In the beginning, roughly 10 billion years ago according to modern cosmology, was the Big Bang. The universe has been expanding ever since. Whether it will keep doing so forever, we do not know. It may be--if the density of matter in the universe is sufficiently great--that gravitational forces eventually will cause the universe to stop expanding and then to start falling back in upon itself. If that occurs, the universe will end in a cataclysmic event that cosmologists call the Big Crunch.
The history of modern science is somewhat analogous. This science appeared on the scene almost three centuries ago in Europe and slightly more than a century ago in the United States. In each case, it proceeded to grow at an astonishing exponential rate. But while the universe conceivably may expand forever, the exponential enlargement of the scientific enterprise is guaranteed to come to an end.
It is not that scientific knowledge must stop growing. On the contrary, if all goes well, it should continue to expand. But the growth of the profession of science, the scientific enterprise, is bound to reach certain limits. I contend that these limits have now been reached. Many of my scientific colleagues persist in the belief that the future will be like the past and are seeking to preserve the "social structure" of science--the institutions and the patterns of education, research, and funding--that they have come to know so well. If I am right, they won't succeed.
The Big Crunch is here (even if it is actually more like a large whimper than a big bang); indeed, in some fields it has already happened. In physics, it occurred about 25 years ago--and we physicists have been doing our best to avoid the implications ever since. We cannot continue to do so. We must address a question that has never even occurred to the cosmologists: what do you do after the Big Crunch?
The situation can be illustrated by a graph. The upper curve--first published in a book called Science since Babylon (1961) by the historian Derek de Solla Price--shows, on a semilogarithmic scale, the cumulative number of scientific journals founded worldwide over the last three centuries. A straight line with a positive slope on this kind of graph means pure exponential growth. If something is increasing that way, then the larger it gets, the faster it grows. Price's curve, he maintained, is a suitable stand-in for any quantitative measure of the size of science. If so, then modern science appears to have sprung into being around 1700 (the Big Bang might have been the publication of Sir Isaac Newton's Principia in 1687) and thereafter expanded exponentially, growing tenfold every 50 years.
Price predicted that this behavior could not go on forever--and, of course, he was right. The straight line in the plot extrapolates to one million journals by the millennium. But the number of scientific journals in the world today, as we near the millennium, is a mere 40,000.
That is only one measure of what is happening, but all the others tend to agree. Consider, in particular, the number of scientists around. It has often been said that 90 percent of all the scientists who have ever lived are alive today. That statement has been true for nearly 300 years--but it cannot go on being true for very much longer. Even with the huge increase in world population in this century, only about one-twentieth of all the people who have ever lived are alive today. It is a simple mathematical fact that if scientists keep multiplying faster than people, there will soon be more scientists than there are people. That seems very unlikely to happen.
I have plotted, on the same scale as Price's curve, the number of Ph.D.'s in physics produced each year in the United States. Like all other quantitative measures of science, this one behaves much like Price's curve. The graph shows that science started later in the United States than in Europe. The first Ph.D. …