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.
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.
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.
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.