Jason Hise
@JasonHise64
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ℂℍ ≅ Cl(3) ≅ M₂₂(ℂ) ≅ SU(2) ⊕ SU(2)i. 4D geometry enthusiast. Physics programmer: https://t.co/0Cfon7p87D
Irvine, CA
Joined December 2012
I've uploaded 3 1080p HD renders of the twister animation to #Wikipedia. Released to public domain as always. https://t.co/RBehO6boXj
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I’ve heard arguments about mathematical criteria various voting systems satisfy. I think this misses the mark. I endorse approval voting because I think it fundamentally *depolarizes society*. Candidate effort goes to gaining policy support instead of villainizing opponents.
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Prediction: the most obvious immediate effect of the new presidency will be that self driving cars hit the roads quickly because regulatory ‘red tape’ has been removed. This will hurt many early adopters and bystanders, and simultaneously advance self driving tech very quickly.
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Happy to see the rhombic dodecahedron exposed as a tesseract projection, with the front and the back indicated by a choice of which four distorted cubic faces to visualize! For space tiling intuition: it is a checkerboard of every other cube, inflated to fill the gaps.
New video: Why 4d geometry makes me sad As I say in the intro, if you even remotely like math, I can almost guarantee that you will be delighted by the solutions to the puzzles here. https://t.co/Adqhkx39AG
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If Escher was Picasso
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I expect the quaternion fish to be 3D and the octonion fish to be a perspective dependent Escherian paradox that is simultaneously eating and anti-eating the quaternions.
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I like living in the contradiction of the superposition of the metric tensor field.
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No context for the argument being made, but the animation is pretty!
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When you unify elliptic and hyperbolic rotations, you unify gentle periodic behavior with asymptotic ‘wrap around at infinity’ behavior. Volume preserving hyperbolic squish-stretching does like to poke infinity as the transformation turns inside out.
Functions like sine and cosine have some pretty nice properties: they're always differentiable and well-behaved (i.e. don't ever blow up to infinity). Apparently. Yet it turns out that such functions are actually impossible, at least over the complex numbers. (1/9)
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My best guess is that the shift amount used to live in the instruction itself, where it could only occupy a fixed number of bits while the high bits were discarded. But does every shift of a 32 bit value by a variable amount still today feed into a 32 case switch statement? 2/2
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Intuitively, it seems like modern hardware and compilers would treat x << N and x >> N as evaluating to zero if N is greater than or equal to the number of bits in x. Yet at best we treat N as (N % bitcount(x)), and at worst it is undefined. Why? 1/2
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This is part of projective exterior algebra in one, two, and three dimensions. The determinants are equivalent to the wedge products of two, three, and four unitized points.
Length of a line segment, area of a triangle, and volume of a tetrahedron in terms of determinants.
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