A Review of Our Mathematical Universe, by Max Tegmark

Knopf, 2014

432 pages

The book opens with a chiller: “A second later, I died.” What follows is not a murder mystery being narrated by the deceased victim, but a whirlwind explanation of cosmology, quantum physics, and theoretical evidence for the idea of multiple universes. Welcome to the world of Max Tegmark, professor of theoretical physics at MIT, whose brain roams across the entire history of human scientific inquiry into the ultimate question: what is reality?

Our Mathematical Universe is Tegmark’s first book-length project, following his publication of over 200 academic papers, numerous essays for popular science outlets, and appearances in TV and radio documentaries. While a book on such a broad, esoteric topic could easily veer off-track into Ph.D. jargon, Tegmark keeps his expansive, quirky voice focused, transitioning smoothly between topics and helping bring the average Joe impressively close to understanding his world with, ironically, as little reliance on math as possible.

Starting from the very first page, Tegmark is very aware of his readers and aims to give them as much transparency as possible. Rather than launching right into the good stuff, he lays out the structure of the chapters in the book, its goals, and a “road map” for readers at various levels of comfort with theoretical physics. A “hard core reader of popular science” is encouraged to skip four of the more basic chapters, while physicists can jump right to the most esoteric, controversial stuff in the second half of the book. As someone with minimal knowledge of physics, I plowed right through all 398 pages of text.

Tegmark calls his book a “scientific autobiography” but acknowledges that the book “is more about physics than it is about me.” I would call that an understatement. Rather than guiding the reader through the labyrinth of physics like Sacagawea leading Lewis and Clark through the unknown American wilderness, Tegmark seems to pop in and out like the Cheshire cat. He often begins chapters with a personal anecdote and indulges in asides about late-night research sessions, but the character of Max Tegmark quickly melts away so that the narrator Tegmark can take over. The book reads more like a very accessible textbook covering the history of physics peppered with Tegmark’s personal stories and quips rather than the chronological narrative of an autobiographical journey of discovery. The structure is even textbook-like, each chapter broken up into chunks around larger topics like “What Is Space?” and those chunks further divided into smaller sub-topics: “The Horizon Problem” and “The Flatness Problem.” At the end of each chapter is a “The Bottom Line” box containing a list of bullet points—the essential ideas that you can summon up at a cocktail party to convince your friends that you really understand all this multiverse stuff.

Tegmark professes, “I love questions. Especially big ones.” Accordingly, the book is structured around sixteen big questions, such as “How could an infinite space get created in a finite time?” and “Are we insignificant?” He explores science’s attempts to answer those questions roughly chronologically, starting with the ancient Greeks calculating the Earth’s circumference by figuring out how many degrees the angle of the Sun shifted between two cities at the summer solstice. He hits all of the rock stars of the physics world: Galileo, Newton, Schrödinger, Einstein, John Wheeler, and Alan Guth. Along the way he includes instances when he got to personally work on a problem that helped to advance the field, and others when he, in his own words, “messed up.” It’s this combination of authority and humbleness that lends Tegmark’s voice so well to guiding complete newbies like myself through the mind-bending throes of decoherence and the “quantum machine gun.”

Though the title of the book states that it’s about his controversial idea that the universe is composed of pure mathematical structures, the first two-thirds of the book focuses instead on “mainstream” physics, covering what we know (or at least are fairly confident we know) about the universe today. Just because they’re mainstream ideas in the physics world doesn’t mean they’re common knowledge, though. Thankfully, Tegmark realizes this and makes masterful use of analogies and pictures to help readers of all levels engage with and understand them. To explain how multiple universes that seem to violate our universal physical laws can exist, he uses the example of a car with no R on the gearshift that requires a huge amount of force to shift into Reverse. “If asked to describe how the car worked, you’d incorrectly assert that, without exception, as long as the engine is running, the harder you push on the accelerator pedal, the faster the car moves forward.” In the same way, the laws of physics appear to behave in consistent ways in our universe, but it might just be that we don’t experience the full gamut of possibilities because of the way our particular universe evolved.

Tegmark’s enthusiasm for physics and sense of humor resurface frequently to help keep the reader engaged. He makes liberal use of exclamation points (a little too frequently for my taste), but they serve the purpose of signaling to the reader that a given statement is an important insight that might not make as much sense to a non-physicist: “A space can be curved all by itself, even if it isn’t the surface of anything!” Many of his analogies are whimsical and memorable, like describing space as a muffin and galaxies as the chocolate chips that move apart from each other when the muffin expands. When expressing the confusion over Schrödinger’s equation that the same electron could be in different places at the same time, he glibly wonders, “If things could be in several places at once, why did we never observe that (while sober?).”

