Not Even Wrong

The Columbia Math department has been doing extremely well in recent years, with some wonderful mathematicians joining the department. A couple items first involving some of them:

• Kevin Hartnett at Quanta Magazine has a great article about developments in the field of technical issues in the foundations of symplectic topology. This explains work by my colleague Dusa McDuff, who together with Katrin Wehrheim has been working on such issues, trying to resolve questions raised by fundamental work of Kenji Fukaya and collaborators. For technical details, two places to start looking are here and here.

  The Hartnett story does an excellent job of showing one aspect of how research mathematics is done. Due to the complexity of the arguments needed, it’s not unusual for early papers in a new field to not be completely convincing to everyone, with unresolved questions about whether proofs really are airtight. The way things are supposed to work, and how they worked here, is that as researchers better understand the subject proofs are improved, details better understood and problems fixed. Along the way there may be disagreements about whether the original arguments were incomplete or not, but almost always people end up agreeing on the final result.

  Also featured in the article is another of my Columbia colleagues, Mohammed Abouzaid, who provides characteristically wise and well thought out remarks on the story.

• Via Chandan Dalawat, I learned of an interesting CIRM video interview with another colleague, Michael Harris. The same site has this interview with Dusa McDuff, as well as a variety of other interviews in English and French.

For some other non-Columbia related links:

• The 70th birthday of Alain Connes is coming up soon, and will be celebrated with a series of public lectures and conferences on noncommutative geometry in Shanghai.
  This year will be the last series of lectures by Connes at the College de France. They’re appearing online here, and I highly recommend them. He’s taking the opportunity to start the series with a general overview of the point of view about the relationship of geometry and quantum theory that he has been developing for many years.
• For employment trends in theoretical particle physics, there are some updated graphs of data gleaned from the particle theory jobs rumor mill created by Erich Poppitz and available here. In terms of total number of jobs, there has been some recovery in the past couple years, with about 15 jobs/year, above the 10 or so common since the 2008 financial crisis (before 2008 numbers were higher, 20-25). As always, an important thing to keep in mind about this field is that this number of permanent jobs/year is a small fraction of the number of Ph.Ds. in the subject being produced each year at US universities.

  The numbers for distribution of subfields separate out “string theory” and lattice gauge theory. There have always been few jobs in lattice gauge theory, appear to be no hires in that subject for the past two years. I’m putting “string theory” in quotes, because it’s very hard these days to figure out what counts as “string theory”. With Poppitz’s choice of what to count, hiring in string theory has recovered a bit, now around 25% of the total for the past two years, up from more like 15% typical since 2006 (earlier on the numbers in some years were around 50%).

• As pointed out here by commenter Shantanu, on Wednesday John Ellis gave a talk on Where is particle physics going? at Perimeter. I’d characterize Ellis’s answer to the question as “farther down the blind alley of supersymmetry”. He spins the failure to find SUSY so far at the LHC as some sort of positive argument for SUSY. The question session was dominated by questions about SUSY, with Ellis taking the attitude that there’s no reason to worry about the failure so far of the fine-tuning argument for SUSY, all you need to do is “ratchet up your pain threshold”. I fear that’s some sort of general advice where this line of research is going.

  About the failure to find any evidence for SUSY wimps that were supposed to explain dark matter, Ellis explained that he had been working on this idea for 34 years, first writing about it in 1983, so with that much invested in it, he’s not about to give up now.

Update: Davide Castelvecchi points me to another new mathematics story at Nature.

Update: One more. A profile of Roger Penrose by Philip Ball. Penrose explains that his main problems with string theory come from two sources. One is the instability problem of extra dimensions, the other is his aesthetic conviction that sticking to four space-time dimensions is a good idea since it is only in four dimensions that you get the beautiful geometry of twistors. Ball raises the interesting question of whether Penrose could have a successful scientific career if he were starting out today:

Worst of all, the career structures and pressures facing young researchers make it increasingly hard to find the time simply to think. According to several early-career scientists interviewed by Nature, the constant need to bring in grant money, to produce papers and administer groups, leaves little time to do any research, still less indulge anything so abstract and risky as an idea.

Every year in Tucson the Arizona Winter School takes place, with a five day program on some topic in arithmetic geometry aimed mainly at advanced graduate students, designed to get them involved in current research-level topics. This year’s topic (Perfectoid Spaces) is drawing a huge number of people there next month, with about 450 participants expected (in the past numbers were more like 100). This should be a veritable Woodstock of arithmetic geometry, with no one I’ve talked to quite able to figure this out, thinking that there probably weren’t 450 people worldwide interested at all in arithmetic geometry. It seems everyone in the field will be there and then some.

