|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
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.|