Thursday, January 10, 2013
The Sound of One Hand Clapping and ( The Foundational Theory)
The Sound of One Hand Clapping
and ( The Foundational Theory)
L. Edgar Otto 09 January, 2013
What we experience or perceive up to the remote, ideal Euclidean plane at zero and null abstract vector seas of singularity, as we may argue there are really no dimensions save by imagining them really higher or lower that we immersed in that space may see such as embedded or forever distant as the world's foundational grounding, the higher and lower if the distinction is made and the choices of what is defined as external or internal with general logic and functions multiple in one direction and singular in another, we may find the plane we see is but a half or flat and single sided plane.
These are deep issues of chirality which I understand it of importance in differences in physical space that seems to determine what exists beyond a state of balance as matter. These differences may be related to the general idea of distance as measurable between pixels or points in a quasic plane (Qs-brane). Or these differences a general space in which by virtual of collective motion the bulk of mass arises.
For we imagine then that the zero polytope (the dihedron polyhedron of two faces and zero volume) if on it we draw a spiral as if a moving form, a loxidrome to the poles of say a Riemann sphere oriented, the spiral turns in the same direction in the sense of handedness as does a reversal of a helix as solenoid. The reversal of the chirality of the spirals we may assume flip over as some boundary of the complex Riemann plane holding this principle significant to explain certain directions of theory- alternatively they may persist on either side of the half mirror as in the magnetic orientation of electrons in the subshells of atomic structure as viewed from outside in all directions as if a perfect spherical system.
So the expressing of this duality as an unfolding of the dihedron into half planes or 2 pixels in the quasic grid, a domino with one double side area and no volume (the distinguishing of this case gives our mind's eye clues as to the nature of the terrain and dangers in the landscape as well as models considered in our dreams, perhaps system of conscience as well as ability to respond and evaluate art and beauty.
But let us recall that the quasic brane having zero abstract volume may really represent n-dimesional division and not simply the prime two in all its continuity of mirrors and powers, presumably where finite can be an intelligible arithmetic and a consistent series of algebraic formulas.
Given this much and trying to imagine or view into the depth over a bounded span of quasic space we find the same thing true as in the geometry of dimensions where we imagine given a series of limits as fractional dimensions that a path may so fill the higher dimensional space it is so inscribed within. In particular the functions in eight dimensions in terms of a system of twists already fill 8 space in the singularity null sea regardless of the sense of the chriality provided we view things from an ideal center as if from the outside (we go on from there to a descending filling of spaces at that mystery still not clear of nine and more dimensions).
This core concept helps explain the patterns in number theory and the self dual 24 cell in four space and its natural toroidal aspects as multiplicity, even triality of the 8 fold recursion of patterns (to which Ramanujan seemed to have insight on the nature of such quasifinte integers as well as the role played in describing not only the well known continuous laws of calculus but the simple yet perplexing nature of what we find as the finite as not a grounding view or just a one sided if not trivial view to established mathematicians. Weyl may be somewhat of an exception here in his scope of considerations.
In any case, again in the counting of these abstract and ghostly integer like entites, for example what we call the time or time-like dimensions, the abstract centers do not necessarily obey our usual concepts of evenness and oddness in the description of connectivity- nor in negative spaces can we simply alternate things distinctly by the nth power of minus one multiplied where needed in our equations.
I look then toward the possibility of current theoreticians as to the evolving direction of our shared and private projects finding a shared insight as a hypothesis with Kea of New Zealand that one possible solution in which our theories of physics may be more unified and thus in a sense have a progress of at least what to each of us seems or is a new physics or discovery, is that of the Surreal numbers, the long developing calculus wherein it seems we treat irrational numbers (I wonder if these can be distinct in some theory that we know or not at what fine extension these are transcendental) such as the square root of two as rational.
I see then someone in the future, as the teleology at least does seem to allow a rebirth and connection of our ideas of merology, measure, explicitly. Yet philosophically we by the natural structures of the world have to go beyond this view of it as if in a reasoning in a rather confined self analysis as if a concrete flat land- the deeper into the infinite earth the more dense it is until we find past the sea level bounds the idea of hell, of more and more infinite heat. Such syntheses of our reasoning freely and nonnecessarily conform to what we imagine the most general laws of reality, and frontiers or limits of what more we may imagine.
