Pilgrims In Another Dimension
Review by Mark Wyman
Lost In Math
How Beauty Leads Physics Astray
Book by Sabine Hossenfelder
Most scientists have never worn a lab coat. The image persists because we like to picture scientists as a distinct class of people devoted to the truth and willing to follow the data wherever they lead. While scientists try to live up to this ideal, Sabine Hossenfelder argues in her insightful new book, Lost in Math: How Beauty Leads Physics Astray, that even scientists can’t escape the human propensity for self-deception. A theoretical physicist herself, as well as a blogger and science writer, Hossenfelder has become convinced that her field has veered off-course in the past few decades. The physicists’ mistake? A romantic belief that beauty should be a reliable guide to uncovering scientific truth.
Hossenfelder, with mainstream credentials and a solid research record, doesn’t have the profile one might expect from a prophet of doom. But as her career advanced (she is now at the Frankfurt Institute for Advanced Studies), she began to accrue doubts about her field. “While I witnessed my profession slip into crisis,” she writes, “I slipped into my own personal crisis. I’m not sure anymore that what we do here, in the foundations of physics, is science. And if not, then why am I wasting my time with it?” When she found herself without research funding, a grim situation that sharpened her anxiety about the field’s health, she set out to discover why others weren’t as worried as she was. This book is the result: a record of Hossenfelder’s interviews with leading theoretical physicists, in which she asks them, in essence, to explain why they haven’t given up. Lost in Math is a compendium of these conversations, interleaved with editorial commentary and summaries of the history and science under discussion. The back-and-forth that results is a sort of skeptic’s remix of Brian Greene’s Elegant Universe, though Greene himself isn’t interviewed.
Like Hossenfelder, I trained as a theoretical physicist in the early 2000s. Our generation was raised on assurances that a new springtime for theoretical physics was just around the corner. Those assurances proved false. While our scientific parents and grandparents constructed a revolutionary and virtually unassailable “Standard Model” of particle physics, we have not had much luck continuing the project despite trying to follow the same blueprints.
The Standard Model explains the workings of three basic forces (strong, weak, electromagnetic), and particles that range from the familiar electron and photon to the more exotic quarks, gluons, and neutrinos.
With a few caveats, it’s fair to say that the Standard Model agrees well with every experiment scientists have done to test it. The recent discovery of the Higgs boson was just the latest of its many successful predictions. The Standard Model doesn’t explain everything, however. It doesn’t include gravity, and can’t account for dark matter, a component essential to describing the distribution of stars and galaxies in the Universe.
But what bothers particle physicists most about the Standard Model is that it is too ‘ugly.’ “I yet have to find someone who actually likes the standard model,” Hossenfelder notes. Physicists have spent the past few decades hoping that particle colliders would turn up new phenomena to guide them beyond the Standard Model. Instead, apart from some small discrepancies, the predictions of the Standard Model keep working. Since recent experiments have ceased producing the kind of unexplained data that has traditionally led to new discoveries, particle physicists have begun turning to non-empirical criteria to judge new ideas.
‘Non-empirical criteria’ is a studiously non-judgmental term for choosing a scientific theory according to taste, rather than by using data to either confirm it or rule it out. This is not a method that people usually associate with the so-called ‘hard’ sciences. Yet, as Hossenfelder points out, physicists have long felt that they should find laws that are not just accurate, but aesthetically pleasing. Beauty, for physicists, means compact equations and dimensionless ratios of moderate size, and clear explanations for situations when two things that look alike behave very differently.
Hossenfelder thinks this may be an unfounded expectation. She doesn’t see why natural laws should look beautiful to humans. While many physicists claim that this kind of beauty has been a successful guide in the past, Hossenfelder counters that there is no guarantee this will be true in the future. Indeed, in a striking final chapter, she gives a précis of the myriad cognitive biases that humans are subject to, and implies that the failure of physicists today to get out of their search-for-beauty rut is radically worsened by a systemic inability to see the psychological cages in which they are trapped.
Hossenfelder’s critique is one that her field needs to hear. Many physicists fear that their experiments will not find anything new for years, or even decades. With pressure to publish unabated, physics research has moved towards ‘ambulance chasing’: absurd mushrooms of activity clustered around tiny experimental discrepancies, which usually vanish when further data are collected. Moreover, lack of impartial criteria has concentrated taste-making power in the hands of a few.
But beauty has a powerful pull to which Hossenfelder doesn’t quite do justice. Hossenfelder feels obliged to explain what “beauty” means to a physicist, but puts her thumb on the scales by quoting a deceptively dry summary by philosopher Richard Daweed: “arguments commonly made by string theorists in favor of their theory are (1) the absence of alternative explanations, (2) the use of mathematics that has worked before, and (3) the discovery of unexpected connections.” Though accurate, this fails to capture the experience of finding a beautiful connection in one’s own work. It feels like magic.
