ABSTRACT
In physics, constraints are external conditions that change trajectories, like a tabletop constraining a falling tennis ball to bounce off in a different direction. The most peculiar of all constraints are sequences, in which changes in the arrangement of one-dimensional patterns modify the dynamic behavior of complex, three-dimensional biological and social systems. Constraints make possible alternative behaviors. In their absence, a falling ball has only one possible trajectory, but when constraints are introduced there are as many different trajectories as there are constraints. They have their limits, however; a tabletop will not constrain a falling piano. You can also think of a constraint as a boundary condition that limits the range of motion available to a system. In constructing and guiding an organism, DNA sequences operate as a boundary condition, giving rise to coherent behavior. Constraints in the living world function through control hierarchies, what is sometimes called downward causation. When you read the instructions to assemble a bookcase, the sequences of text constrain your behavior down to the level of muscle fibers and nerve impulses. Hierarchies are fundamental to understanding how sequences function as constraints. Sequences themselves are organized in hierarchical patterns, what we call grammars.
