"Consciousness as a pathological function" is a phrase I have invented to succinctly describe a concept I have been thinking about in general terms for a while, in some ways related to what I wrote here. It depends on a metaphor that those more skilled in mathematics than me may find somewhat of a stretch, but which seems to at least be somewhat instructive in illuminating the murky problem of mind and brain interaction.

A pathological function, in mathematics, is one in which the relation between x and y, while following a rule, does not produce the type of order, symmetry or pragmatic results that is generally considered to be helpful in mathematics. According to a more technical definition,a pathological function is one that is "continuous but not derivable", but many pathological functions are not even continuous, such as a case where if x is a rational number, y is equal to one, and when x is an irrational number, y is equal to zero.

These functions are in great contradiction to some of the more popular functions that mathematicians study, such as sine waves or the square curve. It is somewhat of a happy mystery that such functions seem to be both appealing to human aesthetics, and very helpful to understanding the world. Gravity follows a very simple continuous function.

To turn to consciousness, if we take the biological and mental processes, one is usually seen to be the function of the other (for a moment, we can lay aside debates about which causes the other). It would seem to be a somewhat workable assumption to assume our brains have some sort of non-pathological function working for them. If we take a group of neurons (or proteins within a neuron, or groups of neurons working together), we might imagine that when one neuron lights up, we think of the number "one", that when two neurons light up, we think of the number "two", and so on, in a pattern that is very obvious. The function might not be as simple as x=y, of course, but most people would assume that somehow there is a correlation between neurons and thought that is somehow decipherable. If we take the dopamine of popular culture, we can imagine that we could derrive some type of relationship between amounts released and happiness experienced.

But what, on the other hand, if the relationship between brain function and consciousness is totally pathological? What if when one neuron fires, we think "one", but then two neurons thinks "zero", three neurons think "ten", and four neurons think "apple"? What if, in other words, any relationship between neuronal activity and thought is so random and haphazard that the function lying behind it is useless to our sense of utility and order? This is of course, something that could theoretically be discovered (and the philosophical implications either way would be staggering), but that is probably beyond any foreseeable technology to investigate. So the issue of whether the relationship between brain activity and consciousness would be an understandable, or a pathological function, will remain a thought experiment for the present.