This is the second part of a series on the mathematical universe hypothesis. Check out part 1.
It shouldn’t be that simple. Yes, I know physics is a bit difficult, and it has taken us centuries to reach our current level of knowledge, and we know we are still far from complete knowledge of time and space. But on the other hand, look at all the technological wonders that fill our lives. Smartphones and GPS satellites and cures for disease. We have all of this because of science, and science works because mathematics is so useful in describing the universe.
We have been doing natural philosophy for thousands of years. And we’ve made progress, that’s for sure. But once we start using math, it seems like there are new revelations every day…because there are.
WHY is math so good?
Maybe mathematics is not just a description of nature. Maybe math IS nature. And the reason it does its job so well is because we have finally, after millennia of attempts, discovered the secret language of nature, just like Galileo said.
Maybe the universe is made of mathematics.
The latest version of this idea comes to us from cosmologist Max Tegmark. I wouldn’t exactly call him a friend of mine – we don’t hang out often enough – but definitely somewhere on the coworker/acquaintance spectrum. Regardless, in 2014 Max wrote a book, Our Mathematical Universe, which describes this philosophy. However, the boundary between physics, metaphysics and philosophy is often blurred. In the book, Max says his idea is physics: it makes testable predictions. To me, and I know I’m showing my bias here, so judge for yourself when I talk about it later, these claims are not that strong, which would place the following discussion in the metaphysical category.
Which is good. There is nothing wrong with metaphysics. Philosophy is useful and important and worth discussing and exploring.
So let’s see what old Max Tegmark has to say about the universe.
Let’s start with the hypothesis. This is an important and debatable question, but we’ll say it out loud and move on: that there is an external, objective reality (that is, we do not invent reality in our minds, and that it exists independently of us, conscious observers). The whole scientific process is about discovering and explaining this external, objective reality, and we use mathematics very successfully to achieve this.
But science is not limited to mathematics. There are very, very human words, concepts and ideas. We may have a beautiful mathematical theory (like GR or quantum mechanics), but we also have a bunch of man-made concepts to wrap around the math, like the wave function, space-time and the equivalence principle, and even mass, charge and force.
Tegmark argues that this is all “baggage.” It is a layer of our subjective, human-centered view of the universe that sits above reality, mathematics itself. We must therefore apply Occam’s Razor: make our perspectives as simple as possible. We have to throw all the luggage overboard because it only gets in the way. The REAL structure of reality will have no baggage. This is created by us, subjective humans. External, objective reality is baggage-free, streamlined, efficient and simple.
And what happens when you remove all the baggage from our physical theories? Bare and raw mathematics.
This is not Occam’s Razor. It’s Occam’s hammer.
Tegmark says that mathematics is more than a useful tool for studying the universe. He says once you get down to business, it’s just math.
Pull up a chair. Remove the luggage. The color. The mass. Atoms. Strengths. Once you remove all concepts of human origin, you’re left with…relationships. Symmetries. Structures.
All you have left is math. Mathematics is the universe, and the universe is mathematics. There is no distinction, no difference between them.
If we work hard enough at physics, then mathematics will not only reveal the universe to us, the universe will reveal itself to be even more mathematical. Some physicists are searching for a “theory of everything,” a single, unified theory describing all the forces of nature. Tegmark says that if he is right, then this theory of everything would not stop there, it would also explain all types of particles, all their possible interactions and all properties of the universe.
You know how I did this episode a while ago about the constants of nature? Yeah, a good TOE would have NO constants: no speed of light, no charge on the electron. Not even the number of spatial and temporal dimensions. It would be a single equation (ok maybe a set of equations) that would explain ALL of reality (including itself! which is kind of crazy to think about if you like that sort of thing).
And because this one mathematical equation could describe all of reality, why not just cut out the middleman and say that the mathematical equation IS all of reality? I mean, Occam’s Razor, right? Why make things more complicated?
