Thursday, December 27, 2012
The Fundamental Foundations
L. Edgar Otto 22 December, 2012
We imagine multivalued functions, as with Riemann's complex plane the "jump" of i2pi (provided we have functions that never cross the excluded negative and zero x axis.) But we make similar restrictions when we have more than one solution to real equations, as the square root in which we take only the positive of a multiple value. Thus the Riemann plane is quite an advanced concept (more than I appreciated having not been familiar with the intuitive steps that lead to a clarity of understanding analysis.)
It seems like little progress has been made since then in the search for more fundamental foundations. But in this presentation, blog, I have the feeling I should take time out for some more formal study- I cannot assume that answers are not there in some form already or that mine reach the level that transcends existing knowledge. I can go back and see what little conversation I had with some teachers after high school that taking their comments as gospel were wrong, trigonometry is a lot more than just identities and the details of developing equations not a simple matter of zaps and duds consumed in a general formula rather than the concepts themselves the grueling work of counting.
That nothing has made fundamental change since the awakening to ideas of the quantum theory I quite imagine it is due to the interpretation of our mathematics on a very foundational level- including that of number theory. Yet in our imperfect system to date there is a great deal of power and beauty. Where there is progress it usually occurs when we imagine some systems from different points of departure where ideas are deeply parallel, sometimes to the point we discover new and unexpected connections.
Philosophically, let us assume that we can have multivalued points, that in some way may differ in duplications yet in the same way have a fixed value. This is fundamental, the exclusion of the zero and negative axis is not, also the cavalier duplication into equal but empty shadows of a system and what seems behind a mirror works but is not clear as to it being a legitimate method to apply blindly.
Nature is at its foundations not a respecter of sign. Where it is, or where we can define complimentary functions such as of the log and exponential, there is no reason to think nature is biased ultimately to what is primary as one or the other. Yet, as in the log, again by tricks we impose this wider space into the lesser dimensions, in a deep sense what is concrete in the mirror function (despite the tricks of successive differentiation and integration alternatively and conceptually cyclically...) said of logs may reverse from some stance of nature. Yet, if and these only we differentiate the logs in complex space we arrive at what is naturally restricted to what we regard as the physical.
The problem, and a challenge that leads me to search the literature, is what sort of things happen if we allow at a point the intersection of three kinds of planes- those of the natural Cartesian dimensions, those of the complex plane, and what I call the quasic plane- each of which seem to share many properties of the same pattern and description. As some of these values must be finite between one and minus one, in a world where we cannot so duplicate or have multiple values despite the beauty of descriptions say of oscillations on a real number line, the convergence of the exponential alone will not give us the deeper secrets of things like the ultimate and unified idea of such objects as branes having charge- that merely extends at this time our bottleneck of the mechanics and formalism of our notations which are useful only in the main in small numbers or as a background for our measure of things by mirror-less probability.
Many anomalies and alternative views can be described or analyzed in this new concept of a wider but accessible next step in mathematics, so that the concrete or soundness of such theories may be discerned. So too if concepts can influence our states of mind, the awakening to new eras of such concepts. Consciousness is not simply something that emerges in the higher analysis complex numbers or not. While it is long time philosophy to merge our ideas of the infinite against the finite, such as with Whitehead's process theology, how can the knowing be complete, say for the ideas expressed by Hawking over the reality of the universe, the Omnium, if we say space is finite in time but time is infinite as imaginary space- these in the mind's eye at least wrapped around our heads as a fact of unity and being?
Can this situation be mirrored as an unbiased stance of nature? Does it not hint of speculation, even principles of metaphysics as well of things involving information theory as in the related issue of where that goes into black holes? Can it be that come convergence in the element is divergence in the filament and conversely, this too mirrored? Do I gain anything, having quasically defined the reason and state of nature for the idea of generations where it applies say in quark theory, if at a multiple point there are these brane like creative or existing entities? That is if it cannot tell us how to find unity again in the concept and the nonnecessity of these quasic functions over the omnium?
Have we not concluded there are models that give us a hint of this in the surprise and anomaly of dark energy and dark matter- even with our familiar physics and chemical models we image something like dark fluid? What is hard to imagine is the consequences of such phenomena should they prove in experiment a direct linking as if some shadow that grounds the reality as if the unity is quasi-metaphysical.
It does little good either if we can only see the outline of such shadows to imagine some dark atoms that work in concert without direct evidence of disproportionate weights when the whole dynamic process suggests that in this higher physics things are creative, that in a sense atoms, and by structure and pattern only, evolve. The memory of the previous states of matter may indeed behind the scenes contribute to the idea of mass along Weyl's lines.
