That book has been on my reading list for a while, but I haven't yet done more than skim the first couple chapters. So, disclaimer: The below is my "HOT TAKE" (extremely unsubstantiated opinion) that you should definitely take with a grain of salt!
I really like the idea of providing code+math together! I applaud their attempt at using code to clarify differential geometry notation, which is very overloaded.
However, I am extremely skeptical that using Scheme (or any Lispy language) is the best choice here. I'm guessing the choice of Scheme has little to do with pedagogical value and more to do with the fact that Scheme was created by Sussman, one of the authors.
I think Scheme is a poor choice here, mostly due to its lack of static types / type annotations. I'm also not a fan of S-expressions, but that's a different can of worms. To me, the lack of type information makes Scheme even more difficult to read than appropriately-parenthesized math notation. I think Haskell, Idris, or Julia might be more effective for clear communication of mathematical ideas.
I think this quote sums up my view nicely:
> "Dynamic typing" The belief that you can't explain to a computer why your code works, but you can keep track of it all in your head. (https://chris-martin.org/2015/dynamic-typing)
The book is probably very effective at teaching differential geometry to a target audience that already knows Scheme inside and out. But to everyone else? I'm not so sure.
Yes, that has always been my feeling about SICM (their mechanics version). It was very helpful to me to see the Euler-Lagrange equations explained in the way they did, i.e. using Spivak's notation for differential calculus, as well as lisp. But they even state in the introduction that the reason they are taking that approach is because the traditional Leibniz-ish notation is full of type errors, so as you say there seems to be a huge question about why they didn't tackle it with a language with a rich type system like Haskell or Idris. I know they did lots of clever things with schema some of which would be impossible to realize similarly in non-lisps, but still.
I really like the idea of providing code+math together! I applaud their attempt at using code to clarify differential geometry notation, which is very overloaded.
However, I am extremely skeptical that using Scheme (or any Lispy language) is the best choice here. I'm guessing the choice of Scheme has little to do with pedagogical value and more to do with the fact that Scheme was created by Sussman, one of the authors.
I think Scheme is a poor choice here, mostly due to its lack of static types / type annotations. I'm also not a fan of S-expressions, but that's a different can of worms. To me, the lack of type information makes Scheme even more difficult to read than appropriately-parenthesized math notation. I think Haskell, Idris, or Julia might be more effective for clear communication of mathematical ideas.
I think this quote sums up my view nicely:
> "Dynamic typing" The belief that you can't explain to a computer why your code works, but you can keep track of it all in your head. (https://chris-martin.org/2015/dynamic-typing)
The book is probably very effective at teaching differential geometry to a target audience that already knows Scheme inside and out. But to everyone else? I'm not so sure.