  It has been known for about a century that psychophysical response curves
(perception of a given physical stimulus vs. stimulus intensity) have a large
dynamic range: many decades of stimulus intensity can be appropriately
discriminated before saturation. This is in stark contrast with the response
curves of sensory neurons, whose dynamic range is small, usually covering only
about one decade. We claim that this paradox can be solved by means of a
collective phenomenon. By coupling excitable elements with small dynamic range,
the {\em collective} response function shows a much larger dynamic range, due
to the amplification mediated by excitable waves. Moreover, the dynamic range
is optimal at the phase transition where self-sustained activity becomes
stable, providing a clear example of a biologically relevant quantity being
optimized at criticality. We present a pedagogical account of these ideas,
which are illustrated with a simple mean field model.
