Sabine Hossenfelder – Lost in Math: How Beauty Leads Physics Astray

Sabine Hossenfelder – Lost in Math: How Beauty Leads Physics Astray

Hossenfelder brilliantly covers the intersection of philosophy, hard science, and social science. She has a lot of wisdom about certainty, error, doubt, and why quantitative analysis is important and useful, but also prone to abuse. Her thesis is that a scientist’s proper goal is to understand the natural world. In that pursuit, many scientists get a little too caught up in constructing elegant mathematical models. Models and equations are useful when they add to understanding, which they often do. In fact, they are often vital to it. But models are a means, not an end.

To Hossenfelder, it is disconcerting how often scientists describe their models and equations as elegant. The word is everywhere. It appears constantly in scientific papers and conferences, in the classroom, and in popular-level books, magazine articles, and documentaries. Scientists sometimes even judge their theories and experimental results to be true or false based on whether they are viewed as beautiful or elegant. Even Einstein fell into this trap with his famous “God does not play dice” remark to express his unease with the Heisenberg uncertainty principle.

This is a problem because the universe does not care if people think it is beautiful or not. f=ma is either true, or it isn’t. Ptolemy’s laws, or Keplers, or Newton’s, or Einstein’s, or the string theorists’ ideas, are each either true or false. The answers do not depend on whether someone thinks they are elegant. Rather than chasing elegant ghosts, a scientist’s goal should be to get as close to objective understanding as possible, given human limitations.

Hossenfelder is a deep enough thinker to realize that our aesthetic sense likely evolved in response to our universe; causality runs both ways. It is not a coincidence that our eyes are most sensitive to the very E-M frequencies the sun sends our way, or that our ears respond precisely to the most common sound frequencies around us. In addition to our sensory organs’ capabilities being determined by evolutionary processes, so too did the way we interpret those sensory inputs.

Aesthetically, people tend to find beauty and elegance in evolutionary success, and ugliness in threats or failures to reproductive success. it is not a coincidence that signs of beauty are almost universally signs of youth, health, and fertility. Most people consider symmetrical faces more beautiful because symmetry correlates with good health, and with good genes. We prefer cleanliness over filth because bacteria and disease are bad for survival and reproductive success. So it makes sense that scientists, as humans who evolved in just this way, both have the aesthetic sense that they do, and that they feel compelled to find it in physics and other sciences.

If a symmetrical face is elegant and beautiful, so is a scientific equation that exactly has a given symmetry, or exactly fits a certain exponent. e=mc2 is much more appealing than, say, e=mc2.1. Some laws, such as this exchange rate between matter and energy, do have this elegant precision. This is fortunate, otherwise humans might never have discovered them! Other phenomena that are just as true are less elegant, such as entropy, the probabilism of quantum mechanics, or the way friction coefficients, alloys, and engineering tolerances all defy perfect precision in practice.

Our search for elegance in scientific research is a longstanding natural impulse redirected in a new and foreign direction. Humans have been a species for perhaps 200,000 years, and proper scientists for just a few hundred years–just a thousandth or two of that time. Our 200,000 years is in turn perhaps a touch more than one three thousandth of the animal kingdom’s existence. Our evolved aesthetic sense is very, very old. As such, it will be some time before evolution is able to adapt to our new social environment and address Hossenfelder’s concerns. Until then, the least we should do is be aware of our elegance problem.

While reading the book, I kept thinking it had just the sort of message that my former economics professor Russ Roberts would enjoy. One of the hallmarks of his approach is a conscious avoidance of certainty, and keeping in mind the difference between good and bad uses of statistics (Russ is also a keen and humble philosophical thinker). As it turns out, Russ had an excellent conversation with Hossenfelder on his EconTalk podcast. It’s worth a listen, especially for those who don’t have time to read the whole book.

Though Hossenfelder’s home is in physics, in several points during the book she acknowledges how her thinking applies to the social sciences. She’s right. Economists in particular would do well to consider her arguments. Her arguments about the parallel uses and abuses of mathematical modeling has some intersection with Jerry Z. Muller’s recent book The Tyranny of Metrics, though Hossenfelder’s arguments are more nuanced and broader-ranging, and have a deeper philosophical foundation.

Lost in Math also reminded me of F.A. Hayek’s The Counter-Revolution in Science, which distinguishes between science and scientism. As Hayek defines the terms, science is the process of learning about the universe and the beings who live in it. Scientism is more about method-worship, valuing mathematical rigor and elegance as its own end. When taken too far, scientism can color results and potentially stunt entire research programs and lines of inquiry.

This has happened in economics. Crudely, science and scientism can be personified as Adam Smith vs. Paul Samuelson–though again, very crudely. Peter Boettke contrasts mainline vs. mainstream economics to make a similar point. Smithian mainline economists are interested in the human condition; mainstream Samuelsonians are a little too interested in technical proficiency and elegant modeling. They would do well to focus a little less on Homo economicus, and a little more on the admirable and real, though admittedly less elegant, Homo sapiens.

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