Interesting. This prank seems to be one you could play on a Logical Inductor, I wonder what the outcome would be? One fact that’s possibly related is that computable functions are continuous. This would imply that whatever computable function Omega applies to your probability estimate, there exists a fixed point probability you can choose where you’ll be correct about the monkey probability. Of course if you’re a bounded agent thinking for a finite amount of time, you might as well be outputting rational probability estimates, in which case functions like f(x)=mod(x+12,1) become computable for Omega.
Interesting. This prank seems to be one you could play on a Logical Inductor, I wonder what the outcome would be? One fact that’s possibly related is that computable functions are continuous. This would imply that whatever computable function Omega applies to your probability estimate, there exists a fixed point probability you can choose where you’ll be correct about the monkey probability. Of course if you’re a bounded agent thinking for a finite amount of time, you might as well be outputting rational probability estimates, in which case functions like f(x)=mod(x+12,1) become computable for Omega.