Monday, August 8, 2011

Intelligibly Condensed Conway Matrices (CCw)

Intelligibly Condensed Conway Matrices (CCw)
L. Edgar Otto August 8, 2011
To start with a link from yesterday and one from today on "phase space" (but I do not think that a very clear description. In any case the quasic informational principles have been here all along for a space model. Seems some are catching up to these wider principles at last.

The graph paper gave me some trouble as it needed a better design... So too when we try to take a template of our ideas and expand or contract them discretely and digitally...

I find it amazing that to really understand good math one has to make the simple numbers and the geometry of it all correspond in our awareness- that is as I was taught it I did not comprehend things beyond counting or shapes thought separately.

[I will be back to post more and make things clearer soon this morning- the problem is to orient the 60 cubes in all possible directions and match the colors- but I must take a break, among other things the numbers of my calculations last night do not add up and I must check them in the morning light- so consider deeply these two links as they relate to my late topics at hand - or the mirror principles of them.]

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Ulla, thanks for the question and comment a post or so back. I cannot answer it as that is not the case as here in the much wider view of what deeper space we cannot see on the surface of what is simple. The higher dimensions in a sense do compress after nine or so as far as curves and volumes and so on- but this view is only part of the picture of dimensions of which the compactification idea is also but part of the picture- I rather call these things condensed. In any case what do you mean by expand?

I also remark about the links here provided that the crystal lattices as I have shown do relate to the ideas of entropy.

Your question is intuitively easy to imagine but hard to explain in a few words.

If one cannot decode the ultimate last pixel in quantum ignorance (so the article says) one cannot readily see these patterns or imagine things in them that we may consider as concrete and real unless we go a little beyond quantum and general relativistic notions - of which many cannot see or see simply that we need to do so.

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Ulla said...

Someone told me that dimensions 4-5 would be expansive and higher dimensions compressive. Can you show how that would be possible?

Ulla, thanks for the question and comment a post or so back. I cannot answer it as that is not the case as here in the much wider view of what deeper space we cannot see on the surface of what is simple. The higher dimensions in a sense do compress after nine or so as far as curves and volumes and so on- but this view is only part of the picture of dimensions of which the compactification idea is also but part of the picture- I rather call these things condensed. In any case what do you mean by expand?

To clear this issue up some, especially from thermodynamic concepts - I have shown in the pages what are the possibilities- as the link on my august 8th post shows the calculation begins in that 8 dimensional field, not the preoccupation with six space- this relates to the simple formulas and differences of the factorial and binary power numbers with the idea of order as an axiom.

As the grid I use is a multi-dimensional ordered matrix we find very interesting symmetries across the main diagonal. For the motions of rotation in four space, 384, we have a diagonal complement of 704, the sum of which is 64 more than 32 x 32.

Our alternative new physics does have a sense of expanding or contracting energetic ideas as if a supersymmetry of sorts- and in strange way our own ideas of what broken symmetry is. For either side of the diagonal can expand or contract, be real or imaginary. So in the squared field the numerical count is naturally asymmetrical if we think of mass or directionality and so on...

The prime or zero pixel or cell is in a sense scaleless and this sort of thing is most important where Pitkanen intuits the role of prime numbers (all of us seem to work with very small dimensions or such numbers- that or I am finally coming to realize in geometric pictures what a lot of physicists and mathematicians are actually doing in the lonely depths of their research in realms we only begin to learn about to the best of our abilities.)

Let me add the link on quantum ignorance can we worked out such that our preference for say the interpretation of consciousness as a quantum effect is surpassed as an issue to higher issues. The opposite is that we tend to see patterns which while they can be misleading are also the possibility our intelligence adapts correctly and intuitively.


But on the level you ask it is a question of what round things fill square things for in the 8 dimensional case the square and round fills the same space then it goes down again from there after things happening we are not sure what in nine space. The vast sea of numbers and dimensions is so wide and while I feel so small, like Newton commenting from the vast shore, I feel I can see a little more of the infinity of the ocean. But I do not know if such a view is not already there, even by the ancients let alone those holy men of science a century ago to which while it is a strength to develop our notions alone- it is very costly to spend our lives reinventing the wheel as original enquiry or not.

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So in the 4 x 4 matrix or quasic grid it is clear we can represent things simply and algebraically as the division of space into the 7 (actually 8) and 8 for 15 or 16 points of the tesseract from a point centered projection. So in the alphabetical labeling of color cubes we can have sets of 8 as if a cube of 8 points and the set of them as if an octahedron with 2 points in the center.

