt in the region beyond the wire in the relative movement of the coexisting electric fields of the conduction band electrons and of the other charges of the crystal lattice of the wire. It is this relative movement of the electric fields which generates the magnetic field.

The nature of magnetic flux

The relationship between moving charges and their magnetic fields can, I believe, be best understood in the following terms.
Electric fields in relative motion to each other have a property which is called magnetic intensity and is represented by the vector . Every moving charge, that is every charge because they are all moving all the time, has by virtue of the movement of its electric field an associated magnetic intensity field. This is a mathematical artefact of the movement of the electric field and has no real existence. The magnetic intensity at a point is the sum of the individual magnetic intensities of all the charges in the universe at that point and we can express this in the equation.

This sums up the combined effects of relative movements of electric fields and the effect of this combined relative movement is to encourage the formation of a magnetic field. We are accustomed to describe magnetic fields by their magnetic induction . We normally write the equation

but I would modify this to

where the sign is read "would like to be equal to".

The vector has been a convenient descriptor for magnetic fields being defined in terms of the ability of the field to exert a force on a moving conductor. However it has served more than anything else as a device for enabling us to avoid wrestling with trying to understand the nature of magnetic flux.

Magnetic flux is first and foremost a form of energy. It is an energy density flux. It cannot be created or destroyed except that at the surface of a charge, it may be generated or adsorbed changing to and from mechanical energy strictly in accordance with the law of conservation of energy. It is subject to the very severe limitation that it can only move into and out of charges parallel to their electric fields. It has directional properties. These properties are best described by the scalar and vector forms of the magnetic energy density.

We as humans are right at the limits of our ability when we try to comprehend the nature of magnetic flux. It is no surprise that we need to periodically rethink our concept of it. We kneed a stating point and so I am going to use an analogy.

The two properties of magnetic flux; energy density and magnetic induction have the same relationship to one another as do the tilth and the furrows of a field. That is a perfect analogy for anyone with a rural background, but may need a little explaining to others. You start with a plain uncultivated field. Below the grass is soil. You plough the field to create a layer of tilth in which to plant the crop. The plough leaves a geometric pattern of ridges running the length of the field which are called furrows. This tilled soil or tilth as it is called is both created by the ploughing and is the substance from which the pattern of the furrows is made.

When we consider a magnetic field, we need to be aware that it has these two properties of tilth and furrows. The tilth is the energy content of the magnetic field and the energy density might be thought of as the depth of tilth. The furrows are the magnetic induction which we characterise by drawing lines of force. The formation and behaviour of the magnetic field is governed by the properties of both tilth and furrow. At any instance, the lines of force must form continuous loops.

The process by which magnetic energy density flux adds and subtracts is most peculiar and can only be understood in terms of the directional properties of the magnetic field. This is rather technically demanding and is discussed in all its mathematical detail within the section on accelerating a charge.

The observed form of magnetic fields depends entirely on the scale upon which we observe them. From close up, all we see is the individual magnetic fields which surround each charge. The intensity of these fields is many orders of magnitude more than that of any magnetic field we might create in a laboratory or in an electric motor. This field forms circular loops about the line of motion of the charge. At this scale we can use the term "field of motion" to describe the magnetic field surrounding the charge. As we move away from an individual charge, the strength its magnetic field falls off until we find it merging into and combining with the fields of other charges. Eventually we reach human scales and see magnetic fields as revealed by iron filing patterns. But to gain an understanding of the nature of magnetism, we need to consider a simple moving charge. Put aside your concept of an electron and consider a fictional entity which I call a pure charge. It has no mass, no angular momentum and no intrinsic magnetic moment. It is simply a hollow spherical surface of charge.

