That is correct. It's just text which talks about concepts that don't have text, like transcendental numbers, infinities, infinitesimals and so on.
There are functions in mathematics that can't be written down in symbols at all, like the integrals of certain functions (which themselves can be written down).
Math text has some useful properties in that certain transformations you can think of as typographical (manipulations of the text) actually preserve semantic properties in a useful way. So for instance addition commutes, semantically; and in the text, this lets us swap the left piece of text for the right one, around the plus sign.
There can be a very close correspondence between typography and semantics (like in Douglas Hofstadter's "TNT": typographical number theory, which he uses to explain Gödel's incompleteness theorem).
> This leads to the alternate conclusion that maybe the s-expression is the underlying set of objects in the interpreter/compiler.
I assure you that it isn't; not in any main-stream Lisp interpreter or compiler.
(Where by "main-stream Lisp interpreter or compiler", I intend to rule out cute hacks like this:
That is correct. It's just text which talks about concepts that don't have text, like transcendental numbers, infinities, infinitesimals and so on.
There are functions in mathematics that can't be written down in symbols at all, like the integrals of certain functions (which themselves can be written down).
Math text has some useful properties in that certain transformations you can think of as typographical (manipulations of the text) actually preserve semantic properties in a useful way. So for instance addition commutes, semantically; and in the text, this lets us swap the left piece of text for the right one, around the plus sign.
There can be a very close correspondence between typography and semantics (like in Douglas Hofstadter's "TNT": typographical number theory, which he uses to explain Gödel's incompleteness theorem).
> This leads to the alternate conclusion that maybe the s-expression is the underlying set of objects in the interpreter/compiler.
I assure you that it isn't; not in any main-stream Lisp interpreter or compiler.
(Where by "main-stream Lisp interpreter or compiler", I intend to rule out cute hacks like this:
https://news.ycombinator.com/item?id=7956246 )