Sunday, October 21, 2012

Elementary Proof of Fermat's Last Theorem (Continued...)

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

L. Edgar Otto   20 October, 2012

We already see, as in the global but suspected nonlocality of computing circuits, that quanta contained as q-bits may be observed across variable scales without a threshold of disturbing the state of the bit and within their boundaries may be transfered between container spaces.   The question then is the finer and finer definition of the mirrors in the microwave probe that contains them.

But in this generalization if we are to insist on a generalization for the sake of approach from a different view in computation, those who take a more continuous group stance (the quasinfiite) in applying ideas of complex numbers, might have a direction to develop with worthwhile effects discovered including more rapid specific computations than existing methods that are already streamlined in the design of patterns to speed up computation as quasic methods alone.

The next frontier of such explorations requires a better understanding of some of the foundations of number theory to the point these are in a sense a reliable ground as if a theory of everything insofar as it relavant to our current human science concerns.

For number itself, from the complex factoring no longer unique in the generalization that makes four space as complex numbers more complicated than the usual idea that some principles and laws are simpler in such space, in particular the first of these is 37.  But in the quasic system as it applies to the gene code in four and eight complex properties of the algebraic system we have this as a symmetric across the quasic main diagonal as the terminator codon whereas Fermat's initiator is 25 all of which begins beyond the space 24 invariant cells.  Note this difference while seeming balanced evokes across the symmetry of numbers ancient property ideas of the division of values by binary halving, that is the viriality in its physical interpretations as Rowlands points out.

In these higher reaches of space with the idea of the physics as concrete living in the top half of the graph that involves zero and absolute values we can now raise the issues of such binary values with the addition of one or the subtraction of one in the superscript of higher powers such that we can know from the ends of a large number some properties without computing those in between.

But, as Singh pointed out these are almost perfect or less than perfect numbers with the overall problem in this general and more or less hyperbolic space of which it is hard to make a picture beyond shadow polytopes at the Euclidean flat and neutral balance (this I intuit in creative object space as intrinsically a grounding of quasifinite momentum balanced but with natural asymmetry. 

Existentially, and  QED, it is clear the scope of the developmental or evolving quasic grid acts at the level of the strength of chemical bonds within each of the four paired bases heretofore controversial concepts as imagined generally or globally for such spaces.  Let us also note the designs in a grid or in decoding that allow us to make the solutions one way easy the other way difficult.  This is built into the reading of natures evolved organisms.

What do we mean then by numbers that are in the difference of powers excessively near and cannot seem to find them...? This is likely beyond the logic at the frontier of this natural difference of hidden mass and asymmetry for example the role of the idea of a monopole or magnetism in general as the last piece of the puzzle assumed as to how black holes eat the momentum of objects falling into them.
What are we to rationally make of the logical design of objects on this level if not wider levels of logic itself?  In terms of mere linguistics rather than emphasis on the finite view of building up errors and math despite the noise all existing proofs, while compelling when understood of the idea of metalanguage are based on this trivial idea of uniqueness of prime factoring thus we need to analyze the primes more so if we are to correctly interpret such proofs, if we are to wade through the noise as if a quasi-chaos to achieve what we have underestimated as the goal and difficulty of unification of our current designs of physics.

I find it gratifying and reassuring many of these principles in my own studies I understood as important and intuitively correct found along the way naturally of which I find so many with these concerns as a new breakthrough in the pointing out of the significance of focus upon them.  Into some new areas on the frontiers of speculation it is a natural result that new territory will be found.  It is also quite likely few can write a paper in the lesser generalization no matter how complicated this is really not original and fundamental more than privious explorers save perhaps to the experience and learning as if new for an individual or for an age, or that age recurring in the scheme of things.

For it is quite at the flatness of which Riemann assumed reached the Pythagorean level and no further or that higher group dimensions were not relevant into the next few dimensions- understandable considering the vast new world of insights concerning zeta spaces and non-Euclidean relations of powers as our usual ideas of natural dimensions.  But this is the reborn flatness that seems to be involved when in fact we logically unify such geometries that stand or fall together as a description of realty- but the next level of spaces, not the mere enumeration of say the view of butterfly cusps as in Rene Thom in four space manifolds, that requires in the unification a deeper understand of the logic of what we mean stands or fall together.  But it is just the flatland of which Fermat had the insight to stand on as a logically, inductively, and intuitively sound basis.

Numbers in the counting may seem magical at first that they fit so well together... so too the patterns they form seems all the more magical or surprising in our time.  It is not a coincidence or artifact of counting that the patterns of numbers, even the algebra of the equations of the pictures, would sum squares of 3 and 4  thus 5 as the ground and that 9 and 4 make 13,  obviously in the symmetry breaking of the 26 in that cosmic string theory...and in the named as magic supposed stability of such numbers in the nucleus of presumed subshells (their naturally in pairs as all issues where it is not explicit or clear what logical method of parity of coloring relations black and white co-exist in higher dimensional lattices.)

