Reality Blogging

If you’re ever looking for a great example of an online technical discussion gone wrong, look no further than the comments section of this post over at Cosmic Variance, from last December.

Now maybe I don’t get out enough, but I haven’t seen anything like this since the Usenet days of yore. It had everything — name calling, anonymous cowards, hecklers, crackpots, vicious ad hominem attacks, a media circus, angry string theorists, elephants and a cast of thousands, and, all the above notwithstanding, two physicists trying to discuss some physics. (In fact, it’s mostly maths — can you embed SL(2,ℂ)×SU(3)×SU(2)×U(1) in a real form of E8 so the adjoint representation breaks up in a particular way? — unfortunately not.) There’s some reasonable background on what started it all at wikipedia.

I feel a little bad about encouraging people to go read this (be warned, it’s long, often tedious, but also strangely engrossing), in part because I think it ends up reflecting rather poorly on both the principal protagonists, not to mention everyone else involved. I know one of them, and have corresponded briefly with the other, and I suspect that the both of them are well meaning, friendly, reasonable people, and contrary to some claims, not crackpots. Quite what went wrong in the above exchange I’ll leave up to you. The whole farce is perhaps a warning against blog triumphalism; this could have been a great example of the potential of online public forums, and in fact at times it threatened to all turn out okay. In the end, however, I’m sure several of the people involved are wishing that the internet’s memory isn’t quite so long. Eventually, one of the Cosmic Variance bloggers closed the thread, with the comment:

“Essentially everyone in this comment thread has managed to be some combination of whiny, obnoxious, incorrect, disingenuous, unhelpful, and plain old embarrassing. “

So why doesn’t this happen in the maths blogosphere? Or is asking tempting fate?

72 thoughts on “Reality Blogging

  1. probably the answer is that in math there’s rarely a question about who’s right. I mean, things aren’t quite as cut-and-dry as mathematicians would like to think, but still, the proof is there, or it isn’t; whereas in natural science things tend to be a lot less clear.

    the internet, however is fundamentally dangerous, I think because of the feeling of anonymity and the fact that everyone comes across as more of a jerk than they are on the internet (even when you take this fact into account), leading everyone else to be more of a jerk in response. I don’t think I’ve said anything really stupid on the blog yet, but I’ve come closer than I would have liked. It’s very easy for things that would be funny delivered in person with the right body language to come across as just assholic on the internet. Also, The “Arrow’s theorem” post is still threatening to break out into a rage voting vs. IRV flame war, though we’ve also managed to have some civil and reasonable conversation.

    So basically, I think math does have some structural advantages over physics (let’s face it, physicists without data are a bit like junkies without smack and math is a lot less tempting to crackpots) in terms of avoiding flamewars, but I wouldn’t uncross your fingers just yet.

  2. “… physicists without data are a bit like junkies without smack…”

    I know you’re just kidding about this Ben, but I couldn’t overlook the irony of this statement given your previous insight that everyone comes across as more of a jerk on the internet. :-) (the emoticon signals my jovial intent!)

    I’m a quantum information theorist, and for the record, I think my field is doing just fine with very little data. After looking at some of the vitriol being flung about willy-nilly on the particle physics/cosmology blogs, I’m really glad that the q-info community seems (typically) more civilized. (This observation is based on a probably very biased selection of physics blogs that I read, so I don’t know how reliable it is.)

    I agree that the reason for the lack of such antics in the math blogosphere is likely due to the (mostly) cut-and-dry nature of the subject matter. But I guess the real question I would like to see answered is not, why doesn’t this happen in the math blogosphere?, but, why does it happen so much in particle physics? And why not other areas of physics?

  3. It can happen. At my own place I was host to a zealot who insisted that my approach to basic calculus was outright damaging to students, despite my consistent statements that each approach had its own merits and that I was merely choosing differently than he would. At Ars Mathematica, someone decided to smear Scott Carter in some very unappealing terms.

    But as often, or as wide-ranging? No, it just doesn’t seem to happen as much. I think part of it has to do with the fact that there aren’t math popularizations out there. The lay audience doesn’t get a garbled view of mathematics and think it knows what it’s talking about, the way it does with physics.

  4. Math blogs have a smaller and more socially connected readership. (Are all of our commenters within three links of each other?) It’s not that anonymous a community. There’s opportunity for troublemakers, of course, but far less so than in physics. We rarely discuss math in ways that involve having an opinion.

