A Beautiful Question

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.

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Random Notes

• The LHC has now finished the first part of its physics run at 13 TeV, with intensity ramping up more slowly than hoped. Total luminosity/experiment so far is about .1 inverse fb (see here), about a tenth of some earlier projections (see here), not enough for any likely new physics results this summer (see here).

According to the latest schedule physics will begin again the second week of August, with beam intensity increasing during the month. Most data-taking is planned for September and October, with a target of 10 inverse fb.

• Yoichiro Nambu died recently, at the age of 94. He was one of the most influential figures in theoretical physics, for his work on many topics, but especially on spontaneous symmetry breaking in quantum field theory. Unfortunately I never got to meet him, it sounds like he was one of the nicest people in the field. There are lots of stories now out about him and his work, I especially liked this one from one of his students.
• Massimo Pigliucci’s Scientia Salon project now has a book of essays out, with the title Scientistic Chronicles.
• There’s a wonderful article out by Rick Jardine on Grothendieck’s great work on homological algebra, known to mathematicians as “the Tohoku paper”. It was written while Grothendieck was in Kansas, and immediately had a huge influence on the subject. Jardine explains not only the background of the article and what’s in it, but some of the later developments that have come out of it.

Update
: Via David Goss, news that the FBI file for Paul Erdos is now available.

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GenCyber

Over the years the NSF has financed various summer camps for high school students, designed to get them interested in mathematics or other areas of science. This summer they’ve teamed up with the NSA to deal with the problem of bad press due to the Snowden revelations by organizing a massive new program of quite different summer camps. The program is called GenCyber, and the New York Times today has an article about it here. This year the NSA/NSF is funding 43 camps (for a list, see here), with 1400 youngsters attending them, the plan is to expand to 200 camps over the next few years.

The NSA official in charge, Steven LaFountain explains how the PR aspect works:

Mr. LaFountain said the agency would not make sales pitches to campers, but hoped that the work of the agency would be enough to lure them into the field.

“We’re not trying to make these camps something to make people pro-N.S.A. or to try to make ourselves look good,” he said. “I think we’ll look good naturally just because we’re doing something that I think will benefit a lot of students and eventually the country as a whole.”

According to the New York Times, one sort of thing being taught is how to crack password files:

“We basically tried a dictionary attack,” Ben Winiger, 16, of Johnson City, Tenn., said as he typed a new command into John The Ripper, a software tool that helps test and break passwords. “Now we’re trying a brute-force attack.”

Others in the room stumbled through the exercise more slowly, getting help from faculty instructors who had prepped them with a lecture on the ethics of hacking. In other words, they were effectively told, do not try this at home.

“Now, I don’t want anybody getting in trouble now that you know how to use this puppy,” Darrell Andrews, one of the camp’s instructors, warned loudly. “Right? Right?” he added with emphasis.

Teaching thousands of kids how to crack password files? What could go wrong with that?

The program at Marymount features indoctrination visits to the NSA together with the hacking instruction, and one of the instructors seems to realize part of the problem:

And here at Marymount University, where campers are staying in dorms for their two-week program, visits to the N.S.A. and a security operations center break up classroom time.

The idea — and the challenge — of the camp, according to its head, Diana Murphy, a professor of information technology at Marymount, is to first teach students how to hack, so they can understand and defend against attackers they might encounter in cyberspace.

“It’s a fine balance for me as a teacher, because you have to teach them some of the hacking techniques, and layer that in with an ethical discussion,” Ms. Murphy said in an interview before camp began.

“They are most interested in the attacking things.”

Update

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My Summer Vacation

When I was young, I recall that a standard assignment when restarting school was an essay on “what I did on my summer vacation”. Now that I’m back in the office after a vacation, here’s a version of that, covering the physics/math aspects:

• In Paris I visited the Palais de la Découverte, the science museum in the heart of the city. This was the site of some of my earliest memories of getting interested in science, back in the late 1960s. I started out by visiting the physics section, some of which looked like it hadn’t changed much since those days. One addition was a video screen with some seating nearby. It was running Particle Fever, and surely someone trying to annoy me had timed things so that I got there just as the part promoting SUSY finished, and the part featuring Nima Arkani-Hamed promoting the multiverse got underway.

Besides revisiting my youth, this made me wonder what the effect of trying to impress the young with glitzy pseudo-science will turn out to be. Will it turn off youngsters looking for something intellectually serious? What would my 12 year old self have made of this?

I soon made my way though to a big LHC exhibit, which cheered me up immediately. This was quite well-done, giving a good idea of what a machine like the LHC really is and what the scientists working there are doing. I quite enjoyed the last part of the exhibit, a recreation of typical grimy offices at CERN that people work in. I’d like to think that I’d have appreciated that, with its unspoken message that these are people who care not about appearances but just about the fascinating work they are doing.

