Figuring Out the World

You don't have to study too much modern science before you figure out the world is weird. Realizing that most of what we see in the objects around us is actually empty space, learning that at its most basic level matter has an uncertainty about it that can't be overcome, and so on and so on.

Scientists have operated under the idea that this weird world is understandable and that even if language can't explain it, math can. As our knowledge of the universe expands past the limits of what scientific instruments can detect, that math becomes more and more important. A theory about what matter is like at its most fundamental level may not be experimentally provable because it deals with forces or particles beyond our ability to detect. But it can make some predictions about things which are observable that, if true, would point in that theory's direction, putting a more solid foundation under the esoteric math and conjecture presented. If the experiments don't pan out, then that math may need to be discarded in favor of other possible explanations.

Sabine Hossenfelder, a theoretical physicist and research fellow at the Frankfurt Institute for Advance Studies, wonders if physicists and researchers have gotten a little too dependent on certain kinds of math or math with certain features. She wonders if that dependence has made it difficult for them to continue to explore the universe around us because they are looking for answers only in places that will confirm what they have already suggested is true. The math they follow seems to have congealed around the ideas of "naturalness" and "beauty," leaving whole areas of inquiry unexplored if they lack those two qualities. In Lost in Math: How Beauty Leads Physics Astray, Hossenfelder explores how those ideas came to hold the power they do and why, exactly, that may be a problem.

"Naturalness" roughly means that scientists prefer certain kinds of answers to questions and certain measurements. For example, if two different experiments on related matters produce very long answers that are only different in their smallest digits, scientists are uneasy. Pi, for example, is the ratio of the circumference of a circle to its diameter. It's a never-repeating, never ending number. If some other geometric ratio were found that matched pi almost exactly, not deviating until the 20th decimal place then scientists would be suspicious of the similarity, which they call "fine-tuning." Either there is a connection that they missed or there is another principle more basic than the two being considered. In the interests of full-disclosure: A person such as myself, mired in my traditional Christian theism, has much less of a problem with a fine-tuned universe than do most scientists.

Scientists are also suspicious of numerical solutions to natural equations and ratios that are very large or very small. If an equation describes a natural process, like the force of gravity, then the solution when some of the variables are replaced with real values needs to be an ordinary kind of number rather than 47 quintillion or so.

The preference for naturalness combines with another scientific preference when it comes to equations, which scientists often call "beauty." That word is often a short-hand for equations that are simply written, symmetrical in appearance, and significant in describing the world. Equations that have values which can't themselves be reduced into other equations are simple. Ones which involve basic rather than complex math on either side of an equals sign are more symmetrical. And ones that describe the actual world around us are significant.

Hossenfelder has no real problem with either of these concepts, noting that they have sometimes functioned as good criteria for evaluating scientific hypotheses. Her first few chapters outline how the concepts developed and how they have been used to advance knowledge. The problem comes when naturalness and beauty become the gatekeepers that decide which theories will be tested by experiment and which ones won't.

She says this has been especially true as scientists explore what is called the Standard Model of Physics. It's successfully described much of the real world on the very smallest scales and offered predictions which later tested out to be true. But it has some gaps and as scientists try to rope the force of gravity in with the other three fundamental forces of the universe, those gaps loom large.

One of the theories that would help bridge the gap is super-symmetry. It has, Hossenfelder says, elegant equations and avoids the perception of fine-tuning. Without going into detail I certainly don't understand, one thing super-symmetry has predicted are certain subatomic particles which have never yet been observed. Even more and more powerful experiments at the Large Hadron Collider have failed to show any confirmable evidence the particles exist. Hossenfelder wonders why that fact has spawned more doubling down on confirming super-symmetry through more expensive and elaborate experiments instead of a flurry of, "Well, what else might be true?"

On the one hand Lost in Math could be seen as a book-length gripe about confirmation bias. Scientists have become so certain that the best and truest descriptions of the universe have more naturalness and beauty that they now assume that situation to be true instead of question whether or not it is.

But Hossenfelder's explorations of exactly how these two concepts came to carry such weight are great studies in the history of science, and show just why many scientists hold to them. She also has clear explanations of a lot of the ideas about the universe that get batted around in the media, mostly it seems by people who could stand to read her explanations. Her writing is clear and a lot of fun, and all the more impressive when you realize she's doing it in another language than her everyday one. Each chapter ends with a list of summary bullet-points that help a reader keep the big ideas in mind before forging ahead.

Hossenfelder includes her interviews with a number of physicists, and a couple of them hint that some of those physicists probably consider her something of a grind when it comes to these ideas. But that's probably a good description of how scientists do their best work: They keep asking questions about stuff, especially the stuff everyone thinks is most certainly true.

Lost in Math has the rare and enjoyable quality of explaining a current scientific situation and what leads to it, as well as the underlying concepts, in layperson's terms while still communicating some of the complicated concepts underneath. Despite the title, it's a book that does not automatically leave a non-scientist reader lost, either in math or theoretical physics.