Whenever I read about the theory of evolution, I’m always struck by the juxtaposition of complexity and simplicity. The theory of evolution is simple: change in the inherited characteristics of biological populations over time leads to new, generally more successful, populations. It’s pretty damn simple. If you’re not equipped genetically to handle the environment you’re born into, you’ll most likely die and leave few descendants. Others who are better genetically equipped will live long fruitful lives and leave many descendants, thus altering the genetic landscape of the population.
The complexity comes into how nature goes about the whole evolutionary process. In the theory of evolution, there’s no guiding plan; there’s no pinnacle that nature is striving towards. Rather nature is discovering various ways of achieving different ends using a variety of similar, but not identical (and in some cases, very different), proteins and atomic structures. Really, what evolution is doing is gradually mapping out the the physical constraints imposed chemically on the universe by the laws of physics, while simultaneously dealing with ever-changing environments and needs.
So when I think of mathematics, it seems to me a very similar process.
I, quite obviously, don’t have the answer to the grand old philosophical question of maths: Is maths real? But the similarities between biological evolution and mathematical evolution intrigue me. To come straight out and say it, I think that maths is a logical feature of the universe which exists outside and independently of the realms of thought. I could be entirely wrong, but it seems to me that mathematics is fundamentally a part of the universe and when we discover such laws as the “Law of logic”, we are discovering inherent properties of the patch of intelligible space that we inhabit (of course, those laws could be different outside of the bounds of our observable universe, whatever that may mean). Maths is real, I think, and we are understanding parts of the real world of the universe when we discover new mathematical techniques (I will throw in a caveat here to say that I think some of our mathematical propositions, while yielding the right answer, could be potential “closest matches” to different underlying mathematics, but at it’s foundation, I do think that maths is a fundamental property of our universe).
Where does Newton come into all this? And what’s up with calculus. Well, when I think of the way that evolution goes about “discovering” new forms and features that are fundamentally grounded in the physical reality of the universe, while also being interesting and diverse ways of solving the same problem, I always think of different people in the history of mathematics coming up with their mathematical strategies to solve problems.
Newton, in my mind, did not “invent” calculus. Rather he discovered that there was a particular way of manipulating numbers that yielded different results. He uncovered, so to say, an extra fabric square in the corner of the quilt of mathematics. In very much the same way that pressures from the outside world will change the genetic frequencies and structures of certain proteins within populations, which will lead to changes within the structure of an organism and its cells; otherwise known as the Theory of Evolution. Evolution is simply discovering the possibilities already inherent in the structure of chemicals, which is dictated by the laws of physics handed down to us from the Big Bang (and if the multiverse theory turns out to be true: that the big bang was just a randomised version of an infinite number of other big bangs, each with their own laws of physics and fundamental properties, then we’re really just discovering a corner of a corner of one of an infinite number of fabric squares that populate the multiverse quilt).
What a grand old universe we live in.