Thursday, March 24, 2011
On the Mirror (Phi-Tau and Concrete Space)
Art in this post-alphanumeric age may not endure as the best concrete ground of human experience and consciousness between it and science, philosophy, and religion.
For we are on the mirror of the dust and shadows of our perceiving. As the coffee shop was down for maintence a couple of days, and we had cold March weather, I went downtown to get ideas from the shops. I speant a few hours in many places and filled a few pages with candle and mould making ideas. Looking back to more innoscent times I find my studies of the last few years- on that virtual world of the internet whose ground is information beneath and finer than the social content and subject of physics in which we are concerned. We dwell in the art of it on some vague general level. We literally eat signs. We crave the imaginary. We are part of a more general nation where the new media is for all practical purposes the ground reality in which only in the face of time or disaster, or if the lights go out, do we confront reality again and the direct dealing with others.
I am amazed how expensive the candles are in the shops since I last tried to sell them in mass, and then charged the same as in 72. Of course a little bit of algebra tells us there are times when charging less for things maximizes the profits. In one case a small Buddah cost $3.00 but it was not as detailed as my own, really it takes a couple of hundred standardized cuts by trained people for the original. I conclude that these people used their small silicon moulds way beyond their lifespan.
I looked up metal cutting and am amazed at the precision of what can be cut- a precison in the world of flat tolerences I need to make things work. I see such percision, not perhaps as detailed as what nanotechonology promises, in the bracelets cut by abrasives and water out of hard wood. But it is the symbolic art of it that the people buy, the sense of reality of the object itself.
In the walks thru the sense of walking on sugar, its lumps and sounds, and up so early in the wind- I found so many new methods and ideas to the point at times I made some mistakes of which a model corrected later (I think, but in the back of my mind I still do not see why it is so hard to make a variable 5 pt. starmould. For all my sense of seeing space now there is something I am missing- perhaps this idea of things in fourspace itself. Where higher dimensions are possible we encounter whole new properties of the symmetry of what we mean by space.
When we add even one more dimension, say from 9 to 10, 10 to 11, from the physical viewpoint we vastly multiply the divisions of space and properties possible.
Rowlands metaphysical principle suggest that nothingness or the vacuum comes into existence with the muon, there is a muon and all that is not muon.
Let us then think of space as if a subtance. One that cannot exactly and abstractly to be said it is something or nothing- both descriptions suggest this idea of substance.
This idea of space moreover can be thought of as continuous and thus perhaps infinitely divisible. Where it is real as a sort of Euclidean geometry, and it is not clear exactly if as Non-Euclidean geometry despite we can say make hyperbolic tessaleations of say seven sided polygons is a complete generalization of space in terms of these familiar and seemingly concrete structures we build. HGere I assume so for now, and I imagine in this space we can have two notions that exist (independently) that of a point and that of a measureable length (a straight line segement or ray).
Recall, that with phi-tau (I use tau, the European symbol for the golden section) that we can have a line segment so as to make a right triangle without area- that is the 1 or tau part of the ratio if flat when tau + 1 and either end of the segment can find these two values as less than or greater than tau or 1. The connectivity in such a line segment triangle cannot exceed the first power of tau. In three space the shortest to the longest ratio of the edges of say a tetrahedron cannot exceed the third power of tau or in all such cases we lose a natural dimension.
Now let us consider a square of the side 1 + tau + tau^2, that squared. We find in fact there are 9 sections 1 + 2tau^2 + 3tau^2 + 2tau^3 + tau^4. But since tau+1= tau^2 we reconditely divide the square into 2 or 4 quadrants. This continues into higher space dividing things (quasically) ino 2, 4, 8, and so on. Furthermore we consider in some higher spaces that we have a sort of fractal like echo of these recondite 4n ratios. Interestingly if we take the first three quadrants only and count the number of squares in them beginning with prime 3, the rest of the values 12,48,192,768... are the rotation groups of orthogons. What this amounts to is the description, perhaps from a view of inversion on the other side of a mirror, of the circumsphere, intersphere, and insphere of the orthogonal subcells (in three space here and so on) for what I thought of as the fsubn functions of abstract motion.
Of course these have square root values as diagonals across the orthogon. In four space it is the square root of 4 or 2 which is the same as the one dimensional unit length. In fact from some center of such an object we encounter 1/2 in the real constructible part right away and all that implies for force laws and so on.
Newton made a major leap in extending Pascal's triangle to the negative values. The -1^n is a powerful notation for alternating values and oscillating values. And on the mirror we have our conventional ideas of -1 as filled space and have to determine in the complex space what exactly do we mean by -i in the scheme of such extended algebra of twistorian considerations.
Of course the general equations of polynomals, the variables and the powers are as far as deeper information goes equal in the effects. In fact we can use these square roots of the natural numbers as coefficients all in informational notation. In a sense that things exibit fields with right angles is also a property of numbers, integers in fact, in this concept of our familar dimensions of space. We recover them further when at a center (as a singularity of points or as a point) we imagine from this side of the mirro things can have discrete shell structures (and the corresponding nothing ground on the other side of the mirror).
Clearly, in these recondite constructible structures we see that in a space representation (tau^2+tau+1)^3 that the largest cube is the sum of the exponents which would be in a sense 6 space, ie 2x nDimensions.
I had some further thoughts that the 24 cell, which is its own dual is in a sense broken down into three beta4 or analogs to the octahedron in three space and these are composed of 8 abstract points. Thus from all directions we have point singularities which involve the division of subtantial space into the 8 octants and so on. I briefly glimped the possibility of a beautiful informational lattice composed of these objects- and perhaps other such resonances of such lattices and yet the fractal like embedding of such obejects tends to balance our idea of scales.
Here, of course we encounter 240, the eight dimensional packing of spheres, as one steridan star before it is broken down, presumably into spaces of ideal jets or points or stretches for observed but relative force values and lifetimes of said particles. Perhaps only abstractly can some such particles present themselves as eternal and irreducible, at least in the short run from all sides of these topological twists and mirrors.
I know these are perhaps very simple ideas of space, then again it could be we have not seen some of the seemingly trivial and too intimate to stand out as obvious that we have long overlooked what is concrete and what is abstract in the art of our notations and notions.
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