Genius at Play

A month or two ago I read the new biography of John Conway, Genius at Play, by Siobhan Roberts (whose book about Coxeter I reviewed here). Since then, writing about it has been on my to-do list, but I wasn’t at all sure what to say. In today’s Wall Street Journal Jordan Ellenberg has done a better job of this than I ever could, so I have a place to start: read Jordan’s review.

Probably the first thing to say about the book is that it’s an excellent portrayal of its subject, who is an unusual and well-known figure in the math community. Roberts spent a great deal of time with Conway, traveling with him and getting to know him rather well personally, then very ably turning that experience into a quite readable and enjoyable book. It’s hard to imagine that a better biography of Conway would be possible.

In his review, Jordan crystallized precisely for me why I was having trouble writing about Conway and the book:

Will you like this book? Here’s a simple test. What’s the rule that produces the sequence 1, 11, 21, 1211, 111221, 312211 . . . ?

This is Mr. Conway’s “look-and-say” sequence, so called because each number (after the first) is what you get when you look at the previous number and say it aloud: “one one; two ones; one two, one one; one one, one two, two ones . . .”

If that makes you laugh with surprise, as it did me, you’ll like Mr. Conway, and you’ll like “Genius at Play.” If not, you might want to quit here and go read something improving about the Greek debt crisis.

I’m afraid this didn’t make me laugh with surprise; it seems that I’m immune to the charm of this sort of thing. While there was a lot of Conway’s story I found interesting and which kept me avidly reading, his mathematical interests are very different than mine. Mathematical games make up a big part of his life and career, but the only aspect of this I’ve at any time found appealing was back in high school, when I remember writing a computer program to run the game of Life. I learned from the book that this is Conway’s most famous creation, a fact he’s not entirely happy with.

I also learned that my one personal experience with Conway is widely shared: at lunch with a group here at Columbia he mostly spent the time explaining how to calculate in one’s head what day of the week any date is. Unfortunately I just didn’t enjoy the idea of spending time on this then, and still don’t.

Conway is one of the main figures responsible for an important piece of mathematics, discovering and working out the properties of some of the sporadic finite groups. This isn’t something I’ve ever known much about, and I was quite interested to learn from the book some more about the subject and the history of how it came about.

I can’t think of any other biography that I’ve read that gives such a vivid impression of its subject. In Conway’s case this is somewhat of a mixed bag. He can be a very entertaining character, but his personal flaws are also apparent, with a suicide attempt and several failed marriages testifying to some real problems. Whenever books like this appear, I think one reaction of some mathematicians (not me…) is “is this good for the public portrayal of mathematics and mathematicians?”. Conway’s mixture of genius, highly accessible mathematical discoveries often related to games, and serious issues dealing with the outside world fit rather well with a certain caricature of what mathematicians are like. In my experience with great mathematicians, very few of them other than Conway fit the caricature. While any book about him would likely reinforce the caricature, at least this one gives a very well-written and comprehensive view of its subject.

Posted in Book Reviews | 30 Comments

Short Items

A few short items:

  • The New Yorker has its own coverage here of the NSA GenCyber summer camp program for children that was discussed here.
  • The LHC is about to start doing physics again at 13 TeV, with beam intensity slowly ramping up in coming days and weeks. You can follow what’s happening here.
  • Some filmmakers are planning an IMAX film about the LHC, more information available here.
  • Online media stories with skepticism about the multiverse continue to appear. The latest one is by Shannon Hall at Nautilus, with the title Is it Time to Embrace Unverified Theories? (I think it’s a general rule that the answer to all questions in titles is No). I like one of the comments on the piece, arguing that some speculative physics is best thought of not as science or religion, but as a game.
  • It’s behind a paywall and I haven’t seen the full story, but this week’s New Scientist has a piece entitled What if .. Most of reality is hidden? A large amount of theoretical activity in recent decades has gone towards ways of figuring out how to hide new physics from any possible interaction with experiment. It seems this is another way of characterizing the problem discussed in the Nautilus article of unfalsifiable theories. Again, since it’s the title of an article, the answer should be No.
Posted in Multiverse Mania | 21 Comments

Multiverses: Science or Science Fiction?

The September issue of Astronomy magazine is now out, with a cover story on Multiverses: Science or Science Fiction? The author Bob Berman does a good job of explaining both the arguments for various Multiverses, as well as the reasons for skepticism about some of these arguments. After quoting Max Tegmark as defending multiverse theory as science since it is a prediction of an “arguably testable” theory (inflation), Berman ends the piece in a way I have to agree with:

Given the current multiverse infatuation, it may be fairest to give the last word to a prominent skeptic. Columbia University mathematical physicist Peter Woit, who maintains the popular multiverse-critical blog Not Even Wrong, pulls no punches.

“Physicists had huge success in coming up with powerful compelling fundamental theories during the 20th century,” he explains, “but the last 40 years or so have been difficult, with little progress. Unfortunately, some prominent theorists have now basically given up and decided to take an easy way out. The multiverse is invoked as an all-purpose, untestable excuse. They allow theoretical ideas like string theory that have turned out to be empty and consistent with anything to be kept alive instead of abandoned. It’s a depressing possibility that this is where physics ends up. But I still hope this is a fad that will soon die out. Finding a better, deeper understanding of the laws of physics is incredibly challenging, but it’s within our capability as humans, as long as the effort is not overwhelmed by those selling a non-answer to the problem.”

