Which mathematical questions can be answered with an n-body computer? An n-body computer is an arrangement of n-bodies moving under mutual gravitation that is prepared in an initial state to answer a specific question. If the solution remains bounded, the answer is "no". If at least one ball shoots out to infinity, the answer is "yes." (I'm quite willing - eager even - to assume the universe is infinite in both space and time.) Of course, such a "computer" is of no practical interest whatsoever. We must be willing to wait an infinite amount of time to be sure of the answer - it is even worse than my laptop.
For example, can we set up an n-body problem to determine the truth value of a given k-variable propositional calculus wff for given Boolean values of its variables? I'll hazard a guess that the answer is "yes". (It is sufficient to consider expressions built using just 5 symbols: 1, 0, (, ), and a symbol for the NAND connective.)
Can we simulate a Turing machine using n bodies?
Is there an effective procedure to determine whether the solution to a given n-body problem will remain bounded? (I don't see how this could conceivably be answered in the affirmative, so I guess I'm asking if it is known that the answer is "no.")