The Big Crunch
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The Big Crunch David Goodstein The following article is an edited version of a plenary lecture given at Pittcon in New Orleans on March 8, 1995. Previous versions of this article have been published as "Scientific Ph.D. Problems," American Scholar, 62 (1993), and "Scientific Elites and Scientific Illiterates," Ethics, Values and the Promise of Science, Forum Proceedings, Sigma Xi, The Science Research Society (February 25-26, 1993) p. 61, and Engineering and Science 56 (Spring 1993) p. 22. David Goodstein is vice provost, professor of physics and applied physics, and the Prank J. Gilloon Distinguished Teaching and Service Professor at the California Institute of Technology.
According to modern cosmology, the Universe began about 10 billion years ago with the Big Bang. It has been expanding ever since. If the density of matter in the Universe is sufficiently large, gravitational forces will eventually cause the Universe to stop expanding, and then to start falling back in upon itself. If that happens, the Universe will end in a second cataclysmic event that cosmologists call the Big Crunch. A vaguely similar theory applies to the profession, or business, of science. The scientific enterprise, which exploded into being around the year 1700, began to run into the limits of growth around the year 1970. Exponential expansion is now in the process of ending, not really in a Big Crunch, but in something much more like a whimper. In the meantime, we are still trying to maintain a social structure of science—research, education, institutions, funding, and so on—that is based on the unexamined assumption that the future will be like the past. Since I believe that to be impossible, I think we have some interesting times ahead of us. The situation is illustrated by the graph in Figure 1 by Derek da Solla Price. It is a plot, on a semilogarithmic scale, of the cumulative number of scientific journals founded world-wide on the vertical scale, versus time in years on the horizontal. A straight line with positive slope on this kind of graph means pure exponential growth. It shows that science seemed to spring into being around 1700, and it expanded exponentially, growing about a factor of 10 every 50 years, until about 1950. Price correctly predicted that this behavior could not go on forever. The
straight line in the plot extrapolates to one million journals by the millennium. Instead, the current number of scientific journals is a mere 40,000. The era of exponential growth in science is already over. The number of journals is only one measure. Another is the number of PhD degrees in physics produced each year in the United States. The graph in Figure 1 shows that the first PhD degree was awarded soon after the Civil War, around 1870. By the turn of the century the number was about 10 per year; by 1930 about 100 per year; and by 1970, 1,000 per year. The curve extrapolates to about 10,000 a year today, and one million a year in 2050. But the growth stopped cold around 1970, and the number has fluctuated around 1,000 per year ev
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