There are a couple of things on Lictor's mind this week, notably Halloween and Terrorism, which are probably what is on most people's minds to some degree today (Wednesday.) I'm particularly steamed about the government's inept or possibly almost criminally cynical handling of the terrorist threat but the truth is I can't settle down to a good frothing rant just yet.
The reason is that I was listening recently to a recorded lecture on the life and teachings of Pythagoras (well, someone has to. Just be thankful it wasn't you, buddy.) The Greeks had a belief that certain numbers were divine. Specifically, the numbers one through four. They, or at least, the followers of that particular branch of Pythagorean philosophy, believed these numbers were the very building blocks of reality. Whatever spirit, force, intelligence or god that had created the universe had used these numbers to define and thus populate the physical world. The number one being required to define a point, two to create a line, three for a plane and four to define a three dimension object. Everything after that is just window dressing, at least when you're creating universes.
In and of itself, it was mildly interesting, possibly only for historical reasons in a 'gee, those Greeks sure were odd,' kind of way. What lies behind it, though, is rather more compelling and frankly has been worrying at the ankle of my consciousness all week, like a rabid terrier.
You see, here's the deal; when you start to look at the abstract concepts behind mathematical principles, even simple ones, you step off the real world into one that is no longer founded in the physical bounds of our fleshy perceptions. The laws that define the relationships between the sides of right-angled triangle aren't empirical in nature, they aren't based upon observing right angles triangles laying around the streets or hanging from apple trees. Indeed, there are no absolute, perfect examples of right-angled triangles, anywhere to be found. The real world is just too messy and imprecise for such things. And yet.. the underlying laws are quite real and do tell you about the way right-angled triangles should behave. (If you can't get your triangles to behave, I'd forget about training that 150 lb Doberman.)
The abstract, non-physical world of mathematics bears directly on the real world; even though it has no direct analogue. What is more, the nature of mathematical insight can often precede any apparent application or mirror in the real world. A mathematical construct which appears delightfully whimsical to a seventeenth century mathematician might describe precisely the behavior of sub-atomic particles discovered four hundred years later. What does this tell us? Well, that there are immutable principles underlying our universe. But why? Why should a purely mental exercise of applying logic to abstract concept have any bearing on nature?
The truth, as they say in the X-Files, is out there. What is fascinating is the appearance of order to the universe. Although reality in all its violent, chaotic and course unpredictability, never conforms to individual instances of predicted, precise behavior, it seems that it is nevertheless true that there is an underlying ghost of mathematical perfection built into the very fabric of time and space. We are all imperfect examples of perfect math.
Perhaps the answer is that the very stuff of thought itself is shaped by the exact same mathematical laws that bound our universe. We have a system of thought, and therefore mathematics, that is based upon the same natural laws that drive galaxies and hummingbirds. It would, in that sense, not be possible for us to conceive of mathematics that do not reflect the very structure of our brains, of the processes that we call thought. And these structures, evolved to exist in this universe, are built with the same tools available to all matter and energy. It would therefore not be possible to develop thought patterns not consistent with the universe in which we exist.
Perhaps there is some deeper truth, or perhaps this is all a self-evident rat-hole of wooly thinking. It's hard to tell. But then, I'm trapped inside the end result of the processes I'm trying to measure, and frankly, I think that's a good excuse for a lack of objectivity. Any lack of clarity I blame on too much Pepsi and too many English Hamburgers.