…and their roles in determination boundaries, embeddings, dynamical techniques, and next-gen LLMs
“A watch for an eye fixed, 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 will need to have been powerful).
The regulation was not put in place to foster violence; quite, it aimed to limit it. The Lex Taleonis envisioned a authorized world the place all the pieces 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 all the pieces of their wake destroyed.
Past the world of retribution, linearity performs an vital function in our desirous about the world: in linear techniques, all the pieces is known. There isn’t a chaos, no difficult maths. All scientists must do all day was remedy these sorts of equations:
For each motion, there’s an equal and reverse response.
— Newton’s Third Legislation 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…