The Concept Of Purity
(Unfinished work)
On a computer, purity is the Turing Machine. In mathematics, purity is the Axiom. In functional programming languages, purity is the Lambda Calculus. In politics and economics, purity is in Game Theory. In chemistry, purity is physics. And in physics, purity is the conservation of energy.
What we mean by "purity" here is whatever you're left with after you reduce a consistent system down to the smallest, atomic building blocks that are still enough to build whatever it was you started with. For big and complex systems, this usually means an awful lot of building blocks. Even when we used to think atoms were the smallest particle of matter (hence their name; "atom" means "indivisible"), millions of atoms are required to make a grain of sand. Now we know that protons, neutrons and electrons make up atoms, and quarks are smaller yet. The only thing we can really find "at the bottom" of physics are a few rules that have never been broken, such as conservation of energy.
The quest for purity got started some hundreds or thousands of years ago when somebody first realized that a thing "could be explained in terms of X", and it blew their mind. It might have been the birth of a new, stranger religion were the central faith is that the whole universe, as complex and perverse as it is, might just boil down to the most ridiculous simplicity.
But more practically, reducing complex things to their simple--pure--components is a way of fighting complexity. Purity is a weapon you can use against confusion if you can somehow establish a fractal relationship between the pieces and the whole. If you can prove, for example, that a Turing machine can compute anything that is computable, and you can prove that a confusing, complicated, awkward and interesting natural phenomena such as weather is computable (by, say, reducing weather phenomena to its pure components), then you know that you should be able to build a computer (Turing Machine) that can predict the weather.
It's a really empowering feeling, the kind that makes you wanna take on the world. Purity is what's implied by the old saying "To a man with a hammer, everything looks like a nail".
The material here is Public Domain.
