Science and complexity

Warren Weaver wrote this short essay in 1948, from the Rockefeller Foundation in New York, three years after a war in which he had headed the US Applied Mathematics Panel.¹ In the same years he was writing, with Claude Shannon, The Mathematical Theory of Communication (University of Illinois Press, 1949), the book that founded information theory.^1,2 The essay asks what science is good for, and answers by sorting the problems science has taken on into three kinds.¹

Problems of simplicity. From the seventeenth to the nineteenth century, physics learned to handle problems with two variables, or three or four: one quantity depending mainly on another. That gave the telephone, the car and the hydroelectric plant. Living things rarely allow it; in them, dozens of quantities change at once, in subtly connected ways.¹

Problems of disorganized complexity. After 1900, probability and statistical mechanics went to the other extreme, to problems with billions of variables. Weaver's image is a billiard table. One ball is easy and three are hard. With millions of balls colliding at random, the problem gets easier again, because averages become predictable: how often balls hit a stretch of rail, how far one travels between collisions. A telephone exchange and a life insurer work this way: the insurer can't know who will die, but knows how many will. The method needs disorder; if the balls were lined up and sent off in parallel, it would fail.¹

Problems of organized complexity. Between the two lies what Weaver calls "a great middle region". It is marked not by the number of variables but by organization: "a sizable number of factors which are interrelated into an organic whole".¹ His examples run from what makes an evening primrose open, to how genes shape an adult, to "On what does the price of wheat depend?", to how to stabilize a currency or avoid swings from boom to depression.¹ These yield neither to two-variable methods nor to averages, and he says science "must, over the next 50 years, learn to deal with" them.¹

He saw two tools coming out of the war. The first was the electronic computer, which he expected not only to handle problems previously too complicated but to "inspire the development of new methods of analysis" for them.¹ The second was the "mixed team" of wartime operations analysis: mathematicians and physicists working with physiologists, biochemists and psychologists on problems such as how large and how fast Atlantic convoys should be. He forecast that much of the next fifty years' progress would come from voluntary mixed teams "effectively instrumented by huge computers", while insisting that scientists who work alone remain essential.¹

The essay ends on limits. Science handles problems whose main factors are logical and mostly measurable; it should not be thought of as "a modern improved black magic", and it does not supply morals or a measure of beauty. His closing line is that "our morals must catch up with our machinery".¹

For anyone modelling a place, the middle region is where the work is. A watershed, a city's traffic or a regional economy has too many interacting parts for a few equations and too much structure for averages. Agent-based models, system dynamics and digital twins are the kind of computer-instrumented methods Weaver hoped for, and the mixed teams they need, of modellers working with ecologists, engineers and the people who know the place, are close to what he described. The reprint carries an editor's note that, nearly sixty years on, the field was still not as far along as Weaver hoped.¹