Peter Scholze is the opening and closing act. The other lecturers who will take the stage have started to put lecture notes for their lectures on the school website.

Some are dubious that there really are 400 or so students in the world with the background necessary to understand this material. See for example MathOverflow where nfdc23 isn’t very encouraging to a student who doesn’t know any rigid analytic geometry, but plans to attend the AWS. In any case, I hear Tucson is quite nice in March.

At some kind of other end of the spectrum of such things, a couple months later experts will gather in Germany to discuss this field (see here). Also for about five days, at the Schloss Elmau Luxury Spa and Cultural Hideaway, the sort of place heads of state go for G7 meetings. Rooms run $600 a night or so, but in this case the tab is being picked up by the Simons Foundation. Sorry, by invitation only.

In the current situation, getting back to finding interesting news about math and/or physics to think about seems like a good idea, but I’ve been having trouble coming up with such news. Besides blogs, many of them listed on the right-hand margin of this one, I also follow some people on Twitter and on Google+. There are quite a few well-known physicists on Twitter at this point. On any given day you can learn something interesting from, for instance, Frank Wilczek or John Preskill (or see an epic throwdown between them).

I’m sure there are many other mathematicians and physicists on social media that I’m not aware of, and open here to hearing suggestions. Part of the problem is that I’m now so old I figure I don’t even know what social media sites are out there. I hear there’s this thing called Facebook, but also that it’s now over as far as the younger generation is concerned. So, if you have a suggestion about where to find high quality news about math or physics on social media, whether it’s on Twitter, Google+, Facebook, Live Journal, Instagram, Pinterest, Snapchat, Yik Yak, Grindr or something else I’ve never heard of, please let us all know in the comments.

After the election it seemed to me that it would be a good idea to ignore what Trump tweeted or said, and wait to see what he and the people he surrounded himself with would actually do. We’ve been finding this out over the past few days, and today the nature of the problem we face is now clear. The actions ordered today that are now being carried out by US officials around the world are the product of a deranged and dangerous personality who has surrounded himself with similar others. This is a national emergency with no parallel in our history.

While the US has never seen the likes of this situation, Europe has, with Trump following a playbook familiar from the history of the 1930s. At this point the US may be one terrorist attack away from full-blown Fascism, this time with nuclear weapons. This needs to be stopped, now.

The Constitution does provide two ways to deal with something like this: either the impeachment process or removal under the Twenty-Fifth Amendment as “unable to discharge the powers and duties of his office.” Many of Trump’s recent statements are clearly the product of delusional mind that is incapable of dealing with reality, and these delusions are now reflected in his actions.

Removing Trump and those he has surrounded himself with will require the cooperation of a significant number of Republican legislators. Anyone who cares about US democracy should be trying to figure out how to get this to happen. Those of us in the US desperately need some good ideas about how to do this. Those in other countries should be pressing their governments and institutions to fight back against the US, as well as doing what they can to keep their own societies from following the US down this path.

I’m moderating comments here and will only post one kind of comment: positive ideas about what to do about this emergency situation. At this point I think what’s needed are ideas way beyond suggestions of a “scientist’s march” to promote rationality. We need to figure out how to fight a new form of Fascism that has just come to power and is starting to rule by decree.

Update: With the Republican Congress so far deciding to sit back and let Donald Trump, Steve Bannon and Stephen Miller rule by decree, all hopes for now are with the Judiciary. Last night a judge issued an emergency stay on parts of the executive order, this was followed by a statement from Miller on behalf of the White House that the order “remains in full, complete and total effect.” The suggestion to donate to the ACLU is a good one, they are on the front lines here.

The President of my institution, Columbia University, at 1 am sent an email to the University community denouncing this executive order and involving the University in this in an unprecedented way:

As I have said on many occasions, it is critically important that the University, as such, not take stands on ideological or political issues. Yet it is also true that the University, as an institution in the society, must step forward to object when policies and state action conflict with its fundamental values, and especially when they bespeak purposes and a mentality that are at odds with our basic mission. This is such a case.

There is a petition being signed by academics here, which likely will have no effect, but I signed it anyway, and you may want to too.

Update: A small glimmer of hope: a joint statement criticizing the executive order by Republican senators McCain and Graham, and a Twitter response from Trump identifying any opposition from them as “looking to start World War III”. World War III between Trump and Republican senators is what we all need to root for.

