Universe Today
This is Part 1 in a series on the mathematical universe hypothesis.
Imagine you walk into a parking lot full of cars. You have in your pocket one single key. It’s the key to your car. The same key you’ve always used, the same key you’ve always trusted, the same key that you always manage to realize that you’ve lost right when you’re rushing out the door.
But have you ever had one of those moments when you walk up to the wrong car? Maybe it’s the same color, or make and model, and it takes you a minute to realize that something’s off about the car, and you stop yourself before you unlock the door and get in.
But what if your key unlocked that other car? That would be weird, right? What are the chances that your key, specifically designed for your car and your car alone just somehow by sheer coincidence unlocked a car very similar to yours?
What if you kept going? What if you tried your key on the next car, and the next, and the next? What if your one key unlocked every single car in the parking lot?
It would seem like magic, wouldn’t it?
In 1960 the physicist Eugene Wigner penned an essay, “the unreasonable effectiveness of mathematics in the natural sciences.” In it, he laid out how in the four centuries of scientific exploration of the universe, ever since the days of Galileo, math has been really, really good at doing the job. He said “the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.”
Math is a key that unlocks door after door after door. So why is math so good? How are we able to make so much progress?
Well, maybe math is more than a way to describe the universe. Maybe it’s more than a blueprint. Maybe…it’s the whole thing.
This is called the mathematical universe hypothesis, and in usual fashion I’m going to do two things: I’m going to tell you what I think up front, but then also try to give a balanced perspective so that you can make up your own mind. And here’s what I think up front: I don’t think the universe is made of math. But you don’t have to agree with me. We’re all good. And either way, it’s a really fun idea to play with, which is why we’re all here in the first place.
To get things started we need to talk about math. For the longest time, at least in the Western tradition, math and physics were different (to the point that physics was called natural philosophy). Math described things that were FIXED, like geometry, arithmetic, musical harmonies and scales, and of course the appearance of the stars and planets. These were all fundamental patterns of the universe that simply WERE, and we could use numbers and formulas and relations (like the Pythagorean theorem for triangles) to uncover those hidden patterns.
Physics, on the other hand, was all about CHANGE. It was about the process of evolution and manifestation and movement. Math did not belong here. After all, there’s no fundamental pattern to a baby growing to become an adult, or a dolphin swimming in the ocean, or fire burning through a log.
And then Galileo happened. Now Galileo did a lot of things, but one of his biggest contributions to physics was the application of math (which, by the way, offended the physicists at the time that there was this lowly mathematician poking his nose in places where it didn’t belong, but that’s a story for another day).He used and applied mathematics to understand what he saw in nature.
He said, “Philosophy [nature] is written in that great book which ever is before our eyes -- I mean the universe -- but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.”
One of his first applications of mathematics to the study of nature was with a pendulum. What’s amazing is that pendulums have been around since basically forever, but Galileo was the first to notice that the period of the swing did NOT depend on the weight of the mass at the end of the rope. It only depended on the length. AND he noticed that big swings took just as much time as little swings. He discovered a deep pattern in nature – the motion of a pendulum – described with mathematics, and used that for all sorts of useful and interesting applications (like making reliable clocks).
And from there the game of modern physics really took off. After Galileo you have people like Johannes Kepler (you know I can’t resist bringing him awkwardly into any conversation), who discovered a literal geometric figure in the orbits of the planets (said geometric figure being ellipses).
And it all comes to a head a century after Galileo with Isaac Newton himself. Remember the whole objection to the application of math to physics was that math couldn’t capture change. It was all triangle this and equilateral that. Newton was SO determined to apply math to his exploration of the universe that he invented a WHOLE NEW MATH, the calculus, to be able to capture change and evolution in physical systems.
With the calculus the whole universe opened up. Everywhere we looked, we found patterns. They weren’t simple geometric figures or algebraic relationships. They were complex, often subtle, and almost always hidden underneath mountains of data. But they were THERE, and the more comfortable we got with applying math to understand the universe, the more mathematical tools we invented (or stole from the mathematicians when they weren’t looking) to look even deeper.
Physics is a mathematical exploration of the universe. We look for patterns, structures, symmetries, and relationships. We use math to capture and describe those patterns, structures, symmetries, and relationships. We take properties of objects that we can measure or identify, like mass or velocity or electric charge, and we find how these properties relate to each other and influence behavior.
I can identify a property, let’s call it mass. And I suppose that the “mass” of an object can influence other objects. I call that influence “the gravitational force.” And I can write down an equation, a simple relationship, that tells me how much mass leads to how much gravitational force, and another equation to tell me how the gravitational force makes another object move.
Galileo found the key. And for four centuries we’ve been opening door after door after door, in the process completely rewriting our understanding of the physical universe. Our perspectives, our views, of how the universe works are RADICALLY different than they were prior to Galileo, and prior to the application of math.
The universe is chaotic and messy and almost incomprehensible. But there ARE patterns, there ARE relationships, there ARE repeatable, predictable behaviors that we can identify, from the orbits of the planets to the Higgs boson. Mathematics is perfectly suited to describe all that.
A little TOO perfectly suited.