Sunday, October 30, 2011
Pinwheel Braids and Quasic Patterns
Pinwheel Braids and Quasic Patterns L. Edgar Otto October 30, 2011
I find it remarkable that more intelligible models of space do not exist in the literature, things like the slow dawning on us that certain ideas of vector products are not very foundational as conventions to describe three space. (as in the link to Matti from Ulla above). My surprise is that I can contribute and that comes with much disappointment that our search for science concepts seems so slow- and yet in principle as in philosophy we may be only at the beginning of long enquiry.
The question has bothered me since my discovery of the quasic 4 dimension chessgame cerca 63 as to how to read the direction of motion between the cells. It worked that I set the order parallel- but this needs not be the case. In fact it is a certain ambiguity and freedom that some systems can be mirrored "perpendicular" so to speak as if complex numbers. But should we not expect this when not only for a quasic cell orthogon complex, a model of 16 hypercubes made of them and so on in four space that at a point in such space we cannot distinguish, in the consideration of the continuity of it all, the directions of time. If we do then we have the general idea of directions of space as if privileged by the quantum theory as in twistors and gravity and collapsing to classical state concepts.
But in the numbering or ordering of a sub-grid of quasic space (the four space of a matrix like 4 x 4 elements or cells is divided into 4 2x2 spaces for the second generation of things (By the way herein I make the fine distinction as to what is flavor and what is generation and the working together of such foundational mechanisms). It follows of course that in a sense the idea of tachyonics is as unclear and not forbidden in the remote view as well as say that we cannot in the relativistic view imagine all events not seen relative to different reference frames.)
The sub sets of binary powers of patterns I call pinwheel (for the windmill patterns are not as general- and these amount to various permutations and the various ways we can organize quasic space by several of these as if a quantized braid, actually quasized, patterns of cells and the variation of matrix maths in patterns.)
It is clear from the start that in the 4 x 4 hyperspace quasic grid or matrix there can be braid-like or quasic-like paradoxical reading of the patterns as to what in the rotations are the inside or outside of things. The former holds one of the four axes fixed and permutes the other three coordinates, the latter does the same for the 24 such coordinates- in a sense we could call these pinwheel cyclic and triality and the later pinwheel quasics and quaternity.
If we increase the generation analogously to three even the cyclic patterns alternate between the magic square sums of the 4D orthogons independent or not from one ordering of patterns. This itself exchanges the within and without of things.
Let us also take note of the quasic coordinate binary notation for we can imagine a hypercube in a hypercube (or more properly a hypercube and its imaginary mirror where the inside and outside of the reading and order is reversed- such that this difference physically kicks in at least in four space and can do so globally that we do find the idea of quantum phases leading to preferred axial directions as part of the picture. In this case we imagine the binary being one digit, or in quaternions two digits, or in octonions four digits as we set a description of the space.
In which case at the octonions we may need a 5 or 4.5 dimensional view such that we can resolve the apparent disconnect between the even and odd numbers under consideration that nevertheless pinpoint the bases of counting. This is why I sometimes divide a quasic cell diagonally- much as Carrol did in his sortisies. And this reminds me I was going to call this post more formally:
Counterchange of the Saltire
But for most people I notice when they fly or wear the union jack such asymmetry can be ignored and they sometimes fly it upside down.
BTW I did some arithmetic on this but it was hard to see at night and I just summarized the concept instead of the explicit patterns. Still, it is an interesting combintorical concept for me that of four color patterns and the rotocenters, we have thirty six of them (not including the permutations) that form a calyptic cube set of six. Sometimes space and numbers seem so coincidental, and we should explore these further for some ideas on higher spaces and higher physics notions of symmetry.
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several orders of magnitude simpler, hmmmmm if that is an advantage.
At last, a surprisingly recent paper on a simpler way and more advanced way to view the plane (as I have posted all along- the quasic plane) and it is much simpler and more general than the link supplied above by Ulla on things like Clifford space.
Now that some theorists realize there can be combinations of what seems complete physics- to ask as you did the difference in physics a and physics p, it is high time we brought it all together.
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I hope someone out there shares the clarity I have come to find lately in our fundamental notions of physics- and I hope that I no longer work alone for in the end the first ones to explore a new land (sometimes by shipwreck on some island with no food before the boars and the colony) cannot be but a Crusoe getting his island on and silent so long speaking perfect Portuguese if he is ever rescued- and if he hopes to build something sea worthy- its a long way to swim by yourself, Mr. Christian...
I should also remark that in the successive changes of three events it is the same thing as the consideration of such events as a totality- only we should recognize the overall unity of the structures beyond the quantum reasoning for such emphases only (save perhaps a better concept of the discrete Fourier transforms for the inside and outside symmetries. Clifford ideas as well as TGD to recognize where there are possible mirror inverses and so on of the whole framework). And keep in mind the vertices that are defined as triality ones in the information. But nothing is to be taken as too rigid a view nor too loose if we are to get a better picture of a unified physicality.
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A stray thought caught my eye- Xe and F 54 and 9 in the periodic table (which is still much confused as to the groups and period names)- and as structure we note on this first discovered unexpected compound in 62 or so- that it is square planar- and that the xenon hexafloride is on the xyz axes (not a hexagon). Now what do these structures and numbers suggest to you?
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