Sabine Hossenfelder’s Lost in Math: How Beauty Leads Physics Astray (Basic Books, June 2018) is a critical account of the disappointing progress in fundamental physics, primarily particle physics and cosmology, since the formulation of the “standard model” in the 1970’s. It focuses on the failure to find new physics at CERN’s $13.25 billion Large Hadron Collider (LHC) and many questionable predictions that super-symmetric particles, hidden dimensions, or other exotica beloved of theoretical particle physicists would be found at LHC when it finally turned on. In many ways, this lack of progress in fundamental physics parallels and perhaps underlies the poor progress in power and propulsion technologies since the 1970s.
Lost in Math joins a small but growing collection of popular and semi-popular books and personal accounts critical of particle physics including David Lindley’s 1994 The End of Physics: The Myth of a Unified Theory, Lee Smolin’s The Trouble with Physics: The Rise of String Theory, the Fall of Science and What Comes Next, and Peter Woit’s Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law. It shares many points in common with these earlier books. Indeed, Peter Woit is quoted on the back cover and Lee Smolin is listed in the acknowledgements as a volunteer who read drafts of the manuscript. Anyone considering prolonged involvement, e.g. graduate school, or a career in particle physics should read Lost in Math as well as these earlier books.
The main premise of Lost in Math is that theoretical particle physicists like the author have been lead astray by an unscientific obsession with mathematical “beauty” in selecting and also refusing to abandon theories, notably super-symmetry (usually abbreviated as SUSY in popular physics writing), despite an embarrassing lack of evidence. The author groups together several different issues under the rubric of “beauty” including the use of the terms beauty and elegance by theoretical physicists, at least two kinds of “naturalness,” the “fine tuning” of the constants in a theory to make it consistent with life, the desire for simplicity, dissatisfaction with the complexity of the standard model (twenty-five “fundamental” particles and a complex Lagrangian that fills two pages of fine print in a physics textbook), doubts about renormalization — an ad hoc procedure for removing otherwise troubling infinities — in Quantum Field Theory (QFT), and questions about “measurement” in quantum mechanics. Although I agree with many points in the book, I feel the blanket attack on “beauty” is too broad, conflating several different issues, and misses the mark.
In Defense of “Beauty”
As the saying goes, beauty is in the eye of the beholder. The case for simplicity or more accurately falsifiability in mathematical models is on a sounder, more objective basis than beauty however. In many cases a complex model with many terms and adjustable parameters can fit many different data sets. Some models are highly plastic. They can fit almost any data set not unlike the way saran wrap can fit almost any surface. These models are wholly unfalsifiable.
A mathematical model which can match any data set cannot be disproven. It is not falsifiable. A theory that predicts everything, predicts nothing.
Some models are somewhat plastic, able to fit many but not all data sets, not unlike a rubber sheet. They are hard to falsify — somewhat unfalsifiable. Some models are quite rigid, like a solid piece of stone fitting into another surface. These models are fully falsifiable.
A simple well known example of this problem is a polynomial with many terms. A polynomial with enough terms can match any data set. In general, the fitted model will fail to extrapolate, to predict data points outside the domain of the data set used in the model fitting (the training set in the terminology of neural networks for example). The fitted polynomial model will frequently interpolate, predict data points within the domain of the data set used in the model fitting — points near and in-between the training set data points, correctly. Thus, we can say that a polynomial model with enough terms is not falsifiable in the sense of the philosopher of science Karl Popper because it can fit many data sets, not just the data set we actually have (real data).
This problem with complex mathematical models was probably first encountered with models of planetary motion in antiquity, the infamous epicycles of Ptolemy and his predecessors in ancient Greece and probably Babylonia/Sumeria (modern Iraq). Pythagoras visited both Babylonia and Egypt. The early Greek accounts of his life suggest he brought back the early Greek math and astronomy from Babylonia and Egypt.
Early astronomers, probably first in Babylonia, attempted to model the motion of Mars and other planets through the Zodiac as uniform circular motion around a stationary Earth. This was grossly incorrect in the case of Mars which backs up for about two months about every two years. Thus the early astronomers introduced an epicycle for Mars. They speculated that Mars moved in uniform circular motion around a point that in turn moved in uniform circular motion around the Earth. With a single epicycle they could reproduce the biannual backing up with some errors. To achieve greater accuracy, they added more and more epicycles, producing an ever more complex model that had some predictive power. Indeed the state of the art Ptolemaic model in the sixteenth century was better than Copernicus’ new heliocentric model which also relied on uniform circular motion and epicycles.
The Ptolemaic model of planetary motion is difficult to falsify because one can keep adding more epicycles to account for discrepancies between the theory and observation. It also has some predictive power. It is an example of a “rubber sheet” model, not a “saran wrap” model.
In the real world, falsifiability is not a simple binary criterion. A mathematical model is not either falsifiable and therefore good or not falsifiable and therefore bad. Rather falsifiability falls on a continuum. In general, extremely complex theories are hard to falsify and not predictive outside of the domain of the data used to infer (fit) the complex theory. Simpler theories tend to be easier to falsify and if correct are sometimes very predictive as with Kepler’s Laws of Planetary Motion and subsequently Newton’s Law of Gravitation, from which Kepler’s Laws can be derived.
Unfortunately, this experience with mathematical modeling is known but has not been quantified in a rigorous way by mathematicians and scientists. Falsifiabiliy remains a slogan primarily used against creationists, parapsychologists, and other groups rather than a rigorous criterion to evaluate theories like the standard model, supersymmetry, or superstrings.
