Amir Alexander reviews *Our Mathematical Universe: My Quest for the Ultimate Nature of Reality* by By Max Tegmark:

Zooming through a Stockholm intersection on his bicycle one morning, 18-year-old Max Tegmark never saw the truck that hit him. The blast of a horn, the screech of tires and a sickening thud followed in quick succession, extinguishing a young life filled with promise.

It never happened, of course. As the adult Dr. Tegmark, now 46, relates in the opening pages of this provocative new book, young Max swerved at the last instant and continued on to school — and an academic career that eventually took him to the faculty of M.I.T. and the top ranks of the world’s cosmologists.

But wait: That fatal accident did happen, Dr. Tegmark writes. Yes, he came through unscathed that day, but he was also killed, and he was severely injured, and slightly injured. He endured every possible outcome, happy and unhappy, that can befall a bicyclist who encounters a speeding truck.

All of these happened, he argues, because everything that can happen does happen — in at least one of an infinite number of universes.

If you find this far-fetched, you are hardly alone. The idea of parallel universes, in which events diverge from those in our own reality, is usually the domain of science fiction. But Dr. Tegmark is a scientist, not a novelist, and he makes a powerful case, leading us step by logical step from well-established mainstream science into ever stranger territory.

Each step along the way seems entirely reasonable, so that by the time we arrive at Dr. Tegmark’s “multiverse,” in which all that can be is, we are left to wonder: Can this be right? And if not, where did we go wrong?

He starts the journey in the ancient world, when Greek scholars used brilliantly creative geometrical methods to estimate the circumference of the earth, the size of the moon and the distance to the sun. From there he moves through the discoveries that established the universe as it is known to scientists today: our solar system, the Milky Way, the innumerable galaxies all racing away from one another as the universe expands and expands. He argues that there is no reason to think the Big Bang was a unique event, so one should assume countless other universes. This is science writing at its best — dynamic, dramatic and accessible.

But then things get stranger. Dr. Tegmark narrows his focus to the building blocks of matter, the elementary particles governed by the laws of quantum mechanics. The position of a particle at a given time is described by its “wavefunction,” but this provides only a probable distribution of locations, not an absolutely determined one.

The classic Copenhagen interpretation, devised by Niels Bohr and Werner Heisenberg in the 1920s, resolved this problem by positing that the wavefunction “collapses” into a specific location when a measurement is made. But Dr. Tegmark rejects this as an improvised and implausible solution. The wavefunction never collapses, he argues, and all its different values continue to exist side by side.

What all this means is that the universe is constantly splitting into more and more realities, in each of which the particle is in one of its possible locations.

Nor is this splitting limited to the microscopic scale of quantum physics. Since we are made of elementary particles, our actions, thoughts and feelings ultimately depend on their position, and our world, too, is constantly splitting into all its possibilities.

Dr. Tegmark’s ultimate reality is one in which anything that is mathematically possible actually exists, but there is nothing that is not mathematical. Our reality, in other words, is not just described by mathematics, it is mathematics.

The vision of a purely mathematical universe, one that can be understood solely through rigorous mathematical reasoning, is far from new. As far back as the sixth century B.C., the Pythagoreans declared that “all is number,” and in the 17th century A.D. Descartes tried to deduce the universe from first principles. Other 17th-century rationalists, including Hobbes and Leibniz, offered their own versions of the mathematical universe.

Such efforts to comprehend the world entirely through mathematical reasoning certainly had their triumphs, none more so than when Einstein upended our universe using nothing more than careful reasoning and mathematical calculations.

But the overall record for such attempts is decidedly mixed: The Pythagoreans, who insisted that everything was made of whole numbers and their ratios, foundered on the discovery of irrationals, and Descartes concluded that matter was simple extension in space, that a vacuum was impossible and that the planets swirled in vortexes of ether.

It is difficult to say whether Dr. Tegmark’s mathematical universe will ultimately be deemed an Einsteinian triumph or a Cartesian dead end. His conclusions are simply too far removed from the frontiers of today’s mainstream science, and there is little hope that conclusive evidence will emerge anytime soon.

Yet “Our Mathematical Universe” is nothing if not impressive. Brilliantly argued and beautifully written, it is never less than thought-provoking about the greatest mysteries of our existence. It may be sheer coincidence that we live in a universe in which Max Tegmark survived a very close call on the streets of Stockholm. But after reading his book, I am convinced we are fortunate that we do.