[Fwd: Re: U-boats and Pop-Sci ??]
Anon.
Felesenstein's reply, which introduces some of the reality into the problem.
Bob
-------- Original Message --------
Subject: Re: U-boats and Pop-Sci ??
Date: Thu, 30 Oct 2003 01:02:16 +0000 (UTC)
From: j...@removethispart.gs.washington.edu
Organization: University of Washington
Newsgroups: sci.bio.evolution
References: <bnn5fs$ekl$1...@darwin.ediacara.org>
In article <bnn5fs$ekl$1...@darwin.ediacara.org>,
<know...@mindspring.com> wrote:
>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
> shrinks in comparison almost to in-
> significance. 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"?
I'm not surprised at Churchill's misunderstanding (or misrecollection)
of the
convoy issue, but I do hope that the Weinberg citation was aimed at
answering
a different question.
While yes, a (very) close-order convoy may have nearly the same probability
of detection as a single ship, if the U-boats then sank all of them once
a convoy was detected, the average fraction of all ships sunk would be
the same
either way. If the U-boat was alone and only had time to sink one or
two boats
of the convoy, there would be some protective effect. In reality multiple
U-boats were steered to convoys once those were detected, and wolf-packs
formed (and their codes were broken, and the story gets more and more
complicated).
A major reason for convoy sailing was not probability of detection but
the defense of the convoy, as one escort vessel could protect multiple
ships, and it would be impossible to escort all ships if they were
sailing individually. I don't think this the issue with fish.
Incidentally, there is an evolutionary connection with convoy issues
(aside from the school-of-fish connection). C. H. Waddington, a noted
geneticist, developmental biologist and evolutionist, headed an operations
research group in World War II as part of RAF Coastal Command. He wrote
a book
about these issues:
Waddington, C. H. 1973. OR in World War 2: Operational Research against
the U Boat, P. Elek (Scientific Books) Ltd.
My postdoctoral advisor, the late Alan Robertson, was a physical chemistry
graduate student at Cambridge University who joined Waddington's RAF group.
At the end of the war Waddington recruited Robertson to join him as a member
of his Institute of Animal Genetics at the University of Edinburgh.
That was
good judgement on the part of "Wad", and the start of Alan's brilliant work
on the theory of quantitative genetics.
--
Joe Felsenstein j...@removethispart.gs.washington.edu
Department of Genome Sciences, University of Washington,
Box 357730, Seattle, WA 98195-7730 USA
Fax: +358-9-191 22 779
WWW: http://www.RNI.Helsinki.FI/~boh/