... It turns out that the overwhelming importance of a trigonometric analysis in the treatment of linear phenomena does not persist when we come to consider non-linear phenomena...
N. Wiener, Cybernetics
Neuroscience is faced with the problem of going beyond the first-pass view of the brain, that which emphasizes the selective firing of single units and the spatial alignment of these units within the cortex. Imposing this view on the cortex can often become quite tortuous once one exits the realm of (lower) sensory areas.
Somehow, we must address both the unity of experience, and the fact that neural events are not necessarily repeatable-- in our brains, the same visual scene is never quite the same, it is always colored by ill-defined variables such as our mood, and our previous exposures. There is no a priori reason to assume that an "average" experience exists, but this is the simplifying assumption underlying cortical neurophysiology. On a mechanistic level, neural processes on the mesoscopic scale, which could underlie the unity of experience, are profoundly emergent, nonlinear, and ill-behaved.
But in trying to face these problems, we are limited to using methods developed for linear, time-invariant systems. All the common constructs of neurophysiology--sinusoidal oscillation, superlinear/sublinear summation, statistically significant deviations--these concepts are so ingrained in our mind, that I think it is important to clearly state their limitations. Namely, these concepts are not necessarily meaningful if the measures in question are not well behaved, LTI, repeatable, stochastically distributed around a "true" value, etc.
