Enough of this arty stuff, let's get back to what is really important, that is, mathematics. I am going through the review chapter on functions and how they work. I never was completely sure about the whole thing but this chapter is a more complete and clearer re-working of the material. One thing that impresses me this time around is that functions and function notation represent a process, as calculus will, rather than simple one-time calculations as in arithmetic. One quantity is processed into another quantity: the input leads to output. x goes through function process f to become y,, hence the function notation y=f(x).

This notation is ambiguous if it points to any actual reality. Is y=f(x) a statement of causality? Does x cause y? When x changes, so does y, in a predictable way described by the function f. But is that predictable change a causal one? It looks that way, but it may not be. A function process may be abstracted from a bunch of data, so that it honestly looks like x causes the change in y. But it could very well be that the two changes are not dependent on each other but simply seem to be changing with respect to each other. The statement of a function f describes a relationship between those two quantities, but is this necessarily causal?

For instance, you could find some sort of causal relationship between unrelated phenomena which happen at the same time, and maybe even create a mathematical statement for it. You'd be right, but the causal reasoning would be wrong. Correlation is not causation, as many a teacher has told us. Mistaking correlation (occurring together) for causality (one thing making another happen) is a common form of bad thinking that may lead to everything from belief in paranormal phenomena and superstition, to what atheists consider religion to be: a mistaken perception of meaning and order in the world.

Or is it possible that there are no unrelated quantities in our world? Is there a function which defines the flutter of that now-famous butterfly's wing which causes the hurricane three thousand miles away? That's chaos theory, something my simple mathematical podging won't get to, perhaps ever. Mathematics on my level is about simplifying things, reductionism, and getting the relationship right, whether that relationship is real or not.

Posted at 3:09 am | link