When you realize your previous approximation leads to a discontinuous function after new data arrives, just roll back your instruction pointer as well as your perception of time.
This ability to retroactively error-correct without affecting perceived continuity could also be affording our brains a greater margin of error.
Maybe, but then it turns out that your brain's cache isn't rolled back when you mispredict, and you have to close your eyes for ten seconds after looking at anything secret until another few hundred generations of evolution fix the bug.
And the brain can rewrite the history it saved if it finds logical errors that came up because of it filling in gaps wrong.
Brains are awesome and scary.