Science is a Small-Numbers Operation, After All

One of the useful structural ideas in Randall Collins' The Sociology of Philosophies is the Law of Small Numbers. He argues that creative intellectual life works when a limited number of networks, representing different positions, gather around a common problem and compete with one another to solve it. He says the minimum number of positions is three, and the maximum is six or seven, eight at the outside. The minimum number comes from the initial claim - "this is a problem worthy of serious attention, and here is our proposed solution" - which, if successful, draws a contrary view; the argument between the two almost inevitably draws a "plague on both your houses" third position. The maximum number of positions is a little vaguer, but seems to be about the limit of the number of competing solutions to a problem that participants can keep track of.

Science today, what Collins calls "rapid-discovery science," seems to be composed of thousands of creative groups pushing along a research frontier, not a small number arguing over a problem for a long time. At first glance, then, science would seem to abrogate the law of small numbers.

If we take a finer-grained look at science as a human enterprise, though, we see that it is composed of many nodes of small numbers gathered around a problem. Moreover, argues Collins, the scientific revolution was really three different revolutions working together. First came a revolution in mathematics, which was driven by developing many new mathematical notations that turned into a technology of discovery. Then began a revolution in scientific equipment, driven more by tinkerers than philosophers, which also turned into a technology of discovery. Only then could there be scientists who use both kinds of technology to attack problems. At that point, they create an attention space organized around a small number of positions competing as fast as they can to both make crucial discoveries and to interpret them convincingly.

The difference between science and philosophy is that science, armed with these efficient technologies of discovery, moves much faster in creating little problems and solving them. This is Kuhnian normal science. Where philosophers might spend decades, whole careers, even generations arguing the same problem, scientists working on a hot topic compete to a solution, solve it, and move on to a new competition. Scientific problems that don't get solved quickly get pushed to the side, where fewer networks will keep working on them; hot problems are not so much the most important ones, as the ones that promise a reachable solution soon.

From a distance and from the outside, science appears to be a vast moving research frontier carried on by millions. Up close, though, science proceeds by many small-numbers competitions gathered around specific problems.