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Arran_Stirton comments on A (very) tentative refutation of Pascal's mugging - Less Wrong
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"So for every extra unit of disutility predicted the probability penalty due to not knowing enough about the current state of the universe becomes greater."
Sure, but the probability shrinks slower than the disutility rises. A scenario in which 1000 times 3^^3 people are tortured has more probability that the probability that 3^^3 people are tortured, divided by 1000. Or more formally:
[P(Mugger tortures 1000*3^^3 people)] > [P(Mugger tortures 3^^3 people)]/1000
Read about Solomonoff Induction to find out why this is true.
I'm treating the current state of the universe as a different thing entirely to the mugger's implied hypothesis about how the universe works. Both a program simulating Maxwell’s equations would obviously win out over a program simulating Thor, but in terms of predicting the shape of a magnetic field in a certain spot, that depends on the current state of the universe (at least the parts of the universe relevant to the equation).
Though if this is an invalid line of reasoning for some reason, please let me know, thanks.
I have no idea where you're going with this.
You use the word "both" but then refer to only one object. Did you forget to include something?
Sorry I'll try to clarify:
If you want to predict the exact state of a system five minutes into the future you need to know the current state of the system and the laws of that system. Call the current state s and the future state s', the laws of the system are simulated by the Turing machine L. Instead of knowing the state of the system, we only know its laws (or rather we take them as a given).
Then any prediction we make about the future state of the system will restrict the range of value for s' that will validate our prediction. The more specific we are about s' the smaller the range of values it can be. In turn this restricts the range of possible values for s (as L(s) = s') that will give s'.
Because we have no information about the current state of the system all possible states are equally likely, and as such the probability that the system will end up in a particular range of s' is the same as the fraction of s (out of all possible s) that will map there.
This is not in relation to any hypothesis about the laws of the system, but instead the current state of the system. I hope this makes my original argument make more sense. If not I'm sorry; please highlight to me where my explanation is going wrong.