    If you want a flame war, start a discussion about what constitutes a proof.

  5. The grumpiness of people involved in fundamental theoretical physics is one reason I’ve pretty much quit working on th subject. The other reasons are probably also why these people get so grumpy: everyone is stuck, nothing is working, and the commercial pop science press is reduced to hyping half-baked ideas.

    Mathematicians are happier and less quarrelsome because they don’t feel like rats stuck on a sinking ship. I cheered up after I jumped that ship.

    But, we mathematicians shouldn’t gloat. It’s easy for mathematicians to succeed than physicists, since math describes all logically consistent universes, while physics is supposed to describe just one.

  6. I personally think math is more structured and there is a limit to vagueness in math, it is really hard to talk about anything in “laymen” terms , you have to precise and definite about the statements you are making…
    In physics people come from more varied backgrounds and there is a tendency to “intuitively” understanding things[ I think partially the influence of Feynman] but then many times people don’t understand it at all [if only we knew the secret to Feynman’s greatness] also there is this general tendency in physics id to try and produce working models which fit the data rather than really probe deep into the models themselves….last but not the least there is immense pressure to try and popularize physics into the mainstream society [something thankfully mathematicians abhor :)] by trying to simplify things too much , which I think is not a great idea at all.
    Is it a good idea to try and popularize these areas which need immense training and hard work into something glamorous like the Hollywood movies?

  7. I suspect it’s just a matter of time. It seems to me that any time people come together — even electronically — to discuss any subject about which (1) they are passionate, and (2) they might be wrong, there is a good chance that intemperate words will be spoken.

    I remember hearing stories from a friend of mine at Berkeley, where Lang would visit Ogus regularly a little after lunch. And during every visit, after a couple of hours, my friend would hear a lot of yelling coming from the office, culminating in Lang’s full-volume announcement, “Bullsh*t, Arthur Ogus, BULLSH*T!” … followed by the slamming of a door.

    If someone with the temperament of Lang or Weil regularly commented on blogs, could there be much doubt about the outcome?

  8. Scott,

    John Baez explains one reason for the bad behavior. The dominant research program in the field has failed to work out and the process of acknowledging this failure and drawing its implications is not a pretty one.

    But I think one huge difference with mathematics blogs is the anonymity issue. Just about everyone participating in the serious math blogs does so under their real name. When you know that your name is on something and you know the identity of the person you are arguing with, you may behave like more of a jerk than you would in person, but like a lot less of a jerk than you might be tempted to if you were anonymous. I can tell you from extensive experience that feeling forced to repeatedly respond to personal attacks carried out from behind the cloak of anonymity doesn’t exactly encourage polite, respectful behavior.

    Since some of the same pseudonymic people in the discussion you link to also submitted similar anonymous comments on my blog, I can see that they’re not random crackpots, but operating from computer accounts at the most prestigious research institutes in the field.

    I’ve repeatedly complained to Sean Carroll about his allowing anonymous personal attacks as part of supposedly scientific discussions, but he doesn’t seem to see anything wrong with this. Before blogs and the internet, if you wanted to attack your colleagues anonymously, no one would print such a thing, so the best you could do was to write on the stalls of your institution’s rest room. Giving people prone to unprofessional behavior a new outlet hasn’t been one of the better consequences of blog culture. Luckily so far this hasn’t infected math blogs, I hope it stays that way. One lesson of all this is that anonymous commenting should be discouraged. There are times it has a legitimate role, but this is relatively rare.

  9. If someone with the temperament of Lang or Weil regularly commented on blogs, could there be much doubt about the outcome?

    I know the answer for this blog, Dr. Barwick: they would get their asses banned in the first week.

  10. To “Ben Webster”:

    There is no proof, indeed NO RIGOROUS EVIDENCE AT ALL, of the ILL-DEFINED HYPOTHESIS that HIV causes so-called “AIDS”.

  11. Heh. I think if Serge wants to comment from beyond the grave, we should probably allow it. Maybe we can get him to write a guest post (on math!).

    Barwick — Some level of obnoxious behavior is probably inevitable, but I don’t think it’ll ever get that bad. sci.math.research has been around for years, and never seems to get all that angry.

    Peter — FWIW, we discussed crackpot policy shortly after starting this blog. The consensus was that a) we don’t have a policy, and b) the individual bloggers are free to delete anything they find obnoxious or inappropriate. It’s basically a zero-tolerance zero-engagement policy, except without any official channels to complain through.

