Book Review: Max Tegmark “Our Mathematical Universe”

Our Mathematical Universe: My Quest for the Ultimate Nature of Reality
Knopf (January 2014)

Max Tegmark just published his second book, “Life 3.0.” I gracefully declined reviewing it, seeing that three years weren’t sufficient to finish his first book. But thusly reminded of my shortfall, I made another attempt and finally got to the end. So here’s a late review or, if you haven’t made it through in three years either, a summary.

Tegmark is a cosmologist at MIT and his first book, “Our Mathematical Universe,” is about the idea that the world is not merely described by mathematics, but actually made of mathematics.

I told you ten years ago why this is nonsense and haven’t changed my mind since. It was therefore pretty clear I wouldn’t be fond of Max’s message.

But. Well. People like Max don’t grow on trees. I have much sympathy for his free-range ideas and also, even though I’ve met him several times, I never really figured out what he was tenured for. Probably not the mathematical universe. Once upon a time, I was sure, he must have done actual physics.

Indeed, as the book reveals, Tegmark did CMB analysis before everyone else did it. This solid scientific ground is also where he begins his story: With engaging explanations of contemporary cosmology, the evolution of the universe, general relativity, and all that. He then moves on to inflation, eternal inflation and the multiverse, to quantum mechanics in general and the many worlds interpretation in particular. After this, he comes to the book’s main theme, the mathematical universe hypothesis. At that point we’re at page 250 or so.

Tegmark writes well. He uses helpful analogies and sprinkles some personal anecdotes which makes the topic more digestible. The book also has a lot of figures, about half of which are helpful. I believe I have seen most of them on his slides.

Throughout the book, Tegmark is careful to point out where he leaves behind established science and crosses over into speculation. However, by extrapolating from the biased sample of people-he-spends-time-with, Tegmark seems to have come to believe the multiverse is much more accepted than is the case. Still, it is certainly a topic that is much discussed and worth writing about.

But even though Tegmark’s story flows nicely, I got stuck over and over again. The problem isn’t that the book is badly written. The problem is that, to paraphrase John Mellencamp, the book goes on long after the thrill of reading is gone.

Already in the first parts of the book, Tegmark displays an unfortunate tendency to clutter his arguments with dispensable asides. I got the impression he is so excited about writing that, while at it, he just also has to mention this other thing that he once worked on, and that great idea he had which didn’t work, and why that didn’t work, and how that connects with yet something else. And did I mention that? By the way, let me add this. Which is related to that. And a good friend of mine thinks so. But I don’t think so. And so on.

And then, just when you think the worst is over, Tegmark goes on to tell you what he thinks about alien life and consciousness and asteroid impacts and nuclear war and artificial intelligence.

To me, his writing exhibits a familiar dilemma. If you’ve spent years thinking about a topic, the major challenge isn’t deciding what to tell the reader. It’s deciding what to not tell them. And while some readers may welcome Tegmark’s excursions, I suspect that many of them will have trouble seeing the connections that he, without any doubt, sees so clearly.

As to the content. The major problems with Max’s idea that the universe is made of mathematics rather than merely described by mathematics are:

1. The hypothesis is ill-defined without explaining what “is real” means. I therefore don’t know what’s the point even talking about it.
   
   
2. Leaving this aside, Max erroneously thinks it’s the simplest explanation for why mathematics is so useful, and hence supported by Ockham’s razor (though he doesn’t explicitly say so). The argument is that if reality is merely described by mathematics rather than actually made of mathematics, then one needs an additional criterion to define what makes some things real and others not.
   
   But that argument is logically wrong. Saying that the universe is accurately described by mathematics makes no assumption about whether it “really is” mathematics (scare quotes to remind you that that’s ill-defined). It is unnecessary to specify whether the universe is mathematics or is something more, evidenced by scientists never bothering with such a specification. Ockham’s razor thus speaks against the mathematical universe.
   
   
3. He claims that a theory which is devoid of “human baggage” must be formulated in mathematics. I challenge you to prove this, preferably without using human baggage. If that was too meta: Just because we don’t know anything better than math to describe nature doesn’t mean there is nothing.
   
   
4. Max also erroneously thinks, or at least claims in the book, that the mathematical universe hypothesis is testable. Because, so he writes, it predicts that we will continue to find mathematical descriptions for natural phenomena.
   
   But of course if there was something for which we do not manage to find a mathematical description, that would never prove the mathematical universe wrong. After all, it might merely mean we were too dumb to figure out the math. Now that I think of it, maybe our failure to quantize gravity falsifies the mathematical universe.

There are further various statements in the book which I can’t make sense of. For example, I have no idea what an “element” of a mathematical structure is. I only know elements of sets. I also don’t understand why Tegmark believes accepting that our universe is a mathematical structure means that differential equations no longer need initial conditions. Or so he seems to say. Even more perplexing, he argues that the multiverse explains why the constants of nature seem finetuned for the existence of life. This is a misunderstanding of both finetuning and the anthropic principle.

There. I’ve done it again. I set out with the best intention to say nice things, but all that comes out is “wrong, wrong, wrong.”

To work off my guilt, I’ll now have to buy his new book too. Check back in three years.