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.

Footnotes

  1. https://mathoverflow.net/questions/38639/thinking-and-explaining