Tuesday, October 30, 2012

Counting out -- 4

Piaget suggested that children's games evolve through three stages. The first is that of the practice game, as when a child leaps back and forth over a stream for the sheer joy of doing so. In the field of intellectual behavior, this might correspond to sitting night after night on a hillside wondering about the stars.

The second stage is the symbolic game, which involves the representation symbolically of an absent object, as when a child pushes a box and imagines it is a car. The box is clearly not an actual car, but it does share characteristics of a car (a movable container) which are precisely the aspects of a car that are important for the game. Science proceeds in an analogous way. If we imagine the Earth to be a perfect sphere of uniform density for the purpose of calculating the gravitational force at its surface, we are symbolically representing the Earth in a way that showcases certain fundamental aspects of the "real" world. We ignore (for the moment) more detailed features of the Earth in the same way the child ignores the fact that her box lacks headlights or a steering wheel.

The third kind of games occurring in a child's development are games with rules. "Unlike symbols, rules necessarily imply social or inter-individual relationships," says Piaget. The rules of science are related to the fact that science is a community activity. In science, as in all games, the requirement of functioning within a given set of rules adds both a pleasurable challenge (an alternative to the frustrating confusion of the Red Queen's chaotic croguet ground in Wonderland) and the stimulation of group play.

Major transformations of the rules by which science is played are infrequent and usually spring from the innovative genius of a mind with a "feel for the game" (Kepler = Knute Rockne). More generally the rules remain unbroken and the occasional spoil-sport is drummed out of the game.

If the rules of science are so rigid how can science, except at times of "scientific revolution," advance at all? Which brings us back to counting rhymes. Kenneth Goldstein, who we met before, observed that while a majority of children hold the counting-out process to be a rigid system controlled by chance, there is still room within the rules for a clever counter to make things bend to his advantage.

I don't want to make too much of these reflections on science and play. But all too often we overlook the fundamental human instincts that drive the scientific enterprise. Play is one of the most basic instincts, to each of us as individuals and to our species. It is not altogether frivolous, I think, to consider even our loftiest intellectual activities as germinating from nursery rhymes and games.