I’d spend as long as I could trying to find the highest possible n.
I’ve considered this problem with just n utils. Basically, pick the highest finite number you could. And consider how much you missed out on because you didn’t square it.
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.
I’d spend as long as I could trying to find the highest possible n.
I’ve considered this problem with just n utils. Basically, pick the highest finite number you could. And consider how much you missed out on because you didn’t square it.
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?”