A process is linear when its response to a superposition of
inputs is the superposition of its response to the inputs
taken separately,
.
We must remark that there can be no purely linear processes
in the nervous system, for if there were, it would mean that
a response to twice the input is always twice the response to
the single input,
and likewise for any amplification of the input,
.
This cannot happen, for neurotransmitters become depleted,
the firing rates of neurons are limited by their refractory
period, etc.
Therefore, processes in the nervous system are at best
saturating linear, that is, approximately linear until
nonlinear saturation effects begin to dominate.
In neuroscience, linearity is always an approximation,
adopted for its mathematical convenience.