(Here, the log(n) is needed to specify how long the sequence of random bits is).
You don’t always need log(n) bits to specify n. The K-complexity of n is enough. For example, if n=3^^^^3, then you can specify n using much fewer bits than log(n). I think this kills your debunking :-)
O(BB^-1) (or whatever it is) is still greater than O(1) though, and (as best I can reconstruct it) your argument relies on there being a constant penalty.
Yeah, kind of, but the situation still worries me. Should you expect the universe to switch away from the Born rule after you’ve observed 3^^^^3 perfectly fine random bits, just because the K-complexity of 3^^^^3 is small?
You don’t always need log(n) bits to specify n. The K-complexity of n is enough. For example, if n=3^^^^3, then you can specify n using much fewer bits than log(n). I think this kills your debunking :-)
O(BB^-1) (or whatever it is) is still greater than O(1) though, and (as best I can reconstruct it) your argument relies on there being a constant penalty.
Yeah, kind of, but the situation still worries me. Should you expect the universe to switch away from the Born rule after you’ve observed 3^^^^3 perfectly fine random bits, just because the K-complexity of 3^^^^3 is small?