Tom Veatch

Flames of inspiration often leave smoke signals behind.
From mine, these.


Negative Dimensionality

Abstracting geometry.

Hilbert's axiomatization of geometry, full of redundancy, led me to a generalization which makes geometric dimensionality a characteristic that can be counted up (as in point to line to plane to space, etc.) and down (space to plane to line to point: etc.) Geometries, by intersecting, create lower-dimension geometries; for example two intersecting 2D planes create a 1D line. Geometries, by projecting, create higher-dimension geometries; for example, two 0D points project a 1D line.

But if there is no upper limit, perhaps there is also no lower limit. The idea that a geometry might have negative dimensionality seems absurd, considered within the assumptions of spatial thinking, yet it derives from the same less-redundant axiom set as the geometries we understand. Suggestions for intuition and use of this idea are also given.

A More General Theory of the Syllogism

Abstracting logic. Aristotle's list of syllogisms missed half of them; there's nothing to them (H!); and we can do better without.

Still it is pretty fun and cool, considering this was the intellectual pinnacle of humanity for 2000 years, and plus I'd say this is not a bad introduction to "term logic", and might be suggested reading for students of computer science, philosophy, classics, and/or math.

Bliss Theory: Emotion in General

On a mathematical represention of emotion, with decomposed functions including Identification which turns out to have a central role.

Math as Language

Underlying intuition reads out as discrete expression.

Math Tutor

Learn your times table.

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Modified: 12/20/2021