From: Damien Broderick (d.broderick@english.unimelb.edu.au)
Date: Fri May 24 2002 - 22:24:25 MDT
At 06:33 PM 5/24/02 +0200, Amara quoted:
>_Falsificationism in Statistics_
>Pg. 171-173, Howson and Urbach
>The Cournot-Popper view overlooks the fact that very improbable events
>occur all the time. Indeed, it would be difficult to name a probability
>so small that no event of some smaller probability had not already taken
>place or is not taking place right now: events of miniscule probability
>are ubiquitous. Even a probability of 10^(10^(12)), which Watkins
>considered to be 'vanishingly small' and to amount to an impossibility
>(1984, pg. 244) is nothing of the sort. [cf.]
>the probability that the atoms in the jug of water on
>this table have a particular spatial distribution at a given time.
This looks like a standard (but perhaps key) confusion to me. For the
purposes of *science*, the improbability of such a distribution is
presumably the very low likelihood that [specific declared distribution D
or something close to it] will be observed in a preparation, or in a
natural experiment, n times out of N observations. In a universe without
any observers, I think that an array of jittery atoms in a liter of gas
that formed the flag of the new nation of East Timor would be no more
special than any of the other zillions of random arrays. But if I announced
in advance that this pattern would be seen at the stroke of midnight due to
the activation of my much ridiculed Kryptonite scanner, finding the atoms
so arrayed would immediately be recognized as strong evidence that my
machine was effective. Indeed, if it *didn't* show that pattern on the
night in question, but someone noticed that the pattern appeared 46.83
hours later, I'm pretty sure we'd be inclined to suspect that the
Kryptonite effect was real but with an unexpected time delay in manifesting
itself.
Damien Broderick
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