MS 473-474 (1903) - Lowell Lecture VII

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while your asumptions would have been utterly without warrant, it would have attained, in the only way possible for any such assumption, the merit of proceeding on a principle that does not cut its own throat.

At this point, I should not wonder if some unwary Laplacian were to say, “There seems to be some reason in what you urge. I think, myself, that it would be a sounder proceeding to assume the different constitutions of the universe to be equally possible. But that is a mere detail, and will alter the numerical result a bit, but that is all.” Well, let us see how much the result will be altered by

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assuming first the different constitutions of the box to be equally possible, and then the different constitutions of the universe to be equally possible. Here is the table for the equal possibility of the constitutions of the box

[table]

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It thus turns out that on this hypothesis, which is certainly not so absurd as that of Laplace, that the odds in favor of the sixth toy being dutiable after the first five are found dutiable are only 7 to 3. Common sense revolts against this. But we ought to have made the constitutions of the universe equally possible. That is, we ought to have neglected the fact of the toys being packed in boxes of ten, which really has nothing to do with the matter and have treated them as if they were packed in boxes of indefinitely many toys. I have made the calculation for 25 in a box, and the result is shown in the following table

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[table]

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We thus find the odds only 5 to 4. If instead of 25 divisions I had made 50 or 100 we should have found it an even chance.

Last edit over 5 years ago by gnox
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