Comments by "Dr Gamma D" (@DrDeuteron) on "Numberphile" channel.

  1.  @lightlysaltedgiraffe7655  GA isn't taught b/c it's not how we teach vectors. We learn them as arrows: magnitude and direction. With that, there's no way to introduce tensors or spinors. If instead, we learned that vectors are the fundamental things that represent the symmetry of space (SO(3)), then it would be natural to look for things that do so, but are not fundamental. From there on would consider other algebras.
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  2. When string theory started, the Standard Model had 37 free parameters, and strings were going to predict them from 1st principles. Now there are 10^272000 solutions.....whoops.
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  3. Water boarding notwithstanding
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  4. 1) The sun isn't stationary anyway, it moves around the barycenter, so a truly heliocentric model is just as messy as a geocentric one. 2) There's a reason Einstein lamented the fact that with General Relativity, he had done away with objective reality all together.
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  5.  @quacking.duck.3243  Fourier series, or better yet, continuous transforms describe a shape f(r) that is a function of the radius vector r as the sum of an infinite number of exp(ikr) where k is a wave-vector. Note that exp(iz) is a circle in the complex plane. k determines the rate it spins (in each dimension), and the size of the circle is determined by the |g(k)| (g is the Fourier transform of f), and where you start in the circle is the phase of g(k)...as it's a complex number.
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  6. ln(exp(x)) = x
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  7. 5001:60012 :: 1:12.....not 10%
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  8. you can also make them a new complex (j) combination of complex numbers, just as complex a made from reals, e.g.: a h = (a + bi) + (c + di)j h = a + bi + cj + dij h = a + bi + cj + dk
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  9. did you need to do 4, 5, 6...or could you just argue it has to be symmetric?
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  10. They look like triangles, but they’re not.
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  11. cos^2 + sin^2 =1 is the root cause.
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  12. 2 & 3 were substation, he just called the new variable "cos(x)" or "sin(x)".
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  13. The scale implements ternary logic, so: powers of 3.
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  14. I can’t figure why you check even caboose numbers, since n(n-1) is always even….and one pattern you can count on is: all these primes bigger than 2 are odd.
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  15. from itertools import chain a = [False] * 100 for m in (chain(*(range(n, 101, n) for n in range(1,101)))): a[m-1] = not a[m-1] for m, v in enumerate(a): if v: print(m+1) 1 4 9 16 25 39 49 64 81 100 are on...weird...squares.. I expected primes. where's my error?
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  16. Magnus would adopt you
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  17.  @rubiks6  well you just me one who doesn't always observe from Earth.
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  18. step one is make it negative. Most ppl think of positive numbers.
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  19. OK. You simply cannot have a circle and call something that is not the radius: "r". It causes confusion and delay.
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  20. what is freaky is that you draw those boxes, say the partitions of N, and then count how many ways you fill them with 1,2,3,...,N so that the number increase left to right and top to bottom....each of those correspond to a subspace of rank-N tensors that is closed under rotations. Moreover, if you take the number permutations in rows times the signed permutations in columns, that tells you how to mix the tensor's indices. Seriously. How did anyone figure that out?
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