…and their roles in resolution boundaries, embeddings, dynamical methods, and next-gen LLMs
“An eye fixed for a watch, a tooth for a tooth.”
— Lex Talionis, Codex Hammurabi
The famed Lex Taleonis is a legislation 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 robust).
The legislation was not put in place to foster violence; relatively, it aimed to limit it. The Lex Taleonis envisioned a authorized world the place all the pieces might 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 enthusiastic about the world: in linear methods, all the pieces is known. There isn’t any chaos, no sophisticated maths. All scientists must do all day was resolve these sorts of equations:
For each motion, there’s an equal and reverse response.
— Newton’s Third Regulation of Movement
Sadly, the fact we inhabit is way 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…
