Thursday, December 6, 2012

PK-ons (Field Nets and 153 Matrix Element Fish)

PK-ons  (Field Nets and 153 Matrix Element Fish)

L. Edgar Otto

06 December, 2012   Next Morning, nothing particular unusual in my dreams except maybe general sense of well being in relation to our ideals at least in the turbulent world, one that moreover bombards us with adverts and nostalgia and half dreams of truths in warnings of some half true or understood indefinite future.

The second illustration, and I feel a little remiss in the presentation and care of the assignment of order and color so abstract if art but the engineering is the bread and butter of some people who enjoy and justly get credit for the effort.  I would like to say this originates with me, from some mysterious depth of genius or intuition- but that does not seem the case, for in the search of my stock of drawings that I regard as mathematical and stored if at all random or surrounded by files lost somewhere in time, I came across the eleven triple circles of incidence.  These this morning suggest to me something like particle structures as if reduced to simplification of the 11 or 12 dimensions into three space.

Of course although I have visited those files before I did not recognize or notice theses circles as significant and yet for this way of relating and explaining highly abstract realms in the coincidence of the idea of a number, of 11 in this case which does seems to be what the physicists talk about to interpret their equations as if some guiding property that is at the foundations of all such integer number properties, I did recognize the utility for my current concerns of the products of partitions and the cube unfoldings.  Yet I must confess that in the search and stumbles it seems as if to the structure another hand was guiding me.  But how independent are we from separation or touch to such quasic field products of absolute contiguity where we share a clear distinction with others and within ourselves?

Let me coin the words, for the art of it only, that imagines these shifted particle colors in shifting dimensions, the little red dots of 14  I style Keaons, and the field of three circles I dub Pitkanenons.  The quasic product, perhaps the pattern like tensors of rectangular numbers involved, would be 11 x 14, that is 154, wherein on this level of combinations and space we may it is legitimate to shift, that is add one in the Eddington insight (to sort out the fives as does Dirac in the 12 colors Rowlands covers in his book) or subtract one, it does seem a foundational three way deal and often not only do some things relatively vanish they add one as a shadow in potential and abstract motion we can assert, as rest perhaps, yet not ground the dynamics or cause from within the theory.  The 3+1 formalism.  My search to have a well oriented Conway Matrix of 6 face colored cubes proves much harder than we suspect especially as we enter the 2+2 aspects of the formalism.

Does it really mean anything to complicate our fields and particles by negative numbers of vanishing as a falling out of some shift when we discuss the absolutes?  How do we find the practical science when all we can talk about is an elaboration of identities, of one, or what can seem to us a lot developed from nothingness?  These "PK-ons" do not necessarily have Keaons which I call that after Kea who worked with the 14 points of the associhedral of Stasheff.  And the circles I call Pitkanenons because from what I can tell in his terminology, certainly from a dynamic view that sets the wormhole mouths as material (massivation?) for rather than the quark terminology he uses the idea of partons (I think he uses it this way but the answer is the same as in my case long ago subdividing the muons as you can find in my illustration of 1968). 

Yet in any case his is p-adic also and concerns absolute values also, in which case the general notation of the PK-on models may be represented or simplified into distinct circles incident or not to a line.  This surely has been explored from the continuous physics viewpoint and the quasifinite aspect of it is independent of the infinity of this axis.

Without knowing or making this distinction with the finite or the interchange of overt or mirror subspace geometries and matter that seems the grounding of lesser theories of everything we might set up alternative cosmologies, for example the Ekpyrotic oscillating universe which does after all begin to deal with the nature of interacting Branes.

But in the quest it is natural not to be so sure of what we think and see- the clarity and transcending our dream in the light of morning, as Pitkanen reports also, seems to me after all the ground we gain, we curious creatures, as we explore theory, and science.

In contrast to the complexity of this theory in the illustration we find basic properties of digits, some mirrored, and the addition hard to argue with in its simplicity.  Yet behind it as if we are missing something we are taught early on, save going through the motions that we in mimicry begin to understand monkey see, monkey do, such as the significance in rapid arithmetic checking of the casting out of nines (but why does this work?) For this quasi-numerology can be seen as some sort of formal number theory- just as mysteriously or in some recorded fact of Greek speculation on numbers carried over to the New Testament the Christ says cast the net to gain 153 fishes of which it seems a maximum as if I catch these number in the 12 by 12 net of the pattern holding grid- whereof by successive sums of the three digits each cubed we eventually reach 153 again from half of all such numbers, and do so at most in 14 steps.  Of course the sum of three cubes can be a cube. But other such applications of powers over orthogonal sub-cells as dimensions and mirrors awaits proofs that elude us still as well the needed more complicated dimensional theory.

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