In the wake of recent swings in the values of technology stocks and the prices of real estate, many people have become (painfully) familiar with the boom-and-bust cycles of speculative bubbles. Although playing out on longer time-scales, student enrollments in the sciences have followed a remarkably similar pattern during the decades since World War II. The characteristic pattern can be seen in several countries, including the United States, Canada, and the United Kingdom. Enrollment patterns, and the specific policies that have been forged at various times to rapidly expand the number of trained scientists, sit at the intersection of science and society; they are where broad societal priorities and the infrastructure of higher education meet head on. Amid current discussions about globalization -- especially fears of potential challenges from booming scientific and technical training efforts in India and China -- the time is ripe to take stock of previous boom- and-bust cycles in our own recent past. How did they take hold, and what consequences have they had on the world of ideas? What intellectual trade-offs have been made, and with what impacts on the direction of scientific research?