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The idea of branch-counting seems untenable when we consider irrational probabilities (which they are, of course, overwhelmingly likely to be),though I think it
by mannykannot 7y ago
The idea of branch-counting seems untenable when we consider irrational probabilities (which they are, of course, overwhelmingly likely to be),though I think it would be begging the question to say, on that basis alone, that branch-counting is the wrong way to look at it. I think the example used to motivate branch indifference would be more persuasive if it used irrational probabilities.
- chr1 7y agoWe do not have any experimental reason to believe that "irrational probabilities" have any physical meaning. There is no method to measure them even indirectly, so a theory that operates only with natural numbers is quite plausible.
- mannykannot 7y agoThat's an interesting point. I did wonder, after posting the above comment, whether frequentists, at least, are ipso facto committed to all probabilities being rational, on account of their insistence that they are only meaningful in the context of repeated trials? (FWIW, I lean towards the frequentist viewpoint, insofar as I have a coherent position on the issue.) But then, what are we to make of physical formulae in which complex, transcendental and other non-rational numbers appear? Are they 'just' tractable approximate models of physical reality? I guess the Maxwell-Boltzmann distribution, at least, could be fairly characterized as such.
- chr1 7y agoAs far as i can understand all our measurements would be the same if all equations using real numbers were replaced by equations with finite precision (containing several hundred digits). The only experiment that could be different is quantum computer, because quantum fourier transform on n qubits requires at least n binary digits of precision on probabilities too. This is why some people think quantum computers won't work.
- lisper 7y ago> it would be begging the question to say, on that basis alone, that branch-counting is the wrong way to look at it. Exactly right. > I think the example used to motivate branch indifference would be more persuasive if it used irrational probabilities. What matters actually is not the probabilities but the branch weights/amplitudes (because you have to square those to get the probabilities). And those are irrational if the probabilities are 2/3-1/3.
- mannykannot 7y agoI take your point about the amplitudes not being rational, but in the examples of branch counting that I have seen, including this particular example, the counting is being done from the probabilities, not the 'raw' amplitudes.