Examining the Copernican Principle, we saw that when Bayes’s Rule is given an uninformative prior, it always predicts that the total life span of an object will be exactly double its current age. In fact, the uninformative prior, with its wildly varying possible scales—the wall that might last for months or for millennia—is a power-law distribution. And for any power-law distribution, Bayes’s Rule indicates that the appropriate prediction strategy is a Multiplicative Rule: multiply the quantity observed so far by some constant factor. For an uninformative prior, that constant factor happens to
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