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Desrtopa comments on On accepting an argument if you have limited computational power. - Less Wrong
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I'm settling for just one quadrillion to avoid dealing with the contingency of "3^^^3 is impossible because complexity". The requirement of testability is not affected by the contingency.
If you assign the threat a probability of, say, 10^-20, the mugger is extorting considerably more dead children from you than you should expect to die if you don't comply.