Imagine bringing a newly cut front door key home, only to discover that it can also open every lock in your house – and your car, too. It would be hard to convince yourself that this was just a fluke, and you’d be tempted to keep trying your special key on new locks, even if the next few dozen didn’t work. And while Hossenfelder is not wrong to criticize some aspects of this pursuit of beauty, I feel she has sometimes elided debatable questions of pure aesthetics with justifiable concerns about the self-consistency of the mathematics underlying the Standard Model. There are aspects of the Standard Model that really do seem odd (e.g. the Large Hadron Collider’s measurements for the Higgs boson suggest that the Universe might teeter on the brink of catastrophic decay), while other apparent peculiarities that physicists dislike have no real consequences.
Despite any quibbles a reader might have with Hossenfelder’s views, the book remains compelling because of her skill as an interviewer. She relays her subjects’ thoughts at length and in their own words. She supplies critical commentary, but in a way that is studiously balanced and fair. She is also quite funny, concluding her summary of non-empirical criteria thus: “I envision a future in which climate scientists choose models according to criteria some philosopher dreamed up. The thought makes me sweat.”
Eschewing the convenience of e-mail or (mostly) Skype, Hossenfelder has done the hard work of scheduling appointments and booking plane flights around the world to conduct her interviews in person. As a physicist herself, she is able to capture how serious physicists think about beauty and how they cope with the fact that current data are all explained by established theories. She deftly portrays, for instance, the influential theorist Nima Arkani-Hamed’s private frustrations and his dry wit. I have personally witnessed Arkani-Hamed bleary-eyed after cereal-fueled all-nighters, and have often marveled at his absent-mindedness and self-indulgence (he regularly fails to catch scheduled flights to conferences) — all tolerated because of his unique gifts. Hossenfelder shows him caricaturing the dismissive comments of non-theorist detractors: “You can make up all kinds of la-la stories, and maybe every now and then, once every fifty years or so, experiment will come along and chop things down. So, great job if you can get it, right? You can just sit around, make shit up, and you’re never checked.” Meanwhile, an interview with elder statesman and Nobel laureate Steven Weinberg begins, “ ‘If you go back to the Greeks of the Hellenic period, up to the time of Aristotle, ‘ …”. Many other personalities, from Nobel laureate Frank Wilczek to surfer dude-cum-physics heretic Garrett Lisi, are similarly well-captured.
For those less familiar with the nuts and bolts of particle physics, Hossenfelder sprinkles in short refreshers. Although these summaries vary in accessibility, they are packed with interesting details, which make them fun reading even for someone (like myself) who knows the material well. The book covers a variety of topics both inside and outside the mainstream, including a fascinating discussion of the problems of interpreting quantum mechanics, but Hossenfelder’s chief target is the idea of Supersymmetry (“SUSY”), which she sees as the gateway drug fueling the field’s present destructive addictions.
SUSY was conceived as a cure for the ugliness of the Standard Model, which it augments with new principles and many new particles. Nobel-Prize winner David Gross calls SUSY “beautiful and ‘natural’ and unique.” Many share his opinion. But in Hossenfelder’s telling, Supersymmetry is in danger of becoming history’s greatest waste of intellectual talent – and grant dollars. Several multi-billion dollar particle detectors, each billed as a potential factory for SUSY tests, have failed to turn up evidence for its existence. Particle physicists, like gamblers beggared by a bad tip, can’t bring themselves to confront the consequences of this failure. String theory carries the abstraction a step further, taking SUSY itself as a given and promising an even deeper, more ‘beautiful’ structure for physical laws.
Unfortunately, a confluence of cosmological observations and ongoing work on string theory have opened a Pandora’s box. Rather than proving that our Universe is beautiful and unique, string theory is capable of describing innumerable possible Universes. Physicists disagree on whether to regard this as good or bad, and Hossenfelder amusingly recounts two versions of the history of string theory. On the optimistic track, she argues that string theory is all the more beautiful for the network of new connections and infinite possibilities that have been revealed. Her pessimistic take, by contrast, closes with the tongue-in-cheek observation that “String theorists’ continuous adaptation to conflicting evidence has become so entertaining that many departments of physics keep a few string theorists around because the public likes to hear about their heroic attempts to explain everything.”
The trouble started with the mysterious energy field that cosmologists have found suffuses the Universe — called, variously, a ‘cosmological constant’ or ‘dark energy.’ A cosmological constant was originally discussed by Einstein, but it is so hard to fit into fundamental physics that one of supersymmetry and string theory’s original selling points was that they might explain why this cosmological constant should be precisely zero. But in the late 1990s, a series of cosmological observations determined that it is not in fact zero, but an extremely small positive number.
