Review of Our Mathematical Universe: My Quest for the Ultimate Nature of Reality by Max Tegmark

Who doesn’t like a good controversy in their popular science books? What’s a philosophical theory about the nature of the universe if it doesn’t ruffle some feathers? No one wants to write a book and then have everyone turn around and shrug at you. That doesn’t sell! So it’s not really surprising that Our Mathematical Universe: My Quest for the Ultimate Nature of Reality is a controversial book by a somewhat controversial physicist. I received this as a Christmas gift a few years ago, and that was the first I’ve heard of Max Tegmark. Since then he has popped up a few times here or there, and now I’ve finally made time to read this long and detailed treatise on the current state of physics and Tegmark’s personal conception of, well, reality.

I don’t actually find it all that controversial, per se—though I should clarify that I’m a mathematician by training, and not a physicist, so maybe the way Tegmark presents these ideas is more insulting or seems more radical when one is a physicist. That being said, I’m also not saying I agree with Tegmark’s Mathematical Universe Hypothesis (MUH), because, despite probably being a mathematical realist, Platonism itself strangely makes me uncomfortable….

Oh boy, I think I’ve already used too many strange terms! This review is probably going to get pretty heady and philosophical at some point, much like Our Mathematical Universe does. So let me spend the first part here just discussing the book, its structure and writing, etc., in a more general way, to give you an idea of whether or not it is of interest to you before you read my whole review. I’ll get to my thoughts about Tegmark’s specific claims later.

Firstly, regardless of any reservations I might have, I still recommend this book. This is a really well-written and approachable popular science work. Tegmark’s style is really accessible—despite going heavy on scientific and mathematical terminology, he is careful to proceed in a systematic way. This is not a book you want to be reading just before bed, maybe, or during a busy commute—it took me pretty much a week, albeit a busy week, to work my way through it. Nevertheless, I think it is a worthwhile use of one’s time.

Tegmark first impressed me with a table at the end of Chapter 1 called “How to read this book”. He lists every chapter of the book, along with three columns: Science-curious reader, hard-core reader of popular science, and physicist. Each column lists the chapters that reader would be best to read/skip—i.e., the science-curious reader should read the entire book; the hard-core reader can skip several of the earlier chapters because they presumably will have seen these explanations before; and the physicist can skip all but the controversial chapters (Tegmark also labels each chapter as “mainstream”, “controversial”, or “extremely controversial”). I love this approach and hope more popular science authors use it. Now, I, of course, ignored these suggestions and read the whole book anyway, because I wanted to see how Tegmark explained the Big Bang, inflation, etc. Yet I confess I skimmed some parts and felt better about it because I knew it was sanctioned.

One reason I’ll recommend this book is simply because Tegmark’s explanations for the origins of our universe, as currently understood by “mainstream” cosmology, are really lucid. He clarified several aspects of the Big Bang and inflation that, until now, I not only did not understand but didn’t realize I didn’t understand. He didn’t just improve my comprehension: he actually showed me parts of my comprehension of these theories that were inaccurate. I am not a physicist by training by any stretch of the imagination (I only took physics up to Grade 12 in high school, and they don’t even get into relativity by then, let alone QM); all of this knowledge is entirely autodidactic, and hence it isn’t surprising a lot if it is inaccurately understood. But I think I’ve plateaued a lot lately because I was having trouble finding explanations that were calibrated for my knowledge level: either the explanations get too technical and lose me, or else I just end up reading the same ground-floor “hey have you heard of this thing called the double-slit experiment?” stories over and over again, which isn’t fun either.

In particular, I really enjoyed Chapter 5, in which Tegmark explains inflation and why it is necessary to account for problems with the Big Bang theory. The idea of the Big Bang itself is now probably within the realm of general public knowledge, assuming a half-decent education (and regardless of whether one “accepts” the theory or prefers creationist nonsense). Yet there are probably as many misconceptions about this theory as there are explanations of it in popular science books, and once any two non-cosmologists start talking about it, we inevitably run into quasi-philosophical walls. Tegmark very clearly presents what the theory actually says; why it is compelling given the evidence; the problems with the theory without inflation and why inflation itself solves those problems.

Tegmark refers a lot to data gathered by several satellites and ground-based microwave telescopes that have observed the Cosmic Background Microwave Radiation (CBMR). He himself worked quite a bit on many of these projects, or with the data from these projects, to help sharpen and analyze this evidence. And this is another reason I enjoyed and recommend Our Mathematical Universe: Tegmark provides a great perspective on how science is done. From conferences to international projects poring over satellite data to writing and publishing papers, Tegmark shows us the act of physics research as much as the end result. He shows us how individual physicists’ opinions of theories will evolve over time. He shows us how people have different specializations, which in turn lead to different predilections and levels of knowledge about parts of physics. It’s really fascinating, and it’s an aspect to the discourse around science that I wish more media would cover.

