created 2025-02-18, & modified, =this.modified
tags:y2025expression
rel: Expression Monad Tutorial Fallacy
I think one reason why one cannot communicate most of one’s internal mathematical thoughts is that one’s internal mathematical model is very much a function of one’s mathematical upbringing. For instance, my background is in harmonic analysis, and so I try to visualise as much as possible in terms of things like interactions between frequencies, or contests between different quantitative bounds. This is probably quite a different perspective from someone brought up from, say, an algebraic, geometric, or logical background. I can appreciate these other perspectives, but still tend to revert to the ones I am most personally comfortable with when I am thinking about these things on my own.1
Quote via a discussion about the difficulty of verbalizing (in the example, math.)
There’s another part
I find there is a world of difference between explaining things to a colleague, and explaining things to a close collaborator. With the latter, one really can communicate at the intuitive level, because one already has a reasonable idea of what the other person’s mental model of the problem is. In some ways, I find that throwing out things to a collaborator is closer to the mathematical thought process than just thinking about maths on one’s own, if that makes any sense. - Terry Tao
Just prior to reading this I was listening to a popular AI company discuss their state of the art models. Under consideration was whether the users of the LLM would use a single instance, or multiple. The team stated that they expected people to use multiple assistants, each with their own conversation history. In my head I saw this as having say a confidant partner, and then maybe a problem solver etc.
These two thoughts seemed connected.
What is the role of the specialization, or upbringing here with Expression?
If you train yourself in something, the documentation comes after.