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If that's counterintuitive, than the most basic physics already teaches you that many things are counterintuive. The 3-body problem does not have an analytical
by Confusion 16y ago
If that's counterintuitive, than the most basic physics already teaches you that many things are counterintuive. The 3-body problem does not have an analytical solution. We can't even properly simulate the solar system a couple of thousands of years ahead. Nearly everything in physics is numerical approximation, despite what theory would lead you to believe. After that, the halting problem is far from surprising.
- archgoon 16y agoThere's a significant difference between "Nobody can solve this problem, despite it having a well defined answer, regardless of the power of the computer and the time given to solve it, no matter how clever you are" and "I can only get an approximation to the solution, but the error will always be well defined, so I can get arbitrarily accurate solutions, say within a nanometer given a few billion years or so."
- Confusion 16y agoAlthough you can't solve the general halting problem, there are many halting problems that can be, and are, solved in practice. To me, that's the same thing as a numerical approximation to something that doesn't have an analytical solution.