## Wednesday, January 26, 2011

### Arithmetica

Arithmetica

I had a most marvelous idea on the way back from the coffee shop- which I cannot post here yet because the details despite a dozen pages are not worked out- in any case this is "My Sputnik Moment" (who is the enemy this time?) So I still write in code, usually poetry (so that things I write could eventually be translated as intelligible) being a child of Kennedy with traces of the cold war mentality for secrets of which lately I have no such claim on important new ideas as not better shared. The question we should all ask ourselves, in the intuitive exploration of vague new enquiry- is if we in the search for some thought from an author and the process or steps leading to it- the claim of some puzzle answered- was it an actual solution that the author leads us to- or did he only understand the direction to find the answer, intuitively the final formulation left vague after translation?

But, as mathematics along the way grows- answers there or not- I offer this today which amounts to part of the new vision in the simple way we can map these things of my recreational concerns to the 81 elements of the hypercube. I begin to not only answer why the world is three dimensional but what happens at the ninth dimension.

In consideration of this I offer some new concepts for arithmetic, a metaphysics of thought that may be the key to some of the decoding and disambiguation of how we see number.

I note today Lubos has an excellent defense of string theory. Clearly his defense is valid to the point it again seems to confirm some of the ideas as alternative that could better generalize that sort of theory (and most likely not make it obsolete). Maybe more on this later when I fully understand some ideas from the other alternative bloggers as they go mainstream in the new physics.

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Constantly running out of symbols or having to overuse them I recalled a post on philosophychatforum where I labeled the subcells of a hypercube by the Cherokee syllabary as I am part Cherokee. This pattern became clear in relation to the Pascal analogs where they trivially seem to add up in the squared formations.

Lampion 01-26-11

Although for every infinite group there is a finite group it is not clear why this should be the most general case. It is possible when an ordinal transfinite number precedes 0 and the natural numbers that from such a presumably non-linear infinity that not a diffuse but a specific ordering or individual value or pattern precedes zero and thus its successors.

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I have to understand the ideas of Looping better but feel it is close to the topological ideas (provided there is a more general treatment of M like theory. But this possibility is worth looking at again even if the terms quantum gravity or sheets of things in TGD theory are still too vague. The same perhaps for any sort of existential view of twists and turns in such theories. But I ask this vaguely.

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The codon bases are part of the structural understanding individually in this sort of encoding by arithmetic and geometry. (this idea from another way came up again)

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Information theory (as with physical effects, numbers, and patterns) itself may present or be an aspect of triviality. The underlying theory invisible to he who makes the computation to which one may imagine a reason for not finding a pattern but cannot in logical principle say that is why we find no such pattern (Lubos).

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The counting of things should consider the internal point as there or not or as a singularity complex or not- which implies the next dimension- even in orthogons.

The information is not only there in the line to a plane but for any such general and more or less disembodied abstract concept of such subcell dimensions. This amounts to a generalization of M theory as it assumes to be not a description of a multiverse. Is it then string theory anymore or closer to a more general physics?

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I may add later an illustration for the above recreational diagram to which we show that the hypercube subcells are broken into three cubes of 27. But the sum of things by this sort of division is different for even and odd dimensions- that is the alternative division is as power one and not the symmetrical Pascal line one.

The 4 space can break into four cubes of 4^3, the sum of such cubes generates the rigid rotations and inversion numbers unto the dimensions in question (ie n!!'s).

The computation of a 2x2x2 matrix in relation to the supercolor pairs can have variations of which the triality and unity is reduced to duality and numbers mixed on the outside of a "geomatrix" of the next higher (perhaps complex) dimension.

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In the exercise of classification of the Soma cubes, 480 or 240 from consideration of the inversion centers and not the surfaces or corners, that is a center singularity- is the C++ notation of zeros and ones usefully non-trivially to generate the cubes by visualization and not blind computation? Are they a quasic notation? In any case whatever the n-omino the grid direction say from xy (if not the notation xy yz zx from three directions) cannot exceed tricube triality. But of course the first piece of the somacube, a trionimino, may like some particles in that zoo of ghostly things, actually be 6 or 9 and so on... Soma More would express in the corpuscular flesh a 30 or 36 cube puzzle to subunfold such things.