  12. I’m glad to hear such sanguineness from experienced blog-goers about the risk of excessively ornery posts on mathematics blogs.

    But, hey, I wasn’t trying to poke fun at Lang. I met Lang briefly shortly before he passed away, and I found him funny and insightful (on matters mathematical), and he seemed to be fully aware that he was perceived as a “colorful character,” and he even seemed to delight in this status.

    I just wanted to point out that we mathematicians have our share of — shall we say — uncomfortably passionate interactions, and that it seems natural enough that this might spread to the internet.

  13. Thanks John A for reminding us of that incident. :-) The funny thing there was I was trying to pay respect to someone whose art appealed to me. I came to the conclusion that part of that person’s (and/or his peers’) art was to be insulting. I will loose respect for them if they discontinue the rude behavior. I will continue to be polite, and expect him/them not to.

  14. [Lang] seemed to be fully aware that he was perceived as a “colorful character,” and he even seemed to delight in this status.

    Within fifteen minutes of meeting him for the first time, he was screaming at me about the proper definition of a conformal map. That afternoon at tea he’d found my undergraduate advisor had been one of his students from when he was at Columbia. He told me I was to “call Bill Adams, and say, ‘Serge had a tantrum’,” before asking him to discipline whoever had told me conformal maps were angle-preserving.

  15. You are wrong. As a non-mathematician, I can tell that most of this blog is filled with things a reasonable person cannot understand. If you read my recent paper on Category Theory and Post-Structuralism — which the Journals refuse to Publish, in spite of my First Amendment Rights — then you will Learn the I Am Right, and that your Univesity Degree DOES NOT Make YOU better THAN NORMAL PEOPLE, AND IN FACT BLINDS YOU OF THE TRUTH!!!

  16. Barwick-

    I wasn’t trying to suggest mathematicians would never have flame wars (after all, we seem to have already started a “trolling-as-performance-art” trend on this thread), but I really think that math has a structure advantage over other disciplines, and Monsieur Lang was actually a very good example. He was a, ahem, passionate guy who got into a lot of arguments, but for the large part they were not about math. I crossed paths with him a number of times, when he was in Berkeley, saw him get in a lot of shouting matches but they were always about HIV, or apartheid, or why cell phones are a sign that Americans don’t have enough sex (though he did have a few terminological bugaboos, like the conformal maps thing that John mentions), all subjects that I don’t expect we will have cause to discuss here (my co-bloggers do a better job of keeping me in mine than that).

    I think we can also be sanguine about this blog in particular, because we are its dictators (junta? politburo?). If things get out of hand, we can always start deleting/disemvoweling comments and banning people. Luckily, this hasn’t really been necessary yet, but I think we’ve been clear from the beginning that we don’t have much in the way of scruples about doing so.

  17. I could be completely wrong, but my impression is that mathematicians used to yell a lot more than they do nowadays. In his Indiscrete Thoughts, Gian-Carlo Rota sketches some portraits of some famous yellers, like Emil Artin (who may have aided and abetted Lang’s own yelling), Solomon Lefschetz, and Willy Feller. My mathematical grandfather, Eilenberg, was reputedly a great yeller, and certainly so was Mac Lane, as well as many others from previous generations.

  18. Todd,
    Maybe I should leave this to the older mathematicians, but I certainly get the feeling it would be a lot harder for a Serge-Lang-like figure to be successful in mathematics nowadays. I’d certainly be willing to believe that behavior along those lines is slowly becoming less socially acceptable. (Of course, people are famously bad at impartially observing social trends like this, so who knows?)

  19. Ben and Todd,

    This is interesting. What do you think has happened that has made it less acceptable to be an enfant (ou ancien) terrible in mathematical circles? Do you see a move toward “professionalism” (by which I mean a bright line separating scientific conflicts from personal conflicts) in mathematics? I haven’t detected this, but I’m actually worse than average (certainly worse than Ben) at observing social trends among academics.

  20. Barwick, this is sheer speculation obviously, but I’d guess that one factor is that there are many more mathematicians than before, drawing from more strata of society, and this has had a certain leveling effect on what is socially acceptable.

