submit these data to analysis, it would embrace in the same formula both
the movements of the largest bodies in the universe and those of the
lightest atom; to it nothing would be uncertain, and the future as the past
would be present to its eyes.”^2
Of course, these statements were rhetorical, but they were made to em-
phasize the far-reaching potential of the solution to the problem. A casual
onlooker, seeing Archimedes use a lever to reposition a heavy rock, might
have said, “OK, that’s useful, but it’s just a rock.” Archimedes could have
replied, “It’s not just this rock—it’s any object whatsoever, and I can tell
you what length lever I need to move that object and how much effort I
will have to exert in order to move the object to a desired position.”
Sometimes we are so impressed with the more dazzling achievements
of science and engineering that our inability to solve seemingly easy (or
easier) problems appears puzzling. During the 1960s, one could occa-
sionally hear the following comment: If they can put a man on the moon,
how come they can’t cure the common cold?
We are a little more scientifically sophisticated now, and most people are
willing to cut science some slack on problems like this, recognizing that
curing the common cold is a more difficult problem than it initially
seems. The general feeling, though, is that we just haven’t found a cure
for the common cold—yet. It’s obviously a difficult problem, but consid-
ering the potential payoff, it’s no surprise that medical researchers are
busily trying, and most of us would probably expect them to find a cure
sooner or later. Sadly, for those suffering from runny noses and sore
throats, there is a very real possibility that a cure for the common cold
may never be found, not because we aren’t clever enough to find it, but
because it may not exist. One of the remarkable discoveries of the twen-
tieth century is a common thread that runs through mathematics, the
natural sciences, and the social sciences—there are things that we cannot
know or do, and problems that are incapable of solution. We know, and
have known for some time, that humans are neither omnipotent nor om-
niscient, but we have only recently discovered that omnipotence and om-
niscience may simply not exist.
When we think of the scientific developments of the twentieth century,
we think of the giant strides that were made in practically every disci-
pline, from astronomy through zoology. The structure of DNA. The the-
ory of relativity. Plate tectonics. Genetic engineering. The expanding
universe. All of these breakthroughs have contributed immeasurably to
our knowledge of the physical universe, and some have already had a sig-
nificant impact on our daily lives. This is the great appeal of science—itxi Introduction