|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.
|Logic constrains biology, biology constrains us, and yet we think and speak and feel. How did we get here, then, and what parts came in what order? This was a lot of fun to write. Includes Tautology, and Cognitive Biology, and Conceptual Archeology.
|Foundations of Future AI
|Towards a New Cognitive Science
|Science can be fun and easy!
Tea Lady is a web app for testing if an assertion holds up statistically. Great, easy, accessible, quick, observational experiments by anybody, anywhere.
Tea Lady applies Fisher's Exact Test repeatedly as you do live data collection.
A predicate, for some category X, and some property Y, is the statement that X's are Y. That could include anything. The truth of it, though, can be empirically tested with the Tea Lady on-line tool. You watch and classify: Observe the X's and Not-X's that occur or come by, and record whether they are Y's or not Y's. Tea Lady keeps count and gives you a P-value or significance measure.
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.
|On the growth -- and decline -- of
species like pine trees, or humans.
An essay toward a parametric model of species success and failure. A clear thought experiment showing how it proceeds, what factors influence it, and how to aim for a soft landing as resource limitations start to squeeze. Relevant to us? I think so.
|(Universal) Gravity is BS
|An argument for Local, Quantum Gravity. Based on the winding problem in which galaxies remain spiralled or barred rather than a smoothly-blended coffee cup of stars, even after supposedly 20 rotations, I propose that gravitational attraction doesn't actually reach out forever, but only to a limited distance from each point of origin. Not only does this explain the mysterious maintenance of spiral galaxy arm coherence but it also explains the interaction of spiral arms with the galactic bar shape, and explains the process of formation of barred galaxies, and it predicts and explains systematic color variation within spiral galaxy arms (which are like tornadoes, spiralling around their centerlines, and detached gravitationally from the galactic center, according to this theory). Current alternative proposals in terms of dark matter and standing waves are demolished. Perhaps the merged projection of such local gravity quanta creates and constitutes space itself, thereby creating the expansion at and after the Big Bang.
|Where I rant and rave against "possible worlds" being used where "concieveable worlds" is intended. But "conceiveable" does not mean (actually) "possible"! So wake up, logicians!
|On the Origin of Life
|Where I speculate on how a single extremely lucky event keyed the the origin of life. Not two.
|Darwinian Selection Logic
|Because although mutation is random, selection is functionally logical. Combined with the Crease of Logic, This resolves the conflict between the evolution-denying God-As-Designer folks and the evolution-affirming atheist folks. Have a look.
|Thoughts about the Pythagorean means: the average, the geometric mean, and the hyperbolic mean. This is surprisingly deep for so simple a topic. Understanding at least 2/3 of it is part of your path to wealth and meaningfulness.
|Some Water Waves
|...A partial typology of water waves...
Water waves come in a small set of types, listed here. Discover the anti-causal wave, the Soliton, the horizontal sheet flow, and other curiosities. Then, try to explain them.
|A careful, accessible introduction to neural networks assuming only high school algebra and a little geometry and differentiation. NNs are defined mathematically, along with how to run them, how to train them (by the usual gradient descent), how to train them better (so I suppose: using 'Newton-Raphson', which really ought to kill!). I also discuss how to understand the training algorithm's implicit reasoning about the adjustments it decides to make; I share an interpretation that backpropagation is like an Anti-Dunning-Kruger learning system (and therefore morally superior to most men?). Then I give a whole Fuzzy Logic re-interpretation of NNs, along with suggestions on how to enhance their logical reasoning capabilities. I tried the wikipedia page, and got so frustrated I wrote my own introduction. So yes, I suggest reading this if you want to really understand neural networks, and if your other resources have made it seem inscrutable. It's a few pages of actual math, yes, but all the steps are laid out: no leaps! It's not short, but you don't have to be a math major to follow along. I encourage your study here if you are interested in really knowing how neural nets work.
|On the Crease of Logic
|Logic from Space
|A solution to the Crease of Logic.
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