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news:bnn5fs$ekl$1{at}darwin.ediacara.org...
> Would some statistically-knowledgeable folk be good enough
> to explain the mathematical/statistical reasoning (or, if applicable,
> the principles which contrave) the following statement by Nobel
> Physicist Steven Weinberg (writing about books on war, not
> about physics) in the most recent (Nov. 6, 2003) issue of the
> "New York Review of Books"?
> Prof. Weinberg writes:
>   "It should have been obvious that the solution to the
>    U-boat threat was to require merchant ships to sail
>    in convoy.  As Churchill later explained in The
>    World Crisis,
>        The size of the sea is so vast that the
>        difference between the size of a convoy
>        and the size of a single ship shinks in
>        comparison almost to insignificance.
>        There was in fact nearly as good a
>        chance of a convoy of forty ships in
>        close order slipping unperceived between
>        the patrolling U-boats as there was for
>        a single ship; and each time this happened,
>        forty ships escaped instead of one.
>   (This is also the reason that fish of many species
>   swim in schools.)"
>
> Putting aside the at best highly questionable (and "scientific"?)
> parenthetical throw-away remark about "the reason" ascribed
> to what "many" fish do, and also disregarding for the moment
> the variable of the role of spying/intelligence, does the Churchill
> quotation really (accurately) "explain" what Weinberg
> characterizes as "obvious"?

This won't be the statistical or scientific answer you wanted, but yes is my
SWAG-ish answer, and the important Churchill quote is: "the difference
between the size of a convoy and the size of a single ship shrinks in
comparison almost to insignificance."

> Does Churchill's (and, implicitly, Weinberg's) use of "vast"
> conflate that word with "infinite" and, conversely, is
"vast"
> itself helpful bearing in mind that, even if a particular ship-
> ping route with respect to one specific ship (or one convoy)
> at one time is not known in advance, the geographical
> parameters of British (or of U.S. or other "allied") shipping
> routes was (more or less) reasonably ("probably"?) predictable?

No, no conflation.  "Vast" is somewhat superfluous, and may therefore only
be of help to the individual reader.  The previous responses are true simply
because we know the far-less-than-infinite parameters of the North Atlantic.
Ironically, the latter half of your comment, above, makes me think that you
may not appreciate how "vast" is the North Atlantic when compared to one
specific ship (or one convoy), the permutations for crossing it, or the
difficulties with visual acquisition.  Remember that, especially in the case
of World War II U-boats, the conning tower (or fin, depending on from whence
you come), was anything but lofty - the horizon was not *that* far away - by
my rough calculations, a submarine on the surface could visually miss a
convey a mere ~20 kms (~13 miles) distant in fair conditions.  This on an
ocean with routes spanning a couple of thousand miles.  Also important is
timing, as the pair (boat/convoy, or boat/ship) generally needed to be in
proximity during daylight hours and in reasonable visibility.  And of course
the bottom (or retrospective) line is that, it worked.

> (And, BTW, what might Weinberg have been referring to
> by his parenthetical reference to "many" fish?) Thanks.

Unclear on your question...  "many species" were implied, not many fish.
Are you asking which species school to minimize predation?  There are many,
of course, though this can be couterproductive as some predators such as
certain shark species, marlin, etc., have "learned" (instinct?) well to
hover above, below and around some schooling fish and periodically and
repeatedly race through the school to eat their fill - sometimes several
predators will quite literally decimate a school together.  Best regards,
Brett.
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