Tuesday, June 5, 2012

The Arithmetic of Symmetry and Dimension

The Arithmetic of Symmetry and Dimension

L. Edgar Otto    05 June, 2012

Debate in physics theories is more about or philosophic interpretations than the mysteries of the universe, what seems some perspective that corresponds to facts.  This applies also to what is intelligible even as a questions we understand enough on a level so to ask or note the lack of answers, or to persist down some direction as if it can reach what we only in doubt can imagine an answer as a goal.

Civilizations rise and fall based on how philosophy becomes our general and personal core values, let us style this "states of the creative theater".  Rome fell by its philosophy as much as by its conflicts or lack of wisdom by the cycles of nature, such as climate changes man made or natural disasters.  Among such artificial ones, intelligibly, are our models of economics.

A the frontiers of golden ages we are closest, if vaguely at beginnings, to raw and unbiased data, the creative intuition that is at the heart of the scales of our absolute and applied existence.  We depart from this, the superstitions as well as the states of fact, forgetting the core of our foundations. At such a place what we hold as fundamental in our base axioms of a theory persists over a theory's development until the end changes ability to view things or it fossilizes into a mature truth- one of the blind who forgot the grounds now buried too far to review again.  But nature has a way that such beginnings may come back independently to unravel ends- this is the philosophy behind the stuff of some cosmologies.

In the long run it is unwise to dismiss anyone who offers a breakthrough in the clarity of our faiths and reasoning- not if we think creatively of ourselves, not if the audit applies to total systems in their creative accounting as well as the people.  At least the governments of this world should be more vigilant than such groups with agendas interpreting the flow and fixity of figures.  These general philosophies of stance or states about ourselves and the universe were once bundling such diverse ideas as oddness and evenness, left and right, male and female at the dawn of Pythagoras.

We have different ways sometimes on the frontiers of the sea of wisdom to express the same or similar things.  The arithmetical and topological ideas as physics, for example the beauty in the concepts of such as Pitkanen, can reduce to frontier and general principles with further depth and generalizations.  We can deny this approach as well and that part of the philosophic picture.  But the physicists who would claim the theory, short of some decisive experiments not forthcoming, who have not done this from arithmetic and geometric principles, have not done it as physics.  In the mysteries of number (or equivalently the ideas of symmetry and dimension) they have answered and tend to use as a matter of practicality in a world of their boundaries of intelligible change or enshrined uncertainty core ideas which even among this generation of number theorists are not solved or grounded as clear and established facts or even goals that may be evaluated as to the the reality.

In the face of the idea of quantum computation it is clear that we have to add to the span of the intelligibility of our core axioms.  It is not enough for encryption to have a dialect of which column in the modual residues some sequence fits in. In itself quantum computation is as a physics too vague and idea for the intelligibilty of the reality of the worlds natural design.  Technically a mechanism like this would be an achievement and would confirm our abstract ideas and intuitions, but is it an enterprise that was direct or necessary so to understand what we want to find which is after all something to logically design that is what we want to describe.

The use of primes as an idea of uniqueness is a powerful one, in particular that some large numbers are the sum of their powers, as with squares, these primes not yet put into some pattern intelligibly as a totality if that is possible or if in a wider view possible and impossible as states of existence at the same time.  We can imagine the sequence of primes from the small to the larger as absolutely there or not as well the wild card of a color or center of symmetry so described. Some things in this non necessity are paradoxically absolute.

I imagine then new proofs as such where we represent a binary number if the squares of the primes are to be uniquely summed.  Again, it is a new look at the plane, its congruences in topology and number theory, and branes with or without the singularities that involve layers or superposition of designed or real coordinates.

I image also that such sequences of binary numbers can involve the difference of cubes, a sort of hexagonal congruence and primacy where three space is the ground or emphasis for physical theory.  In this sense we ask what can be added by the usual rules of number theory as plus one when some prime is doubled.  Did Pitkanen find his 89 this way in relation to 19 ?  Would there be a physics of say the 37th Fibonacci number and so on... or does it have to be in some sense over all the powers a prime (that a partial mystery in a world of partial results of computation.)

The vision and grounding of such ideas as physics are light years away or ahead of those would would try to incorporate them with lesser vision than the likes of Pitkanen.  That physics can apply to number theory and general mathematics is complimentary to that sort of analysis applying intelligibly to what we regard as physics.

This genie is finally out of the bottle and while he may grant a wish or two, do not forget that one cannot wish for a thousand more wishes and so on without the natural concept now forgotten but faced again of the gender of the cosmos as multiple or singular.  From my view, from perhaps a little deeper core and faith, some efforts or ideas offered us in our times seem to me very comical if the worlds situation was not leaning closer to the tragic, but philosophy in the end shares the ideal of objective science- only for some philosophers we have not give up the value and measure of our higher spirits of humanity.

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