In this future project, possibly obtainable with existing mathematics if we include some of the ideas still said not understood of Ramanujan, will be to consider the measure in the abstract space of such quasic brane distances (that is over the general stance of the reality as if the sum total and variations, the Omnium - my and Penrose's term which by the way seems to me a little wider than our pretensions of theories of everything) such that in the general integral abstract values we find the digits of the irrational number to some level of accuracy explicitly of which to have some standard value of things like the fine structure constant of which in the detail of the measure it is neither 137 of Eddington nor an ideal dimensionless value that may as well be an integer anyway as he maintained. In a sense we really do not have other than by definition an explicit value for the velocity of light as a standard measure.
I hope moreover that in the wider interrelations between such mathematical entities the refinement makes intelligible and accessible sense in explicit measure of abstract mirror shadow counting and encoding. Quasic motion laws supply the general geometrical model for this. It should be emphasized that the golden ratio is very special and useful as a key measure in four dimensions as a number, the inverse of 89 in particular gives the digits of the Fibonacci series as would other significant quadratics relating to integral numbers.
We do need better notations for some of the more general ideas such as factorials, exponential, and what I call recondite theory from the remark of Fermat on what Gauss does with modular numbers and quadratic reciprocity and yes on higher levels beyond the scope of the general discussion in Gauss's presentation he only remarked upon.
I think it worth saying again that practical uses of these new theories will certainly be to aid our understanding of the complexity of things involving our organic chemical systems, DNA and so on that narrows the burden of blind experiment and unforeseen consequences by our usual methods. That science meets these abstract consideration of physics at the foundations and already we find new ways to literally see the universe at this horizon of foundations.
While this suggests within our universe we need not appeal to vague mysticism, in the freedom of the wider logic with a wider generalization the foundational theory is not closed to the possibility of radical new discoveries we have not even remotely imagined of concepts and technologies, the mathematics of it all open to a better grounding of our ideas of our current use of numbers as systems embedded and defined by a metalanguage.
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And the Foundational Theory
I suggest that some of the issues we find difficult to explain in the fundamental theorem of algebra in relation to the complex plane,
a shifting toward the periphery of a central point to which there is one mapping of a polynomial to it and of which any point on the plane so limited to the idea of a fixed span of integers of a certain finite value with the intuitive understanding that these can be many-fold closed twists or turns,
some such higher analogs to complex (two, four, or eight) spaces that can be many-fold or in a vague meta-space have no such polynomials that correspond,
that the fundamental theory does not immerse us into necessary proofs, contradictions down a path of reasoning,
nor a grounding closed of such symmetry applied to three space in terms of scalar plus vectors involving a zero point so limiting higher ideas of symmetry (or even a virtual duplication of the algebra say of quaternions as with Rowlands this as developed intelligibly for nilpotent Dirac algebra)
that more is there than the symmetries imagined to vanish in properties at eight dimensions, octonions, a new generalization of the number and counting idea exists wherein with what haunting similarities we seem to find in parallels of our theories so to encompass and internalize,
claim them into our focus of views explaining or dismissing others as but a lesser analog to our perspective held a theory of everything to the point we find paradoxes of open or closed processes of identity and unity,
we find beyond Eddington's Fundamental Theory and beyond that fundamental in algebra and geometry, the Foundational Theory of the diverse and deep connections where they apply in mathematics as physics over the universe as the Omnium
with influences of non-necessity as paradox in the null potent singularity count that grounds the source and intelligibly of creative entities and objects that persist dimensionless as quasifinite monomarks or monads (See Eddington and Leibniz) grounding interactive levels of the reality where we can imagine deeper laws of quasi-conservation and action...
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A lot of this is a deeper foundational consideration of nil points in our methods of the usual ideas of limits and so on in analysis... but do these points, of convergence or devergence expressed as some series as in exponentials or logs act isolated as a single origin or do they act transitively over a space or sea of them? In a sense since from the discrete view we deal with the unity of some interger, we may ask the same thing- is there but one unique prime point or number or many of them that grounds the reality of mirror fields and particles over the evolving structure and order we interpret as a property of our universe? In this abstract realm of reasoning it is not necessarily the case that in mathematics or physics one instance undermines the propositions of the whole- nor the lack of any instance evidence there is no general and unique phenomena over many or one unified theory.
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