## Drama in ƒ: ℤ₂ ⨯ ℤ₂ → {0,1}

$\dpi{300} \bg_white f: \mathbb{Z}_2 \times \mathbb{Z}_2 \to \{0,1\}$

I don’t find numbers particularly interesting, in and of themselves. Mathematics’ folklore suggests that, even if you’re misled into thinking that, for example, 1729 is an uninteresting number, you may be wrong. Whatever. I’m just not a numbers person.

But you can combine numbers to get interesting things. When you put enough numbers together you get Toy Story. Beyond interesting: it was moving. All of the polygons and sound waves (1-D functions of time) are mathematical, and the movie was ultimately encoded as bits — so Toy Story is one long number.

Drama can be built up with much less. Consider the set {Jun, Kiko}. There is a function which maps pairs from the set to {0,1}: a two-place relation

• ƒ(Jun, Kiko) = 1
• ƒ(Kiko, Jun) = 0

{0,1} is isomorphic to {true, false} and the two-place relation’s name is “Love”. True, Jun loves Kiko. False, Kiko does not love Jun

See what I did there? ƒ(a,b)=1 && ƒ(b,a)=0 ——functor—→

• Love(Jun, Kiko) = T
• Love(Kiko, Jun) = F

The possibilities take the shape of the vierergruppe:

A love triangle isn’t far off. And now you have my attention if you want to talk about cohomology or something. Oh, the cohomology of a love triangle? The cohomology of unrequited love? Yeah. I could get interested in that.

This is why I read mathematics. Not because numbers fascinate me. Not because deduction is fun. Because with math you can think about sh_t in a totally new way.

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“…Toy Story is one long number”
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^^^^^^^^^^