Thursday, December 27, 2012
L. Edgar Otto 25 December, 2012
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.
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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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