Worth watching: news reports that the Trump administration is defying court orders requiring access to lawyers by detainees at Dulles airport. A decision by Trump and his people to defy court orders would provide grounds for impeachment.

Update: Just wrote the following to a correspondent, thought I might as well also post it here.

My advice would be to consider focusing on the following, and not getting distracted by the blizzard of appalling things one might reasonably find concerning about the current situation:

• It was unclear who would actually be running things in a Trump administration (since Trump himself clearly neither knows nor cares about anything other than getting attention) until the past couple days. The answer now seems to be that it’s Steve Bannon of Breitbart. Bannon is a self-described “Leninist”, see for instance.

  His self-described goal is to tear the country apart: “to destroy the state… destroy all of today’s establishment.” This means he’s not just our enemy, but is also the enemy of much of the Republican Party, including for example John McCain and Lindsey Graham. He’s also not about to let himself be thwarted by the courts. I think we’re already seeing defiance of court orders, with a lot more of that to come.

• There’s always the possibility of something like a military coup, but the only constitutional way out of this is impeachment or the 25th amendment route. This requires convincing a sizable number of Republican legislators that they have to abandon Trump and support his removal. To me, the big question here is what can be done to make that happen. How does one get the Republican establishment (legislators and/or Fox News, Wall Street Journal, etc.) to turn on Trump? My guess is that where they are now is that they know they have a problem on their hands, but are deathly afraid of Trump’s supporters, of ending up with their heads on a pike.
• There’s not much time here. Looking at history, what happens next in this kind of situation is some episode of violence gets used to rally the country to the leader and justify his assumption of emergency power to rule by decree. We’re one episode of some enraged person shooting a lot of people away from that happening, in a country full of heavily armed angry people.
• The best, most successful thing to hope for here is something I and maybe many of you find a depressing prospect: President Pence. But, there we are.

Hoping I’m wrong about all of this…

Update: Thanks to commenter Fred P. for the link to this. For something sensible from a conservative, see this by Eliot A. Cohen, which includes:

For the community of conservative thinkers and experts, and more importantly, conservative politicians, this is a testing time. Either you stand up for your principles and for what you know is decent behavior, or you go down, if not now, then years from now, as a coward or opportunist. Your reputation will never recover, nor should it.

Update: There was an incident last night (in Quebec City) of an enraged person shooting a lot of innocent people, killing 6 and wounding 8 others. Since the shooter was an Islamophobe and the victims were Muslims praying at a mosque, so this was of no use to Trump/Bannon, this has gotten just about zero attention.

Update: The Quebec City shooter was a Trump fan radicalized by Marine Le Pen.

Update: Terry Tao has a blog entry about this, emphasizing the damage to the math community.

Update: Leonard Susskind has also decided to issue a statement warning about Fascism and the Trump administration, using his YouTube channel.

Update: For commentary from historians of the rise of fascism in Germany on analogies with the current situation in the US, see Ron Rosenbaum and Isabel Virgina Hull.

A few links for your weekend reading:

• If you just can’t get enough of the Multiverse, Inference has commentary on Max Tegmark from Daniel Kleitman and Sheldon Glashow.
• Coverage of the important topic of blackboards is to be found here. To those ill-informed sorts who think that blackboards are the past, whiteboards or some other technology the future, I’ll point out the following. When I came to Columbia back in 1989, there was a recently installed modest-sized whiteboard in the math department common room. Everyone hated it, and after many years it was replaced by a similar-sized blackboard. Last year, in a renovation of the lounge, that blackboard was replaced by a better one, and one whole wall of the room was replaced by a floor-to-ceiling blackboard. A year or so ago, a newly renovated Theory Center was unveiled here in the Physics department: floor-to-ceiling, wall-to-wall blackboards. That’s the future, the whiteboard is the past.
• The latest CERN Courier has a long article by Hermann Nicolai, mostly about quantum gravity. Nicolai makes the following interesting comments about supersymmetry and unification:
  

  To the great disappointment of many, experimental searches at the LHC so far have found no evidence for the superpartners predicted by N = 1 supersymmetry. However, there is no reason to give up on the idea of supersymmetry as such, since the refutation of low-energy supersymmetry would only mean that the most simple-minded way of implementing this idea does not work. Indeed, the initial excitement about supersymmetry in the 1970s had nothing to do with the hierarchy problem, but rather because it offered a way to circumvent the so-called Coleman–Mandula no-go theorem – a beautiful possibility that is precisely not realised by the models currently being tested at the LHC.

