Lost in Math

Listening to experts argue can be one of the better ways to learn about a new field. It does require some basic orientation and grounding or can be confusing or, worse, wildly misleading, so some advance research or Internet searches are warranted. But it provides some interesting advantages over reading multiple popular introductions to a field.

First, experts arguing with each other are more precise about their points of agreement and disagreement because they're trying to persuade someone who is well-informed. The points of agreement are often more informative than the points of disagreement, since they can provide a feel for what is uncontroversial among experts in the field.

Second, internal arguments tend to be less starry-eyed. One of the purposes of popularizations of a field is to get the reader excited about it, and that can be fun to read. But to generate that excitement, the author has a tendency to smooth over disagreements and play up exciting but unproven ideas. Expert disagreements pull the cover off of the uncertainty and highlight the boundaries of what we know and how we know it.

Lost in Math (subtitled How Beauty Leads Physics Astray) is not quite an argument between experts. That's hard to find in book form; most of the arguments in the scientific world happen in academic papers, and I rarely have the energy or attention span to read those. But it comes close. Hossenfelder is questioning the foundations of modern particle physics for the general public, but also for her fellow scientists.

High-energy particle physics is facing a tricky challenge. We have a solid theory (the standard model) which explains nearly everything that we have currently observed. The remaining gaps are primarily at very large scales (dark matter and dark energy) or near phenomena that are extremely difficult to study (black holes). For everything else, the standard model predicts our subatomic world to an exceptionally high degree of accuracy. But physicists don't like the theory. The details of why are much of the topic of this book, but the short version is that the theory does not seem either elegant or beautiful. It relies on a large number of measured constants that seem to have no underlying explanation, which is contrary to a core aesthetic principle that physicists use to judge new theories.

Accompanying this problem is another: New experiments in particle physics that may be able to confirm or disprove alternate theories that go beyond the standard model are exceptionally expensive. All of the easy experiments have been done. Building equipment that can probe beyond the standard model is incredibly expensive, and thus only a few of those experiments have been done. This leads to two issues: Particle physics has an overgrowth of theories (such as string theory) that are largely untethered from experiments and are not being tested and validated or disproved, and spending on new experiments is guided primarily by a sense of scientific aesthetics that may simply be incorrect.

Enter Lost in Math. Hossenfelder's book picks up a thread of skepticism about string theory (and, in Hossenfelder's case, supersymmetry as well) that I previously read in Lee Smolin's The Trouble with Physics. But while Smolin's critique was primarily within the standard aesthetic and epistemological framework of particle physics, Hossenfelder is questioning that framework directly.

Why should nature be beautiful? Why should constants be small? What if the universe does have a large number of free constants? And is the dislike of an extremely reliable theory on aesthetic grounds a good basis for guiding which experiments we fund?

Do you recall the temple of science, in which the foundations of physics are the bottommost level, and we try to break through to deeper understanding? As I've come to the end of my travels, I worry that the cracks we're seeing in the floor aren't really cracks at all but merely intricate patterns. We're digging in the wrong places.

Lost in Math will teach you a bit less about physics than Smolin's book, although there is some of that here. Smolin's book was about two-thirds physics and one-third sociology of science. Lost in Math is about two-thirds sociology and one-third physics. But that sociology is engrossing. It's obvious in retrospect, but I hadn't thought before about the practical effects of running out of unexplained data on a theoretical field, or about the transition from more data than we can explain to having to spend billions of dollars to acquire new data. And Hossenfelder takes direct aim at the human tendency to find aesthetically appealing patterns and unified explanations, and scores some palpable hits.

I went into physics because I don't understand human behavior. I went into physics because math tells it how it is. I liked the cleanliness, the unambiguous machinery, the command math has over nature. Two decades later, what prevents me from understanding physics is that I still don't understand human behavior.

"We cannot give exact mathematical rules that define if a theory is attractive or not," says Gian Francesco Giudice. "However, it is surprising how the beauty and elegance of a theory are universally recognized by people from different cultures. When I tell you, 'Look, I have a new paper and my theory is beautiful,' I don't have to tell you the details of my theory; you will get why I'm excited. Right?"

I don't get it. That's why I am talking to him. Why should the laws of nature care what I find beautiful? Such a connection between me and the universe seems very mystical, very romantic, very not me.

But then Gian doesn't think that nature cares what I find beautiful, but what he finds beautiful.

The structure of this book is half tour of how physics judges which theories are worthy of investigation and half personal quest to decide whether physics has lost contact with reality. Hossenfelder approaches this second thread with multiple interviews of famous scientists in the field. She probes at their bases for preferring one theory over another, at how objective those preferences can or should be, and what it means for physics if they're wrong (as increasingly appears to be the case for supersymmetry). In so doing, she humanizes theory development in a way that I found fascinating.

The drawback to reading about ongoing arguments is the lack of a conclusion. Lost in Math, unsurprisingly, does not provide an epiphany about the future direction of high-energy particle physics. Its conclusion, to the extent that it has one, is a plea to find a way to put particle physics back on firmer experimental footing and to avoid cognitive biases in theory development. Given the cost of experiments and the nature of humans, this is challenging. But I enjoyed reading this questioning, contrarian take, and I think it's valuable for understanding the limits, biases, and distortions at the edge of new theory development.

Rating: 7 out of 10

Reviewed: 2020-03-23