Frank Wilczek’s new book, A Beautiful Question, is now out and if you’re at all interested in issues about beauty and the deep structure of reality, you should find a copy and spend some time with it. As he explains at the very beginning:

This book is a long meditation on a single question:

Does the world embody beautiful ideas?

To me (and I think to Wilczek), the answer to the question has always been an unambiguous “Yes”. The more difficult question is “what does such a claim about beauty and the world mean?” and that’s the central concern of the book.

Early chapters are of an historical nature, searching out the roots of such ideas, going back to the Pythagoreans and their beliefs about number and harmony, and then on to Plato and Platonism. The discussion of physics begins seriously with Kepler and Newton, and emphasizes very much the nature of light and color, topics about which Wilczek is currently actively pursuing new ideas. Maxwell then appears as the foundation of our modern understanding of light and electromagnetism.

Notions of symmetry (gauge symmetry) then begin to appear, as well as the surprising notion of quantization of wave motion. The basic ideas behind the Standard Model are extensively developed, emphasizing the connections to symmetry and beauty. Wilczek tries to make some changes in the conventional terminology, calling the Standard Model the Core Model, fields “fluids”, etc., in an attempt to bring the subject closer to a conventional language that might give the average person some feel for what is going on. He also brings in some of his personal experience: he is of course most well-known as one of those responsible for the final stage of the development of the Core Model.

Wilczek has been traveling a lot lecturing about this recently. You can for instance watch or hear him speak here, here and here, read extracts from the book here or here, find reviews here and here. The Wall Street Journal has “a week in the life” here. I very much like Wilczek’s comments in an essay here which explain how the book came about and who it was written for. His conclusion that he had written it to speak to himself as a child or adolescent very much resonates with my own experience writing a popular book.

The later parts of the book deal with more speculative questions about particle physics, and here I find that truly difficult issues appear: can we hope to agree on what beauty is in this context? Wilczek has never been a fan of string theory, and the various problematic claims about its “beauty” really don’t come up. He is however a fan of supersymmetric GUTs, and there issues of beauty become problematic. Yes, the fact that a family of SM fermions can be organized into a spinor representation of SO(10) is a beautiful fact, and likely indication of something deep about the world. But there’s a serious problem with getting unification by putting things into larger symmetry groups, without at the same time having a compelling idea for what breaks the larger symmetry to the smaller one we see. Just postulating a new set of GUT Higgs is not so pretty.

Similarly, the general idea of supersymmetry has beautiful aspects, but its implementation as a specific extension of the Poincaré group starts to become seriously unbeautiful once one introduces structures needed to break the supersymmetry to correspond to observation. I think one reason for Wilczek’s fondness for this idea is his involvement in the first calculation of coupling constant unification in such theories. A parent always thinks their child is unusually beautiful, but may not always be a very good judge of the matter…

Wilczek has made some bets that SUSY will appear at the LHC, but I think he’s going to be losing them. Garrett Lisi has an account here of one such bet, which had a problematic time limit. By next summer I think there will be enough data to start making a judgment about whether SUSY is there at LHC accessible energies. I’m quite curious to see how Wilczek and others of his generation that had so long invested their hope in this will react to a negative result. Will SUSY start looking a lot less beautiful?

**Bonus item**: In today’s Wall Street Journal there’s another profile of a particle physicist, of George Zweig, a co-discoverer of the quark theory which ultimately was vindicated by the later discovery of asymptotic freedom by Wilczek and others. Zweig is now starting a hedge fund, I hadn’t realized that he worked for quite a while at Renaissance, the Jim Simons hedge fund.

**
Update**: This does seem to be the week for profiles of mathematicians and physicists in the media. There’s a wonderful one about Terry Tao in the Sunday New York Times magazine.

I haven’t read the book, but I suppose Wilczek discuss at the beginning of the book (or somewhere) what he means by “beauty”. I remember many years ago reading Weinberg’s “Dreams of a Final Theory” that the analogy for him of beauty was with a “beautiful horse” and that “a beautiful horse wins races”. So this was a subjective idea that had an objective way to be tested. The same would hold for physics theories (beautiful theories are the ones like QED that are also objectively successful).

