I made a [fork](https://github.com/ahalma/cats-of-jasnah) that allows for some internationalization. Now you can play the game in Dutch or Spanish as well (or extend it for your own mother tongue).
How to compute the geometric product of
unit orthogonal basis blades (3/3)
If we represent each basis vector with a specific bit in
a binary number (e1 = 001b, e2 = 010b, e3 = 100b),
computing the geometric product of basis blades is
exactly the xor operation on binary numbers!
(e1^e2)(e2^e3) = e1^e3
011b xor 110b = 101b
We have to take care of the signs though:
- basis vectors have to be rearranged into a specific order before
they can annihilate each other (this rearranging causes a sign
change in the result). This can also be computed binary.
- signature of annihilated basis vectors can change the sign as
well.
Does it relate in any way to Von Neumann's trick[1] to create a fair coin from a biased one?
In short: if you don't trust the fairness from possibly biased coin flips, then don't look at individual outcomes in a sequence of (H)eads or (T)ails, but only at H,T or T,H combinations.
You can set the language via an URL parameter:
https://ahalma.github.io/cats-of-jasnah/index.html?lang=es