Thus we can label the sides or surface colors A to O and the negation on the six sides of a cube representation so as to find three vectors for each of the 15 cubes, and the number 15 here is a group that relates to more than 4-space as always dimensions are a bit hard to define.

We can of course make geometrical analogies which are a little mysterious but intuitively feel valid by the old methods- the expand and contraction of things, the expanding and truncation of centered 4 space objects, but to do this I would have to say that the utility (of information) of the Conway matrix as depth or span- that in the depth there are spaces of further depth to explore. Isospin conceptually may be such an analogy, at least in the vague spirit of it.

In the division of the 4x4x4 or 2^6D or 4 x two 3D cube doubling (halving) we note the algebra of 9 of the 15 alphabetical letters in the corner of the 4x4x4 matrix and 3 and 3 on the equator and 1 = 16 for a surface or 2D representation of this 6x6x6 core in a pattern I call the Hexcon or Hex Concon.

Such symmetries where their are some cubes left out which in effect are neutral or merged they can be a positive number such as 8 and i8 to subtract 16 to make 240 or add 8 to make 248 for the generalized concept of 8 timelike dimensions. This also may shed light on the Fermat problem in that a proof may lie with such doubling and squaring of the side of the triangle which has such a square difference when we try to extend it cubes, I suspect. The number 80 or 2x40 (5D close packing) comes up a lot in these simple calculations.

It occurs to me that the solution to this quasi-three space in matters of total inclusion of vectors and internal color matching contiguity that this may be a solution to the old DOS (for I recall beyond 216 of the ascii code that certain messages could ride on the packet to mess up the operation of say the IRC chats.) It reminds me of the movie Pi where the secret code was 216 or 6x6x6 (a perfectly good and intelligible triangular number) as if the "Number of the Beast". But superstitions aside in deeper Conway Matrices could there be analogs of this system of use to calculations? I mean to keep the system secret while it was very hard to solve did help develop the technology- but perhaps at the cost of general theory.

Whatever the actual facts in areas I am most likely not proficient in that may reach beyond my intuition or cause false estimations of what are but trivial coincidences, the general question of physicality, of the felt need to shore up what is concrete and classical from theories more advanced, in the more concrete concepts of our theories we perhaps need something beyond the quantum and relativity, like perhaps my quasics as a primary physics, to shore up issues of encryption and security of our human transactions. If life and nature are founded on better understood quantum principles, the universe does not necessarily have to exist based on ignorance.

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Let us not underestimate our artistic sensitivities. Sometimes on idol our mind benefit from free play and there is a point where such games add more then they detract from enquiry. Flag design, here a rare new principle I look for thru the cracks of the overly done like love poems, has a certain raw and primitive logic and traditions of color. But what is magenta but off the spectrum of a rainbow, and is it socially the Pink? Or in this evolving planet of us apes is the flag of the gorillas pink with a large vertical black stripe?

I would like to add per this link again:

While these ideas are most interesting they are not as general as the notions presented in this creative science and philosophy blog but are on the right track. The vision goes much deeper than that offered in this article and more concretely as to essential ideas like relative locality- It is not just a matter of the results of combining "momentum space" and "spacetime" if we must have that distinction, so again phase space is not quite the right term for even this article's level of vision. Anyway, the issues of this article just synchronously (if by its vision this term makes sense) to what is done here in at least 8 space as a matter of viewing ensembles and duplications of "cubes" as objects of orientation, momenta, and that part which contributes to ideas of mass or gravity and other inertia- one can in fact find the gamma burst reference in this blog. But I must give Smolin an A for imagination. Thus those in the know now can see that as wide as this new view is it is but putting our toes in the water of a vast new beautiful and wonderful sea.

Then again the article says it points toward and is not a theory of everything, or in my terms a higher theory of the Omnium to use my and Penrose's independently coined term.

Another article in science daily suggest that number sense and mathematical sense is inborn and the ability is developed culturally- well, this issue comes up periodically and seems especially relevant to the philosophy of science part of my recent posts. I disagree with the part of the article that says such ability is determined if there in adolescence or by social and cultural conditions- unless I understand that having high counting ability is dampened by some early methods of how we teach arithmetic. This perhaps introduces the stage where our idea of mental computation reaches quantum level notions of uncertainty- and is perhaps a stage that is difficult mentally for some people to go beyond to a more real view- in fact just as with the number sense of the lower animals, say the crows, the ability to count does not mean the ability to comprehend if our world view is yet not developed as to what is regarded as a complete theory or not such that the idiot savants are not aware of their conceptual limitations are some of our working theoreticians.

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