This is interesting as beauty has been one of the big arguments for SUSY (I recall John Ellis’ “why I love SUSY” in 2011) but SUSY has been very unsuccessful in the way Weinberg discussed. I don’t get how at this point SUSY can still be beautiful but I suppose I need to read the book.

Peter,

I agree with your opinion on SUSY. But I would like to claim more definitely: Spontaneously broken SUSY is totally ugly; it can never been a truth.

Just because the result of a broken symmetry is very ugly, doesn’t mean the underlying symmetry is less likely to be true. I’m talking about SUSY here. If SUSY is so beautiful, does it matter if breaking SUSY leads to an ugly-looking theory? I thought the general trend was that as you go higher in energy, things look more beautiful. So if you go at high enough energies, SUSY is restored, and everything is nice and beautiful again. So why is the ugliness of broken SUSY a reason for thinking SUSY isn’t true?

There is a fascinating profile of Terry Tao in this Sunday’s NY Times Magazine:

http://www.nytimes.com/2015/07/26/magazine/the-singular-mind-of-terry-tao.html?hpw

Does Frank Wilzeck mention “low Kolmogorov complexity” as one of the driving criteria of “beauty” as mentioned for example here? The postulate being that:

Among several patterns classified as “comparable” by some subjective observer, the subjectively most beautiful is the one with the simplest (shortest) description, given the observer’s particular method for encoding and memorizing it.This sounds very correct. Theories with a low-complexity “core description” and no extraneous “ifs”, “thens” and “buts” and randomly tucked-on stuff, all of which would increase the KC (however given) by a factor of 2 at least are indeed what one likes to see.

Walter,

The argument that “my beautiful idea only applies at high energies where it can’t be tested; at energies where we can do experiments it doesn’t apply and doesn’t say anything ” has some obvious problems…

in your opinion are GUT theories of unification like SO(10) promising? is there any GUT you find promising? what do you think is a promising avenue for unification? are there any well motivated theories of GUT, unification, as well as no unification of strong and electroweak forces? thanks

Unification,

There’s a chapter in my book about GUTs, it’s a complicated story, but I don’t think anything much has changed since I was writing that chapter a dozen years ago.

What isn’t really discussed in the book is the construction that Wilczek describes in detail in his, how to make a generation of fermions out of the spinor representation for SO(10). This is “beautiful”, there’s something important going on there, but I think we’re missing some important ideas about what this means.

You can think of the SO(10) spinor representation as what you get from a collection of 5 fermionic oscillators, this is described in detail in my notes at

http://www.math.columbia.edu/~woit/QM/qmbook.pdf

For a good discussion of the relation to GUTs, see the article by Baez and Huerta

http://arxiv.org/abs/0904.1556

That NYT article was great – not because it was about Tao but because it contained some lovely thoughts about mathematics in general. The article would be more appropriate if Tao actually solved the twin prime conjecture or Navier-Stokes.

A general point here. One problem with using “beauty” as a criterion for scientific theories is the lack of a precise definition. In the case of female beauty, though, there is a well-defined unit called the Helen (H), named after Helen of Troy. As this is a large unit, people prefer to work with the millihelen (mH), which is defined as the beauty required to launch a single ship.

If Ptolemy’s epicycles worked, would we consider them to be beautiful?

Isn’t SU(5) also very beautiful?

Carl Sagan in an episode from the Cosmos series stated that the Universe need not be in harmony with human ambition. The human ambition to find a ‘beautiful’ theory of the laws of nature is meaningless since ‘beauty’ is subjective.

Bernd,

The SU(5) vs. SO(10) question in GUTs is a good example of where relative magnitudes of beauty are clear. To describe one generation of fermions using SU(5) you need two irreducible representations, of dimension 5 and 10. Using SO(1o ) (more accurately, Spin(10)), you just need one representation, and it’s a special distinguished representation, the 16 dim spinor representation. So, the SO(10) case is more beautiful…

One has 16=10 +5 +1, so SO(10) also includes a singlet, which is just what one expects for a right-handed neutrino.

Walter,

Spontaneously broken SUSY implies the existence of Nambu-Goldstone fermion, which was experimentally excluded. If one appeals to super-Higgs mechanism by using supergravity, it implies that quantum-gravity effect cannot be neglected in the energy region of the Standard Theory. Furthermore, quantum supergravity cannot be global-SUSY invariant, because the anticommutator of supersymmetry generators in quantum supergravity cannot have the spacetime index of the translation generator.