    I mean, for example, that within the comparatively small number of mathematicians who got their PhDs in the 50’s (say), there may have been a kind of stylistic inbreeding within a school like Princeton, where there may have been a certain cache to being an enfant terrible, or flaunting a certain type of otherworldly weirdness, so long as you excelled at mathematics. For the younger ones taking their cues back then, there may have been fewer different kinds of personality types to emulate.

    (Actually, I have no idea; this could be complete BS!)

  21. Todd’s theory is in the direction of a trend that surely has some social truth to it. People quarrel more when they are stuck with each other. If everyone has a lot of lateral social mobility, then most people wander away when you fly off the handle instead of shouting back. This is as much a matter of rational incentives as irrational psychology.

    There is no question that math departments are less stifling than they once were. We have the Internet and cheap air travel. As a result, there is a lot more long-distance communication and a lot more conferences and seminars; and there are more good math departments. So you can jump into a rant-fest if you feel like it (as in the Monty Python sketch, “I’m here for an argument!”), but you’re not usually obliged. That does a lot to cool people’s tempers.

    Of course it does not explain how physics is different; and for the most part, it isn’t. I don’t put much stock in these “physicists are from Mars, mathematicians are from Venus” discussions. What is true is that in either discipline, there are always a few people who are angry about something or other. After all, mathematics just had its own tempest in a teapot involving Perelman, Yau, et al. (Maybe even two tempests in one teapot.)

  22. Let’s not forget the very tense exchanges and dramas that occurred in Peter Woit’s blog over Perelman & Yau and Penny Smith’s ill-fated announcement about the Navier-Stokes equations. In those cases, there were a number of people hiding their real identities, and the discussion did get nasty. Mathematicians are not immune to flame wars, although I have to say that most of the math blogs have been rather congenial places on the whole compared to the physics blogs. I used to look at the physics blogs out of curiosity, but have grown very discouraged by the discourse.

  23. I agree— I see no reason why mathematicians could not have flame wars such as the one cited.

    In this particular case, the media was the root cause of the initial blowup, and it seems to me that the reason this happened is because of the imprecise nature of the goal “Theory of Everything.” In mathematics, most of the most celebrated goals are precise conjectures that nobody doubts are stated correctly, so either you prove it or you don’t. So at least, if you prove it, everyone should be impressed because they couldn’t prove it. Nonetheless a flame war could result from doubts as to whether the proof is indeed correct.

    I wonder if, were there blogs and the internet when Einstein came up with his theories of relativity, if there would have been a flame war about that.

    On a different note, looking at the flame war I was really surprised how tame it was given the discussion here and elsewhere about it. It didn’t really seem all that bad to me. Sure, it wasn’t “professional discourse” but the “blogosphere” is partly a social environment.

    I think that it would be better not to have anonymous postings in general, although even if it were not expressly an option, people could make up a name and email etc. So it probably can’t be really stopped (without excessive effort).

    Finally, now I’m curious — John — what did Lang say is the proper definition of a conformal map if not one that preserves angles? Looking now at Google Books, I see on p. 35 of Lang’s Complex Analysis the sentence “A map which preserves angles is called conformal” — the first definition of the word “conformal” in the book.

  24. travis,

    In practice it is not difficult to put a stop to unprofessional anonymous comments. Blog software allows them to be deleted in seconds, and in my experience people quickly stop writing such comments when it becomes clear that they will be deleted.

    Richard,

    Thanks for reminding me of the mathematics flame-war incidents, I’d forgotten about those. My initial idea at the time of the Perelman-Yau New Yorker story was to allow comments on my blog on the issue that provided accurate information, even if anonymous. It quickly became clear that this was a dumb idea, since the Tian-Yau situation was so partisan and toxic. Unfortunately, discussion of anything related to string theory has taken on some of the same character. In both cases, allowing partisans to operate anonymously turns out to destroy the already slim hopes for reasoned discussion.

    One thing you can say about Serge Lang is that he was someone extremely unlikely to make his opinions known anonymously…

  25. I had a look at the discussion of Smith’s Navier-Stokes attempt on Woit’s blog, and I must say, I found it very disturbing. Having anyone — even an anonymous crackpot on the internet — speak to me that way about my work would really upset me. I have no idea how Smith retained her composure as much as she did. Perhaps I’m overly sensitive, but I would have been devastated by that kind of talk. It’s one thing to state directly and precisely where errors persist in a preprint (or, better, to brainstorm about how to sidestep those errors), but to call a mathematician’s professionalism into question in the harshest imaginable terms simply because she’s had to withdraw a faulty preprint is inexcusable.

