Neurobiologist; Professor of Pharmacology and Physiology, George Washington University
Ophthalmologist and Neurobiologist, University of California, Davis

Here are three of my unproven beliefs:

(i) The human brain is the most complex entity in the known universe;

(ii) With this marvelous product of evolution we will be successful in eventually discovering all that there is to discover about the physical world, provided of course, that some catastrophic event doesn't terminate our species; and

(iii) Science provides the best means to attain this ultimate goal.

When the scientific endeavor is considered in relation to the obvious limitations of the human brain, the knowledge we have gained in all fields to date is astonishing. Consider the well-documented variability in the functional properties of neurons. When recordings are made from a single cell—for instance in the visual cortex to a flashing spot of light—one can't help but be amazed by the trial-to-trial variations in the resulting responses.

On one trial this simple stimulus might elicit a high frequency burst of discharges, while on the next trial there could be just a hint of a response. The same thing is apparent when EEG recordings are made from the human brain. Brain waves change in frequency and amplitude in seemingly random fashion even when the subject is lying in a prone position without any variations in behavior or the environment. 
And such variability is also evident when one does brain imaging; the pretty pictures seen in publications are averages of many trials that have been "massaged" by various computer programs.

So how does the brain do it? How can it function as effectively as it does given the "noise" inherent in the system? I don't have a good answer, and neither does anyone else, in spite of the papers that have been published on this problem. But in line with the second of the three beliefs I have listed above, I am certain that someday this question will be answered in a definitive manner.