So the first 6 or 7 chapters of this book are excellent, and I recommend reading at least those. After Chapter 8, Tegmark introduces the more “controversial” content. As I said above, I don’t see it as controversial so much as a bundle of claims that are either uninteresting because they are obvious or unappealing because they are largely unintelligible. Now we arrive at the part of the review that gets technical.

Let me refer you to Scott Aaronson’s review. He is a computer scientist and much more well-versed in this stuff than I am, so his review goes into more depth behind the mathematical/physics claims that Tegmark makes. I found myself largely nodding along and agreeing with most of Aaronson’s opinions there.

You might think that I, as a mathematically-inclined person, might seize upon the idea presented here. Tegmark’s MUH says not only that we can describe the universe using mathematics (a notion almost axiomatic to our physics) but that all of our physical reality itself is literally mathematical. That is, our entire subjective human experiences are simply the consequence of certain facets of a certain mathematical structure within a superset of structures, the entirety of which comprise the Level IV multiverse, i.e., the sum total of all existence and anything that could ever possibly exist.

It’s tempting. And yet….

Years ago I read The Grand Design. This was back in my university days, mind, when I was high on philosophy classes of all kinds and armed much more to purpose for these kinds of throw-downs. Nowadays, my memory of the differences between ontological and epistemological arguments requiring jogging from Wikipedia, I’m not so sure I’m up to the task. Yet one idea has stayed with me from Hawking and Mlodinow’s book: that of model-dependent realism. They proposed that the reason we are having so much trouble finding a “theory of everything” to unify the physics of the big (relativity) and the physics of the small (QM) is because no such theory exists. Rather, different theories are required depending on the situation one is trying to model. It is an intriguing idea, one I hadn’t really encountered in a science book before. And I really liked how it short-circuited many anti-realist objections to scientific realism.

Tegmark appears to move in the opposite direction. He backs the ToE horse (which is fine) by insisting that the ToE is reality. And then he kind of dodges the question of whether that means we will ever actually find a ToE (because if we did, wouldn’t that mean we just have … reality?).

That’s what I mean about the MUH being uninteresting and unintelligible. He starts off by talking about how the movement of time is an illusion, all very much standard stuff depending on how you define spacetime, etc. Yawn. When we get into the more “controversial” material, his argument just sort of breaks down. He starts making a whole bunch of probabilistic paradox arguments, like quantum suicide, the doomsday argument, etc.—the kind of thought experiments that are fun to put into a first-year philosophy textbook but that have little connection to, you know, reality. These thought experiments rely explicitly on making assumptions to make up for our near-total lack of knowledge about a situation. The whole point is that, as we acquire more certain knowledge, we are in a better position to see if we are indeed a representative sample or if, perhaps however improbably, we are not.

Tegmark’s MUH is also, despite his claims to the contrary, completely untestable/unfalsifiable. He insists that we will uncover evidence and create theories which logically imply the MUH, and that’s just silly. The MUH is untestable because we currently have no alternative to mathematics as a way of describing physical theories of reality. It is unfalsifiable, because even if we can get past the testing problem, how will we know if we’ve discovered a physical law or property that violates the MUH? Almost by definition, the MUH can take nearly any observational evidence and somehow fit into its framework. Tegmark claims that if the MUH is false, then we will one day run up against an insurmountable “wall” in physics beyond which our knowledge of reality can progress no further, since our mathematics will no longer be able to express reality. I disagree. I think model-dependent realism would be an effective way to counteract such a wall: maybe to progress, all we need do is abandon the search for a ToE and instead create theories of everything.

The last half of Our Mathematical Universe is a wild ride of philosophy of mathematics and science. I loved reading it. I found parts of it very convincing, but I don’t think those parts (combined with the other parts) necessarily add up to the whole that Tegmark calls the Level IV multiverse, the Mathematical Universe Hypothesis. I think he is incredibly enthusiastic about this idea and has clearly spent a lot of time thinking on it—which is great. I loved that I got a chance to read it. But I don’t think his arguments are as sound as he thinks they are. I say this not from a physicist’s position (because I’m not one) nor even a mathematician/logician (because, let’s face it, my memory of higher math dims with each passing day) but as the target demographic for this book, the hard-core popular science reader who is looking for a new hit to bring on that theoretical physics high. It’s a nice try, Tegmark, and you almost had me going.