From what I understand, TAoCP is building up to that compilers book! When initially tasked with writing about compilers, he realized all the background necessary for building them and planned out these books as an overview of computational techniques that would be helpful to use.
Having been interested in APL, but never taking the plunge and learning it, I've seen this article "Notation as a tool of thought" (this is linked in the submitted article as well) thrown around: https://www.jsoftware.com/papers/tot.htm
The paper kicks off with a quote by George Boole: "That language is an instrument of human reason, and not merely a medium for the expression of thought, is a truth generally admitted."
Having a terse language in itself can lend itself to thinking about problems and playing around with them in your head more effectively. I know when I'm thinking about an algorithm to be implemented in something like java there isn't room for all the boilerplate in my head. Stuff like "public static void main..." gets fuzzed out when thinking about a solution, to be replaced the idea of "place where main method is".
I like the idea of boiling down useful abstractions to the most simple symbols we can manipulate mentally, to be able to fit the most possible high level abstractions in our mind at the same time. This should make it possible to be able to play more with constructing solutions. Never feeling particularly locked down because you have to manipulate a lot of syntax and curly braces to implement or think about an idea. That you only have to switch around a few symbols for a change in semantic meaning.
Having never learned something like APL myself, I can't speak personally about the effectiveness of this idea.
I'm jealous! He was my first year computer science teacher, probably the person who most instilled love for functional programming in me. I still at some point want to go back to take a compilers class with him someday. Until then, while you are a FOO I'll be at the BAR :p
God, The Scsh reference manual has my favorite acknowledgements section in all of media. I urge all of you to read this.
https://scsh.net/docu/html/man.html
See the "future plans" section of his website: https://www-cs-faculty.stanford.edu/~knuth/taocp.html has volumes 6 and 7 as being on compilers.