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鈥檚 The
Universal Computer: The road from Leibniz to Turing you should be able to
demonstrate conclusively that 鈥渘o X are Y鈥�.
Were I a mathematical logician myself, I would leave my review at that.
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New 杏吧原创 readers are, however, more demanding. Which is the
point, since Davis鈥檚 book claims to be 鈥渁bout the underlying concepts on which
our modern computers are based and about the people who developed those
concepts鈥�, it is really about giving readers a (sometimes not very basic)
tutorial in mathematical logic.
Davis鈥檚 idea is a good one. First, examine key figures behind the development
of logic鈥攖he mathematicians and logicians Gottfried von Leibniz, George
Boole, Gottlob Frege, Georg Cantor, David Hilbert, Kurt G枚del and Alan
Turing. Then tell us about their innovations, such as Boole鈥檚 new algebra or
Turing鈥檚 鈥渦niversal鈥� computer, and about their lives: Cantor鈥檚 depression,
Turing鈥檚 homosexuality and so on. Finally, consider the relationships between
them.
The result should be that we appreciate these scientists鈥� 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鈥檚 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 鈥淒epression and tragedy鈥�, Davis talks mostly
about the mathematician Cantor鈥檚 transfinite cardinal numbers. Then he glosses
over Cantor鈥檚 depression as 鈥渨hat is now viewed as manic-depressive illness鈥�.
This is, of course, not the same thing at all as depression. Davis gives the
simplistic explanation that 鈥渋t is now generally understood that the disorder鈥檚
fundamental cause is rooted in defective brain chemistry鈥�.
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 鈥渢his episode pretty much
marked the end of Cantor鈥檚 ground-breaking work鈥�. 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 鈥渇ollowed the
lives of a group of brilliant young innovators鈥�, whose contributions 鈥渁dded up
to the intellectual matrix out of which emerged the all-purpose digital
computer鈥�. I don鈥檛 believe he has done anything of the sort. He suggests in his
final sentence that this story 鈥渦nderscores the power of ideas鈥� and he has shown
that 鈥渢hose who provide scientists with the resources necessary for their lives
and work try to steer them in directions deemed most likely to provide quick
谤别蝉耻濒迟蝉.鈥�
This is nonsense. The 鈥渄igital computer鈥� (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.