Ben, "[my statement] seems to incorporate the assumption of a "finite period of time" because a finite set of sentences or observations must occur during a finite period of time."
A finite set of observations, sure, but a finite set of statements can include universal statements. "Fractal image compression is computable." OK, yea, scratch the example. The point would possibly be valid if fractal compression relied on a superset of the Mandelbrot set's math, since the computability of that is still open as far as I know. "Based on a finite set of finite-precision observations, there is no way to distinguish Wei Dai's black box from a black box with a Turing machine inside." Sure, but the more observations, the longer the description length of that turing machine, so that at some point it will exceed the description length of the uncomputable alternative. --Abram ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
