Great writeup! I ended up following a few of the links and came across perhaps my favorite hand waving of all time for the validity of "The Spaghetti Code Conje

Great writeup! I ended up following a few of the links and came across perhaps my favorite hand waving of all time for the validity of "The Spaghetti Code Conjecture"[1]. Basically: For N=0,1: the problem is trivaial/degenerate. For N=2: the Turing machine must go back and forth between states or else it'd just be stuck in one state forever, which wouldn't be very busy beaverish. For N=n+1: well we just proved it up till n, so it seems pretty unlikely that n+1 would be different, things don't really just suddenly change like that y'know? QED So I'm not too surprised that this conjecture is being called into question. [1]: https://nickdrozd.github.io/2021/01/26/spaghetti-code-conjecture.html https://nickdrozd.github.io/2021/01/26/spaghetti-code-conjec...