Peter,

I understand your point, but my question was meant to address your thoughts on SUSY leading to the ugliness of having a lot of extra particles. I understand how that can be viewed as ugly. But if the underlying, fundamental theory, valid at the Planck scale (whatever it is, no assumptions here) is “beautiful”, even though it leads to a million fundamental particles from the TeV scale to the Planck scale, why should these million particles negate this? That’s all I was asking.

I have problems with beauty as a scientific criterion. This would imply that our anthropocentric point of view is the same as the view how nature works in its deep structure. Keplers mysterium cosmographicum was a concept derived from beauty but was totally beside the point . I lectured about SUSY several times but while being perhaps a mathematically beautiful framework I never found it beautiful from a physical point of view. The same holds in my view as to string theory.

It is important to understand the biological and psychological roots of a concept like beauty before one can decide if beauty is a useful scientific concept.

Walter,

The issue isn’t number of fundamental particles, it’s whether they’re tightly constrained by a symmetry argument. The simplest SUSY extensions of the SM have a new particle for each of the ones we know about, which is twice as many particles, but SUSY tells you their properties. You can argue whether this is more beautiful than the SM (more symmetry, but a symmetry that tells you only about unobserved particles, nothing about the observed SM particles), I happen to think not.

The big problem with SUSY though is that these simplest extensions don’t work (since they predict superpartners we don’t see). So, you need to make the theory more complicated by adding degrees of freedom that will cause SUSY breaking. This is where it gets completely ugly, and it’s at the level of the fundamental theory.

I remember as a kid learning the gas laws PV=nRT. I thought that was incredibly beautiful – so much information packed into one equation – and then I learned that this equation is inexact, and that a more accurate equation devised by van der Waals was more accurate, but it had different coefficients for each type of gas!

That made me rather cautious about appeals to beauty in physics.

Maybe every appeal to beauty implicitly assumes there is no deeper structure to mess things up (the quantum structure of molecules in the above example, which give molecules finite size and intermolecular forces).

I agree totally with what David Bailey says. The problem is that most of our theories are only effective theories being approximately correct on a certain level of resolution. In a sense there is no real reason that such theories should be beautiful. On the other hand, in the realm of mathematics there is ample room for beauty. This is the platonic point of view uttered by many great mathematicians (recently by e.g. Allan Connes). Nevertheless even there this philosphy is a little bit vague.

@Peter Woit: So the real issues come not from SUSY itself, but from the modifications to the simplest ideas of SUSY in order to have it be compatible with observation?

Would these extra degrees of freedom you refer to be yet another (undetermined by SUSY itself) particle (something like the Higgs, given their role in symmetry breaking)?

manfred Requardt:

“It is important to understand the biological and psychological roots of a concept like beauty before one can decide if beauty is a useful scientific concept.”

I think this is a very important point. And there is a nascent field about that, neuroaesthetics.

http://old.unipr.it/arpa/mirror/pubs/pdffiles/Gallese/2009/DiDio_COP2009.pdf

Even more on topic, you may want to look at this fMRI study co-authered by Atiyah:

http://journal.frontiersin.org/article/10.3389/fnhum.2014.00068/abstract

I wonder whether Wilczek mentions that in his book.

The article on Terence Tao doesn’t really say anything new, I’m not sure why you consider it ‘wonderful’. Tao certainly deserves all the plaudits and praise bestowed upon him, but I’m not sure that such hagiographies give any particular insight. It might be good for scientific outreach I guess.

In any case, on another Tao related matter, the comments on this post

https://terrytao.wordpress.com/2015/07/20/a-nonstandard-analysis-proof-of-szemeredis-theorem/

make interesting reading from a viewpoint of scientific sociology.

Thomas, many thanks for your helpful hints and remarks! By the way, there is a related discussion concerning the conventionalism in science as being introduced by e.g. Poincare (see the nice biography by Jeremy Gray). This is a purely pragmatic criterion without aesthetic qualities (apart perhaps from simplicity and economy of thinking). But, nevertheless, it is obvious that there is some peculiar structure underlying our universe.

