The deepest and most profound insight in science is that mathematics somehow models reality. There is no known reason WHY this should be
so – it just IS. Sometimes it is said that discovering extraterrestrial life, especially of an intelligent variety, would be the greatest discovery in the history of science. This is not true. Once we figure out a mutual language of communication – almost certainly based on mathematics in general and probably prime numbers in particular – the first thing we will ask aliens is whether or not they have figured out why mathematics models reality. If they say yes, and tell us, THAT would be the greatest discovery in the history of science. More likely, that’s what THEY would ask of US – and be disappointed when we said no because we didn’t know.
Over the centuries, humans have achieved greater and greater insights into how mathematics models reality. We discover whole numbers model sheep in a field of grass, and so the human endeavor of accounting is born. We discover calculus models the motion of air flowing over the wing of a jetliner taking off from an airfield, and the human endeavor of aviation is born. We discover matrix algebra models the interaction of subatomic particles in a quantum
field, and the human endeavor of quantum physics is born. In every field throughout history, NEWLY DEVELOPED math is the key to reaching deeper and deeper levels of understanding – and mastery – about the reality which surrounds us.
There is no reason at all to believe this process of developing new types of mathematics and finding new ways it models reality has stopped, and every reason to believe it will continue. Arithmetic and counting sheep is pretty well figured out by now (we’ll leave a discussion of Godel’s theorem for another day) but there are new branches of math puzzling us today as much as the mentally taxing switch from a vague “many” to precise counting of sheep puzzled our caveman ancestors.
Like so many other current areas of human endeavor, the pace of change and progress in mathematics development is accelerating. Just as microscopes have provided biologists with a new window into a previously unknown microworld, just as telescopes have provided astronomers with a new window into previously unknown deep space, so have modern computers provided mathematicians with a powerful new window into a previously unknown world not just of numbers, but of new unsuspected relationships about math and the nature of reality. And these new relationships mathematicians are discovering between numbers and reality are just as philosophically profound as the implications of DNA complexity or the vastness of the universe.
Example: fractals. At first glance, the equations of fractals don’t seem that different from a 2+2=4 equation you would write down on a sheet of paper. But when you write down the “4” in that arithmetic problem on a sheet of paper, you’re finished. When you write out a set of simple-looking fractal equations, you’ve only just begun. To solve a fractal equation, your first answer gets fed back into the equation and you compute its answer all over again. Then you take this second answer, feed it back into the equation yet again, and compute the third answer. And the fourth. And the fifth. And the millionth. And it goes on like that forever. You can’t possibly write out all of these different answers by hand; it would take a lifetime just to get started. But by using your personal computer as a type of microscope and as a type of telescope, you can generate a lifetime-long list of fractal equation answers in a fraction of a second.
So what? Well, fractal math is so new we aren’t really sure what it all means just yet, but it is virtually impossible to deny that somehow fractal mathematics have a profound relationship with reality that we have never appreciated before. As an example, the millions of fractal numbers that are churned out of one set of fractal equations somehow mimic how the millions of plant cells in a fern leaf form such a distinctive fern-like shape. These fractal equations are like a recipe for making a fern, but you won’t find them encoded in a fern’s DNA. So…how does a fern spore DO that??? It’s like an incredible magic trick, only the magic is not fake or coincidental but REAL. It’s like this certain fern-leaf shape or structure is mathematically encoded into the very fabric of space or reality.
If it works like this for fern leaves, could it work like this for brain cell layout? Is the key to the mystery of consciousness not in DNA at all but in fractal mathematics instead?
Stay tuned and in the next Part of this article I’ll make a leap-of-faith jump from fractals to prime numbers…