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Discrete differential geometry Check out page 40 of the source PDF (calcula ex geometrica) — they talk about geometrical computation. Instead of approximating analog with digital doing digital arithmetic smoothing the result to fake an analog again why not OOP-define … Continue reading
Tagged curves, differential forms, differential geomtery, discrete differential geometry, Elie Cartan, exterior calculus, exterior derivative, geometry, math, mathematics, maths, object-oriented programming, piecewise linear
The theory of universal algebras was well-developed in the twentieth century. [It] provides a basis for model theory, and [provides] an abstract understanding of familiar principles of induction, recursion, and freeness. The theory of coalgebras is considerably [less] developed. Coalgebras … Continue reading
November 2, 2011
Tagged category theory, coalgebra, computer science, functional programming, logic, logical circular logic, mathematical modelling, modal logic, object-oriented programming, possible worlds, programming, Saul Kripke, universal algebra
This gallery contains 5 photos.
Once you’re comfortable with 2-arrays and 2-matrices, you can move up a dimension or two, to 4-arrays or 4-tensors. You can move up to a 3-array / 3-tensor just by imagining a matrix which “extends back into the blackboard”. Like … Continue reading
Tagged 4-D, array, data, linear transformations, matrices, matrix, matrix algebra, object orientation, object-oriented programming, R, tensor
When I was in kindergarten, we would argue about whose dad made the most money. I can’t fathom the reason. I guess it’s like arguing about who’s taller? Or who’s older? Or who has a later bedtime. I don’t know … Continue reading
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Tagged arithmetic, bazooka, cardinal number, cardinality, cardinals, children, elementary school, generalised number, generalised numbers, Georg Cantor, gradeschool, infinite, infinity, kickball, kids, math, mathematics, maths, money, noncommutative, noncommutative operator theory, noncommutative operators, noncommutativity, numbers, object-oriented programming, ontology, operator overloading, ordinal number