beriukay comments on Demands for Particular Proof: Appendices - Less Wrong

26 Post author: Eliezer_Yudkowsky 15 February 2010 07:58AM

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Comment author: Unknowns 21 February 2010 07:26:53PM *  3 points [-]

The point was that you can easily have a sum of an infinite series that adds to some small finite amount. Assuming "Earth 5000" is defined differently from "Earth 500" (which it must be in order to have new hypothesis), your different hypotheses will different complexities depending on the complexity of the number. Overall (but not in every single instance) the higher the number, the more complex the hypothesis, so the less the probability will be changed. There is no reason for this infinite sum not to converge to an extremely small quantity.

In any case (and this may be Peter de Blanc's point), these probabilities are smaller than the sensitivity of the human judgement: so in fact, subjectively you don't need to feel obliged to change your opinion at all based on them.

Comment author: beriukay 22 February 2010 03:15:21PM 0 points [-]

That makes sense. I guess as long as the sum of the infinitely many absurdly contrived possibilities remains less than rounding error and/or sensitivity of human judgment, I have no qualms with your original point.