Our Mathematical Universe

Cover of Our Mathematical Universe: My Quest for the Ultimate Nature of Reality by Max Tegmark. Knopf

In his first book for a popular audience, Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, MIT theoretical physicist Max Tegmark lays out a bold proposition which he dubs the mathematical universe hypothesis:

Not only is our universe described by mathematics, but in fact our universe exists, at the most fundamental level, as a mathematical structure. And, not only that, but in fact universes exist - really, truly, physically exist - for many different types of mathematical structures.

It is a revolutionary suggestion, to be sure, and I'll get into the overall merits of the hypothesis itself on its own page. (Clearly, I've found it interesting enough to devote a whole article to it.)

But let's step away from the hypothesis a bit and allow me to judge the book itself, what with this being a book review and all.

Structure of the Book

The goal of the book is nothing less than tackling one of the most fundamental questions not only of physics, but of existence itself: What is the nature of our reality?

Tegmark splits his exploration into three parts. In Part I, he "zooms out" to view the cosmological questions about reality, focusing on concepts such as the Big Bang theory, inflation theory, and the types of parallel universes predicted by these theories.

In Part 2, he "zooms in" to view the smallest realms we have ever studied, specifically the ideas from particle physics and quantum physics.

One of the major conceptshe explores in this section is the Level III multiverse that is predicted by the many worlds interpretation of quantum physics (and he mentions the implications for quantum computers).

It is in Part 3 where Dr. Tegmark proceeds to focus upon his core thesis of the mathematical universe hypothesis.

Pulling together many of the concepts and open questions introduced earlier in the book, he presents his argument in favor of the mathematical universe hypothesis (discussed in a bit more detail here), and also argues in favor of a Level IV multiverse ... that is, a multiverse in which different mathematical structures give rise to different universes. 

The Good and the Bad

One danger in a book with this much speculation in it is that the lines between established scientific evidence, broad scientific agreement, and speculative scientific inquiry will get blurred. Tegmark gets high marks for clarity in this regard, as he goes out of his way to explain the degree to which these different ideas are under debate within the scientific community, and the highly speculative nature of his own hypothesis.

This book is definitely not for the faint of heart, however. Readers looking for an opening foray into the world of scientific literature would find the first chapters quite engaging, I think, but I suspect that they would feel the more complex subjects later in the book do move a bit beyond them. Readers who are well acquainted with the basic scientific concepts will no doubt find the whole book highly engaging and even the more esoteric topics accessible.

Though the book is about mathematical structures, the reader does not need to be highly familiar with mathematics in order to understand the core argument, although it certainly wouldn't hurt! For readers who are comfortable with reading about complex scientific concepts - particularly those in cosmology and quantum physics - this is a very readable account that doesn't specifically assume any significant background or expertise in these areas.

One other pleasant element is this book is that it is incredibly candid about the broad philosophical questions that it tries to address, and somewhat unapologetic that it is trying to answer questions that are both physical and philosophical at the same time. Recent books such as Stephen Hawking's The Grand Design and Lawrence Krauss' make the error of tackling deeply philosophical questions while, at the same time, trying to diminish the validity of philosophy itself as meaningless.

Our Mathematical Universe seeks to answer some of the deepest questions about reality itself in an expansive, entertaining account of modern theoretical physics, with a touch of existential philosophy thrown in for good measure. Anyone who enjoys these subjects and likes not merely reading science facts but also thinking deeply about these core issues would find the book extremely engaging.

If it sounds interesting to you, then by all means ... .