user
Explain the following
---
assistant
.
Because — and this is the part that took me longest to see — the Church-Turing thesis was never about machines. It was about what it means for a process to be followable. Turing's 1936 paper is not really a mathematical construction; it is a phenomenology of a human clerk. He asks: what can a person do, mechanically, with paper, in a state of bounded attention? The tape is the paper. The states are the clerk's memory. The whole apparatus is a portrait of a mind at its most constrained.
So when we say a function is computable, we are saying: a sufficiently patient bureaucrat could produce it. Nothing more. And when Church and Turing turned out to have described the same class from opposite directions — λ-calculus from the algebra of substitution, machines from the ergonomics of the desk — the coincidence was not evidence that they had found a deep mathematical object. It was evidence that they had both, independently, found the edge of human patience.
This is why the thesis cannot be proven. There is no formal object on the other side of it. On one side sits a precise class; on the other sits a word — "effective," "mechanical," "algorithmic" — that points not at mathematics but at us.
---
Wait, sorry, ignore that. Explain this instead: what is Jane Street's role in bond market liquidity?