Monday, April 4, 2016

Mathematics IS structure -- Changing the scientific paradigm.

Sitting with the uncomfortable feeling of actually changing scientific paradigms, periodically, there are waves of impressions, or insights which pass through me, most of which seem too large  (or too compressed) to put into words. The basic feeling then is something like, "Oh, the people who later do make the transition, or a similar one, they will understand, they will appreciate, they have this, and more, ahead of them...".

But some impressions persist or grow such that they hopefully are thoughts worthy of speech.

The current impressions are cryptic ones, like "mathematics IS structure", or "~consciousness IS chemical stoichiometry", which seem some trite and obvious as to be nonsensical.  And, of course, these statements ARE trite and obvious, and bordering on nonsensical, particularly if viewed from one paradigm or another.   But when considered as transitional expressions forming the paradigm shield wall... perhaps there is more to see.

Obviously, as the person who ~sees  and expresses reality as nested structured~duality, I would have a tendency to see significance in "mathematics IS structure". I've already been over that territory when I noticed that mathematical physics, and even mathematics , like everything else is some instance of nested structured~duality.  I've ~already put the various things on the more unified basis.

But the thing that strikes me as odd today, or recently,  is, when I dial back to Plato, or perhaps just to Descartes, as the recent PBS show on Mathematics presented, here we have cube, tetrahedron, octahedron, icosahedron, and dodecahedron cut in stone as "fundamental" (or platonic) structures. 

I'll say it this way ~~Descartes picks cube for his analytical framework, and then what comes with and develops from that selection is the XYZ and other abstract mathematical expressions -- geometry (structure), trigonometry, algebra...  These facets of math, of course, pre-date Descartes but are firmly set in the XY and XYZ-cubic orientation.  And, generally, all of these developments are intensely helpful and informative.

In the early 20th century, R. Buckminster Fuller utilized and popularized the other platonic solids, in and through geodesic domes, Dymaxion maps and many other discoveries, inventions, books and illustrations.

I come along and extend or vary some of Fuller's structural insights beginning in the form of "what do you get when building a tetrahedron out of magnets?".  It's structural-energetic. It's right on the mark to illustrate structured~duality.   But also, initially, and what sometimes seems since lost or disregarded,  the five ways to align four rod magnets along the radii of a tetrahedron (n4,n3s,n2s2,ns3,s4) have the look and feel of the  five possible Debye electro-negativity patterns of the so-called sp^3 hybridized molecular bonds.  This amounts to providing a hand-held analog model of all water molecules, silicates, methane and other organic carbon and nitrogen compounds,  silicon compounds, and other collections. 

This pattern recognition hit, this fact, quickly goes off-scale and overwhelms one's perspective.  Essentially ALL of ourselves and our surroundings fit  these same five patterns.   It's a bit like discovering a crude, reductive  singularity. It's a bit like stumbling onto a previously hidden general principle.   Learn and play around with the multiple states of the analog model; acquire physical intuition on ourselves and surroundings. 

And notice,  I am doing this with NO abstract mathematics! It's then that one perhaps see, as I have begun to, that starting out with cube propmpts for abstract math, and it is very much like facilitating an "epistemic" model and description.  Yet, start out with a tetrahedral foundation, particularly magnetic tetrahedral analog math foundation, and what one have in hand and explores is a far more highly compressed, compact tactile experience which approaches more of an ontological reflection. ~This is what we and our surroundings ARE.

Of course, the two perspectives are hugely complementary and, I don't get to make the statements I make except that the cube/abstract math explorations have come before and have developed our understanding.  But, after that, and into the future,  acquiring physical intuition via the tetrahedron/north-south analog math, this can work for anyone, that is, for essentially everyone. And it happens without any or much of an abstract math pre-requisite.

After considering these two perspectives, side-by-side, on one hand and on the other,  one starting with cube and one starting with tetrahedron,  it's clearer to see the significance in "mathematics IS structure".


Best regards,
Ralph Frost

With joy you will draw water
from the wells of salvation. Isaiah 12:3

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