New Experiences of an Old Universe

(part 2)

 

[Ceptual Commentary Bulletin #4]            . . .  "I reasoned ... shouldn't the universe be more properly perceived
as extensive interactions among pluralities of entropy groupings, all moving in different yet interconnected gradients, with differing rates, different relevances, different entropy/neg-entropy directions?"  J . . .

This means that the concept of  environment  takes on thoroughly new levels of integration . . . environment isn't only that which 'surrounds' an entity or system, now it includes anything and everything  internal  or even constructively  precursive.    It is more than "place", it is  relationships  of dynamic processes.  And that is open and unlimited -- boundaries and forms being transitory pieces of energy/matter coming together to enact whatever they do.

And what about "mathematics"?  What does this imagery tell us about mathematics?  In very straightforward fashion it informs us that it too is a gracefully smoothly integrated whole.  Functions, equations, factors, relations, inferred qualities et al exist completely with all the others in cohesive integrated co-ordination.    What ever equations or operations or factors are being used, all the rest are there in the wings, accessible if appropriate or needed.   Mathematics is an ediface of qualities and quantities so interreticulated that it has a singular Unity no matter how complicated, involuted or hyper-infinite.  All familially bound.  And all those prospective entropies, and all the consider-able environments ..?.. how does this view of mathematics relate to the model we are conceptually evolving about real-world force dynamics and interactions and connectedness?   It means that the discerned relationships of systems malleating other systems should have a presence in the language, form and structure of mathematics.

We have for generations built Mathematics from the patterns and behaviors in the world around us.  Our mathematical house embodies the relationships we discerned and patterns which implied the existential reality of other real-world patterns that may not have been directly observable -- like quantum mechanical forms, like relativity -- until we developed devices sensitive enough to encounter and verify those pre-ceptual goings-on.

In order to be consistent and coherent, the physical universe perforce must include the relational equivalents of David Bohm & Basil Hiley's "Undivided Universe" and my "topology of confluencial dimensions".   Like the opening moments of a dim then burgeoning light giving us conceptual contact with a place and time, these nascent concepts are informing us about the collage of systemic structurings of which we are built, the core of our composition, our arisings, and our potentials.   I was fortunate enough to speak with supersymmetry physicist S.James Gates (reference URLs), University of Maryland, a few weeks ago.  I needed to get his views on the number of dimensions seen to be involved with supersymmetry models of the universe, and more specifically, couldn't there be an equal number of temporal dimensions in pair with spatial dimensions (the Integrity model).  Without getting into details he replied that the topology of supersymmetry to date hasn't been developed that way, that it is organized with only one of the ten or so being "time".  So I switched gears in order to plumb an alternative connection between Integrity and Supersymmetry.  After reading and listening to discussions about the recent Proof of Fermat's Last Theorem, it occurred to me that there was an underlying organizational theme to the Proof which was reminiscent of super-string topology.  Prof.Gates gave me the terse reply, "Funny that you should mention that.  It seems that, yes, there is a link, in an area called Modalities.  But nothing's proved yet and its just now being explored by some folks."

Humans experience the world, interact with it directly, as well as with codes and representations, which we respond to with equal surety because they accurately stand for the relational experiences.  There are no guarantees, but if you see a fast moving object disappear behind a building, one of the possibilities is to guage the trajectory and momentum, and judge where it will show up again in your view, emerging past the impeding ediface.  Such "filling in" gestalt happens everywhere, every day, and no less in Mathematics.  We cohere the mathematical universe by filling in the mechanisms and substance of connections between ideas and functions, in spaces that were un-attended to before, which content we were innocent of.  

And we explore those spaces with conjectures about their content.  Sometimes we get it correct, right from the first effort.  Sometimes not.  And sometimes the accomplishment is attained by tweaking and fine tuning, making sure to include all possible impinging factors.   But over all, the guiding rule is consistency.   What works here must work there -- or show the bridling conditions why not.   This is the exploration of the undivided universe, now championed by Hiley since Bohm's passing.  This is the exploration of a mathematical topology that can account for and combine pluralities of nested integrated entropies.    It's not that we are mechanical representations of mathematical principles, no.  It is that mathematics --  systemic dynamic mathematics -- enables the profusion of lush organic existence.  And that includes what we used to consider "in-organic" or "not life".   And in keeping with the theme of these two specific ICI Bulletins (4 & 10), it includes the notion that, like the proverbial cluster of blind people, each touching a different part of an elephant yet trying to incorporate each other's isolated "observations" into a coherent single description of the animal and how, where, why the disparate pieces fit together, that it takes a little extra effort on each of our parts to recognize that our mathematical descriptions may be wildly different from each other -- some simple, some intricate, some narrowly focussed, some trans-general -- but that they merely represent alternate descriptions and aspects of the extensively diverse universe we are part of.

In hopeful anticipation of blending my perspectives with that of Basil Hiley, I see that we are both dealing with describing a universal/mathematical structure in which all parts have accessible communication with all other parts.  We are looking to develop such structure which accounts for content tranference, for conditions that produce specific distribution restrictions (relativity), for conditions of the same ediface that allow zero-temporal restraints (non-locality), for information transduction and coding, for the underpinning quality/ies which we have interpreted as something else, broken and separate, but which really are different applications of the same a priori quality.

To this last case, it is my thesis that we are on the verge of a cleaner, crisper, simpler yet broader definition of Entropy... one which can be applied not just to energy dissipation (of which there are now at least 4) or unknown vs known information, but to transcendental mechanisms themselves ... time, space, sequence, bit variables, etc.    I quote from my Feb 10 1998 email to Prof Hiley:

"The key possible mechanism that would gather together the divergent phenomena is the application of an aspect of entropy to dimensionality in general, rather than just to energy.  I view entropy not simply as a fundamental directive of energy distribution, but as a result of an underlying response to spatial and/or temporal deformations imposed by the presense of energy/matter.

Entropy is the process of moving toward a state of "least deformation" (least stress) of all pertinent factors or constituents.{my definition} That "least deformation" can even be extended to dimensional scalings. Eg, I've often wondered why orthogonality was such a special relationship in general, even underpinning hyperbolic descriptions. It turns out that orthogonality is the state of "least deformation" when transposing between dimensions and is in fact the fundamental a priori of Lorenztian transformations. Orthogonality is afixed by the impact of entropy on dimensionality (extension of plural dimensions).

Entropy is a smoothing function which can be applied to energy, to time, to space. It can be discerned in localized/bounded cases; it affects factors singly and plurally; it can be used to model interactions of nested levels of systems (electron vs atoms), and so on.

I surmise that one version is Hooke's Elastic tensor, and another even related to your concept of Osmotic Velocity. I project that non-locality can be alternatively discussed in terms of dimensional compaction . . . that for all intents and purposes avoids the deformation stress and transmission limitations found in "n" dimensions, by retaining information content in coded "n-1" and "n-2" etc dimensions. This state is always present and so will always show up as non-locality even in the presence of fully formed "n" dimension conditions.

Bottom line?...communication links are always present, only the dimensional configurations change. Some configurations have transmission-time restrictions (relativity), others don't (QM, non-locality). The universe, ultimately, is a vast communications network, processing incredible varieties and forms of information through its topology.  Confusion only comes to us because we don't have a fully integrated comprehensive model yet that allows for causality that may be widely variable in "sequencing".  Which variability is not a refutation of causality, but its larger frame of reference and verification."

Feb 12, 1998

 

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