On the Consistency of Matrix Methods

On the Consistency of Matrix Methods

In an earlier Lubos Motl post in taking an overview of string theory he pointed out his concern with consistency in the theory. Of course this is also a discussion in general on the logic of things, consistency and completeness of Godel.

I often regret engaging others with my quasic theories- that is developing them in almost total isolation and in a sense losing my innocence of play and world view.

I hope my remarks have not made Ulla angry for any reason, that was not my intention- nor ever with anyone to discourage enquiry and objective criticism. But she raised some interesting thoughts at a time when I see Kea's work as growing interesting indeed and my own caution taking a new look at the problems- said to be solved in the next generation, indeed, of the M and Eternal Inflation cosmology.

She insisted that my mention of a benzene ring of 7 carbon atoms (one in the center) was an incredible idea that was not the case. I recall, way before the age of computers so prevalent to the general public, an article that such an arrangement of carbon was achieved in a laboratory- and that in the large dusty books on organic chemistry some such pictures were listed but only in case such were discovered as they had unusual symmetries.

I searched the net but found nothing. It seems that there is so much on the new forms of carbon chemistry, that so amazing, that if it is on the net anywhere it would be buried rather deeply. Any carbon chemists out there care to enlighten us?
Perhaps if true it could have some interesting uses or sources for new theory and should not have been a forgotten experimental result.

But I hoped Ulla was right and I was wrong- for so long has my work seemed consistent and not fallen totally in worldview for half a century- to be shown an inconsistency would be a refreshing experience and a good cleansing of cobwebs.

She goes on to say there is nothing there in the ring- and apparently things that I have misinterpreted what Kea was doing. Thing is, I am not sure what she is trying to do from my methods of mathematics. We share some of the same results and methods even ones I understand but do not think was the best way to develop things like the Fourier and the ways we try to say the complex numbers apply.

Yesterday, after seeing her post, I half expected she would seek the higher case which I assume that is what is meant by the 248 dimension. I include the chart I was going to earlier- thinking that the algebra of it would make a short project to solve the higher problem if such a structure was not the answer already. But as I am only familiar with my own excursions and had not finally found the relevant validity in such a space, and we have some vastly different terminology, I just could not whip off a representation to post as a solution. But I wanted to know why I did not understand this work of Kea in totality that "even a child could understand".

So it raised some philosophical questions which I thought would be an interesting post for this creative blog also part of philosophy. But when I thought about it a little more the answer to much of this seems to me right under our noses. In particular we are considering the differences of mass of particles of which as far as structures are concerned they could be symmetric and the same. The first example is the recent interest of more compact planets (not of equal mass nevertheless) and what it means in a general law of the formation of solar systems (of which others too seem to consider Bode's law again where solar systems are views as highly variable- certainly not my early idea of the planets created in pairs.

The other obvious model to hint at these structures is the atom itself, it uses KLMNOPQ if taken to the 5! elements only in a sense the NOPQ are internal and hidden. In general there is a symmetry difference in the duality of structures that results in a sort of nucleation (here kernels of the chemical properties of atoms- how do you explain XeF4 Ulla?) In any case I am not sure this is a question of the division of space, at least continuous group space, into imaginary mirrors. But in any case, according to B. Diaz on the octet nature code in the appendix of Rowlands new book of which I read and understand this notation last night- I do not see the world as a division between spaces involving diverse edifices as to orientation (the 101 question Stasheff asked me to determine on what level of topology I was asking my question.

In the diagram above apparently we have to double things, KLMN OPQR and then find that left from the 256 for the 8 timelike ones included or excluded. But I hoped it would be a better matrix of simpler forms like the 28 somehow instead of merely the assertion of duplicating things justified by ideas of complexification.

n!/(n-1)! = n after all. Are all diagonal matrices not a Jordan block matrix?. So the spacious center of such things be they some idea of the infinite or of emptiness, perhaps taken literally as mass, little solid things that face the right way with a little bit of emptiness between them, are not classes of numbers or multidimensional singularities and so on- but solid balls to count of some sort- a finite view in the endless extent of continuous space. Of course some also are not comfortable with there being any absolute nothingness at all and that solves a few things emotionally, as would say forbidding the infinite regress or looping things back in recursive, and yes complex, fractal structures.

Now, in a matrix, one that sort of reduces down to some representation or compass of concern for a choice of particle structures (with or without the representation of color RGB or CMY (one way Rowlands also suggests we can label things) it is a matter of the columns that multiply by the rows for some twists and answers. But in my system already it is built in that the f and change of coordinates if they are to interact already have this property of (an at the same point and time too) of merging the multiplication aspects with the addition ones. In a sense the f motions are after all binary or intelligible or meaningful sums of binary at a point.