A worrying concern with the standard model with its twenty-five fundamental particles, complex two-page Lagrangian (mathematical formula), and seemingly ad hoc elements such as the Higgs particle and Kobayashi-Maskawa matrix is that it is matching real data entirely or in part due to its complexity and inherent plasticity, much like the historical epicycles or a polynomial with many terms. This concern is not just about subjective “beauty.”
Sheldon Glashow’s original formulation of what became the modern standard model was much simpler, did not include the Higgs particle, did not include the charm, top, or bottom quarks, and a number of other elements (S.L. Glashow (1961). “Partial-symmetries of weak interactions”. Nuclear Physics. 22 (4): 579–588. ). Much as epicycles were added to the early theories of planetary motion, these elements were added on during the 1960’s and 1970’s to achieve agreement with experimental results and theoretical prejudices. In evaluating the seeming success and falsifiability of the standard model, we need to consider not only the terms that were added over the decades but also the terms that might have been added to salvage the theory.
Theories with symmetry have fewer adjustable parameters and are less plastic, flexible, less able to match the data regardless of what data is presented. This forms an objective but poorly quantified basis for intuitive notions of the “mathematical beauty” of symmetry in physics and other fields.
The problem is that although we can express this known problem of poor falsifiability or plasticity (at the most extreme an ability to fit any data set) with mathematical models and modeling qualitatively with words such as “beauty” or “symmetry” or “simplicity,” we cannot express it in rigorous quantitative terms yet.
Big Science and Big Bucks
Much of the book concerns the way the Large Hadron Collider and its huge budget warped the thinking and research results of theoretical physicists, rewarding some like Nima Arkani-Hamed who could produce catchy arguments that new physics would be found at the LHC and encouraging many more to produce questionable arguments that super-symmetry, hidden dimensions or other glamorous exotica would be discovered. The author recounts how her Ph.D. thesis supervisor redirected her research to a topic “Black Holes in Large Extra Dimensions” (2003) that would support the LHC.
Particle accelerators and other particle physics experiments have a long history of huge cost and schedule overruns — which are generally omitted or glossed over in popular and semi-popular accounts. The not-so-funny joke that I learned in graduate school was “multiply the schedule by pi (3.14)” to get the real schedule. A variant was “multiply the schedule by pi for running around in a circle.” Time is money and the huge delays usually mean huge cost overruns. Often these have involved problems with the magnets in the accelerators.
The LHC was no exception to this historical pattern. It went substantially over budget and schedule before its first turn on in 2008, when around a third of the magnets in the multi-billion accelerator exploded, forcing expensive and time consuming repairs (see CERN’s whitewash of the disaster here). LHC faced significant criticism over the cost overruns in Europe even before the 2008 magnet explosion. The reported discovery of the Higgs boson in 2012 has substantially blunted the criticism; one could argue LHC had to make a discovery. 🙂
The cost and schedule overruns have contributed to the cancellation of several accelerator projects including ISABELLE at the Brookhaven National Laboratory on Long Island and the Superconducting Super Collider (SSC) in Texas. The particle physics projects must compete with much bigger, more politically connected, and more popular programs.
The frequent cost and schedule overruns mean that pursuing a Ph.D. in experimental particle physics often takes much longer than advertised and is often quite disappointing as happened to large numbers of LHC graduate students. For theorists, the pressure to provide a justification for the multi-billion dollar projects is undoubtedly substantial.
While genuine advances in fundamental physics may ultimately produce new energy technologies or other advances that will benefit humanity greatly, the billions spent on particle accelerators and other big physics experiments are certain, here and now. The aging faculty at universities and senior scientists at the few research labs like CERN who largely control the direction of particle physics cannot easily retrain for new fields unlike disappointed graduate students or post docs in their twenties and early thirties. The hot new fields like computers and hot high tech employers such as Google are noted for their preference for twenty-somethings and hostility to employees even in their thirties. The existing energy industry seems remarkably unconcerned about alleged “peak oil” or climate change and empirically invests little if anything in finding replacement technologies.
Is there a way forward?
Sabine, who writes on her blog that she is probably leaving particle physics soon, offers some suggestions to improve the field, primarily focusing on learning about and avoiding cognitive biases. This reminds me a bit of the unconscious bias training that Google and other Silicon Valley companies have embraced in a purported attempt to fix their seeming avoidance of employees from certain groups — with dismal results so far. Responding rationally if perhaps unethically to clear economic rewards is not a cognitive bias and almost certainly won’t respond to cognitive bias training. If I learn that I am unconsciously doing something because it is in my economic interest to do so, will I stop?
Future progress in fundamental physics probably depends on finding new informative data that does not cost billions of dollars (for example, a renaissance of table top experiments), reanalysis of existing data, and improved methods of data analysis such as putting falsifiability on a rigorous quantitative basis.
(C) 2018 by John F. McGowan, Ph.D.
About Me
John F. McGowan, Ph.D. solves problems using mathematics and mathematical software, including developing gesture recognition for touch devices, video compression and speech recognition technologies. He has extensive experience developing software in C, C++, MATLAB, Python, Visual Basic and many other programming languages. He has been a Visiting Scholar at HP Labs developing computer vision algorithms and software for mobile devices. He has worked as a contractor at NASA Ames Research Center involved in the research and development of image and video processing algorithms and technology. He has published articles on the origin and evolution of life, the exploration of Mars (anticipating the discovery of methane on Mars), and cheap access to space. He has a Ph.D. in physics from the University of Illinois at Urbana-Champaign and a B.S. in physics from the California Institute of Technology (Caltech).
