>>13748512Interestingly, this is almost true, in the sense that any system in our current theories, whether classical, quantum, or relativistic, can have its motions calculated to arbitrary precision. Of course, it might take so long with our current tech that the universe ends via heat death or whatever before it finishes the calculation, depending on the precision you want.
>>13748833>>13750252>>13750846Uncomputable numbers exist, but their existence is usually considered irrelevant because (see above) we can just compute something arbitrarily close to it. One way to think of "uncomputable" real numbers is that we can't come up with a program that does, "I want the nth digit of this fixed real number", and have it work correctly for ALL digits. If the real number in question is uncomputable, there are an infinite number of digits wrong, and we can't use a computer to figure out which ones they are, in the general case.
In a more specific case, however, you can use an approximation algorithm, so you can guarantee that the first however many decimal places are correct, for a finite, but arbitrarily high number of decimal places.
