You’re mixing up two layers of uncertainty. There’s an outer uncertainty. This would include things like I made a mistake, this is all a dream, etc. This outer

You’re mixing up two layers of uncertainty. There’s an outer uncertainty. This would include things like I made a mistake, this is all a dream, etc. This outer uncertainty pervades all problems. It’s often useful to ignore that outer uncertainty. We create a framework where we take certain things as true (shared reality, mathematical axioms). This framework may or may not have uncertainty inside of it, which we could call inner uncertainty. Questions of probability have inner uncertainty. Questions of geometry do not. This makes them qualitatively different. If you frame the initial task as something like “do your best to lead people to believe your sequence is random”, that makes sense. If the task is “make it so they can’t tell if it’s random”, that’s a bit off in some way. At the very least, it’s because you’ve presented the spotting of randomness as something that can truly be done to a logical conclusion (random/not or true/false). This violates both the outer and inner uncertainties of randomness.