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Physics + MathPhysics & Math

Why We’ve Underestimated Not Only the Size of Our Cosmos, But Also Our Ability to Understand It

The Nature of RealityThe Nature of Reality

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The Higgs Boson was predicted with the same tool as the planet Neptune and the radio wave: mathematics. Why does our universe seem so mathematical, and what does it mean? I believe 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.

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Credit: Flickr/playful.geometer under a creative commons license

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, 1/2 and 1. Physicists call these properties electric charge, spin and lepton number, but those are just words that we’ve made up; the fundamental properties of an electron are just numbers, which are 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 also has only mathematical properties–for example, three, 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.

Max Tegmark ponders the mathematical universe.

Thinkers as far back as the ancient Greeks recognized that our universe is “approximately described” by mathematics, meaning that some but not all of its properties are mathematical. When I say that the universe “is mathematical,” I am going a step further, arguing that all of its properties are mathematical, in other words, it has no properties at all except mathematical ones. If I’m right and this is true, then it’s good news for physics because it implies that, if we’re intelligent and creative enough, we can in principle understand all the properties of our universe.

This challenges the common assumption that we can never understand consciousness. 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 non-human animals, unresponsive patients and future ultra-intelligent machines, with wide-ranging ethical, legal and technological implications.

As I argue in detail in my new book Our Mathematical Universe , 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 eight, 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 eight 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 hubristically view these equations as the “Theory of Everything,” but as information about our location in the mathematical atlas of the ultimate multiverse.

It’s easy to feel small and powerless when faced with this vast reality. Indeed, we humans have had this experience before, over and over again, each time we’ve discovered 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 brains as large as ours, 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 wrote my 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. After all, this quest belongs not just to me and my fellow physicists, but to all of us.

The groundhog image above is courtesy of Meia Chita-Tegmark. He’s not really called “Max Tegmark” either, but “Mr Hoggles.”