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Re: Marilyn (redux)



On Tue, 12 Aug 1997, brian whatcott wrote:

There is a wise essense which witholds lists when for a moment they lose
their cool... as when a prof gives uncritical approval for a
mathematical construction which applies exactly to some world that does not
exist (such as a year of exactly 365 or 366 days, and as many birthdays,
but which errs in the case of brute reality, where the year measures some
fraction more than 365 days, but birthdays number 366)
In any case, it is unbecoming for me to gloat, so I won't. :-)

Huh? Oh well, since you *aren't* gloating I suppose it would simply be an
academic exercise for me to wonder what it is that you might otherwise
gloat *about.* ;-) After all, wasn't it *you* who wanted to put the
numbers d=365, and n=365,366,367 into the formula in the first place? And
wasn't it you who then wondered how to account for the results? If it was
merely "brute reality" you were concerned with, I thought David explicitly
and clearly addressed that issue in the very same note in which he gave
the formula.

As I wrote last week (in an apparently "unpublished" note),

brian whatcott wrote:

Unfortunately, the probability of 366 people having the same
birthday is not exactly one.

That's what to account for....

Ahem; to put it more succinctly...
It is possible to collect 366 people, no two or more of whom have
the same birth day number and month number.

Of course, *we* all know that, but how is the poor formula supposed to?
It can only speak intelligently about the answers to questions it was
designed to address; feed it any other question and it can only stare
blankly and, on a good day, drool. Thus, if you tell it that there are
365 distinct outcomes (i.e., "d=365"), 366 instances (i.e., "n=366"), and
ask it for the probability that at least two of those instances will be
identical (the only kind of question it understands), it will give you the
correct answer-- exactly 100%. Well sure, being mathematical, it might
complain a bit and mumble something about needing to deal with limits more
elegantly, but physicists are pretty good at beating uppity mathematical
formulas into submission.

John
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A. John Mallinckrodt http://www.intranet.csupomona.edu/~ajm
Professor of Physics mailto:ajmallinckro@csupomona.edu
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