Group Theory

Group theory supposedly belongs to “higher mathematics” but it’s more like a preschooler playing with coloured blocks than it is like abstruse journal articles full of pointy symbols.

Say you have a collection of things. And then you do stuff to them. Maybe there is only a finite range of options of what to do, as in

  • tying a knot
  • turning your mattress (apparently you’re supposed to do that every season)
  • paging through a book
  • playing with a belt
  • solving Ernő Rubik’s cube
  • rotating your car tyres (not spinning them; taking them off and interchanging them)
  • turning over a piece of paper
  • opening and closing a cupboard
  • spinning around in a circle to make yourself dizzy
  • the Tits Group … I’m not sure where you would encounter it in life, but there is only a finite number of things you can do
  • playing peek-a-boo

An example (ways to re-arrange 4 things) tomorrow.

You’ll see that the only rules in abstract mathematics are the ones you make up. I’ll add, breaking the rules of math is exactly what led to advances in particle physics, music theory, crystallography, machine learning, cryptography, and organic chemistry.

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