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The Easiest Way to Memorize the Algorithms of Rubik's Cube: 7 Steps
Learn to solve the Rubik’s cube in no time by taking advantage of your visual memory. You’ve probably been playing with Rubik’s cube and wondering how to solve it. Eventually, you may have succeeded by following an online tutorial. While there are several methods to solve the 3x3 cube, these techniques usually consist of a number of algorithms that look something like this: T R Ti Ri Ti Fi T F.

Some people can memorize such sequences without difficulty. But what about the rest of us who are better at remembering peoples faces rather than their names? The good news is that the algorithms can be converted into easy to memorize graphics so that you don’t need to spend days learning the sequences by heart!
diy  puzzles  visuo  spatial  explanation  howto  math.GR  rec-math  wordlessness 
july 2017 by nhaliday
5/8 bound in group theory - MathOverflow
very elegant proof (remember sum d_i^2 = |G| and # irreducible rep.s = # conjugacy classes)
q-n-a  overflow  math  tidbits  proofs  math.RT  math.GR  oly  commutativity  pigeonhole-markov  nibble  shift 
january 2017 by nhaliday
Mikhail Leonidovich Gromov - Wikipedia
Gromov's style of geometry often features a "coarse" or "soft" viewpoint, analyzing asymptotic or large-scale properties.

Gromov is also interested in mathematical biology,[11] the structure of the brain and the thinking process, and the way scientific ideas evolve.[8]
math  people  russia  differential  geometry  topology  math.GR  wiki  structure  meta:math  meta:science  interdisciplinary  bio  neuro  magnitude  limits  science  nibble  coarse-fine  wild-ideas  convergence  info-dynamics  ideas  heavyweights 
january 2017 by nhaliday
soft question - Thinking and Explaining - MathOverflow
- good question from Bill Thurston
- great answers by Terry Tao, fedja, Minhyong Kim, gowers, etc.

Terry Tao:
- symmetry as blurring/vibrating/wobbling, scale invariance
- anthropomorphization, adversarial perspective for estimates/inequalities/quantifiers, spending/economy

fedja walks through his though-process from another answer

Minhyong Kim: anthropology of mathematical philosophizing

Per Vognsen: normality as isotropy
comment: conjugate subgroup gHg^-1 ~ "H but somewhere else in G"

gowers: hidden things in basic mathematics/arithmetic
comment by Ryan Budney: x sin(x) via x -> (x, sin(x)), (x, y) -> xy
I kinda get what he's talking about but needed to use Mathematica to get the initial visualization down.
To remind myself later:
- xy can be easily visualized by juxtaposing the two parabolae x^2 and -x^2 diagonally
- x sin(x) can be visualized along that surface by moving your finger along the line (x, 0) but adding some oscillations in y direction according to sin(x)
q-n-a  soft-question  big-list  intuition  communication  teaching  math  thinking  writing  thurston  lens  overflow  synthesis  hi-order-bits  👳  insight  meta:math  clarity  nibble  giants  cartoons  gowers  mathtariat  better-explained  stories  the-trenches  problem-solving  homogeneity  symmetry  fedja  examples  philosophy  big-picture  vague  isotropy  reflection  spatial  ground-up  visual-understanding  polynomials  dimensionality  math.GR  worrydream  scholar  🎓  neurons  metabuch  yoga  retrofit  mental-math  metameta  wisdom  wordlessness  oscillation  operational  adversarial  quantifiers-sums  exposition  explanation  tricki  concrete  s:***  manifolds  invariance  dynamical  info-dynamics  cool  direction  elegance  heavyweights  analysis  guessing  grokkability-clarity  technical-writing 
january 2017 by nhaliday

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