In the idea concerning time, tachyonic or even paradoxical aspects, it is natural that at the 25 sandwiched power flatland foundation these arise as a consideration to be explored and refined or resolved until vanishing for a more general theory.  In the flat Euclidean and Pythagorean triple it is clear that excesses in the power lattices that could involve a proof inductively or in infinite decent of the inequality that at the heart of the 4 unit side the deeper algebraic formula (and even in the computation of the perimeter we fly into the four-space to come back down to our familiar space again as if this computation done in some space not real or at least unseen) we have the power of two  ie  2mn with m^2-n^2 summed to the ancient pre-Euclid m^2 + n^2.  Structurally we quite image a slice of this hyperbolic space scale condensed with the illusion of different areas, as in a pseudo-sphere or Escher disk, that at least 2 lines can be drawn parallel to a third at a point- but 2 is involved here in the sense at the simplest impossible equations by zero division two is in a sense equal to zero uniquely for is this not the difference in the sum of subcells in orthogons, 2 in odd dimensions and 0 in even dimensions... but odd and evenness is not the only thing that distinguishes integers on a defined foundational level.

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(Part IV  Some Footnotes):

The abstract boundaries in 4D super space, complex or not, at 24, I call Fermat's razor.

The source of light as a concept, physically or in a sense metaphorically subjective, needs not be dependent on the stage or frame of light, this a statement of non-necessity.

The psychological model of Carl Jung, essentially a thermodynamic model, suggests these subtle differences in the stereonomic geometrical and arithmetical structures along the lines of logical balances is an intimate connection to our ideas of thermodynamics including a breath of extended grounding for synchronicity over some interval of time much as observed in such mysteries of quantum principles.  This of course begins with the description of heat flow in relation to complex number spaces over idealized planes that synthetically amounts to a division in an equation of the real and imaginary parts.

From this view the steps and the proof of Fermat's Last Theorem as worked out in its multi-page effort covering a wide variety of mathematics and the parallels of some of the mirrors of methods, for example the elliptic questions- all of which on the more general level are in the fifth operation in arithmetic at the raw structures involved at grounding and unifying or resolution of consistencies, these a higher order dialectic as if thought too can be so described thermodynamically along these lines- so reduced then and quite less general than the nature of space quasically envisioned... reduced then these mirrored real or virtual forms that naturally begin with subtle differences, the take or put as active and the lose or find as passive as the logical possibilities refined then to the intellect and intuition to which the science, more certainty in grounding or not as a working mathematics and symbol system balances with sensation and feeling.  All such models may be limited in application and computation of the states of mind thus debatable as to further complication of such dualities and dimensions and the presumed higher reaches of the idea of symmetry or color.

What I have imagined as a dynamic process I call teleoscoping intuitively a physics principle and arising from consideration of organic DNA code patterns is also the mathematical aspect felt needed for that more rigorous grounding as logical certainty of laws presumed. But I realize as I translate and compare it to existing concepts so applied in the invention or discovery, the noise and count, information and meaning, the time and temperature of our ideas of entropy and energy is a property of arithmetic itself to so be resolved into the still unexplored, evidently symmetries as applied to say replicate tiling as in quasi-crystals in the steps dealing with the effort of recovering memory or laying it down as a steppingstone in the proofs with mathematical induction not in the endlessness of the infinite but in what Singh in the book calls the compromise of clock time in the heat from computations, the spectrum also reduced of irrationals into a circle...

In string theories it is the partitions that also limit the defaulting themes in a stereonomic dimensional structure I maintain as the grounding choice available in all the landscape (and in the book the mere exchange of such strict symmetry of two of the 10^87 said numbers of particles in the universe I presume is the logical possibilities along the lines of Eddington's vision, the matrix as the physical description of the observable universe and its mirror shadow in the continuum depending on the axiom of the velocity limit of light. 

The focusing of these non-linear possible structures that we ground the particle zoo is in a sense a physical quasi reduction of similar counts, an intermediate teleoscoping so to speak which philosophically does raise the metaphor of teleos or purpose with a directionality or even continuum with irreversibility where that stands out and seems to apply that is grounded more generally into the stratosphere of our dark matter metaphors.  The definition of numbers, such as the nature of division and subtraction, its idea of fractions is after all a sort of space or landscape of such clock looping and precipitating teleoscoping of which we can imagine the idea that in the physical processes at least for organic systems the idea of sentience as well as life physical structures given the thermodynamic space will inevitably everywhere at least potentially arise.

But we cannot just assume a limit to these emergent processes so implied as participated cycles isolated and independent of the simple idea of multiverse and many world totalities resolved in consistencies or not- we can try to understand it but in general, and even as a physics of statistics of chance, the emptiness if every a true vacuum in the stratosphere tends to participated around the material atmosphere as the deep parallel logic of all such groundings.

A little distant in contemplations on numbers it appears that although immersed in the seemingly obvious this pattern of numbers is as amazing and deep in concept that challenges us and drives our light of enquiry as we can more easily from that breath and safety of the repeatable and real if we are strong enough to look into it at that unknown vague sense we may feel about an absolute nothingness as if it a certain ground.  The idea of sensation in this breath of contemplation as if a spacious surface, a skin over the bare structure of branes and black holes suggests our ideas of sensations go even deeper into the freedom and emptiness of space than mere mechanical and imaginative methods of perception have considered heretofore, thus beyond the now familiar idea of the strange logic of quantum and other elaborate and advanced theories.

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