Two priors could indeed start out diverging such that you cannot reach one from the other with finite evidence. Strange loops help here:
One of the hypotheses the brain’s prior admits is that the universe runs on math. This hypothesis predicts what you’d get by having used a mathematical prior from day one. Natural philosophy (and, by today, peer pressure) will get most of us enough evidence to favor it, and then physicist’s experiments single out description length as the correct prior.
But the ways in which the brain’s prior diverges are still there, just suppressed by updating; and given evidence of magic we could update away again if math is bad enough at explaining it.
Two priors could indeed start out diverging such that you cannot reach one from the other with finite evidence. Strange loops help here:
One of the hypotheses the brain’s prior admits is that the universe runs on math. This hypothesis predicts what you’d get by having used a mathematical prior from day one. Natural philosophy (and, by today, peer pressure) will get most of us enough evidence to favor it, and then physicist’s experiments single out description length as the correct prior.
But the ways in which the brain’s prior diverges are still there, just suppressed by updating; and given evidence of magic we could update away again if math is bad enough at explaining it.