Searching for scale invariance in neurons and behavior

Many biological systems exhibit dynamics that span a wide range of scales.  One possibility is that there are many distinct processes, one for each discrete scale.  Another possibility is that interactions among many internal degrees of freedom generate a near continuum of scales.  By analogy with physics problems that we understand quite well, the emergence of such scale invariance would point to some deeper underlying theory.  But searching for scale invariance is subtle.  In animal behavior, correlations that extend over long times are tangled with individual differences.  In networks of neurons, the dense connectivity can make it difficult even to say what we mean by scale.  I will discuss new approaches to these problems in the analysis of experiments on the behavior of walking flies and the patterns of neural activity in the mouse hippocampus.  The results provide evidence for precise scale invariance over several decades, with scaling exponents that are reproducible, sometimes to the second decimal place.