Analysis of the growth of radio and X-ray astronomy in the 1960s suggests that future reductions in the size of entering cohorts of new doctorates in astronomy may lengthen the time needed to exploit future innovations, discoveries or breakthroughs. This may well lead to slower rates of advancement in astronomical knowledge. Most scientists making up the early growth of these two problem areas hadrecently earned their Ph. D's, and, it was found, the probability of initiating research in radio or X-ray astronomy declined with the age of the scientist. Since smaller entering cohorts of new scientists would imply an overall aging of the astronomical community, the rate at which scientists will move in to exploit future innovations will probably be slower than during the periods of peak growth in the 1960s.