I’ve considered this problem with just n utils. Basically, pick the highest finite number you could.
If in doubt write really big numbers that look kind of like “9 → 9 → 9 → 9 → 9”. Is there a standard operation notation available that is more ridiculously excessive than Conway Chained Arrow? Preferably one that is easy to express rapidly in a format accepted by Omega.
I suppose I am then faced with a new problem, that of maximising the number that I can express to Omega. Do I stand there chanting Conway Chains at Om in all my waking hours until I die? Do I engage in or fund mathematical research into and popularization of ways in which to more efficiently express stupid numbers? Perhaps I ought to dedicate my entire existence to creating an FAI which would then necessarily dedicate all accessible entropy in the future light cone to answering Omega for me or through a post-human me.
Here I encounter a recursion. It seems that the rational response would be the “attempt to create an FAI to facilitate answering with a bigger n” for exactly the same reason that a big n is good in the first place. A stupidly excessively big payoff makes a tiny chance worthwhile.
If in doubt write really big numbers that look kind of like “9 → 9 → 9 → 9 → 9”. Is there a standard operation notation available that is more ridiculously excessive than Conway Chained Arrow? Preferably one that is easy to express rapidly in a format accepted by Omega.
If in doubt write really big numbers that look kind of like “9 → 9 → 9 → 9 → 9”. Is there a standard operation notation available that is more ridiculously excessive than Conway Chained Arrow? Preferably one that is easy to express rapidly in a format accepted by Omega.
I suppose I am then faced with a new problem, that of maximising the number that I can express to Omega. Do I stand there chanting Conway Chains at Om in all my waking hours until I die? Do I engage in or fund mathematical research into and popularization of ways in which to more efficiently express stupid numbers? Perhaps I ought to dedicate my entire existence to creating an FAI which would then necessarily dedicate all accessible entropy in the future light cone to answering Omega for me or through a post-human me.
Here I encounter a recursion. It seems that the rational response would be the “attempt to create an FAI to facilitate answering with a bigger n” for exactly the same reason that a big n is good in the first place. A stupidly excessively big payoff makes a tiny chance worthwhile.
Pretty much anything involving the busy beaver function. See also Scott Aaronson’s “Who can name the bigger number?”