Imagine we find our charge moving some distance away from any other charge. Nevertheless, the region it is moving through is permeated by the presence of the electric fields of a universe full of charge. It is against this background presence that we measure the velocity of our charge, because it is its relative motion to that background presence which generates its magnetic field. We will consider simple changes in the motion of the charge. First let us accelerate the charge in the direction it is moving. We are increasing the magnetic field and its energy content increases. The magnetic energy density is becoming greater. This means that magnetic energy flux has to be created at the surface of the charge and move outwards. If we calculate the rate of increase of energy in the field of motion of the charge, we can then use the idea that there must be a continuity of presence and movement of the magnetic energy density flux, to calculate the speed with which energy density flux is emerging from the surface of the charge. At this level, we can apply Faraday's law using the velocity with which the energy density flux is moving from the surface. We get the correct answer. That is to say that the force we get is the force required to do the mechanical work to increase the energy content of the field of motion of the charge.

Newton's laws

The mathematical analysis can be done for an acceleration in any direction. We find that acceleration is always resisted by a force which is proportional to the acceleration. The other two factors governing the magnitude of the force is the magnitude of the charge and its radius.

The first important result of the proof is that the property we call inertia exists for a pure charge and can be wholly accounted as an electromagnetic interaction.

The second is that starting from a modified understanding of the nature of magnetic flux, we have taken the laws of Biot-Savart and Faraday and proved that Newtons second law of motion, , applies to a pure charge. With this, the laws of mechanics can be deduced.

Faraday's law revisited

It is hard for us imagine how difficult Faraday's original experiment must have been for we are familiar with sensitive moving coil galvanometers. These however did not exist. The galvanometers of the day relied on electrostatic forces and were very insensitive. The famous experiment of Faraday in which a magnet is moved into and out of a coil producing a voltage in the coil has a sequel in which the coil is moved over the magnet and then removed. These two experiments led Faraday to conclude that it was the relative motion between the magnet and the coil which generated the voltage. This concept of relative motion is fundamental to the accepted theory, but it hides from us the real process.

I want to look at the situation where the magnet is moving. In the absence of any coil, we are quite happy to calculate that the moving magnetic field generates an electric field. This is consistent with the theory of the propagation of electromagnetic radiation discovered by Maxwell. The electric field results in an electric polarisation of space. That results in a displacement current flowing which in turn generates a magnetic field which in turn..... And the result is a travelling electromagnetic wave. What is not quite so obvious is the fact that if we place a test charge in the way, it will feel the electric field induced by the motion of the magnetic field pulling in one direction while it finds that the polarisation of space pulls it in the opposite direction with an equal force. So the movement of the magnet should have no effect, but it does.

The answer is far more subtle. The electric field of a charge extends throughout all space falling off in intensity according to the inverse square law. As it moves, the effect of its motion is felt everywhere because of its contribution to the magnetic intensity. We have defined magnetic intensity as and we know that the magnetic energy density is given by . We also know that . When we substitute these equations into each other, we get a most interesting result.

The significance of this result is that the magnetic energy density at a point in a magnetic field is equal to the sum of the energy densities of the individual fields of the individual charges. These contributions can be positive or negative depending on whether the motion of the individual charge is contributing to the magnetic field or lessening it at that point. Now magnetic energy density flux can only move within the confines of the electric fields of charges. If we assume that each charge has its own personal energy density field which is influenced by the prevailing magnetic induction, we find that variations in the magnetic field around a charge will cause magnetic energy density flux to move into and out of the surface of the charge as its position relative to magnetic fields changes.

Let us try to imagine a very well defined situation in which a region of strong magnetic field moves towards the charge. So long as the charge remains outside this region of magnetic field, the energy content of the magnetic energy density flux belonging to the charge remains fairly constant. As soon as the charge moves into the region, there is dramatic change because the energy content now depends on the distance of the charge from the boundary of the region. The charge is moving away from one boundary towards the other and that means that magnetic energy density flux is flowing out of the charge on one side and into it on the other. It is this process which generates the force on the charge. Now the effect on the charge is opposite to the effect of the charge on the field. That means that if the motion of the charge relative to the field is such as to have no effect on the field, then the field has no effect on the charge. The more the motion of the charge affects the field, the greater the force on the charge.

