This post in the link gives an intuitive connection between canonical forms in mathematics and easy-to-understand examples in day-to-day conversations. It was motivated by the following question I posed to myself:

  • Why do mathematicians value canonical forms?

I think this addresses an important class of communication problems that people experience, and that's especially true of intelligent people that see the world through the lens of specialized knowledge. It's easy to trap yourself inside your head when you learn to (usefully!) pile on the complexity. Canonical forms offer one strategy for escape.

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I found your categorization of three ways to improve explanations to be useful, and they seem like they cover most of the issues.

However, I feel like the brunt of the article itself was too short to give me a good sense of what canonical forms are like in math, or how to apply them conversationally. In particular, I think having more examples (or making the examples clearer) for each item on your list would have been helpful.

Also, I personally would have also enjoyed a more technical explanation of how to think about canonical forms mathematically. (Which I would guess would help me understand the connection to conversations.)