Two of Hossenfelder’s interviewees – Steven Weinberg (mentioned above) and recently deceased string theorist Joe Polchinski – were instrumental in making the connection between string theory’s problem of too many solutions and this new observational fact. Weinberg pointed out many years ago that the structures necessary for any kind of life –galaxies, stars, and planets– could not arise unless the cosmological constant was very close to zero. He concluded that if there could be many Universes with different values for this constant, all the ones that could contain beings studying science would necessarily have cosmological constants in a special, narrow range.
Polchinski and his colleague Raphael Bousso demonstrated that string theory could give Weinberg what he wanted: a huge menu of universes, each with a different constant. This zoo of possible universes is now called the ‘multiverse.’ Polchinski initially abhorred this solution, as Hossenfelder recounts: “ ‘I wanted this to go away, but it didn’t go away,’ Joe says. ‘Even after people started working on this and started to study this, I wanted it to go away. I literally had to go to the psychiatrist over this. It made me so unhappy. I felt like it was taking away one of our last great clues as to the basic nature of fundamental physics, because things we had hoped to calculate now became random.’ ”
Physicists thus found themselves in a strange position. The beautiful, unique solution they hoped for didn’t look viable. In its place: a multiverse that seemed to rob science of its ability to make predictions.
Proponents of the multiverse claim that accepting this new view is an act of scientific humility akin to the move from geocentrism to heliocentrism. But Hossenfelder, together with many others, isn’t sure that it’s science at all. “I can’t believe what this once-venerable profession has become,” she writes. “Theoretical physicists used to explain what was observed. Now they try to explain why they can’t explain what was not observed.” Predictions based on the multiverse might neverbe testable, even in the future — not because of technological limits, but because such experiments may simply be impossible.
She further worries that Multiverse proponents are underestimating the challenge of coping with an infinite number of possibilities. As she recounts from a penetrating discussion with physicist George Ellis, “Physicists nowadays seem to think they can treat infinity as just another big number. But the central nature of infinity is quite unlike any finite number. It can never be realized no matter how long you wait or what you do—it is always beyond access.”
Though clear about her concerns, Hossenfelder seems unsure whether her patient is terminal – or just in need of an aspirin. Her final words in the main text are: “Physics, it might seem, was the success story of the last century, but now is the century of neuroscience or bioengineering or artificial intelligence (depending on whom you ask). I think this is wrong. …The next breakthrough in physics will occur in this century. It will be beautiful.” Maybe Hossenfelder herself has fallen prey to one the human biases she describes: the tendency to avoid expressing opinions that will be render one socially unacceptable.
Another cognitive bias is avoidance of socially undesirable thoughts, like that fact that physics may be running up against the limits of what experiments can unveil about in the Universe, even in principle. If this is the case, our conclusions about what is true are going to depend on metaphysics and philosophy. While Hossenfelder tries to give a fair hearing to philosophers on the subject of non-empirical criteria, she expresses the vague disdain felt by many scientists about philosophy: nice words, but not very helpful in actually advancing the study of physics.
I have always felt this to be a category error. If physicists are going to rely on metaphysical criteria like beauty, they should not hold the field hostage to said criteria without spending significant effort to make sure they are rigorous and objective. Some physicists share my view. George Ellis, a cosmologist of long standing, is dismayed by his colleagues’ unwillingness to reference prior knowledge of this subject. He complains, “These are scientists who haven’t understood basic philosophy, like the work of David Hume and Immanuel Kant.”
Indeed, there is a grand mystery underlying foundational physics: why are we humans capable of this work at all? Hossenfelder asks why humans should expect our notions of beauty, that emerged from our species’ Darwinian evolution, to make judgments about the structure of a quantum world unknowable to our ancestors.
I’m tempted to argue that we should listen to Plato: if humans have souls, we have an immaterial essence that can interact with an immaterial order. If there is a pre-existing being that is the common origin of both nature’s structure and our immaterial essence (a being we typically call God), then we would have a reason to expect our notion of beauty to continue to have purchase in the quantum realm.
This is an uncomfortable direction for many – scientists especially – that usually results in harrumphing about abandoning science for witchcraft. But I worry that the multiverse is something worse. We can either suppose that there is still beauty to be found, or we can spend the next few decades making uncheckable guesses about an infinite collection of unobservable Universes, hoping to discover that our world does not look special. Personally, I’d rather bet on beauty.
Mark Wyman received his Ph.D. in theoretical cosmology from Cornell University, then worked as a postdoc at the Perimeter Institute, University of Chicago, and NYU. He has been working in quantitative finance in Manhattan since 2014.