Will Crichton

If I'm pulling out a term for additional analysis or explanation, it's usually easiest to draw a box around it so my brain can maximize structural sharing, instead of creating new values in-memory every time.

As an aside, this is the main reason I haven't been able to switch to live-TeXing notes: my text editing workflow can't match the expressivity of freehand annotation in multiple colors.

I have a whole ensemble of thoughts around "grouping" expressions. It might be helpful to start with an analogy. As a native English reader, I don't sound out characters individually; each word is roughly an arrangement of pixels or lines that maps to a concept in my brain.

I've noticed that mathematics works similarly: a fluent user will read or write xᵀy or Σᵢ₌₁ xᵢyᵢ as "inner product", like a single word, without thinking about what each individual i or xᵢ represents. But a learner will try to interpret each individual symbol.

Unfortunately, mathematical expressions do not reliably separate conceptual "words" with whitespace, especially when the "words" are factors, so it can be difficultforlearnerstovisually gloss an expression at the correct level of granularity.

As I become more familiar with a domain, I learn how to read the words and not the letters, and have less of a need to draw circles and boxes everywhere.