  There is growing effort in the "physics of behavior" that aims at complete
quantitative characterization of animal movements under more complex,
naturalistic conditions. One reaction to the resulting explosion of data is the
search for low dimensional structure. Here I try to define more clearly what we
mean by the dimensionality of behavior, where observable behavior may consist
either of continuous trajectories or sequences of discrete states. This
discussion also serves to isolate situations in which the dimensionality of
behavior is effectively infinite. I conclude with some more general
perspectives about the importance of quantitative phenomenology.