Evolving atoms would certainly explain processes that even the reversal of brightness of supernovas could make the higher half of our natural occurring atoms as well the explanation of gamma burst on all scales. A quasar like creative object may disintegrate into many systems of stars as if the materialization of its multiplicity at a point of its hidden yet mirror atoms.
This I have hinted at in my last post of cosmic chemistry and this in a vague form I have considered for years. In the mass extinctions over a million years or so, why do we assume the layer of iridium is other worldly? And do not the planets themselves appear to be formed in pairs as most things, as perhaps the nuclear shells of nucleons?
Clifford was as close in the usual mathematics, as a sort of finite model, the dimensions taken from the power of some number, to my idea of quasics- this quite a challenge in 1995 to my idea of originality in research as well the haunting similarities when string theories reared their heads. Yet, I persisted down a path not as if any of these theories were blocking the way- so why? It must be from a wider standpoint concerning the continua and numbers involved- for the power as a dimension or the dimension as a power can be fundamentally mirrored, and that is not a simple matter of fractions or zero divisions to avoid should we encounter such as singularities.
But such exclusions do seem to make the world work, especially where in its consistency it does seem one sided and asymmetric in the relationship to creative things we describe as if heat of a more general nature to which one sided logs only is not a bad model to suspect we reached the limit of the power of our calculations, accepting some conditions in the world as illusions.
To this end in the manuscript (I am still debating to post as an illustration in the raw) I chose the yod symbol or a simple degree sign as a product analogous to the dot product vector operation. Perhaps this explains the idea of the continuum of a power set greater than the R... not really a paradox, then again Tarski's makes some sense by such mirroring too. In any case as workable as some of our formulas are that apply to systems of physics, If my quasic view is write, too much is depending on our insistence of solutions that have separate formula for the odd and even number in a series. That then an example were wider intuition and speculation may transcend the bottleneck of our established formulas, these not as elegant as they could be, that may constrain us in the symbols that to new useful physics we do not transcend.
Deeper than that, some variation in the basic values like the velocity of light or Planck's constant may not be visible on one side of the mirror as if not things of multiplicity. Why then should we regard a space of h cubed as important as such a space when its boundaries, are described only in the usual concept of dimensions. We cannot really say in matters of our conservation laws that what around a boundary, a quasic one as well, that what vectors and properties coming into a system are the same as that which leaves.
Surely, if the dynamics in this world conform over many regions and scales, and these apply to our phenomenon of consciousness, if this concept of multiplicity is right then vaguely defined ideas like autism is indeed a result of the multiplicity of sensitive gene regions on a chromosome. As such one may debate if this is the cost of survival of the fittest as to if such states of mind are descended into past states or maybe lead to a new and advanced species. If right the ideas can tells us how to heal such problems without invasive procedures changing the inherent identity of an individual while our experiments contradict the intent, and the doing no harm, and no current explanations are to be easily found if in our present state of wisdom they can be.
All of this seems nevertheless to be, in the physical and material applications at least, lesser than the next few levels of general theory now hidden to us of which the complexity of this theory even with no other explanations to be offered, will seem like a logical and natural extension of existing theories done with better clarity- that or in the looking back all we know for the last couple of a myriad of years will seem all to simple, obsolete, and coming so near the future truths. The ideas here, as if an expansion of fusion and fission into super-duper fission and fusion for some indefinite but creative singularity of potential real atoms in a creative object multi-singularity complex, are neither models with the parsimony of reduction nor so wide that the mechanism could conceivably give us access to more energy than say that in theory of a complete merging of matter and antimatter.
One stray idea of which the foundations of counting goes to a little more general idea than that of arithmetic, in a philosophical sense the old 2 + 2 = 5, is that if the boundary of a quasic region (of any natural representational dimension defined by the usual conservation of the count) is the distinct but indefinite boundary wherein to cross it it can be any number of such brane regions in the path and not necessary of uniform or crystalline quasic space pixel dimensions- provided the entry into another region may reverse the usual group signs of things while in effect the object in motion thinks it is in the same place with same orientations- and unlike in the complex plane in a sense it is as well of all such nearly the same or the same coordinate places.
So I do not need to post the notes after all- save perhaps the last entry that asks: Can we store natural energy- matter into the condensed (but of multiple hyperbolic parallels from this side of the mirror) into a dark matter or black hole like object- store information? if so how much more over these stances of natural processes?
Such treatments as I have presented in color and hypercolors relate to the real world of four space as natural dimensions... It would be of interest to do the same thing for the higher symmetries in such four space for the great grand stelleations of the analogs to the icosahedron. But that would be beyond the present scope of the level to which we are trying to expand our understanding.
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