Wednesday, August 31, 2011
Plyctals (Reconsideration of Folding Hypercubes)
Plyctals (Reconsideration of Folding Hypercubes)
L. Edgar Otto August 31, 2011 (note: Plytals is a general term but I prefer Plyctal or folding, the interesting case in higher space as posted tomorrow will be more like the n-space multiply density for such lattices and space fillers.)
From an informational approach the list of the 261 unfolded hypercubes is done by pairs of cubes of the total. But this considers only the outside space and not the more right angled quarter twist of the surface and internal spaces. I want to see in the case of the eleven cubes of six faces if these make a set with interesting matching properties in three space (which they do not in two space). I also see new functions in hyperspace for these primitive functions of folding and cutting as a possibility.
The cut edge is akin to the idea of a string or quarks in that if we cut a string it still has two ends. Thus the 5 quarter rayguns are in a sense strings in that the unfolding of them doubles the count of the edges. Thus 7 edges unfolded are 14 and the five rayguns are 19 (with 8 to make 27 for a general intelligible count globally). In any case the objects together in this notation make 7+5 or 12.
These are not string like nor a question of combining the complex space with other counting spaces in some method (such as the Minkowski count +++- and so on where we try to match the imaginary and real parts) In the surface-internal quasic like spaces we do not try to twist things in multiples of pi such as a rotation that comes back after 360 or 720 degrees. The resolution of these methods is one conceptually between such spaces and not an operation by any one of the views unless that is the goal of finding a needle in a haystack if it is there after all. Not to say there is anything wrong with these methods- after all our view as to what is continuous and physicality verses the discrete and virtual where these are metaphysically distinct in a more general view of physics and mathematics.
Now I have to reconsider these abstract objects from the standpoint of what we mean by science or a pseudo-science in terms of what is the overall view of things as to when it is useful to apply ideas of infinite regress and inelegant recursion formulas. In a sense this is like the brief time when some particle physicist bet their careers on bootstrap ideas of space and of time as a paradox. Most of the hidden debate in the world views of physics, especially cosmology, seems to be centered around these sort of issues (after we enter the next stage of the physical and possible cosmic background, the Omnium, we find such ideas may be resolved better than say in the relativistic Minkowski formalism and any complex number ideas or for that matter the p-adic concept of strings, p-adic strings.) Again we can understand the problems but have to struggle to visualize the solutions. In a sense we have a world that is a combination of useful regress and irreducible even unobtainable reduction in terms of compactification and my flange or condenser topology.
* * * (Post later here illustration: Tired Old Turtle (or for turtles all the way up and all the way down, softshelled...)
The lowly turtle in a sea of dark, unknown how wide the river only that as one thing in existence if he dwells in a small point he dominates and exhausts all creatures therein...
For there are degrees of non-existence as their seems degrees of existence.
An entity is one thing, it is nothing at all, it is countless copies or nuiances where what seems the physical boundaries infinitely and exquisitly blend into each other- the paradox and problem of uniquess again.
If the structure of the universe were circumscribed by a ring, and that ring could be compressed into a singularity- would it describe only one universe that can seem isolated from the others- the certainty of the one totality or brane?
Or in a compromise of the bootstrapping of space and time- all such states of some location or entity are in a sense present at once, not at all, and for all directions in indefinite seas of time?
The fractal, save perhaps at the final summation to become plane filling and in a sense a continuity of its compass, at some instantaneous point perhaps or something only pushed further away and remote so never reached in our concept of number and limit, is but a pale and quasi-unique copy of the unitary universe to which in that it is iterations and recursive in tricks and paradoxes of time, it does not describe the local condition of something like mass even sorted out in the seething proximity to a singularity.
There are realms in this sense were something may be neither holographic nor fractal, the placiticy of the mind and human language comes to mind. So, as with so many of the topics in science fiction, and abhorances that justly or do not classify whole trends and views of creative physics as weird science. It is this many-world and multiverse problem that has long enchanted and limited the imagination of man- not so the thought that since all was created by the Creator our role is one of fantasy for what is left?
The simple constructions of viewing what is not as simple as it seems from our crude understanding and scale of things where the finest crystals fade into a background of rocks of no particular shapes, or the detailed symmetries of leaves become a random shifting forest of green, says for these views that the planes or squares that compose them are whole universes or branes in the various connections. As such what is proven within one, the same as another physcially, intersecting, or not, is that which must do more than prove the deep law that seeks a monological unity and yet must do more in the natural generalization of dimensions than establish physicality or its mirrors as if non-linear were the greater state of things as an interconnected randomness. Behold this view that seems to solve some of the philosophic problems of our time as the Poly-omnium PyOm. But it is not the ultimate even when the existing paradoxes and prejudices would pain the world with say imaginary numbers and shifts of space and time to reduce to their limited style of what are the singularities. The brane complexes are intelligibly structured and counted as the notions of their intelligible parts.
What then are we to make of a theory where our best digital approches which also raise from their assertion as to the whole of mathematics, and these are equally as powerful as any other human construct, that outside of their scope they can only keep at bay the paradoxes and not solve them at the level of computation in progress?
I have asserted intuitively and metaphysically, at first blush of some idea I stumbled on too long ago not to question now with deeper insights, while watching a cloud of gnats and trying to see a connection between them (yes we can assume they are in synchronation by some physical principle applied to biology- but that is not unexpected as part of the explanation in an intelligible universe. that a fifth or greater natural dimensional chessgame would play itself. Thus we see that this idea does raise the usual ones about initital conditions, and entropy remote or not as to its nature, and still asks the nature of the arrow of time. I find it perhaps true in this polyomnic view if we so allow the reiteration of or bootstrapping of the quasi-unique branes as part of the infinite games to be arranged in self-hierarchies and played. This area seems to me to come closer to the ideas we need, show a place for real science that is a clue that I do not feel can be undecidable or a dead end.
The idea, similiar to that of TGD of the wormhole (and mouths) between parts of the organic structre should consider such ideas for the universe would be multiply p-adic and other systems where it is p-adic at all. For even in the frontiers of black hole concepts and in the fairly well popularily understood physics assumptions of the sci-fi writers we may ask- can the wormholes be held open? Is the surface of a black hole rather thin? And if light, the photons is the issue then ideas like with Kip Ward, the travel between them around a black hole as if a gate or wormhole into time would cause its own collaspe by the "duplication of the photons" - again the frontier of these questions of creative science and philosophy as physicality. But such a theory as this may have some intelligible part to play in the new physics.
It is enough for now that we may see a particle and quite differently make some interpretation of what it is or how it decays and so on- not something as simple as the quantum formulations of the idea of wave and particle. What after all in this theory is the general idea that would define these disputed ways evidence and experiment show that such radical but still hidden descriptions seem to apply?
* * *
Note to Pitkanen a comment that may clarify my question some from the other side of a real surface to the continuous groups from the finite groups as to what is the ultimate proof of the uniqueness of any particular number theory:
interesting and educational posts to which I strive to address such issues.
Is the swan logically black or white?
While this more relativistic idea of rotation is useful I think it needs more of a generalization - I think you might find my last post of interest where I post Plyctals or the folding and cutting of cubes.
* * *
It is not that humanity, as with any hypothetical sentient beings, will one day only reach so far because they stumble on an idea that accidently destroys their planet so we do not see much of civilization enduring in the immensity of space and time. But it is that we do not strive soon enough to reach a certain technical level where we have command of our own evolving and can survive the affronts of nature in her unforseen encounters. The species that will endure will be those who take science and philosophy seriously, and with their creative human heart.
* * *