BOSTON—From the arc of a baseball to the orbits of the planets, mathematical patterns are everywhere. But according to physicist Max Tegmark of the Massachusetts Institute of Technology in Cambridge, it’s not enough to say that math governs our universe. Rather, he believes that reality itself is a mathematical structure. What the heck does that mean? We caught up with Tegmark after his presentation at yesterday's symposium “Is Beauty Truth?” at the annual meeting of AAAS (which publishes ScienceNOW).
Q: What makes a mathematical theory beautiful?
M.T.: For me, it’s usually when there’s an unexpected connection between two things I thought were unrelated. Imagine if you walked into an art museum and saw a very beautiful sculpture in one corner, and something else in the other corner, but there’s a big veil between them. And then suddenly someone lifts the veil and you see that the two things are just parts of a much grander structure. Seeing that whole makes you understand the pieces much better.
The beautiful mathematical regularities that have been uncovered have typically been unifications, where instead of having one mathematical description for this and a different one for that, we realize there’s a single mathematical structure that encompasses all of it. So for me, it would be a natural conclusion if everything could be unified, if there’s a single mathematical structure that is our reality, and all of the mathematical structures that we’ve discovered before are part of this more beautiful whole.
Q: Wait a minute. What do you mean, the universe is a mathematical structure?
M.T.: So right now, I’m eating an orange, which is made of cells. Why do they have the properties they do? Well, because they’re made of molecules. Why do the molecules have their properties? Because they’re made of atoms put together in a certain way. Why do the atoms have those properties? Because they’re made of quarks and electrons. What about the electron? What properties does it have? And the cool thing is, all the properties that electrons have are purely mathematical. It’s just a list of numbers. So in that sense, an electron is a purely mathematical object. In fact, there’s no evidence right now that there’s anything at all in our universe that is not mathematical.
Q: You call this idea the mathematical universe hypothesis and say it’s a fundamentally optimistic way of looking at reality. Why?
M.T.: We’ve discovered again and again that reality is bigger than we thought. People were really shocked to realize how big Earth was. Then they were shocked by how big our solar system was, and how far away the stars were, and that we were just a small part of this galaxy, which is one out of gazillions of others. Now there’s a lot of fuss about our whole observable universe just being part of a much bigger space, with lots of parallel quantum realities.
If there are parts of reality that we can’t observe with our telescopes or travel to with our rockets, some people might feel it’s a bit of a bummer, that we’re fundamentally limited in what we can observe. But there’s a cool twist here. If the mathematical universe hypothesis is true, we can actually learn things about the parts of our universe we can’t see or visit. Not with a telescope but with a pencil—and a lot of ingenuity.
Plus, if the mathematical universe hypothesis is false, that means that the future of physics is ultimately doomed. We’re ultimately going to hit a roadblock beyond which we just cannot proceed. Whereas if I’m right, there is no roadblock. The road ahead is open, and our future understanding is really only limited by our imagination.
Q: I'm not a mathematician. Why should I believe your theory?
M.T.: We should believe scientific theories if they make predictions that can be tested, and possibly proved wrong. Some people argue that, well, if there’s a theory that predicts a bunch of stuff that you can never observe, that’s not science. But that’s actually an incorrect viewpoint. For a theory to be falsifiable, we don’t have to be able to observe everything that it predicts. Just at least one thing. And if that prediction is wrong, flush the theory down the toilet.
Gravity is a great example. Einstein’s theory of gravity predicts exactly what happens inside of black holes. Should we dismiss that as philosophical blah blah blah? No! Because this theory also predicts exactly the time delays of the GPS satellites. And if Einstein were wrong, we would get totally lost when driving around in our cars these days. Because it’s so successful in the things that it predicted that we could test, we were forced to take seriously its other predictions as well.
This interview has been condensed and edited.