After five chapters of a crash course in the basics of cosmology comes, in my opinion, the most successful and interesting part of the book. Chapter six, “Welcome to the Multiverse,” introduces us to the first two of four levels of multiverse that make up Tegmark’s theory of reality. He clearly explains why the previously explained theory of eternal inflation (the universe expanding forever in certain places) predicts the existence of multiple universes: unequal rates of expansion and decay. Since the universe expands twice as fast as decay gets rid of the inflating substance, the total size of space triples while one third of space stops inflating, like our universe. This process happens over and over again, resulting in the inflating part of space doubling forever and therefore producing non-inflating universes like ours in the process. “In other words, what we’ve called our Big Bang wasn’t the ultimate beginning, but rather the end of inflation in our part of space.” These universes together make up the “Level I multiverse” and are each governed by physical laws that are consistent throughout the universe, which is why the laws we observe appear to apply without exceptions. Inflation is constantly driving those universes apart, so those universes can be thought of as making up a larger, “Level II multiverse” where the discrete universes can have different expressions of the laws of physics, like the car that we aren’t aware can shift into Reverse.

After reaching this point, I felt surprisingly comfortable with the idea of multiverses; for the first time, the possibility of their existence made sense to me. But then I got to chapter eight, “The Level III Multiverse,” and encountered, in Tegmark’s words, “Quantum weirdness.” It turns out that while Level I and II multiverses are predicted to exist in physically distant parts of space, the Level III multiverse exists in the same place and time as ours. Famously exemplified by Schrödinger’s Cat, this is the theory that particles exist in all possible states in an infinite number of alternate universes, so there are essentially clones of you in other universes living varying degrees of different lives, but your brain can’t perceive the weirdness because it happens faster than your neurons fire. I start to struggle at this point; despite lots of drawings of the probabilities of a playing card landing face down or face up after being balanced on its edge, I find it challenging to cognitively wrap my head around the concept of multiple copies of me of which I’m unaware.

Finally in chapter ten Tegmark starts talking about his mathematical universe theory. Until that point, I’d forgotten that this is the “main point” of the book, because I’d needed to learn so much about the currently accepted ideas about reality to get there. Under the Mathematical Universe Hypothesis, lots of strange things happen. It implies that spacetime, and everything within it, is a mathematical structure, and that we humans are complex braidlike structures in spacetime. Additionally, nearly everything we perceive is an illusion; the flow of time, our own perceived realities, etc. And the main reason we needed to learn about multiverses 1-3 is that MUH predicts a fourth multiverse in which physical existence equals mathematical existence; anything that exists mathematically also exists physically in this multiverse. As evidence for this point, Tegmark cites various examples of how computers are able to transform math into physical things and vice versa; express letters typed into a word processing software as a string of numbers, convert coded numbers into vibrations that in turn are interpreted by your ear as music.

At this point, the book shifts from what I would call the realm of physics to the realm of metaphysics. The thought that you and I are simply “self-aware parts of a giant mathematical object” is a little far-fetched, even accepting the idea that we perceive ourselves as more than mathematics because our brains contain a model of the universe through which we interpret our world. Tegmark’s proofs and arguments to support MUH are complicated and hard to follow, involving other theories and possible ways the multiverse(s) might end.

The book concludes with what is usually looked down upon in physics, which Tegmark refers to as “the A-word:” anthropocentrism, or the belief that humans are the metaphorical center of the universe. Tegmark claims that the only reason anything in our universe has meaning is that we make it so, and makes a bit of an abrupt turn toward a “let’s make a difference” message that was not hinted at anywhere else in the book. The last third of the book, while the crux of Tegmark’s argument, is also its Achilles heel. It’s clearly the most personally meaningful to him, and what he’s put the most of his energy into, but it’s just “out there” enough to make one’s eyes glaze over rather than burn with excitement. It’s a bit of a let-down after the much clearer, well-articulated “physics” part of the book, which I feel is more informative and helpful to the average reader hoping to gain a better understanding of this mysterious thing we call the universe.

Perhaps upon re-readings, Tegmark’s vision will become more clear, but I now feel the need for a long walk to clear my head of all these multiverses. But perhaps along the way I’ll wonder if there’s an equation that describes how tree branches heavy with buds sway in the spring breeze.