• Now that scientific bookstores are gone in New York, checking out the ones in Paris is a high-priority when visiting there. This time I bought a few books in French, one of which was a new biography of Grothendieck, by Georges Bringuier. I’ve read widely among the many sources emphasizing Grothendieck’s mathematics, this is one that instead focuses on his life, including quite a bit about the years after he left the IHES in 1969. This is an amazing story, and there’s much in the book that I didn’t know, especially about Grothendieck’s mystical views.

The last years of his life he was a hermit, just about completely isolated and perhaps paranoid, but still supposedly writing (the biography explains his view that one shouldn’t read mathematics, but write it). Perhaps someday we’ll find out what he was writing about, for some information about this, see here. While in the earlier part of his career Grothendieck wanted nothing to do with physics, associating it with the Bomb, evidently at the end he had physics books in his home rather than mathematics ones.

One person Grothendieck was in communication with in the early 1990s was Robert Thomason, see a letter available here. Thomason died in Paris in 1995, his notebooks have just become available at this site.

• Another book I found in Paris was from a few years back, about the “unification of mathematics” by Parrochia, Micali and Anglès. The topics are Clifford algebras, abstract algebraic geometry (a la Grothendieck), and the Langlands program, wrapped up in an argument that these provide a unified framework for mathematics. The point of view is the very French one emphasizing the “philosophy” of a subject, and much of the argument is that philosophers of science should be paying close attention to the “Langlands philosophy” and its significance as a unifying set of ideas. They also argue that physics should fit naturally into this sort of unification, an idea I’m very fond of, but they don’t seem to be very aware of the actual connections between physics and the Langlands story (they refer only to the classification of branes by twisted K-theory).
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Summer Break

Heading out soon for summer vacation travels, this time to Ireland and France, back in about two weeks. While away comments will be shut off.

My vacation will spare readers commentary on the rest of the Strings 2015 talks, which at some point will appear here. It seems that the conference included the usual publicity campaign for string theory, with Ashoke Sen continuing to demonstrate a sense of humor by telling the press that

In string theory, we are essentially following in the same steps

as the 50 year story of the Higgs mechanism, the Standard Model and the discovery of the Higgs particle. It does put modern HEP research in perspective once one realizes that its greatest success (the Standard Model) and greatest failure (string theory unification) are essentially the same…

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Anomalies Revisited

Some of the talks at Strings 2015 have now appeared online, and one of them I found quite fascinating, Witten’s Anomalies Revisited. Some of his motivation comes from string perturbation theory and M-theory, but the questions he addresses are fundamental, deep questions about quantum field theory (and not just any quantum field theory, but exactly the sort of qft that appears in the SM, spinors chirally-coupled to gauge-fields/metrics).

The fundamental issue is that these are theories where the path integral does not determine the phase of the partition function. Part of story here is the well-known story of anomalies, perturbative and global. One interesting point Witten makes is that vanishing of these anomalies is not sufficient to be able to consistently choose the phase of the partition function, and he gives a conjecture for a necessary condition that is stronger than anomaly cancellation.

The standard story of QFT textbooks is that once a Lagrangian is chosen, the corresponding QFT is well-defined. But quantization really is a lot more subtle than that, and the anomaly phenomenon is just one indication of the problem. In earlier parts of my career I spent a lot of time thinking about anomalies; the connections to some of the deepest mathematics around (K-theory, index theory and much more) are truly remarkable. In recent years I’ve been thinking about other things, but Witten’s talk is a strong encouragement to go back and revisit the anomaly story (some of his best work has “revisited” in the title…)

In particular, Witten emphasizes a particular case I’d never paid much attention to: the 3d massless Majorana fermion. One would think that this is among the simplest quantum field theories around, but Witten explains how this is an example of a theory with a potential inconsistency (no way to consistently choose the sign of the partition function), even when the anomaly vanishes. This theory also appears in a hot topic in condensed matter physics, the theory of topological superconductors. One reference Witten gives to related work is to this recent paper (there’s a typo in his reference, should be 1406.7329 not 1407.7329).

Witten ends with:

I hope I have at least succeeded today in giving an overview of the tools that are needed to study the subtle fermion integrals that frequently arise in string/M-theory. A detailed analysis of a specific problem would really require a different lecture. Write-ups of some of the problems I’ve mentioned – and some similar ones – will appear soon.

I look forward to those write-ups, with the theories he’s talking about of a lot more interest than just their role in string/M-theory calculations.

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Convergence

Another conference that starts today is the Convergence conference at the Perimeter Institute. The concept is explained by Neil Turok here. His point of view is one I’m very much in sympathy with:

Turok explains that the “large bandwagon” of the last 30 years has not found experimental support. The bandwagon in question is the Standard Model of particle physics established in the 1970s, which, he says, people have been elaborating ever since. “Grand unified theories, supersymmetry, string theory, M-theory, multiverse theory,” he lists. “Each is not particularly radical, but is becoming ever more complex and arbitrary.”

