…and their roles in choice boundaries, embeddings, dynamical programs, and next-gen LLMs
“A watch for a watch, a tooth for a tooth.”
— Lex Talionis, Codex Hammurabi
The famed Lex Taleonis is a regulation of proportionality. You’re taking my eye, I take yours. You’re taking my tooth, I take yours (being a Babylonian dentist should have been robust).
The regulation was not put in place to foster violence; somewhat, it aimed to limit it. The Lex Taleonis envisioned a authorized world the place every little thing may very well be described by linear equations: each crime would create an output proportional to its enter. And because the punishment for an offense was proportional to the crime, it prevented extreme retribution and explosions of violence that left every little thing of their wake destroyed.
Past the world of retribution, linearity performs an vital position in our serious about the world: in linear programs, every little thing is known. There is no such thing as a chaos, no difficult maths. All scientists must do all day was resolve these sorts of equations:
For each motion, there may be an equal and reverse response.
— Newton’s Third Regulation of Movement
Sadly, the fact we inhabit is much from this linear utopia. Historical past is ripe with examples of the world responding to small issues in extremely disproportional methods: the Defenestration of Prague sparking the Thirty…
