## Saturday, 21 March 2009

### Crisp Anyone?

Matter is a twist in the aether. To fashion matter out of the aether, the aether has to create an energy sink. The aether does this by working in opposition to itself. A vortex is the only way in which a fluid may move through itself. At the core of the vortex, the aether divides itself into a double helix. The double helix is made up of the aether moving in two different directions. We now have two vortices which are joined, one to the other, by their centres of rotation, and gives us a shape something like an hour-glass, or a bow-tie perhaps.

Draw a double helix on a piece of paper, and ensure that you have an even number of turns. It needs to be an even number (2,4,6...). Add a loop at either end of the double helix. The double helix is the aether moving in two different directions. If you follow the course of the aether moving down one side of the helix, round one loop, and back down the other side of the helix, and then round the next loop - you should find yourself repeating the course once again. You should find that the direction inside one loop is opposite to the direction of the other loop. In one loop the direction is clockwise, and in the other it is counter-clockwise. I think, we now have the basic premise to polarity.

We can even reduce the double helix to a point where the two loops simply join to make a figure-eight. If you follow a course around the figure-eight you should find the same thing as before - one loop follows a clockwise direction, while the other loop follows a counter-clockwise direction. The direction changes each time the middle of the figure-eight is crossed. You can follow the top loop round in a clockwise direction, but when it crosses the middle of the figure-eight to enter the bottom loop, then the direction you follow becomes counter-clockwise.

The energy flows quite happily around the figure-eight any number of times without interruption, but we can make the observation that in one loop the direction of flow is clockwise, while in the other it is counter-clockwise. The direction of the flow of energy is rather dependent upon the observer. In the same way I suppose, that if you hovered directly above the north pole, the Earth would appear to rotate in a counter-clockwise direction. But if you were able to observe the Earth from the south pole, it would appear to rotate in a clockwise direction. It all depends on the position of the observer.

The figure-eight is a rather ingenious way in which a uni-directional flow of energy can be made to appear as if though it works in two directions. The figure-eight is an interesting shape. On its side it becomes the mathematical symbol for infinity.In maths, the shape is also known as the Lemniscate of Bernoulli (pictured at the top of the page). If we think of it as a 3-dimensional shape (as in the picture directly above) it begins to look a bit like a saddle, or a Pringle's crisp. In mathematics, there is a particularly grand name for the shape of a Pringle's crisp - it's a hyperbolic paraboloid.

When you say - hyperbolic paraboloid - it has such a resounding brevity, that surely, it's something to be savoured when you manage to toss it (rather like a live hand-grenade) into a conversation. Something like someone asking you, "Did you see the game last night?" And you might say, "Yup." Then they might add, "Did you see Beckham's freekick? What a blinder. Talk about 'bend it like Beckham'!" Then you say, "Bend it like Beckham? Bend it like Beckham? It was more like a hyperbolic paraboloid." And the person will probably just LOOK at you.

The hyperbolic paraboloid is a three-dimensional curve that is a hyperbola in one cross-section, and a parabola in another cross section. I'm pretty new to the names of these shapes (even though we are all familiar with the shapes themselves). I found this site useful for a quick dose:
http://www-prod.pen.k12.va.us/Div/Winchester/jhhs/math/lessons/calc2004/apphyper.html

Basically, a hyperbola is a curve in mathematics. A hyperbola is derived from a double cone. A double cone looks a bit like an hour-glass, or a bow-tie perhaps. I'm grateful to the following site for easing me in a bit more gently:
http://www.intmath.com/Plane-analytic-geometry/6_Hyperbola.php

Also, this site has pictures of hyperboloid structures, out-there, in the big bad world:
http://deputy-dog.com/2008/09/hyperboloid-structures.html

"A quadratic surface of which there are two basic forms: a hyperboloid of one sheet, generated by spinning a hyperbola around its conjugate axis, and a hyperboloid of two sheets produced by rotating a hyperbola about its transverse axis. The hyperboloid of one sheet, first described by Archimedes, has some particularly remarkable properties. In 1669 Christopher Wren, the architect who designed St. Paul's Cathedral in London, showed that this kind of hyperboloid is what mathematicians now call a ruled surface – a surface composed of infinitely many straight lines. This fact enables a close approximation to a hyperboloid to be made in the form of a string model. Two circular disks, of the same size, are held parallel, one exactly above the other, by a framework. Strings are then run through holes near the circumference of one circle to corresponding holes in the other circle that are a fixed distance further around the circumference. Each string is perfectly straight but the surface that emerges takes the curved form of a hyperboloid. For the same reason, a cube spun rapidly on one of its corners will appear to describe a hyperbolic curve when viewed side-on. "
http://www.daviddarling.info/encyclopedia/H/hyperboloid.html

That last sentence reminds me of something once said by Einstein; "The Theory says a lot, but does not really bring us any closer to the secret of the 'Old One'. I, at any rate, am convinced that he does not throw dice."

For my eyes, the hyperboloid resembles the inner core of a torus. Indeed, the exact shape of a vortex is a hyperboloid, or a hyperbola of rotation. If we were to wring the waist of a hyperbola like it was a dish-rag, then it would give us a hyperboloid. If we were to wring the hyperboloid to such a degree that the waist constricted to a point, then we would have, once again, something like a double cone. If you draw a double cone, I find you can impose a hyperbolic paraboloid over it, by drawing round the double cone, and treating it like a figure-eight. Indeed, if you induce the flow of energy as being counter-clockwise in the top cone, then you find the flow of energy appears to be clockwise in the bottom cone.

If energy was moving inside the hyperboloid, then at the waist, or vertex, we would thus find the energy being condensed at this point. Occasionally you might spot a hyperboloid that wants your money. You start with a coin at the rim and let go. The coin revolves around the funnel in spirals in its descent into the vortex at the centre. You can see one here: http://www.funnelworks.com/index.html

Is the hyperboloid describing the centre of our 'atomic' torus? Does energy descend, and ascend in spirals inside a hyperbolic funnel? If it does, then it's worth noting that these spirals will be condensed into ever-decreasing circles at the vertex. Are the ascension and descension of this energy describing centripetal and centrifugal forces? Are these forces dictated by the direction, clockwise or counter-clockwise, taken by the energy inside the hyperbolic funnel? It could be that the movement of this energy is describing how electromagnetic radiation is emitted by matter.

Many thanks to everyone:

http://www.math.hmc.edu/~gu/curves_and_surfaces/surfaces/hyperboloid.html
http://www.cosmosmagazine.com/node/1566
http://glafreniere.com/sa_light.htm
http://mysite.du.edu/~jcalvert/math/hyperb.htm
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html http://www.ipfw.edu/math/Coffman/pov/spiric.html