The Universal Computer: The road from Leibniz to Turing by Martin Davis,
Norton, $26.95, ISBN 0393047857
LET X be the class of mathematical logicians, and Y the
class of good popular science writers. By reading Martin Davis’s The
Universal Computer: The road from Leibniz to Turing you should be able to
demonstrate conclusively that “no X are Y”.
Were I a mathematical logician myself, I would leave my review at that.
Advertisement
91av readers are, however, more demanding. Which is the
point, since Davis’s book claims to be “about the underlying concepts on which
our modern computers are based and about the people who developed those
concepts”, it is really about giving readers a (sometimes not very basic)
tutorial in mathematical logic.
Davis’s idea is a good one. First, examine key figures behind the development
of logic—the mathematicians and logicians Gottfried von Leibniz, George
Boole, Gottlob Frege, Georg Cantor, David Hilbert, Kurt Gödel and Alan
Turing. Then tell us about their innovations, such as Boole’s new algebra or
Turing’s “universal” computer, and about their lives: Cantor’s depression,
Turing’s homosexuality and so on. Finally, consider the relationships between
them.
The result should be that we appreciate these scientists’ contributions,
their intelligence, and their ability to see beyond the immediate into a complex
abstract world of relationships, reasoning and alternative systems of logic. The
actual result is that we are treated to a set of sketchy vignettes, drawn and
badly re-edited from secondary sources which reveal little or nothing of these
people’s lives. Davis would prefer to write books which consist entirely of
sentences of symbolic logic and have footnotes containing
the same, consuming entire pages. You have to admire logicians for their
enthusiasm for the subject even if it drives out any thoughts of style, humour
or analysis.
For example, in his section “Depression and tragedy”, Davis talks mostly
about the mathematician Cantor’s transfinite cardinal numbers. Then he glosses
over Cantor’s depression as “what is now viewed as manic-depressive illness”.
This is, of course, not the same thing at all as depression. Davis gives the
simplistic explanation that “it is now generally understood that the disorder’s
fundamental cause is rooted in defective brain chemistry”.
But what we would really be interested in is what this meant for Cantor as a
person. How did it affect his professional and social relationships? Instead,
Davis dismisses him with a wave of his hand, saying “this episode pretty much
marked the end of Cantor’s ground-breaking work”. Exit Georg Cantor, consigned
to the backwaters of chapter four, with defective brain chemistry.
Davis sums up what he has accomplished for us, saying he has “followed the
lives of a group of brilliant young innovators”, whose contributions “added up
to the intellectual matrix out of which emerged the all-purpose digital
computer”. I don’t believe he has done anything of the sort. He suggests in his
final sentence that this story “underscores the power of ideas” and he has shown
that “those who provide scientists with the resources necessary for their lives
and work try to steer them in directions deemed most likely to provide quick
ܱٲ.”
This is nonsense. The “digital computer” (as Davis quaintly calls it) emerged
from a complex set of social, ethical, technological, political, commercial and
financial circumstances, and only partly as a result of the efforts of those
innovators discussed in this book.
It will, however, be a howling success at the annual Association for Symbolic
Logic conference, which Davis will no doubt attend, and at which his fellow
mathematical logicians will applaud by calling out abstract logical expressions.
