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gjm comments on [Open Thread] Stupid Questions (2014-02-17) - Less Wrong
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This is probably a stupid question:
How is rounding error not a fatal flaw in brain simulation? Meaning, even if you could copy the workings of someones brain perfectly, it's presumably still a calculation done on some computer in some way. So even if you store the first X digits of every number in the calculation, it would at some point diverge from what the real brain did, even if it took a very long time.
Therefore is it fair to call that copy that 'person' or rather do you have to switch to speaking in terms of fidelities: that copy is Y percent the original person and diverges at a rate of Z percent every so many steps?
Yes, the two will diverge. But then, so they would even without rounding error, on account of quantum mechanics.
Neither of them is "the original person" (you are not, now, quite the same person as you were a year ago). Both are, so to speak, descendants of the original person. There are many (apparently) possible descendants -- you never know what might happen to you, after all. A good enough simulation would be as much like one of those as they are like one another. (I suppose that's a definition of "good enough".)
You don't even need quantum mechanics. The closest thing you can use to describe the way that cells actually function is 'noisy differential equations'. With emphasis on 'noisy'.