    Peter’s observation about Lang is particularly interesting. The picture I’m starting to imagine here is that while mathematicians may be less provocative and “uncomfortably passionate” face-to-face these days (as Todd suggests), some seem to see no problem with going undercover on blogs to publicly humiliate someone unfortunate enough to use his/her real name (as Peter and others suggest). If that’s true (and I sincerely hope not), then this is not a move toward professionalism, but toward insincerity and passive-aggressiveness.

    So the question I have is this: Is there any truth to my imagination? If so, is this an intrinsic problem with anonymous or partially anonymous internet discussions? Or is what we are seeing merely the result of widely circulated hype regarding a small number of difficult problems with cash rewards attached thereto, combined with the accessibility of online discussion forums to a wide variety of rude and ill-informed wingnuts?

  26. One thing you can say about Serge Lang is that he was someone extremely unlikely to make his opinions known anonymously…

    Oh, I can only imagine the screeching scorn he’d heap upon anyone craven enough not to sign his name to his own thoughts.

  27. It’s cause mathematicians are fermions, physicists are bosons.

    Good call! In that case, I’d rather be an anyon.

    A CONFORMAL MAP IS AN ISOMORPHISM IN ZE CATGORY OF LOCALLY HOLOMORPHIC MAPS!

    Professor Lang, can you tell me whether Q-bar equals the algebraic closure of Q in C, or whether they are merely isomorphic? I have heard from both Dan Bernstein and Tal Kubo on the matter, but I am still undecided.

  28. Travis,

    Actually those discussions on Peter’s blog were worse than appears now because he wisely deleted some of the nastiest comments.

  29. Is that a direct quote, John? If so, I’m not understanding the difference between Lang’s notion of conformal map and a biholomorphic map. (If I’m being stupid here, so be it. At least Lang isn’t here to scream at me.)

  30. I think I have a partial answer to my question: from what I glean from Google, the notion of locally holomorphic mapping X –> Y doesn’t seem to require that X and Y be complex manifolds (and in that case my worry seems to be nonsensical).

  31. I remember reading the comments section on Not Even Wrong after the Navier-Stokes paper and feeling very depressed. Gosh… thanks for reminding me :-( To anyone who thinks the mathematical community is somehow immune to that kind of thing: please read that entire affair, and weep. Ultimately we’re all the same human beings with the same kinds of insecurities and fears.

  32. I’m surprised. It seems to me that the word “conformal” is specifically chosen to refer to angles. And, as mentioned, why not use “biholomorphic” or at least “locally biholomorphic” if that is the meaning desired? Not to reiterate that *Lang’s own book* uses the definition of conformal using angles…

  33. Like with other academic activity highlights are more interesting than cases were things went wrong. Thus a more interesting question is: what is the potential (if any) of scientific blog discussions (and even debates) when they go right. Do you have examples of online physics/math technical discussions which were good?

  34. There are lots of technical discussions over at the n-Category Café which have productive outcomes. For example, recently John Baez put up a paper he’s co-authoring with Mike Stay, inviting patrons to submit their comments. And Urs Schreiber pretty much uses it as a sounding board for his ongoing research (where he posts voluminous technical entries and asks numerous questions). Tom Leinster has also gotten a lot of feedback from that blog (e.g., on his recent Metric Spaces entry). Those are just a few examples.

  35. As Todd says, there are lots of examples of productive technical discussions to be found at the n-Category Cafe, and many other mathematics blogs (such as this one).

    I think the summarizing statement at Cosmic Variance was overly harsh. Sure, there was a lot of bad feeling in the exchanges there, but it was too conveniently simplistic to suggest that everyone (or “essentially everyone”) was at fault. Some people were making serious efforts to keep the tone professional and civil. It can be hard to do that without coming off as whiny or preachy, but that’s the sacrifice you make.

    As Bertrand Russell pointed out, no one goes to war over whether Iceland is in Africa. If someone suggests such a thing, they simply expose themselves to ridicule. Arguments only become heated when the truth of the statement being argued over is hard to settle. Mathematics is the study of things that can be made precise, and if we can’t quickly decide the truth of a statement then we usually come to the agreement that it’s a challenging and interesting conjecture.

