On Sat, Jan 18, 2025 at 2:45 PM Jesse Mazer <laserma...@gmail.com> wrote:
*> my central point that Godel's theorem places no limitations on our > ability to understand/predict dynamics over finite time periods, and that > this is the sort of question physicists are almost always concerned with in > practice* *That's true but I think Alan Turing's Proof that there is no general solution to the halting problem and it's corollary that some things are true but uncomputable, is more relevant than Godel's theorem. In general there is no way to determine if a cellular automation, such as Conway's Game Of Life, will keep on growing forever, or start repeating itself, or die out completely; all you can do is watch it and see what it does, and you might need to watch it forever. * *And the first five Busy Beaver Numbers are 1, 6, 21 , 107 and 47,176,870, and we know for a fact that even if we had a mechanical computer that strictly followed Newton's laws and even if we had an infinite amount of time at our disposal, we will NEVER find the 745'th Busy Beaver Number even though it's well defined and it definitely exists. The same thing could probably be said about the sixth busy Beaver Number, although we are not certain about that, all we know for sure is that it's greater than 10^15. * *John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis>* 4jj > > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion visit https://groups.google.com/d/msgid/everything-list/CAJPayv0atLeCF4RcZ5sb-k9ece4jCnZ67%2Bhw9%3DkujME2PDybww%40mail.gmail.com.
