Monday, February 4, 2013

From Icosian Twist Triaconway Games to (The Unity of Number Theory)

Icosian Twist Triaconway Games
to  (The Unity of Number Theory)

L. Edgar Otto      04 February, 2013

In the intuitive universe it helps in comprehension of the unity of a theory system, beyond the draw of working out a puzzle for the doing sake- thus a recreation, to have pondered the structures of number theory and its description as geometry, principles discovered on one's own at the frontiers of inquiry, as if in the flow of a subject's history done independently or not.  It also helps to learn of others who have gone down a certain path and discovered something at the frontiers.

In the quest for a total theory as it is at least the structure as a mental model, our states of mind when disrupted in its span of internal or external working if it understands something of this quasi ideal totality has a core a strength to which eventually a mind can heal, return again to the unity of this quest albeit with the broken view of a thousand new eyes.  Of course there is no guarantee at ground that any creative entity, the intuition thru our minds or that of the  freedom of development in the universe of intuitions as if it is something like sentience itself, that any chance soul may become more in our collective wisdom than a large gaseous planet we can think of as a failed star.

There is consolation even in the failure for the joy of the quest aware or not of purposes drawing us in our doing.  This is an overview itself as a philosophic comfort that will imagine our efforts and uniqueness has a sense of legacy or immortality that endures in this world- yet, this is to be realized in the lives and minds of others, unknown souls in other worlds, or somehow preserved in the universe that the question of our work reaching great heights so thankful for our being may or may not so vanish.

Another consolation is that science as if to give equal weight to our variety of paths of thinking operates blindly, this we value if not the world, the ideal that it is just as important to learn from negative experiments and encounters the awakening of our scientific wisdom.  The universe in the main has a long time, and sufficient time to find the unity from its intuitive stance if even it thinks of itself as deterministic as a mindless machine.

But this is the frontier question as to what are the influences and impediments from emotional considerations only- simply because we can overwrite memories with others, superimpose them in ambiguity, and expend energy in the expediency of resolving paradoxes of motion and rest as to energy requirements, balance and compensation or ever divergent runaway paths as our unity evaporates. 

Unity, as much as the Null grounding has such paradoxes of which we try to go around what is finite, continuous, or in the diversity and exceptions of our patterns, mathematics, we find ways to describe useful working inquiry methods. We find in the logic of it all a way to express simple addition in computation.  We are careful regarding the reality of mirrors and images by such zero division and its hierarchies, its continuum paradoxes and matters of choice, to which we can say reality has its nonnecessity of stances to reason of which we tend to expect only our ideal in our total images.

I have found it quite startling, beautiful, and rewarding to find a book that lists the achievements and unsolved problems of number theory- some of the long time unsolved problems as simple as a few arithmetic equations or as difficult as what proofs we are not quite sure of in the number of steps as computer researched,  have made whole careers and established reputations even when the circumstances of the world at war or some epidemic easily cured in retrospect interrupted this activity of which, especially with topology, has its applications years later for the value of its doing for society in general.

Intuitively, at least, I see so many of the problems as part ot the unity of integer and of ideas, especially continuous in its ideas of geometry, as obviously solvable or in near reach of our doing so.  I also find some simple concepts which while seemingly trivial have significant and profound influences from those dedicated or who tinker and dabble with the number game.  The core relevance of arithmetic and space structure, visualized, seems the greater part of the tools of ideas to reach this state of accessing the frontier.

Some of the axioms or theories in special cases are very ancient, at least since the birth of our writing but in a sense these are timeless in their weights.  We need to come together on this basic issue of our views as to what is a unification of physics from those who are dominated by the continuous view and those still exploring the discrete.  In the continuous approach sub-dominant in number theory some may underestimate the power of simple relations of the variety of number theorems in its simple counting.  These are useful to see how both views apply.

In this background of the list, and I am barely thru the first few entries, I understand the grounding that has always been perplexing as to what I think a contribution, that which began with the Quasic grid - but such patterns have been the foundation also of whole new areas of mathematical investigation such as was determinants and matrix theory. I see how this consideration, really of two locations or points needing only the compass and not the straight edge in the treating of distance so to speak beyond this tried method that justifies some of the use for angles in the physics, as certain of the vision as any such startling weighed in our minds and peer review, only it more highly generalizes the method over all the points in a unity of our vision.

With the finite (or quasifinite) view I can readily understand the very obscure conclusions and paradoxes of those with the continuous view of which the training to it suggests Olympian gods out of reach of our common assumptions, yet I see these do not go deeper into what part of their unity may describe what happens near some small limit region.  In this Platonic, seemingly mystical division of things I built the mythology of Quinadad, the idea of the Christian Trinity (a model for space as mentioned in Dostoyevsky) only extended it to five and more [this the origin of my sister term for quasics, quabics]. 

I now see the influences of bits of the wisdom here and there I encountered (but not all, who knows what I still miss?) and I see the logic of my own development even if in the casual passing I did not know this such a formal law- of course I do recall stopping once on the way to grade school in Afton park struck by the laws of motion of Newton and better never than late I decided I wanted to know more in school.  This of course not far from the spring day and sunlight in the leaves of the park, nor that I walked along a new pathway beyond my direct usual way as influences.

This tract or post has two titles because I am in transition between the return to relaxed mathematical recreations of which I have filled up the page of notes with a vast new array of puzzles and principles of which my first gimps of them as solved and elegant I did not see had wide new applications and developments.  I give you a rough skeleton sketch of the Icosian (from Hamilton's icosian calculus whatever that is) Triaconway Game where we learn more combination theory with the aid of color, and some new game theory models itself of various ways to play given pieces and the dodecahedral structure. At the other end of this transition I may make the Game of Numbers utilizing all these new distilled core results with the said unity in mind, those listed in Darling's book.

I have a lot of reading and work to do so forgive my crude sketch so informal.  I have from time to time said that I had other things never posted- eventually I have posted them being by nature not one to feel at home with secrets- a defect perhaps yet respecting those of others, that fleeing from the self control we learn but not by the censoring our poets.  Now I have a vast new world of things I have not posted of which I did seem to reach ever closer the blank page that we from time to time feel we have nothing more to explore or say.  I and all of us may get around to this.

We in intuitive computations if casual need not fall into the acceptance of mystery into some Platonic conception or the disdain for the infinitesimal and absolute nothingness, nor for the sake of our formalism in the mindless and algorithmic brute solving- all these things have their place and their probabilities, yet where casual we are grounded in that this aspect of the available energy does is minimal as to ideas we feel need the unlearning, once, as if  a primitive substance it is left to run free in its open inquiry.

Forgive my connectives in English of one that stands out as complicting the hard work of clear writing- the "as if" but then in its rare use in mathematics and physics,  quasi-, at this time I find that connective between such abstract concepts to be indispensable.

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