[GlobalTraveler]

Is there anyone on hacker news that could explain me secion 6 in this article? Overall the article is very interesting but I am not sure if the waterfall argument is valid.

The waterfall conjecture was stated as : 'Given any chess-playing algorithm A that accesses a "waterfall oracle" W, there is an equally good--chess-playing algorithm A', with similar time and space requirements that does not access W.'

From this we can assume that the article is a metaphor for us as external observer given semantics for computation. Thus by providing the reduction we showed that the computation in and of itself does not have semantics. However, why would we assume there to exists A'? Even if there is A', can't we reduce A -> A', and if we can reduces W to A, then by proxy W -> A'?

Could somebody help me?

[solusipse]

Well, author tries to prove it's not. And, btw, oracle is something more than just an external observer, it can be used, for example, to solve the halting problem in classes for which it would be impossible with nondeterministic machines.

[GlobalTraveler]

In my hastly typing i forgot to add 'in' to valid.

Could you elaborate on the oracle approach? Because I interpreted it as being the external observer in this case. From computational complexity I know that an oracle solves NP problems in polytime by a nondetermnistic turing machine, but I am not sure how this oracle stuff loops back to the philosphical argument.

The proof provided by Aaronson is really opague as to what and how it proves that the argument is invalid.

[eru]

The main problem with that section is that the author tries to engage with a particular objection (the waterfall argument) that is itself a bit obscure.