  36. If mathematicians ARE fermions, I realize that it might not be well known among them, that that description of them, as compared to physicists being bosons, is due to Alain Connes. The blog post by AC has a link labeled “attempt” which used to go to the famous (at least among those interested in noncommutative geometry) essay but no longer does. It might come up in a google search like this one, or at least references to the essay.

  37. Mathematics is the study of things that can be made precise, and if we can’t quickly decide the truth of a statement then we usually come to the agreement that it’s a challenging and interesting conjecture.

    That’s an important point. Much of the heat one sees in online theoretical physics discussion is due to the friction caused by less-than-well-defined language applied to sophisticated issues.

    This allows participants of the discussion to have different ideas on what is at stake. All sides feel they know what the physics more-or-less-folklore is really about and are shocked by the sight of someone not adhering to that interpretation.

    One rarely sees a heated theoretical physics discussion about an issue which can be phrased entirely in terms of classical mechanics. That’s because there a rigorous, well-defined and agreed-upon formalism is at work, symplectic geometry, which allows to settle all questions in principle.

    Most arguments usually inolve quantumness and field theory in one way or another. There the problem is that no general framework, comparable to symplectic geometry for classical physics, is quite available yet.

    It’s possible, as shown by evidence, to have heated discussions about “quantum anomalies”. At least part of the reason for that is that a quantum anomaly is a phenomenon with maybe four different more-or-less precise definitions, the relation between which is unclear, arising in a context (QFT) which itself has in turn maybe four different more-or-less precise definitions, the relation between which is unclear.

    I think there are practitioners who have sufficient control of this somewhat shaky framework to actually be able to judge what is wrong and what is right. But without the tedious but effective step-by-step procedure of rigour, it is possible to drive them up the walls by insisting on not following their interpretation.

  38. Most arguments usually inolve quantumness and field theory in one way or another.

    Although “quantumness” in and of itself is completely rigorous. That is, quantum probability, or what the physicists call quantum mechanics, is rigorous. Quantum field theory is not rigorous, and neither is stochastic field theory. And, of course, quantum gravity is largely undefined even nonrigorously.

  39. what the physicists call quantum mechanics, is rigorous

    Of course that’s true. And still, there is always wiggle room for physicists, since they may simply opt not to accept your rigorous set of axioms for what they are doing.

    One of the big discussions in the early days of physics blogging was a fight about how to think of the mere quantum harmonic oscillator. (Due to a proposal somebody made saying that the standard rules for describing it should be revised in the light of, guess what, quantum gravity…)

  40. they may simply opt not to accept your rigorous set of axioms for what they are doing.

    Maybe that sounds more dismissive than it should. Actually to a large degree it is what makes theoretical physics interesting: the need to not just follow axiom sets, but to perpetually search for “better” ones. The most famous achievements in the history of theoretical physics have been refinements of the axiom sets.

    But this freedom is also what makes some discussions problematic.

    There had been some heated discussions on some blogs with proponents of the “AQFT” axiom set, which says that QFT is all about nets of local operator algebras, and nothing else. Disagreement about that is from the mathematical point of view meta-disagreement, since it cannot be decided by working out consequences of some axioms.

    We have seen the striking communication difficulties which can result from this here in the discussion section. But this wasn’t restricted to blogs, I have seen the same kind of problem over the same issue at a conference.

    It’s rather noteworthy what the problem in that case had been: not only did people disagree whether somebody had provided a proof or disproof of some hypothesis or not, the disagreement was actually about whether the mere statement that was to be proven had anything at all to do with the concept people had originally in mind.

    Imagine conversely mathematician A saying: “I present a proof/disproof” of a conjecture stated by B.” and B replying: “No, no, that wasn’t my conjecture at all.” and an argument ensuing not about the proof, but about what the conjecture actually is.

  41. And still, there is always wiggle room for physicists, since they may simply opt not to accept your rigorous set of axioms for what they are doing.

    Well, one of the reasons that I like quantum information theory
    is that it has, ironically, done a lot to get rid of this wiggle room. An analogy: In the earliest days of computability or recursive functions, people philosophized a certain amount as to what it meant to think, or compute. The Church-Turing thesis cleared the air, by positing that all interesting definitions of computability are equivalent.

    Likewise, you could say that quantum information theory is developing a “Copenhagen thesis”, that all interesting models of quantum probability are equivalent. My preferred description is that it is just non-commutative probability, as in von Neumann algebras. There have been a ton of interesting results in quantum information theory lately, but none of them have come from any perceived wiggle room in the axioms of quantum probability.

