Tuesday, July 12, 2011

Reading, 'Rriting, 'Rithmetic, and R^3

Reading, 'Rriting, 'Rithmetic, and R^3
L. Edgar Otto July 12, 2011

Let me start by showing the links to comments on Lubos and Pitkanen's blogspot posts today (I really should post before I read them as the ordering of thoughts can be distracting and it may not show how our themes touch synchronously in a given day. Our languages are so different and it is quite an achievement really to even grasp some of these abstract ideas of which of our theoreticians we should all understand and be justly proud of our expertise.) But who are we to imagine we play God or are God-like in the careful husbandry or even conquest of the world by science? These issues are in my review of the scientific and philosophic continua page the issues of what I called the Theotericontinuum and its paradoxes, but that needs fresh contemplations and speculations. The page on the quasic graph theory perhaps shows something we cannot find or see without other pictures as forerunners- so this does speak up for these pictorial methods of the great human concept of higher dimensions. Not to say the algebraic approaches are less important- for Kea's way has the same essential idea to ground certain aspects of ordering needed to better define the arithmetic of things and the idea of the special role of both translations and the phase angles and signs of the determinants unto the dimensions and braided spaces. This for me is the apparently linear but complicated ordering of the intelligible and unique logic and such.

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Matti :-)

I had to look up what Bourbaki was but I agree with your analysis and that of the evaluations of it in the link. I find several areas of which I would be in direct disagreement with its style- for us the inclusion of topology and for me in particular the possibility of pictures.

Lubos has a most interesting post today (for we are all three concerned with this issue) and it is a different language again as mine where certainly such languages are incomprehensible to ourselves (few can be fluent in more than one language).

Your persistence to our purpose will lead to a long life bypassing the third part of our gene. The 1100 or so maths are wide but not devastating. There is time enough for one language of these notions and the wideness is life giving just as much as our stable relationships with others.

A little bit of worry is a good thing, but in moderation.

Last night looking at this problem again I see as the same sort of frontier notions I may have shifted my thoughts on such summations and clearly each of you theoreticians here have a part of the ingredients in the new physics bigger picture.

The PeSla
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This post has very important ideas relevant to many areas and lately I have read such ideas gently whispered by others like Peter Rowlands. I like your take on it and that you see the importance. That you also see there is more to these ideas of symmetry and dimension than just the complexification formalism. The use of 240 in the equations (which indeed stand out regardless of the language, as well as the essential Diracian 12, stands out regardless of the spoken language. Of course this relates to string and M theory ideas- and these a stepping stone to more. I am surprised there are physical experiments to find some of these values. Oh the deeper understand of what we mean by vanishing even numbers- right on!

The PeSla

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So, I may wonder if my Teleoscoping idea has to be less fixed as a concept- and thus maybe a more useful concept in considering new ways to see these questions of information as the area or the n-volume. After all the idea of symmetry as invariants does seem to suggest (as Lubos boldy asserts...there just "is" and no infinity here) some sort of closure or vanishing or normalization with and of infinity, but I do see a sort of shifting symbol: |{ or C cleft of the information as if a quasic multiplication for a wider field of vectors) of which we clearly have a difference or limitation if we see things only in polar phase terms.

Turns out all the ingredients in my post were there as I said all the notions were there in our existing maths if we but look at them. My surprise is that we can with such worlds of shifting infinity matrices find the influence, numerically and intelligibly so, of my notions of the Conway Cw sorts of grids.

The main problem with these special uses of planes is that of translation that can be outside the description of what is dynamic- a vanishing into the flatness of things... that and the defaulting into loops of what seems to be an arrow of action. For we simply do not have, yet do not supersede the notion of vector and scalar spaces, that is for any R^n x.x = (sums of axes of so many natural dimensions that of course relate to the reduction by ideas of the triangle inequality). I mean that the nature of dimensions and of R^n is much richer in structure than we have dared to imagine- in a sense, and as a caution to theoreticians, it is clear to me that these are good working mathematical models but sometimes the establishing of these as proofs to aid in the work to be done in corollaries- carries over to the whole system of some limited totality but self referential vision, all the fundamental errors.

In the particle physics, at some pixel of unity- it occurs to me that the essential starting pixel or quasic unit cell plane (after all we can have symmetry breaking that is natural and neutral and thus we can show it to be an arrow of occurrence as if in the deeper dimensionality it is spontaneous after all as in the string theories in a dynamic manner) Is not the upper corner in this unified quasic and arquasic grid without an underlying grid - a null grid as we imagine in the first place (so it does act more Cartesian in general which we should expect where so much of our physics and its mathematical pictures work out well) but one shifted down into these abstract and non-degenerate Conway fields to so shore up the notions of group and set symmetries of these even more abstract dimensions. In any case this should be true where the biological codes apply. This is a predictable evolving of our higher insights and debates as to particle theory that made the distinction between partons as such and quarks- for this establishes what sort of particles and their mirrors may distinctly carry the color force or technically exclude it for example.

Yet, as a principle of the paradoxes of non-necessity, I still would like to work out the dials of these interwoven infinite and still singularity dimensions with the realization it is the total picture these aid in the computations and dynamics- and that as far as the establishing of a unique theme in the centered music the falling into loops outside the logic of the context is after all an advantage.

Let us not forget that in this sort of factoring and a more x-ray vision of how vectors and matrices work may ultimately and abstractly exchange what we mean by those sums which are continuous and those discrete. It follows too that the Cw matrix can be in a sense deep into some level of the quasic theory or any normal matrix theory which is intrinsic to space and not just a skeleton for its description in the sense some state of it crosses all the quadrants, intelligibly.

I guess one cannot solve a problem that we clearly do not know has no solution when we get to a bigger picture- yet, is it not in a sense so solved?

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From Astronomy Picture of the Day I found this most interesting link which reassures me there is a wide field for workers in scientific enquiry and that there is a welcome complexity in the world to explore. Interestingly, algorithmic ideas have come of age when it was not in the topic of the mathematicians Matti mentioned today.


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