Coordination without binding through scarcity

In “Binding Through the Fovea”, Paul Cisek and Martine Turgeon propose a partial solution to the binding problem based on selectivity.

Within the traditional "information-processing" view of brain function, the shifting focus of attention has been seen as a mechanism for dealing with the limited capacity of the perceptual systems. Neumann (1990) argues that this has things backwards. Selection is not needed because capacity is limited. Instead, capacity is limited because selectivity is required to guide action; it is a deliberate feature of brain function which serves useful roles.

The idea that limited resources is actually beneficial to constructing a goal state, like a particular motor behavior, is corroborated by the work of Peter Smiley and Michael Levin showing that morphogenesis works better when the cells are competing over a finite reservoir of resources instead of an infinite reservoir. This is surprising because we normally expect that removing constraints makes it easier to do things, but these papers show that removing too many constraints can actually make it harder for the parts of a system to construct desired outcomes.

Motor behavior and morphogenesis are the same thing, so there must be a deeper principle underlying the shared observation that constraints are helpful for constructing target states. I think it’s an economic principle: both motor behavior and morphogenesis are economic processes whereby a collective state is reached through the coordination of many parts. Economics relies on scarcity, and scarcity means resource constraints. Without capacity constraints and finite reservoirs, there’s no economics and thus no economic coordination.

The easiest way to understand the role of scarcity in coordination is by understanding the role of scarcity in competition. Competition is a vital concept in economics, and it also plays an important role in morphogenesis and in motor behavior. Competition requires scarcity because without scarcity, what are you competing over?

In Enemies Coordinating on Abstract Conditions, I point out that although two competing basketball teams have diametrically opposed goals in terms of their concrete ends—each team wants to score and to stop the other from scoring—there is a high degree of coordination between the team trying to score and the team trying to stop them because each team agrees on the abstract condition of marginal benefit = marginal cost. Specifically, both the offense and the defense want to converge to areas of the court where the value of the next shot is worth more and away from areas where the value of the next shot is worth less.

Each spot on the court acts like a reservoir of expected points that gets used up as the offense takes more shots there and as the defense guards more there. For example, if a spot on the court is worth a lot of points, say 2 per shot, then the offense is going to shoot a lot there, taking worse and worse shots there until the value of the marginal shot at that spot isn’t higher than elsewhere on the court. Similarly, the defense will defend more there again until the marginal value of a shot there equilibrates with the rest of the spots on the court.

If there were no reservoir of points to use up, then the game would become dull. The offense would just take shot after shot from whichever spot happens to offer the most points, and the defense wouldn’t put any additional effort into guarding that spot. To get interesting and dynamic constructions on the court—basketball morphogenesis—you need a finite reservoir.

Agreement on abstract conditions via scarcity is how the price system works. No two economic agents in an economy need to agree with each other about anything concrete to agree on equilibrium prices. This is a simple version of why the binding problem isn’t a problem: you can have immense amounts of coordination without having to stick anything concrete together.