**From**

**Icosian Twist Triaconway Games**

**to**

*(The Unity of Number Theory)***04 February, 2013**

*L. Edgar Otto*
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

**(from Hamilton's icosian calculus whatever that is)***Icosian***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***Triaconway Game***utilizing all these new distilled core results with the said unity in mind, those listed in Darling's book.***Game of Numbers*
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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