  A spiking neuron ``computes'' by transforming a complex dynamical input into
a train of action potentials, or spikes. The computation performed by the
neuron can be formulated as dimensional reduction, or feature detection,
followed by a nonlinear decision function over the low dimensional space.
Generalizations of the reverse correlation technique with white noise input
provide a numerical strategy for extracting the relevant low dimensional
features from experimental data, and information theory can be used to evaluate
the quality of the low--dimensional approximation. We apply these methods to
analyze the simplest biophysically realistic model neuron, the Hodgkin--Huxley
model, using this system to illustrate the general methodological issues. We
focus on the features in the stimulus that trigger a spike, explicitly
eliminating the effects of interactions between spikes. One can approximate
this triggering ``feature space'' as a two dimensional linear subspace in the
high--dimensional space of input histories, capturing in this way a substantial
fraction of the mutual information between inputs and spike time. We find that
an even better approximation, however, is to describe the relevant subspace as
two dimensional, but curved; in this way we can capture 90% of the mutual
information even at high time resolution. Our analysis provides a new
understanding of the computational properties of the Hodgkin--Huxley model.
While it is common to approximate neural behavior as ``integrate and fire,''
the HH model is not an integrator nor is it well described by a single
threshold.