Whoa, intense. We’ve got to toss the multiverse if we care about physics!

Of course, if an infinite multiverse does exist, some other Woit is out there saying the exact opposite.

The same issue of Astronomy has a “Web Extra” entitled What happens if string theory is wrong? It mentions the 2013 poll of theorists discussed here, which had a large majority (73%) answering the question “Do you think that String Theory will eventually be the ultimate unified theory?” with a “No”, then goes on to link to a 2007 article by Sten Odenwald. Some of that article includes quotes from an interview with Lenny Susskind, which Odenwald recently included here. It will be interesting to have an update on that material in a year or so once 13 TeV LHC results on supersymmetry are in.

Bonus material: Quanta magazine has a great interactive map of “Theories of everything”.

Posted in Multiverse Mania | 59 Comments

Math and Physics Summer Camps

With the kids shipped off to NSA summer camp, now is the time for mathematicians and physicists to head off to their own summer camp experiences. Some of these have websites where the rest of us can participate a bit virtually. These include:

  • Out at Stony Brook, in mathematical physics there’s the Simons Center Workshop going on now. This features lectures at the nearby Smith Point beach.
  • Down in Princeton, the summer PiTP program for this year has just ended, with the topic New Insights Into Quantum Matter. In recent years many HEP theorists have given up on applying duality arguments to string theory unification and have gotten interested in condensed matter physics. Links on this schedule will take you to lectures that include three by Witten on Fermions and Topological Phases.
  • Utah has been the center of the algebraic geometry world for the past few weeks, with the AMS Summer Institute in Algebraic Geometry held in Salt Lake City ending today. This is one in a series of big events held every ten years and as usual was preceded by a bootcamp for graduate students. Also as usual, the NSA is helping out with the funding.

    Overlapping with this, some algebraic geometers were at camp up in the mountains nearby, at the Zermatt Resort, for the PCMI Summer Session, this year the topic was Geometry of moduli spaces and representation theory.

  • Later this month, SLAC will host the 43rd SLAC Summer Institute, with topic this year The Universe of Neutrinos.
  • For Spanish-speaking mathematicians, around the same time the place to be will be Cusco for AGRA 2015. Michael Harris has notes for his lectures and has started blogging in the appropriate language.
Posted in Uncategorized | 2 Comments

This Week’s Hype

Symmetry, the FNAL/SLAC run online magazine funded by the DOE, today is running a piece of multiverse mania entitled Is this the only universe?. It’s a rather standard example of the pseudo-scientific hype that has flooded the popular scientific media for the last 10-15 years.

Besides the usual anthropic argument for the size of the CC, the evidence for the multiverse is string theory:

For further evidence of a multiverse, just look to string theory, which posits that the fundamental laws of physics have their own phases, just like matter can exist as a solid, liquid or gas. If that’s correct, there should be other universes where the laws are in different phases from our own—which would affect seemingly fundamental values that we observe here in our universe, like the cosmological constant. “In that situation you’ll have a patchwork of regions, some in this phase, some in others,” says Matthew Kleban, a theoretical physicist at New York University.

No mention is made of the fact that there is no evidence for string theory, with the multiverse given as the usual argument for why this is so.

Kleban also claims the theory is testable in this way:

it may be possible to experimentally induce a phase change—an ultra-high-energy version of coaxing water into vapor by boiling it on the stove. You could effectively prove our universe is not the only one if you could produce phase-transitioned energy, though you would run the risk of it expanding out of control and destroying the Earth. “If those phases do exist—if they can be brought into being by some kind of experiment—then they certainly exist somewhere in the universe,” Kleban says.

No word on how to do that.

Nomura says the way to test the idea is by looking at the universe’s spatial curvature (which, according to Planck is zero within the experimental uncertainties). According to Nomura, the implications for the multiverse of possible more accurate measurements of the spatial curvature are

  • If it remains zero, that’s consistent with the multiverse.
  • If it is negative, that’s “strong evidence of a multiverse”.
  • If it is positive, that’s a problem for some multiverse models, but not evidence against the multiverse, because you can’t have evidence against the multiverse:

    a positively curved universe would show that there’s something wrong with our current theory of the multiverse, while not necessarily proving there’s only one. (Proving that is a next-to-impossible task. If there are other universes out there that don’t interact with ours in any sense, we can’t prove whether they exist.)

Kleban and Nomura are quite excited by this, because the multiverse has the wonderful implication that we can all give up on trying to find a better fundamental theory and do something more useful with our lives:

If there were different universes with different phases of laws, we might not need to seek fundamental explanations for some of the properties our universe exhibits.

Posted in Multiverse Mania, This Week's Hype | 16 Comments

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.

: 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.

Posted in Book Reviews | 37 Comments

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.

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

Posted in Uncategorized | 10 Comments


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.”

: CNN has an article up today about this here.

Posted in Uncategorized | 39 Comments

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).
Posted in Uncategorized | 16 Comments

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…

Posted in Uncategorized | 2 Comments