We’re going to use Solomonoff induction, or (if you want it to be computable) an approximation like AIXI-tl, so we’ll need a prior over all Turing machines. Let’s go with the speed prior for now.
At each bit, choose the bit which has lower probability according to this predictor.
This sequence is entirely deterministic, but can’t be predicted without self-reference.
It does make sense, and there’s a way to do it!
We’re going to use Solomonoff induction, or (if you want it to be computable) an approximation like AIXI-tl, so we’ll need a prior over all Turing machines. Let’s go with the speed prior for now.
At each bit, choose the bit which has lower probability according to this predictor.
This sequence is entirely deterministic, but can’t be predicted without self-reference.