I have recently come across Weber electrodynamics. In my view this is an extremely beautiful theory, but it seems that it just doesn’t work. If so, this would be a nice example of beauty being deluding, and probably it is not an exceptional case in the history of physics.

“The great tragedy of science – the slaying of a beautiful hypothesis by an ugly fact.” – Thomas Henry Huxley –

Magnema,

There’s an infinite variety of ways to get SUSY breaking and explain away the non-observation of superpartners. But all involve postulating additional, otherwise unmotivated, physics beyond a simple SUSY extension of the SM.

It seems to me that “beauty” is largely being used where simplicity is really meant in much of this discussion. IMHO beauty is way too subjective to enter into any discussion in physics, whereas simplicity is much easier to agree on — PV = nRT is simple, the van der Waals equation is certainly less so. Few would disagree. The Standard Model is far from simple. That’s what all the fuss is really about—find the overarching simple set of concepts that unify and simplify that mismash of fields and adhoc “constants”. Only the means differ.

SU(5) was beautiful till the protons refused to die

A 78 year old is starting a hedge fund. I think we’ve hit the top.

Speaking of Zweig, the Wikipedia profile of him points to this CERN colloquium talk he gave in November 2013, which is a history of particle physics leading to the development of the concrete quark model. (It starts with a review of the stage-setting prior to World War II. In 1947 Zweig was 10 years old.)

The talk has probably been widely read, but I had never come across it before. It’s extremely readable, with many fascinating anecdotes about the wrangling that led to the concrete quark model. (It also indicates that Zweig turned to neurobiology by the end of the 60s—earlier than I had thought.)

As Jim Eshelman says, simplicity is certainly an important aspect in this field. The concept of symmetry in all of modern physics is an example. On the other hand, even this quality is not entirely clear. Einsteins field equation are looking simple but threy are in fact very complicated if one tries to solve them (non-linar partial diff.-equations). Sometimes only the mathematical representation of an actually complex situation may appear simple.

I tend not to like the terms ‘beauty’ (or especially ‘elegance’) when describing scientific endeavors. In my opinion, these phrasings seem to be an effort to persuade one towards the author’s belief system absent grounded technical evidence.

Ground Loops. Fadeev-Popov ghosts. Eventually, there is messiness underpinning beautiful experiments and theories.

GoletaBeach,

“Fadeev-Popov ghosts”

Exactly. This is one part of the Standard Model that isn’t beautiful, and isn’t completely satisfactory non-perturbatively. I think that’s a strong argument that it should be getting a lot of attention as an aspect of the SM that we don’t properly understand, for which there is a more beautiful, more compelling explanation, one that would teach us something about the fundamental theory.

Faddeev-Popov ghosts and BRST are not a fundamental part of the Standard Model, are they? Since there are other ways of fixing the gauge that don’t involve ghosts, aren’t they mostly a calculational device? But, for what it is worth, I personally find Faddeev-Popov ghosts and BRST to be a technically quite beautiful and elegant calculational device, since they magically automate a lot of the gauge fixing while allowing you to largely do calculations in a gauge-invariant set of variables, as opposed to an awkward and arbitrary choice of reduced variables. I use “magically” on purpose, since the idea of “negative” degrees of freedom embodies in ghosts still seem magical to me to this day.

anon,

Faddeev-Popov/BRST is the only covariant gauge-fixing procedure I know of (for the non-abelian case). Non-covariant gauge-fixing introduces a different set of technical problems and uglinesses. The only way of dealing with gauge symmetry that I know of no technical problems with (perhaps just because of ignorance…) is what the lattice people do: don’t fix the gauge, integrate over all gauge choices. But you can’t get the perturbation series this way.

I agree that the introduction of anti-commuting variables to deal with gauge symmetry is not ugly, but a quite beautiful idea. It’s closely related to very deep mathematics: homological methods in representation theory. The fact that the same “trick” (introducing anti-commuting variables, a complex, and looking at the cohomology of the complex) occurs throughout modern mathematics is a good reason to believe that it’s the right way to handle the problem, and well deserves to be thought of as beautiful.

Thanks Peter, I hope a beautiful solution to the ghosts emerges.

As the old joke goes, when Fermi asked God how to solve Ground Loops, God simply replied `Never could solve that problem.’