  In fact, the reduplication of internal quantum numbers predicted by N = 1 supersymmetry is avoided in theories with extended (N > 1) supersymmetry. Among all supersymmetric theories, maximal N = 8 supergravity stands out as the most symmetric. Its status with regard to perturbative finiteness is still unclear, although recent work has revealed amazing and unexpected cancellations. However, there is one very strange agreement between this theory and observation, first emphasised by Gell-Mann: the number of spin-1/2 fermions remaining after complete breaking of supersymmetry is 48 = 3 × 16, equal to the number of quarks and leptons (including right-handed neutrinos) in three generations (see “The many lives of supergravity”). To go beyond the partial matching of quantum numbers achieved so far will, however, require some completely new insights, especially concerning the emergence of chiral gauge interactions.

  I think this is an interesting perspective on the main problem with supersymmetry, which I’d summarize as follows. In N=1 SUSY you can get a chiral theory like the SM, but if you get the SM this way, you predict for every SM particle a new particle with the exact same charges (behavior under internal symmetry transformation), but spin differing by 1/2. This is in radical disagreement with experiment. What you’d really like is to use SUSY to say something about internal symmetry, and this is what you can do in principle with higher values of N. The problem is that you don’t really know how to get a chiral theory this way. That may be a much more fruitful problem to focus on than the supposed hierarchy problem.

• Progress in geometric Langlands marches on, with a new paper yesterday from Aganagic, Frenkel and Okounkov on the Quantum q-Langlands Correspondence, a two-parameter generalization of geometric Langlands. Among many other things, they formulate (Conjecture 6.3) a conjecture generalizing the characterization (using BRST methods) of affine Lie algebra representations at the critical level that from the beginning of the subject described a major aspect of how geometric Langlands works locally (for details on this, see Frenkel’s book Langlands Correspndence for Loop Groups).

I’m about to head off for a short New Year’s vacation in West Texas, but wanted to recommend a wonderful article that just appeared at Nautilus. It’s a memoir by Bob Henderson (who I met when he wrote about me, see here), appearing under the title What Does Any of This Have To Do with Physics? (although the title of the web-page, What Graduate School in Theoretical Physics is Really Like, is more descriptive).

Henderson was a graduate student at Rochester in theoretical physics, working with S.G. Rajeev. He later went to work on Wall Street, and more recently in journalism. His Nautilus piece is the best explanation I’ve ever seen of what it’s like to start working in this field as a graduate student, should certainly be required reading for anyone thinking of going into the subject. It’s also somewhat of a profile of Rajeev, who has worked on a wide variety of topics in theoretical physics.

One of the main themes of the piece is Henderson’s thinking about how and why he left theoretical physics, why he “quit”. Something to keep in mind is that this kind of decision is what most people who get Ph.Ds in the subject end up facing. There are 5-10 times more people getting Ph.Ds in this field than there are permanent positions doing research in it, so the career path starts out with a game of musical chairs that you are highly likely to lose. Different people make the choice to quit the game and do something else at different points and in different ways.

Henderson does an excellent job also of explaining what the real problem is with doing this kind of research: that of figuring out what the right thing to calculate is. For everyone, but especially for those at the beginning of a career, the subject is a huge collections of topics one doesn’t understand. One has to somehow choose a direction to pursue, and it most likely won’t go anywhere:

Writers talk of the terror of facing a blank page, but it’s no different for theorists like Rajeev trying to choose which path to take. There are an infinite number to choose from, and most go nowhere or back from where you came. The clock is always ticking and you spend so much time in the dark that it can make you not only question your path, but your own self worth. It can make you feel stupid.

Sticking with this and making a career of it involve some combination of good luck (being in the right place at the right time), ability, self-confidence, not having a family to support, and a host of other factors. As Rajeev explains to him:

Without naming names, he ticked through a catalog of his contemporaries who’d succeeded in theoretical physics even without having the towering mathematical intellect that I was sure it took and that Rajeev surely has. They’d made it, Rajeev explained, by focusing on problems that played to their strengths, or by taking advantage of computers, or by collaborating with peers who had complementary skills. Some socially gifted but not so mathematically talented types had gone quite far this way, earned a lot of renown.

Anyway, the whole piece is well-worth reading. Another recently published Nautilus piece that I learned about from a link on this one is The Universes of a Woman in Science. It’s by Kate Marvel, who shares with Henderson (and hundreds if not thousands of others…) the experience of getting a theoretical physics Ph. D. (string cosmology in her case), and then leaving the subject for another field (in her case, climate science, which she blogs about here).