Saturday, October 20, 2012

Elementary Proof of Fermat's Last Theorem

Elementary Proof of Fermat's Last Theorem
and Physical vs Logical Quasic Living Space  Atmospheres

(Part I  Reason and River)

L. Edgar Otto    20 October, 2012

On persons romantic notion can be the ground for another persons routine experience of certainty.  Somewhere in between, sandwiched in the operations and mysteries beyond one and one is two, the coating, the skin, the breath, the atmosphere where life or thought, is possible- between the geometry of dimensions and numbers is the vertigo of our sensing, awesome respect for the design of the world, and the questions of beginnings, end-time, and the Fall.

But science and mathematics itself can be perplexing and paradoxical in design in this manner as we gaze upward to the skies or imagine something downward beyond the solidity and emptiness our stories and structures as if tall buildings, pavilions of trees confused with castle towers in the  landscape as if in reality there dwells the denizens of our dreams.

Parallels develop wide diffences between language and nations while these come back again to the simple unity that one persons certainty within the powers and primes unravels that similar to another persons and in the lesser creative role as the totality too the source of motion and light, science echoes the role of certainty offered by faith in religion to which if flails itself before the workaday explorations armed by the working hypothesis that the logic once discovered does not change at the foundation as law seen as ubiquitous on which the mass of commerce and civilization builds and to which so many feel alive in the battle to dramatically take on an angel, play chess with some soul hungry one, honor the sacrifice when the town and gown together can put you in the goal if only for the illusion there is freedom and for the entertainment for gatherings at the gladiator games.

A bridge between the isolated dreams of the thousand islands of mathematics once built solid over the shallows and the shelf so long we cannot see the end of the causeway nevertheless, the bridge itself is then indistinguishable from the solid ground and the islands save time and effort for a long journey although not steep the mountains of learning.

I gaze down the river itself from the concrete and metal bridge, the river low and the old pilings poke thru from a hundred years ago when Ginny Whipple the steamboat brought things from distant place and  away such as paddle boats send South the young and glory hopeful soldiers.  These pilings in the center of the river were places to tie to against the flow.  But what is a river but an island as the Native Americans so imagined, out of sight the next oxbow is a different place and village, and the river is a road?

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(Part II  Foundational Views of Genius)

Evidently, within the potential diversity in its development and freedom of enquiry in a mind there is a fine line or breath of space more defined and focused and contained within bounds as to what grounding principle is profound or what amounts to triviality, the tinkering with the world or with ideas we hold as models and as a consensus, reasonably and scientifically apparently, as genius.

In particular what mysteries and miracles seemed exposed by the inventor pragmatically at least may be seen in the ideological interests of a new state in its beginning as genius.  Or in a sense of social genius as the contemplation of self referential disciplines of intellect the Olympia and distant realm, the image greater than a truth, or the hopes of some truth worth the social investment as a cost benefit, a gamble and insurance against decay and true scarcity, beginning with the priesthood in the isolated goings on of Pythagoras, the highest and nobelist goals of such a gathering of minds may decohere from its golden age and the power of the priesthood as distant and empty as that accrued by the great sultans persisting while hidden the corruption of their courts.

We cannot then judge the truth of genius although we can speculate on all sides of propaganda, social concerns reduced to pointless marketing and advertizing that in reality no one heeds in this abstract battle of logos and flags.  There are subtle philosophical slogans or saying to which we also give the benefit of doubt as worth the risk of something at the end of an interval of enquiry that so justifies the hope,
That some of our prophets and law makers are experts on the way. 

Such sayings as "There is something of the child in the genius" - that fine distinction between childlike and childish that at bottom speaks of the physics of beginnings. Or in the economic realm as a basis of politics we make the subtle distinction between egoism and egotism and all the religious and psychological stances that tries to define a self.
Philosophers also in the atmosphere, stratosphere for the not yet enlightened, consider that between eternal and everlasting of which the common sense mixes informally as one idea.

What then of Fermat as that in his state of mind as true genius rather than a lifelong hobby of numbers?  What was he thinking in his relations beyond mere proof and certainty of such speculations in the margins?  Was his pursuit trivial or profound?  Some hold him as a minor mathematician while we could say his will lead, as the concepts appear magical and genius as they are beyond the concern of the average man of the day that some see him as one of the greatest of mathematicians. 

Ramanujan, in his simple sensitivity to numbers, that we intuitively as children learn as if to touch them in the counting on our fingers, nevertheless in depth, in the logic, they hold him as a model to the children of genius.  Gauss and Riemann too are of a profound and leading the direction realm of great men but they too seem to see deeply into and ask what to many can be seen as mundane and trivial-  Let Einstien be seen also as such a genius to so consult while his is more a mystery of the view, the Platonism of the likes of Godel of which this can when at least partially understood gain admiration from the masses.  But such genius is of a different quality and is grounded on some simple idea at the source of a beginning- what then was Fermat thinking when he put his great claims and puzzles in the margins.  Do we really find his intuitions verified?  It seems so, but on what fact elementary and right before us gives him such intuitive certainty?

I find myself, in this vague world of parallelism, making the same sort of conclusions at the foundations of number, see others following similar paths in wide directions, see the gain in ideas and new areas of math along the way... the islands we inhabit of our isolated musings in this world at least seems to have a common unified thread or theory to which the distinctions that persist between them. One mans focus is anothers tangent and developing chaos at the heart of what is possible and may not be proven or unified in the alien bridge between people made of touch and ideas.)  But this is perhaps beyond the idea of genius, more like the chance ground, the choices, and the long hard work that as creative we find the source and foundation a shadowing of Love.

Yet in these speculations and tangents a wider theory is there that we may so analyze and bring to science, possibly, the certainty of mathematics, at least as steps on the ladder along the way.  In what stratosphere of our unique minds and intellects can we safely ground the how and the why of our thinking?  What was this sort of genius, Fermat, thinking?

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(Part III  Certainty and Uncertainty in Numbers as Stepping Stones Building Thoughts)

What then is the picture; the algebra, arithmetic, and geometry involved in the quasi-certain principles that finds parallels in what Fermat was thinking and feeling for him what was recondite in numbers as deep mystery so to make assertions and claims of elementary proofs?  I propose the relationship to my subtle ideas of quasic theory especially as it applies to the demonstrations in nature of our organic codes and the issues of symmetry and end-beginnings beyond the usual and from a finite basis the ideas of complex numbers and parallels or deep bridges between and unexpected landscapes and rivers of our mathematics.

But this technical part of the posting will be continued in the next post... it suggests a proof of sorts or a wisdom to better understand the integration and differentiation of organic entities, like ourselves.  There is more to four space than in its great complexity meets the eye and the truth of Fermat's theorems stand universal to science as we now know it.  The technical part, for the record, came before the social speculations and in some cases developed from a few terse scribblings. 

Inspired by the reading last night also of Fermat's Enigma by Simon Singh I causally pulled off a shelf in the library for something more than computer texts to read... in it I saw more, and after all this posting understood more, of what I read and of what others in the various alternative physics think they have found in the higher reaches of physics as number theory.  Especially it seems obvious to me, even without quasics. the idea of 26 as the unique number sandwiched between a square and a cube is relevant to the elementary proof... but consider this you Einsteins, 26 certainly comes up in interesting places like the base of the Beautiful Mind Nash in solving singularities- and its place in some string theories.  But let us also realize that with the issues of viralitry (twoness and so on) Fermat may have envisioned these things at the bottom of the Euclidean flatland as powers as geometric figures rather than just algebraically- thus with the quasics we note the general logic of our still ill defined dimensioned differences.

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