A charge does not have to be within a magnetic field to be affected by it when the field is varying in size and/or strength and/or orientation. The transformer relies very much on this principle. Conventional wisdom has it that magnetic flux moves outwards from the turns of the primary coil into the core as magnetic field builds, then moves back into the turns as the field collapses. In this process, it is said to cut all the turns of wire both of the primary and of the primary coils. This in fact does not happen! There are two factors which contradict this picture. The first can be seen if we imagine a loosely wound coil and draw lines of force for increasing currents. What we find in our two dimensional picture of the expanding magnetic field is that there are zero points between the turns of the coil. The lines of force cannot pass these points. What happens is that lines of force moving towards these points thin and appear to part to join with other lines on the far side of the point. The result of this is that local to each wire, we only find magnetic flux moving outward from the wire. We do not see the flux of the whole field cutting the individual turns as the field changes. The second thing is that within the magnetic core, the process of magnetisation and demagnetization is accomplished by movement of the boundaries of the individual magnetic domains of the material. This involves individual electron orbits changing orientation so that their flux links with neighbours on one side rather than on the other. If we were to attempt to draw diagrams of the movement of the lines of force during this process, we would again find the movements to be local. The mass movement of magnetic flux just does not happen in the way the theory imagines. There has to be a second mechanism which accounts for the induced emf in the coils. It is the process I have described in the previous paragraph.

What the reader needs to understand is that analysis of the workings of a transformer are based on a model which is consistent with energy conservation. It is this consistency which enables the theory to supply answers which are the same as the observed behaviour of the components. The actual mechanism which I have described is also consistent with the conservation of energy and so accounts for the match between theory and practice.

The intimate connection

The process which I have described above becomes more important as we reduce the scale on which we look at a group of charges. Let us imagine that we have a stream of moving charges forming an electric current. The combined effect of the individual movements of the electrons forms the electric current and this generates a magnetic field. We might think of a long thin wire as carrying the current and we find that the surrounding magnetic field has a given energy content per unit length of the wire. If we now stop one electron dead in its tracks, we find that it resists being stopped exerting a force and transferring energy to whatever stopped it. Now the energy which the electron transfers comes from two sources. There is the energy stored in the magnetic field surrounding the electron and we can think of this as the kinetic energy of the electron. Then there is the energy which the electron contributed to the magnetic field which the current generates. But the removal of one electron from the group would mean that the the current is reduced and the surrounding magnetic field needs to shrink. This loss of energy from the magnetic field results in equal amounts of energy have to be transferred to each electron of the current. This flow of energy into the surfaces of the individual charges results in the generation of a force tending to accelerate each electron in the direction of the current. I call this the intimate connection because it links the motion of all of the electrons which constitute the current. A collision which decelerates on electron accelerates all the other electrons. This is the essence of the effect which we call self inductance.

If we come down to the scale of an atom, we find that this process continues. The motion of the electrons is totally chaotic, but basically takes the electrons along sections of curved paths. I call this process pseudo orbiting. The process of moving in an arc should be accompanied by the field of motion of the electron rotating with it, but this process is limited because the further we are from the magnetic field, the faster the magnetic field would have to move. We reach a region where the magnetic energy density flux is literally left behind. If we had a single electron orbiting a nucleus, then the result would be the establishment of a stable orbital magnetic field. Let us imagine that we had one electron orbiting a helium nucleus so that we can imagine a second electron being captured by it. We now have an extremely complex situation in which the resulting orbital magnetic field is composed of energy from both electrons. The electrons interact producing chaotic pseudo orbiting and all the time, magnetic energy density flux is moving into and out of their surfaces generating forces on them. If the change in motion of the electrons is such as to increase their common magnetic field, then the forces on each electron as the magnetic field attempts to grow will tend to lessen the growth in the field, but then if their change of motion is such as to decrease their common magnetic field, the forces generated by the movement of magnetic energy density flux into and out of their surfaces will oppose this tendency. What we can say is that fluctuations in the magnetic fields within and around the atom provides a mechanism for energy exchange between the electrons which has an additional effect on their motion.

What we will find when we attempt to model this and to try to understand the chaotic behaviour of electrons within an atom is only to be guessed at. Will we be able to account for the atomic spectra. Is it possible that some brilliant mathematician will produce phase space models of the chaotic behaviour identical to the present probability distributions of quantum mechanics? One thing is certain: there is more to magnetism than we ever imagined.

© Copyright Bruce Harvey 1997.
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