Sliding the boundary in mathematical-physics.

One of the compelling advantages of  going through a paradigm shift and then noticing that "reality is ~structured duality" is, at various moments thereafter, other tectonic plates in the contemporary terrain can and do slide about, theoretically, or potentially resulting in incredibly useful, yet highly unsettling new perspectives.  It is as though we tie off the bungee,  trudge out past the thin ice warning markers  and swan dive, soon arriving safely,  disconnecting some ~60-odd levels of organization below the ill-formed, shattering crust.


We look back and think, just for a moment, of  adjusting the boundary line in mathematical-physics a couple of notches into the physical. Symbolically, and simplistically, mathematical-physics begins to become mathematical-phy-sics, or simply convolutes into physical-mathematics.

Of course, in the contemporary, dominant world view, such a proposal is completely insane, clear evidence of a psychotic break in progress.  Why, yes, the interface between the abstract math and physics IS murky and clearly entangled in uncanny, ineffable ways, but doesn't everyone know that the abstract math symbols and expressions are the pure, unadulterated  truth?  And yes, right at the interface obviously one can slide the viewframe window one way or another which does, in fact bring different sorts of intersections into focus. But seriously?  Can one truly expect to hit another,  more stable, more informative harmonic just by  sliding a little bit into the  analog math?

Preposterous.

Or is it?

The odd thing is once one fiddles just a bit in this region and sees the unseen while saying what has previously gone unspoken,  relocating the dividing line in mathematical physics into the analog math region --let's make it extreme and definite-- from the idealized ephemeral way over  in the sp3-hybridized, molecular bonding region, then, if one does survive the shock, again, basically, all we are talking about and doing is shifting from the old cubic XYZ structural (aka, mathematical)  orientation and upgrading into the naturally occurring, functional tetrahedral structural coding. We are, as advertised,  merely making a shift in ~structured duality; changing from beginning with a cubic, to a tetrahedral format or bias. 

How is it that we can say and do this? Or how does this infinitesimal distortion prove beneficial? 

First off,  going back through part of the litany, the analog math symbols and expressions still do turn out to be primary and always the origin and source of ALL the secondary abstract math symbols and expressions. For purists, this may  be an uncomfortable pill to swallow, but that makes it no less true. 

Secondly,  if one relaxes in the soft embrace of analog math and gazes back toward  where the boundary used to be, down in the valley, somewhere IS the artificially inserted, idealized XYZ-cubic framework.   It ~works and is productive in spawning  ALL sorts of  the uncanny abstract math imagery,  but it is still very artificial, external and arbitrary.  It is a wonderful initial approximation; a case of Descartes taking a leadership position and deciding to "do something, even if it is wrong".   It gets us here.   Yet once we arrive,  here we are facing the need for a small, slight adjustment, needing to let go of the scaffolding and step through  a  small paradigmatic revision.

The benefit, once it can be seen as that, hits on a couple of fronts.  Inside each cube are two tetrahedrons. One tetrahedron is sufficient to sketch out a cube.  Essentially all of the molecules making up our biologicals flit fitfully in the sp 3-hybridized  tetrahedral states. Our own "thing itself" is tetrahedral. Life and consciousness are carbon, nitrogen, water based and thus, tetrahedral.  So, the unified tetrahedral  analog math is obviously working. 

If one adds increments of length, L,  equal to the sum of the six edge lengths of a tetrahedron, the increment connects midpoints of the tetrahedral edges to subdivide each  tetrahedron into an octahedron surrounded by four "half-sized" tetrahedra. Adding another increment of  length, L, repeats the same subdivision at every level, providing a very  simple, accessible "quantum  gravitational model".  Adding increments of length,  L,  has the effect of  increasing total length and  complexity while keeping the the sum of the areas of all faces of tetrahedra  at every level, constant. 

Out on the fringe, almost too bizarre to describe or consider from the perspective of our dominant world view, is the connection between where and how we conceptualize and locate the boundary between math and physics and the economic and thus life support systems that we implement and run.  Here, I will try just one analogy  and then stop.  It's not clear by any means.

Consider, for example, if mathematicians, when they came up, say, with the symbol for taking the integral of some function, they decided to copyright and trademark and restrict the free use of the math integration symbol -- that one had to purchase copies of the symbol to understand and use it.  We all say, well, that is crazy. Math is free and one of everyone's "rights".  It is innate. It is just the way things are. People have a right to the knowledge and to the symbol and tool.

Now slide the boundary in mathematical-physics over into the analog math, where the new  math symbol or expression truly is physical and physical intuition of it can only be acquired through a tactile or haptic experience with a specific physical artifact.  Are you beginning to see?  Sliding the boundary between mathematics and the physical reveals that the location of the boundary is also  entangled with our economic system.  If math is free, yet now physical then certain physical circumstances are now also free to all.  If this is the case, how far might this extend? Are knowledge, water, food and shelter all  rights of all  members of the hive?

Admittedly, I'm doing a poor job of clarifying this new-to-me notion.  At once it smacks of physical idolatry and beyond that, a deep and unfamiliar brand of altruism. 

Being off the mark in our mathematical-physics -- having a low level flaw in our scientific paradigm --  naturally induces all sorts of twisted difficulties in our socioeconomic and cultural systems.   Repair the flaws,  make an improvement in the scientific paradigm and after a fashion, the socioeconomic and cultural   systems will strike a new resonant tone. 

-- Ralph Frost


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