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“great minds think alike”

I don’t really know to what extent the good doctors of intellectual history still prescribe reading Thomas Kuhn’s .

I went to Princeton when that book was in its heyday. Post Future Shock. Pre Hunger Games.

Anyway, part of what we did, when discussing how paradigms give way to one another — not only in the hard sciences (and mathematics), but of course in politics all the time — was look for quintessential examples.

Fascism begets its opposite and yadda yadda. Dialectical whateverism. Paradigms have a half-life.

Just wait, and things’ll be different.

What came to me later, after Princeton, was a different paradigm in maths, but an easy one, nowhere near the high bar of a “Minkowski space” and yet one could claim it was non-Euclidean.

Grade schoolers might get it, in other words.

You would not need years of background in XYZ, before getting your head around this simple alternative.

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Enter the IVM.

Instead of cubes filling space, we have dodecahedrons. Weigh them as six, relative to a unit volume tetrahedron.

What? Could this be?

Indeed, a new paradigm, and therefore a fine example to retroactively insert into the curriculum segment on Kuhn.

So who does that? Stanford? Harvard?

The IVM is heavily into naming the “” (see Regular Polytopes) of its participant tetrahedrons and octahedrons, called A & B (stay tuned for nuances).

Five-fold symmetry ala quasi-crystals, fat and thin zonohedrons, those kinds of topics… yes, check. Accessible!

For that family, we have modules named T, E & S (more orthoschemes and such).

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When your course gets around to Kuhn, and they start dishing out examples, do they mention a different take on 3rd powering as an option?

If not, did you miss your American heritage?

A lot of students come to America expecting to be steeped in what’s uniquely American (otherwise why not just stay home?). But if you didn’t get the IVM, did you get what you paid for?

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