I really like that essay, and it was linked here before. I would have liked to enroll in the course.

The key insights I took away from the paper are:

• No, a waterfall isn't simulating a chess program, because the mapping from one to the other would be "doing all the work". IOW, you can only say one computation implements another if there's a polynomial time reduction between the two that benefits from having the other as an oracle, which is not the case for waterfalls and chess.

• Different choices of language have no asymptotic impact on complexity of descriptions, except to the extent that it limits expressive power. If you couldn't represent the concept of a differential equation, then Newton's gravitation would be no simpler than Ptolemy's epicycles: both would require a lot of table lookups to predict motion.

• The Turing Test, as well as human-run tests in general (like a quiz in school) can be subsumed into the concept of interactive proofs, where assumptions about the subject plus random probes of their knowledge suffice to prove what they are capable of, without knowing how they implement or represent it.

• When considering whether a machine can pass the Turing Test, the relevant question is not if it's theoretically possible, but if you could do it while only using resources that increase polynomially in the length of the test (rather than e.g. a superexponential lookup table).