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And this was the sort of vision, that and the idea of three sets of five things when they share a point- that is 8 becomes 7. We map the soma cubes to this answer I long sought not in the back of my book but now with the wider view of higher space find it within reach and a matter of calculations, busy work. The realization is that we can map these cubes in higher space so as to see them readily, something we feel we might be able to do with numbers as to their primacy and digits- but that is a much harder problem.

If it is amazing when different areas of math magically seem to be connected, especially if we do not have the opportunity to explore or access to our earlier works, then it is all the more amazing that works of art and mathematical methods seemingly so different and each my independent discovery so magically fits together.

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From Today's post by Luboš Motl :

"What could happen - although it is extremely, extremely unlikely - is that a consistent, non-stringy competitor to string theory that is also able to predict the same features of the Universe as string theory can emerges in the future. (I am carefully watching all new ideas.) If this competitor began to look even more consistent with the observed details of the Universe, it could supersede or even replace string theory. It seems almost obvious that there exists no "competing" theory because the landscape of possible unifying theories has been pretty much mapped, it is very diverse, and whenever all consistency conditions are carefully imposed, one finds out that he returns back to the full-fledged string/M-theory in one of its diverse descriptions."

I agree pretty much with Luboš here with the exception of the part I placed in bold type- for there are those in the string field who imagine "a string theory without strings". I offer such a unifying theory as do many bloggers here. Let us not confuse the map with the terrain they say... The consistency of things like 2+2=4 or the reference frames does seem to allow for phenomena that are physical but not observed or observable directly- that does not mean there is no gravity or Higgs (well, it but one minor particle and not the all pervasive field idea) and yes I did suggest iotas which one could in trying to see the world as some sort of conservation and symmetry in terms of energy and its encompassing reality (while still not all there is of the physical let alone possible metaphysical like consciousness as a real and maybe independent source and phenomenon we experience). One can be assured there is no challenge to the string view, it in a sense is a steppingstone but like quantum and relativity itself not the isolate be all TOE.

I am glad the line calling some idiots is revised I think- an emotional rant not fitting of formal science but perhaps a good political tool in the blogosphere culture. But I do have a problem with his statement concerning the old "where does the information go into black holes?" This as a classical as well as relativistic concern for today's physics. So, it does not vanish, does not return to us to churn up the "swampland"? Loops in somewhere else in say some other action at a distance or parallel universe? Where does this information go- into braneworlds that lose their stringy origins? Perhaps, it goes (all these issues of dark or opaque matter aside) into a much greater theory, with I agree our mathematics at hand) well beyond even its marriage to what we imagine of the various dimensions, symmetries, and topologies. As Luboš foresees but does not see, this a proof of sorts of a challenge to the now established string-like framework. This only looks like a paradox or complimentary contradiction- I can agree that quantum theory and general relativistic ideas, being a little less emphasized in the pursuit of physics, will not go away either. Perhaps the information goes into the various TOE's in the great external black hole we call the blogosphere.

In the face of swampland (perhaps a more general uncertainty principle if all is Otto-Motl statistics) does a statement, while reasonable in our scientific skepticism, like his " extremely, extremely unlikely " have any meaning or relevance to the new unified physics at all?

Even in the vast and deeper dimensional worlds beyond our ability to observe or disprove as measure, things intelligibly arithmetical at least over infinity, we find alternate levels of dimensions or things like them where we may distinguish what in a group of objects has increasing discrete mass or what has mass of a more symmetrical variety. This issue is a vision of mass that is not that easily dismissed as magical or metaphysical at all- if we desire physics as a primary description of the world. Let us not into string theory bring the same old confusions and contradictions of our ideas of uncertainty and the reference frames as if on steroids- such complexity is a challenge but does not explain the omnium.

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Yes, 'string theory without strings' (or rather, an arithmetic M Theory) is a pretty good catchphrase for understanding the new theory. Lubos will soon be given proof that this is essentially the only possible scenario.

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