To illustrate the lack of experimental support for these ideas, Turok describes how many people were hoping string theory would represent a radical development; but since string theory – as currently interpreted – leads to the multiverse, Turok describes it as the “least predictive theory ever”.

Indeed, experimental support has not been found for other extensions of the Standard Model either. “We have discovered the Higgs and nothing else,” says Turok, “yet the vast majority of theorists had been confidently predicting WIMPS (weakly interacting massive particles) and supersymmetric particles…Theorists are walking around in a bit of a stunned silence.” He adds that it could turn out to be right that all sorts of other particles are needed along with the Higgs – but that thought seems to be misguided.

“My view is that this has been a kind of catastrophe – we’ve lost our way,” he says. “What we need are ideas as simple and radical as in the start of the 20th century with quantum mechanics.”

So what might these ideas look like? Turok explains how observations have shown that the universe is simpler than we ever expected – in contrast to our theories, which are becoming ever more complex.

It’s great to see this, very encouraging to think that a more reality-based point of view on fundamental physical theory may finally be emerging. My only criticism is that the program doesn’t seem to include any mathematics or mathematicians (except perhaps in the context of history and Emmy Noether). If you have a structure you don’t understand, which is unusually simple, with surprising explanatory power, you might want to ask mathematicians about it…

The schedule is here, there’s a blog here.

There is no difference that we know right now … between the story of divine intervention and the multiverse.

It’s great to see a conference on fundamental physics where the multiverse is coming in for some appropriate skepticism.

Update: One thing to say about the multiverse, it does provide an excuse for an endless number of popular articles mulling it over. Just today, there’s Caleb Scharf and George Johnson.

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Strings 2015

Strings 2015 gets underway in Bangalore tomorrow, and so far the press coverage I’ve seen consists just of two articles that aren’t what I’d guess string theorists would like to see:

• In The theory that may have been stringing scientists along for years Robert Matthews starts with

Over the next few days, the southern Indian city of Bangalore will be playing host to an exclusive group of people.

No amount of money can buy you membership and it doesn’t matter how well connected you are. But rumour has it that it helps if you have a brain the size of a planet.

but soon moves on to

There’s just one problem: there’s not a shred of evidence to support it. And that is now leading to awkward questions about just what all these very smart people have been doing with their time and funding.

He then goes on to discuss the recent New York Times Op-Ed, as well as a Physics Today piece

The American Institute of Physics has now gone further, with an editorial in Physics Today asking if the insouciance of string theorists over the issue of testability may harm public faith in science.

Finally, there’s an accurate discussion of the relation of string theory to the search for superpartners in Run 2 at the LHC

The real fun and games will start if the particles are not found. That is because, even after all these years, string theory is not tied down very tightly.

As a result, theorists can tweak their equations to explain away the failure.

Such flexibility is a classic symptom of pseudo-science, and it is what particularly irks physicists about string theory – along with the arrogance of some of its practitioners, who insist it is the only way to complete Einstein’s quest.

But there is another source of resentment, and one with which we can all sympathise: that an entire generation of brilliant minds may have been lost to an esoteric mind-game.

• The other string theory news story is at The Telegraph, a Calcutta paper, which has Physicists too can have fun. The article is about Ashoke Sen’s bizarre hep-th article Riding Away from Doomsday, which was the topic of an April 1 posting here. Since then, Sen has shot down any idea that this was a hoax, and has turned it into a major research program, with a technical hep-th article and a talk scheduled for the opening session of the conference tomorrow. The article argues for the importance of computing the decay rate of the universe since it

is important for planning our future course of action if we are to adapt this strategy for increasing the life expectancy of the human race.

String theory is supposed to provide this calculation, but Sen characterizes the status of that calculation with

it is probably fair to say that we do not yet have a definite result based on which we can plan our future course of action.

which shows that, despite what some people say, he definitely has a sense of humor.

Given press coverage debating whether string landscape research is pseudo-science or a joke, I wonder what prominent string theorists gathered in Bangalore now think of the string theory community’s decision over the last ten years to mostly go along with the idea of the string landscape as an excuse for why string theory predicts nothing. This all started about ten years ago, and it’s interesting to take a look again at the panel discussion at Strings 2005, where the panelists were in favor of the landscape, but the audience not so much. The last ten years have shown conclusively that any hopes for predictive science coming out of the landscape were misguided, but will that or bad press cause anyone to re-evaluate their stand on this?

