Max Tegmark's Our Mathematical Universe asks some big questions, including the very nature of existence itself--and explains all of them with math, arguing that everything around us is made out of it. Here, Tegmark explains why.
The Higgs Boson was predicted with the same tool as the planet Neptune and the radio wave: with mathematics. Why does our universe seem so mathematical, and what does it mean? In my new book Our Mathematical Universe, I argue that it means that our universe isn’t just described by math, but that it is math in the sense that we’re all parts of a giant mathematical object, which in turn is part of a multiverse so huge that it makes the other multiverses debated in recent years seem puny in comparison.
WHERE’S THE MATH?
At first glance, our universe doesn’t seem very mathematical at all. The groundhog who trims our lawn has properties such as cuteness and fluffiness – not mathematical properties. Yet we know that this groundhog – and everything else in our universe – is ultimately made of elementary particles such as quarks and electrons – and what properties does an electron have? Properties like -1, ½ and 1! We physicists call these properties electric charge, spin and lepton number, but those are just words that we’ve made up and the fundamental properties that an electron has are just numbers, mathematical properties. All elementary particles, the building blocks of everything around, are purely mathematical objects in the sense that they don’t have any properties except for mathematical properties. The same goes for the space that these particles are in, which has only mathematical properties - for example 3, the number of dimensions. If space is mathematical and everything in space is also mathematical, then the idea that everything is mathematical doesn’t sound as crazy anymore.
That our universe is approximately described by mathematics means that some but not all of its properties are mathematical, and is a venerable idea dating back to the ancient Greeks. That it is mathematical means that all of its properties are mathematical, i.e., that it has no properties at all except mathematical ones. So all you need to do to falsify this is to find a single property that isn’t mathematical — and as I argue in the book, breakthroughs in physics have so far undermined all such claims.
CAN WE EVER UNDERSTAND OUR UNIVERSE?
If I’m wrong and the mathematical universe hypothesis is false, then physics is doomed to eventually hit an insurmountable roadblock: we’ll still lack a complete understanding of our physical reality, but there would be no further mathematical regularities left to discover. If I’m right, on the other hand, it’s good news for the future of physics: there’ll be no roadblock in our quest to understand reality, and we’re limited only by our imagination.
CAN WE EVER UNDERSTAND OURSELVES?
The mathematical universe hypothesis challenges the common assumption that we can never understand consciousness. Instead, it optimistically suggests that consciousness can one day be understood as a form of matter, forming the most beautifully complex structure in space and time that our universe has ever known. Such understanding would enlighten our approaches to animals, unresponsive patients and future ultra-intelligent machines, with wide-ranging ethical, legal and technological implications.
HOW BIG IS REALITY?
As I argue in detail in my book, it also implies that our reality is vastly larger than we thought, containing a diverse collection of universes obeying all mathematically possible laws of physics. An advanced computer program could in principle start generating an atlas of all such mathematically possible universes. The discovery of other solar systems has taught us that 8, the number of planets in ours, doesn’t tell us anything fundamental about reality, merely something about which particular solar system we inhabit — the number 8 is essentially part of our cosmic ZIP code. Similarly, this mathematical atlas tells us that if we one day discover the equations of quantum gravity and print them on a T-shirt, we should not hübristically view these equations as the “Theory of Everything”, but as information about our location in the mathematical atlas of the ultimate multiverse.
HOW SMALL ARE WE?
It’s easy feel small and powerless when faced with this vast reality. Indeed, we humans have had this experience before, over and over again discovering that what we thought was everything was merely a small part of a larger structure: our planet, our solar system, our Galaxy, our universe and perhaps a hierarchy of parallel universes, nested like Russian dolls. However, I find this empowering as well, because we've repeatedly underestimated not only the size of our cosmos, but also the power of our human mind to understand it. Our cave-dwelling ancestors had just as big brains as we have, and since they didn't spend their evenings watching TV, I'm sure they asked questions like “What's all that stuff up there in the sky?” and “Where does it all come from?”. They'd been told beautiful myths and stories, but little did they realize that they had it in them to actually figure out the answers to these questions for themselves. And that the secret lay not in learning to fly into space to examine the celestial objects, but in letting their human minds fly. When our human imagination first got off the ground and started deciphering the mysteries of space, it was done with mental power rather than rocket power.
I find this quest for knowledge so inspiring that I decided to join it and become a physicist, and I’ve written this book because I want to share these empowering journeys of discovery, especially in this day and age when it’s so easy to feel powerless. If you decide to read it, then it will be not only the quest of me and my fellow physicists, but our quest.