Interesting. Here's a possible way out. Suppose the universe is always changing according to some state-transition function that gets you to time t to time t+1. We have a machine existing in this universe which is trying to predict the state at t+1. You point out this is impossible because the transition function might suddenly change for some particular t+1. But if the change is massive enough, it will also destroy the internal workings of the prediction machine. Conditional on the universe retaining enough regularity for the prediction machine to survive, maybe it would be possible to make "universal" predictions.
The universe (U) itself would be the prediction machine.
To be fair, there would be no definition of "circular" without the universe.
The reality we - or habitants from other universes or other domensions - can measure seems to be some kind of "Fractal collapsing" at the dimension/universe that the "measurer" is located.
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Kind of related:
Dostoiévsk, in his book notes from underground proposes an interesting problem.
I paraphrase it below:
What would you do if you receive from god himself a manuscript of the actions (down to the minimum possible dt) that will maximize your "satisfaction function" considering all your life?
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Rick and Morty also explored this using another analogy:
Psychologists are like horses in a caroussel trying to understand it's mechanism. They'll do their best, but in the end won't help much and feel terrified.
