Once Upon a Number by John Allen Paulos, Basic Books, $23, ISBN
0465051588
THE acerbic Austrian physicist Wolfgang Pauli, suspicious of attempts to
unify the fundamental forces of physics, used to waggishly advise: 鈥淟et no man
join what God hath set asunder.鈥� While Pauli may yet prove to have been too
pessimistic about the unification of physics, his aphorism can surely be applied
with complete confidence to other attempts at bridge-building: finding a
connection between quantum theory and pre-Raphaelite art, say, or politics and
truth. Some things are just plain different, and no amount of bending, twisting
or spinning will make them otherwise.
In Once Upon a Number, mathematician John Allen Paulos boldly
ignores such admonitions and sets out to show that, despite appearances,
mathematics and storytelling are linked in ways that help each field to clarify
the other. Have you, like Paulos, ever pondered 鈥渢o what extent can the logical
and psychological gap between stories and statistics鈥攁nd the related gaps
between subjective viewpoints and impersonal probability, informal discourse and
logic, and meaning and information鈥攂e closed, or at least clarified?鈥� No,
me neither. And in this single direct quotation you have the central flaw of
this book: a pretty dull thesis, explored in a deadly dull way.
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Frankly, I can hardly believe that Once Upon a Number has been
written by the same person who gave us Innumeracy, that brilliantly
clear, original bestseller about the consequences of general mathematical
ignorance. I can still recall the excitement of reading that book, and my
amazement at its wonderfully fresh and apposite illustrations of how, say, the
mathematics of coincidences can catch us out. His Beyond Numeracy and
A Mathematician Reads the Newspapers were no less insightful.
Which is why the stale, rambling and opaque style of this book comes as a
shock. Whole chunks of it read like the sort of guff one would expect from an
author challenged to write like a postmodern philosopher for a bet. Take, for
example, Paulos鈥檚 defence of his basic thesis, that we should try to bridge
cultural divides, even if we do not always succeed: 鈥淏iculturalism ought to rein
in our individual cognitive homes, and souvenirs of travels and travails in
foreign disciplines are one way to help further this.鈥� What does this mean? It
makes a bit more sense if 鈥渞ein鈥� is a misspelling of 鈥渞eign鈥�, but not much.
Sadly, there is plenty more where this came from along with many a tired old
topic written about more clearly and to better effect elsewhere: Ramsey theory,
complexity theory, G枚del鈥檚 theorem, randomness.
There are some bright patches in this thick fog of a book. The material on
extensional and intensional logic and their uses seemed interesting, though it
was covered in such elliptical language that I may well be wrong. Bizarrely,
near the end of this book, Paulos admits that he himself has doubts about the
cogency of his thesis. I fear that anyone who buys it will be left in no doubt
whatsoever on that score.