From: scerir (scerir@libero.it)
Date: Fri Aug 30 2002 - 01:32:42 MDT
Damien
My recollection of Pohl's original discussion
is that this was his term for dimensionless numbers,
ratios that show up most unexpectedly in different
situations apparently implying some common cause.
Frederik Pohl, 1980, _Beyond The Blue Event Horizon_, Del Rey,
NY, pg 251:
Then I turned to the tapes. I let the semi-Albert, the rigid
half-animated caricature of the program I knew and loved,
lecture me on Mach's Principle and gosh numbers more
curious forms of astrophysical speculation than I had ever
dreamed of.
[Courtesy of John B. Grosh]
Yes actually most "gosh" numbers are dimensionless. Well, I would
not say that all "gosh" numbers are dimensionless (this reminds me of
a certain numerical factor, for radiative corrections, in particle physics,
0.07, which has been called, after Bruno Touschek, the "Bond factor").
According to F. Pohl infinity is also a dimensionless number, since you will
get the same value no matter what unit of measurement you use. But Pohl
wasn't a good mathematician, see what James A. Landau wrote recently.
<< Frederick Pohl liked to use mathematical tidbits in his science fiction
stories. Unfortunately he had no real mathematical training, and this led to
some amusing errors. In his story "The Gold at the Starbow's End" (in the
magazine Analog Science Fiction in 1972) he cited a certain number as being
impossible to factor with any reasonable number of computers. In fact it
could be factored by hand.
(Pohl did not realize that a^m + b^n is no harder to factor than is a + b.
He was further embarrassed by having x^y^z, which was part of the number as
he originally wrote it, get truncated to x^y somewhere between manuscript and
publication, thereby making the number as published ridiculously small for
what he was describing.)
I met Pohl at the 1972 World Science Fiction Convention. He told me about
the missing exponent, admitted his lack of knowledge of factorization at the
time he wrote the story, and added that this mathematical blunder actually
worked to his advantage. All the skeptical readers (including myself) had
concentrated on his math and had overlooked a much more embarrassing
blunder---he had had the Hale telescope (on Mount Palomar in California)
looking at Alpha Centauri!
I have only read one of Pohl's more recent books, "The Coming of the Quantum
Cats" (the title refers to the paradox of Schroedinger's Cat, which however
plays no part in the story.) In this book Pohl correctly points out that a
binary number such as 100110 can be easily handled by humans simply by
breaking it up into groups of three bits, in this case 100 110. However, he
fails to realize that he has simply created the octal number 46.
However, Mr. Pohl is entitled to laugh at the staff of Computerworld (a
weekly newspaper in the computer field) who once gave out buttons that read
THE SPIRIT OF 100110
This was supposed to be "The Spirit of '76" (for non-US list members, the
reference is to the US Declaration of Independence in 1776). However, these
professionals had managed to leave off the trailing zero, so that the badge
actually read "The Spirit of 38". >>
For sure there is a special set of "gosher" numbers. They have the form ...
$ x,xxx.xx
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