Update: Slides of the talks are appearing here. One of them is so interesting I’ll devote a posting to it…

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Multiversal Journeys

One of the many efforts to promote the Multiverse to the public way back when (2005-2007, some of their advertisements are here) was an organization called Multiversal Journeys. Back in 2006 they got $77,000 in funding from the Templeton Foundation (via FQXi). Since 2007 they seemed to have disappeared, with no more scheduled public events as far as I could tell. Now they’re back though, with an upcoming event defensively called Clarifying theoretical physics and cosmology misconceptions for SF Bay Area journalists. It’s unclear exactly what they think the misconceptions are that such journalists need to have clarified. One of the three announced speakers (John Terning) might actually be able to do some clarification, but the other two seem more devoted to the spreading of misconceptions. Yasunori Nomura likes to promote the idea that the landscape and the many-worlds interpretation of quantum mechanics are one and the same thing (see here and here), a claim I believe few serious physicists have ever been able to make sense of. He also claims that the multiverse can be used to make predictions about physics, and back in 2009 used the multiverse to predict that the Higgs mass would be 141 +/- 2 GeV (see here). This prediction played a central role in the film Particle Fever, which featured David Kaplan and Nima Arkani-Hamed during the period leading up to the Higgs discovery explaining how a 140 GeV Higgs would mean the multiverse was right. Will Nomura clarify for the journalists any misconceptions they might have about what scientists are supposed to do when their theory’s well-publicized prediction is tested and shown to be wrong? The other speaker is Texas Tech chemist William Poirier, who has some sort of “Many Interacting Worlds” theory, which supposedly shows that the observed behavior of particles indicates the existence of parallel universes (see here). Again, I’m curious what misconceptions about physics he plans to clarify to journalists. Update: I see that this event will be funded by at$5750 grant from FQXi to Multiversal Journeys (Fall 2014 Mini-grant).

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Ordered from the more to less serious…

• On the geometric Langlands front, there’s video posted today of this talk by Dennis Gaitsgory. Michael Harris has already commented here about the local geometric Langlands conjecture in terms of 2-categories that Gaitsgory discusses. Today’s arXiv listings have a new paper on geometric Langlands by Witten, which begins with his version of a formulation relating the categorical point of view and quantum field theory.
I wrote recently here about a talk by Jacob Lurie that alluded to an explanation of this categorical equivalence for the simplest case of G invertible complex numbers (rather than the case of G a general semi-simple Lie group that Gaitsgory and Witten are discussing). I’m still far from being enlightened concerning that simplest case, but have learned a lot from Alexander Polishchuk’s Abelian varieties, theta functions and the Fourier transform which I take as treating the global versions of this equivalence.
• Witten has been busy, with yesterday’s arXiv listings including a 429 page paper with Gaiotto and Moore (does anyone know of a longer hep-th paper that’s not a review article?). There’s also a companion shorter summary paper. The motivation here is again a categorical picture expressed in terms of quantum field theory models, but for more insight you’ll need to find someone more expert than me on this topic.
• Strings 2015 will be held in Bangalore in a couple weeks. Talks titles are now available, so you can see what the hot topics in the “string theory” community are. Of Gaiotto, Moore and Witten, only Witten will be speaking. Perhaps his talk on An Overview of Worldsheet and Brane Anomalies will shed some light on the 429 page paper.
• On the Mochizuki/abc front, hopes rest on a planned workshop at Oxford this December. Fesenko has circulated a letter about the workshop, which gives suggestions about how to approach the subject.
• Via Chandan Dalawat’s Google+ page I found out about this autobiographical piece by Misha Gromov. One thing it made clear to me is why I couldn’t get anything out of the couple times I’ve heard him lecture.

Being trivial is our most dreaded pitfall: you say stupid things, not original things, outrageously wrong things – all will be forgotten when the dust settles down. But if you pompously call a+b=c “Theorem” in your paper, you will be forever remembered as “this a+b guy”, no matter you prove bloody good theorems afterwords…
I was introduced to the idea on September 1st 1960 at the then Leningrad University when our analysis professor Boris Mikhailovich Makarov said to me after our first calculus class – he expressed this in somewhat metaphorical terms – that I should’ve kept my mouth shut unless I had something non-trivial to say.
Further encouraged by my teachers and fellow students, I tried to follow his advice and, apparently, have succeeded – I hear nothing disrespectful about my mouth for the last 10-20 years. Strangely, this does not make me feel a lot happier.
“Trivial” is relative. Anything grasped as long as two minutes ago seems trivial to a working mathematician.

Another thought this raises is that I’ve just spent the last 3 years of my life writing something trivial

• I really like Jordan Ellenberg’s suggestion of Cold Topics Workshops.
• Mathematics makes it into the Guardian with an article about mathematical modeling.
• With the LHC inactive, some LHC physicists have had to spend their time studying plots (trigger warning, and NSFW).

Update: One more, far more serious than anything above. Sabine Hossenfelder brings up an important and rarely discussed topic here.

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