The Modern Forgery Hypothesis

[Jorge_Stolfi]

Here is a fun exercise of the Bayes formula.   An old oak trunk with brass trimmings, with "J.S.T" written on the lid, is said to contain N tokens, with distinct numbers 1 to N.  You don't know N, but from the size of the trunk and of the tokens you are sure that it is less than 10'000. Other than that, any value of N seems equally likely.

1. The trunk is well shaken, then someone reaches into it and picks a token at random.  It bears the number 19.  Now what is your probability that N is less than 50?

2. That exercise is repeated four more times, and the numbers that come out are 4, 7, 18, and 40 (in some order).  Now what is your probability that N is less than 50?

I am too lazy to do the computation myself, but I would guess that the answer to (2) is very high, much more than 50%.

The point is that, from the numbers on the front pages, we can safely guess that the set of all the books that ever existed with Jacobus's name on them had only 50 books or so.    

Would that be a plausible value for the number of books owned by someone like Jacobus?

All the best, --stolfi