Thursday, February 05, 2009

Dimension Talk

From the Wanderers list:

> If Physics is mathematical, is it "a miracle" that
> something physical is described by a mathematical
> formula? What does e=mc-squared mean anyway,
> what is gravity anyway? Is its essence mathematical.
> Or is the mathematical formula a partial descriptor
> of one or some of its realities?

Note that in buckaneer world we don't say e=mc-squared. Whoever saw the play at PCS might remember he always says "to the 2nd power".


Because using a square to model 2nd powering is a cultural convention, not anything "proved" or "necessary", not a "law" mandated from on-high.

Likewise a tetrahedron models 3rd powering just fine, plus is more economical in terms of edges and faces, is the minimum polyhedron (hence simplex) in terms of having an inside and outside in Kantian conceptuality (= ordinary experiential time/space, whereas that so-called "flatland" of "2 dimensional objects" is just a lot of cartoons about triangles on paper with talk balloons, "seeing" each other as line segments etc., Abbott's book having set the stage for the next 100+ years of inventive fiction along these lines).

We don't teach kids to "question authority" around "dimension talk" or even explain to them that there's more than one authoritative language game using it, i.e. "fourth dimension" in Einstein-Minkowski lingo (world lines etc)., is not the same as "fourth dimension" in Coxeter-Conway lingo. Coxeter himself is authoritative on this point.

Fuller's "4D" is yet different again, simply identifies the primitive 4ness of the tetrahedron (4 corners, 4 faces) with our Kantian experience of spatiality as beings in time.