The difference, things centered like we do those six dimensional spaces compactified, and my notation is subtle and with both being useful and consistence in addressing the unknown (of which how can we really declare the negative of some case before a certain point of complexity or understanding?) we should look for a more general picture and one that does not fix our methods and world view where they can be different. Some issues are not there which are the concerns of others- but of these we should know why they are not- if we can. The anthropocentric issue raised by science as merged with metaphysics is a good general concern even if it is the eventual case but the defense of this or railing against it should have a better basis of how we understand the various algorithms applied or the cosmic (natural) codes.

It is clear to me that my 4D chess game of years ago is the representation to apply to three space graphics. Each is consistent. Each is subtly different. Each has its utility (and as with the first illustration) there are better methods and faster methods for such programming.

I use the word ultrafinite, it will do for now, not exactly what I meant other than the ultranscontinum-finte issues raised with the Ekpyrortic and M clashing brane worlds. It is almost a statement of the consistence of all or parts of arithmetic and as such leans toward he intuitionist view.

But what does it mean if we are consistent ultimately, the human personality seems to me much more diverse than the countless string theories- it is an interesting drama and the paths to reach some real conclusions are interesting in themselves?

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But as much an emotional reaction and rant as this seems I leave with a positive note for those invested with interest and inspired by the sciences. The idea is consistent to some extent as a democratic theory that scientist compete red in tooth and nail- but when a final truth or consensus is reached the greater purpose has so many fall behind the new theory.

Ulla posts that my links on the latest news on DNA is a source of inspiration as well they are to me. She has a knack for bringing to my mind relevant and interesting links too. She has loyalty to her sphere of friends.

But what after all is the consistency of things in a physical sense- Imagine a proton as the WMAP surface we see as if that is the totality of the universe and a theory of everything- at least for our place in the big picture and in time. The past if it is in a sense there at all would be the whispy interior (or at the beginning of higher space structures where all the non-Euclidean geometries that apply then differentiate to more exotic shapes) One is consistent but if one falls then logically so do they all.) the consistency of every variation of time and space toward or away from some center or new beginning- In short everything past and present in infinite detail for our unified theory of everything. Alas, this is but a dot on even our simplest visions of a multiverse. Conway erects a continuum on every position or point on the number line, and every point is a multiverse- even a multiverse of multiverses with all the perplexity we have not but begun to work out or accept- even if some representations (we being a long time creature of simple familiar mass and three space) and as always this idea of nothingness or emptiness on one hand and our voices shouting and drowning in the indefinite immense unknown. But the density, consistency of physicality is a model that in its complexity simplifies to itself- moving to everywhere an nowhere, self- perpendicular its mysteries.

So I come again to Coxeter, amazed that his program so long rejected is mainstream- what is not found in Coxeter is something I sometimes feel? So, on a deeper level Ulla's question is quite inspiring and important. What after all is in the rings of the bases- nothing? A place where electrons have zero probability of being- a transmission from base to base in the DNA as if stacked their aromatic properties? How are we to regard such transmissions that seem to move thru the nothingness and made of nothingness? Are we forbidden to put something in the rings so as to count the structure there as deep and comprehensive as such topologies on a higher scale? Of these hints there are things to find along the way which are the proper field of science first and foremost- whether the structure and time are ghostly or given and we can see enough now to seriously begin to consider, even ask such a question.

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I want to add that as complex as my illustration looks, and of course we use the hexadecimal notation of Baez here also. That the overall general picture to put this into some sort of matrix and arithmetic may turn out even more complicated- that is if we do things like square things all around into even higher abstract dimensions. Of course those working in such large dimensions use very high numbers routinely.

I saw the link of Kea on functors- what a basic word not to wonder if I understood it. What an interesting path to take just as the one that considers those parts of numbers related to the path of associiahedra. Some of the number or topological classes in classes are real enough and seem to me to be the next step of these sorts of descriptions.

But what sort of matrices does it take if we regard some position or pixel in a quasic space as a brane itself- that is not just a simple question of two of them in some sort of coherence and clashing? What then if in such a brane there is so much of these abstract concepts of higher dimensions anyway- how do we begin to find the proper general algebra to put into matrices of some sort that not only finds the restrictions and directions of paths, but suggest some sort of unity of coherence and path differentiations, and dead ends, of such multiverse of multiverse becoming our comprehensive unitary ground of the real and common in our experience?

The sciencechatforum com today has a programmer who asks a thought experiment question of course in computer space. No one seems to reply to him that such a thought was addressed by Penrose in his contemplations on "quantanglement".

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Happy Enquiring!