shot. After all, it doesn’t seem so unlikely that Cook’s techniques for dem-
onstrating the equivalence of NP-hard problems could be modified to
show that a hole in one algorithm must necessarily result in holes in oth-
ers. I’m not capable of moving these pieces, but I really believe that I can
see them move.
Falling Off the Train
Whenever one considers memorable prognostications that have proven to be
incredibly wrong, one has to at least mention a classic that occurred a couple
of decades ago. The Soviet Union had just collapsed, the United States was
the world’s only superpower, and Francis Fukuyama produced a widely
publicized essay entitled “The End of History?” This less-than-prescient
comment is taken from that essay: “What we may be witnessing is not just
the end of the Cold War, or the passing of a particular period of post-war
history, but the end of history as such: that is, the end point of mankind’s
ideological evolution and the universalization of Western liberal democracy
as the final form of human government.”^3
Karl Marx may have been discredited as an economic theorist, but he
really nailed it this time with his observation that when the train of his-
tory rounds a corner, the thinkers fall off.^4 Even conservatives would
likely welcome the universalization of Western liberal democracy as the
final form of human government, but the events of the last two decades
have shown that the millennium, at least in the sense of the ultimate ful-
fillment of Fukuyama’s prediction, is not yet at hand.
In retrospect, Isaac Asimov had a much clearer view of how history un-
folds. Asimov may not have been the first of the great popularizers of
science (my nominee would be Paul de Kruif, author of the classic Mi-
crobe Hunters), but he was undoubtedly the most prolific. He has works in
every major category of the Dewey decimal system except philosophy,
which he perhaps resisted because his academic background was in bio-
chemistry rather than physics. It is rather surprising that his popularized
science works are written as rather straightforward presentations of facts
(“the moon is only one-forty-ninth the size of the Earth, and it is the near-
est celestial body”), because his fame originally came from his highly
entertaining and often-prescient science fiction. He was one of the three
great early writers of science fiction (Arthur C. Clarke and Robert Hein-
lein being the others), and his ideas were often unbelievably ingenious.
One of his earliest published stories, “Nightfall,” describes the difficulty
experienced by a civilization in trying to discover the mysteries of gravi-
tation in a planetary system with six nearby stars. I found particularly
242 How Math Explains the World