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".

Enjoy.

Best regards,

Ralph Frost

With joy you will draw water

from the wells of salvation. Isaiah 12:3

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