**The Thinker**

**25 December, 2012**

*L. Edgar Otto*
After the hustle and bustle of the holiday, we try to do more than we can in travel and visiting
than what goes according to our plans.
Gatherings cancelled, meetings missed, quiet again and the work'a'day
resumes; after over sleeping with dreams of cashing checks in Canada only in
increments and not the whole with freedom to travel anywhere, the details of
the border town, I returned to a few notes on the foundations not at all sure
the analysis of the fundamental axioms of arithmetic are sound or original.

I received a framed
gift of a photo of my second grandson his parents picked because of my
flirtations with philosophy, the symbol of The Thinker. I connect this with the profound and
influential sci fi movie, the Star Baby in that in my advancing years the
series of rooms in reflection on my selves and the awakening as if for wisdom
it all has to begin from a new born perspective again, hopefully new and
original.

Whatever else we may
be in the great conversation as we learn thru time as debaters and lurkers in
the rooms of the founders and moderators on line, and the bureaucrats, we all
stand at the expanding frontiers to bond or just socialize, and yes to solve
mysteries if we try in creative science and philosophy.

* * * * * * *

Let me call this no-numerological stance of dealing with numbers, the integers in particular,
pseudo-arithmetic, that term to dwell among the other terms of what becomes the
opposite of senses, the irrational, imaginary, metaphysical and so on...
The reality, the consistency of facts that connects the real or apparent
consistency of imagination, the old 2 and 2 are 4 rather than say 5, is the
general question of our ontological curiosity, a journey and deep connections
in the math and mystery of our being.

I still have a
difficult time communication the excitement and profound sense of what such
contemplations mean to the general and yet still wider picture of what we are
as genetics, for one barrier is that such studies, even among the wise can be
seen as something there, yet exceedingly boring. Let us just note then that the implications
in my view of things holds very worthwhile pictures that may awaken us in our
time to a bigger picture of the whole, perhaps make our lives easier.

In the hours since my
last post, times of waiting and the easy flow of writing and thinking to which
we may as well do something with our time- I have nine posts for this last part
of December which I will post after this update, for reference. I am not sure these are of the best quality,
then again for those as in a booklet of poems around a similar theme we can see
the growing clarity of such visions as if the universe itself has a stage of
learning.

Included in the post
and the continuity of thought developing, there at the frontier of what is
objective universe and sentience, the
pseudo-arithmetic as numerology and methods that precipitate into clarity does
seem to transmit to the total vision its forms of haunting connections and
methods to the final products and unified integration of what is left of the
personal paths that designs our discernment.

We see my use earlier
of the profound numbers such as 666 which is essentially a triangular number
and 153 with the digits the cubes summed reaching that number again. All this may be obvious in number theory, yet
it seems a little more obvious to me in patterns and pictures.

In particular, the
possibilities where lines or circles interconnect at a point or not, of a
system with a real center or not, these extended naturally at this count of
possibilities by structure alone of the intersection of singularities to which
as our abandoned but early suggestions for notation of that division by zero
concept is not solved and is inadequate where at the extremes our equations
still break down intrinsically.

I have some obvious
if still vague projects that need to be factually sorted out, and that
intuitively hold my attention to which my earlier generalizations may have been
too naive and but the beginning of new systems of facts and dreams. The paths of 32 edges meeting each point
twice on the hypercuble, or the wider extension of Conway's color matrix of
matching colors to which I have to abandon my order and sense of labeling come
eight cube colors to match and yet in the wider development in this direction
(or I have followed others) of generalizing such simple arithmetical methods
are examples of my current directions of informal research.

In the Conway type
matrices the color matching with the restraints of what pixels are singularity
centers in a given dimensional space the solution of what matches may be
obvious and simple in four space- but the lack of general clarity in this
applying to theories of how we ground our physics seems to me a matter of
debate and confusion also as to the possibilities near our adjacent dimensions
including the errors we often make such as doubling of dimensions beyond the
natural, and usually irrational expected volumes in our flatland thinking.

In the labeling of
such hyper-Conway counting and matching matrices the general idea of
compliments and mirroring do give rise to shadow or ghostly combinations of
apparently constrained sets of colors, unitary, bicolor, quadracolor, and in
the intuitive idea the octonions follow of octonion 8-color when these things
condense or combine, thus shadow symmetries and particles in our psephos
(calculus) of these quantities of departed ghosts so to speak.

But it is the very
subtle differences within a clearer labeling and count of such mathematical and
physical entities as broken subsystems that can give us useful ideas as to how
in some various level, as if the differentiation of cell tissues, we can understand
and influence how such complicated and diverse biological systems work that in
experimenting with them we know more of what we are doing.

What do we gain if in
the core axioms of arithmetic we follow in complexity the logic of these
assumptions as if only this foundation is the concrete? For in this intrinsic uncertainty of
arithmetical operations thus the idea that in the metalanguage we do not prove
Hilbert's program as he envisioned, if these assumptions philosophically are
incomplete?

In the nilpotent (and
to this as relative systems we add the tachyonic like principles to Rowland's
metaphysics of the vacuum and the muons) concept generalized clearly we could
as foundationally a non-necessary state of things in its widest application
that zero times (that is a jot or yod form of the operation) a number is not
just a zero, but can be the number. 0
(,) n = n, an axiom of mirrors... after all in the widest concept of mirrors we
might considers reversal of time as concretely negative or that such can be the
negative probabilities, the possibility as concrete the idea of negative
distance.

What is the number
after the sequence 2, and 42 ? I seem to vaguely imagine 153 arises, but this
is but the hint of something happening when we simplify the geometric
picture. Such vague thoughts widen our
scope of possible useful intuitions as well as the design of physics,
mathematics and logic systems also.

I may have missed
some steps in the still not posted series to which, as that was not written to
post, I will include later. These terse
notes scattered conserving paper can at least in their content be an
interesting game of reasoning wherein the necessity of such shadow logic is the
question and by which even my own methods has sometimes limited the ability by
labeling of more concrete systems of wider scope, as seems one of the hazards
of our development with ideas as we assert interesting and awakening things in
our contemplation.

Of course for those
competent with algebra and number theory such connection with this sort of
pseudo-geometry would be most welcome as a standard to define the wider
paradoxes and contradictions of this game as to what we can be sure of is the
case.

* * * * * * *

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