    Certainly some sort of geometric axioms are missing from our axiomatic description of reality. Maybe the correct axioms of quantum gravity will shed light on why quantum probability is true. Or maybe not, who knows.

  42. I wish I could remember the exact details of Lang’s “conformal map” rant, but it wasn’t as bad as what people are describing up-thread. That is to say, he had a good point hidden somewhere in the rant. The main point was two-fold, first that the way people used conformal confused students into misunderstanding stuff like f(z) = z^2, the second was that as a matter of principle you should be using language compatible with category theory (some notion of homs, and then isos are invertible homs). But it’s been a few years and I only saw the rant second-hand, so I can’t remember the details.

  43. Yes, Noah is right. I left out (repressed?) the part of his rant where he’s holding up counterexamples. z\to z^2 defined on the entire complex plane, for one, and z\to\bar{z} on the upper half-plane for another.

    I didn’t say that he didn’t have a point. In fact, he did have a very good point, which I’ve probably mangled a bit in my memory, but which Noah is more or less right about. I’m just saying that my very first interaction with him I was literally afraid for my physical safety.

  44. Thanks guys. It sounds like he doesn’t accept that a function f holomorphic in a neighborhood of z is actually conformal there if f'(z) = 0, and that seems sensible to me.

    I can think of maybe two mathematicians who have really shouted at me — one was Saunders Mac Lane (someone I came to love over time). I think emotional flare-ups came naturally to him, and he was not the least bit inhibited in giving them full expression. Part of the social milieu he had become accustomed to.

  45. Oh dear, I don’t understand either John’s comment 49 or Todd’s comment 50. John: what’s z |–> z^2 on the entire complex plane a “counterexample” to? And Todd: I thought *no one* accepted that a function f is conformal at z if f'(z) = 0? (Have I misunderstood you? Or did you mean \neq 0?)

    The definition of conformal that I learned was that a holomorphic map f is conformal if f'(z) is nonzero for all z.

  46. Tom: that’s essentially equivalent to the formulation Lang would prefer. Locally it’s an isomorphism, since there’s a neighborhood where f'(z)\neq0, and in that neighborhood the inverse function theorem works.

    What he was screaming about was that in response to what I thought was a casual, semi-rhetorical question, I gave the standard rough answer that everyone hears in a first course: “angle-preserving”. Those words paper over a lot of technicalities, though, about which angles, what orientation, what points…

  47. Well, anyway, if the derivative is zero, then the angles aren’t preserved at that point: z -> z^2 indeed multiplies angles at the point zero by two.

    I understand that (locally) biholomorphic (i.e., holomorphic with a holomorphic inverse) is better to use than conformal, but I just think that the word “conformal” is designed to refer to angles, and indeed in the case of holomorphic maps from C to C, conformal just says derivatives are nonzero == there is locally a holomorphic inverse…

    As for the complex conjugation map, one could make the case that this doesn’t preserve oriented angles … but we’re definitely digressing here.

  48. As for the complex conjugation map, one could make the case that this doesn’t preserve oriented angles

    Me: “Okay, oriented angles.”
    Lang: “NOW YOU ARE HEDGING ABOUT ORIENTATION! ZIS IS A MASSEMATICS COURSE, NOT A BIOLOGY COURSE OR A POOLITICAL SCIENCE COURSE! ZERE ARE REAL ANSWERS!”

  49. Relax, Tom. You’re right — no one accepts, etc. It’s just that for some reason I had no idea what Lang was driving at according to John’s recollection, until I reminded myself what conformal actually means (and made a mental connection with “locally biholomorphic”, as travis said out loud). Just think of it as me clogging up the blogosphere with my mumblings.

    John, those are some pretty vivid evocations – lol!

  50. There is one BIG difference between theoretical physics and mathematics: if an analyst proves an important theorem that the algebraic geometers were hoping to prove themselves, it doesn’t result in the whole field of algebraic geometry being thrown out the window.

  51. one was Saunders Mac Lane (someone I came to love over time). I think emotional flare-ups came naturally to him, and he was not the least bit inhibited in giving them full expression. Part of the social milieu he had become accustomed to.

    Todd, I’m curious what you mean by this; are you saying that he was accustomed to a social millieu where it was normal to have emotional outbursts, or one where people put up with his emotional outbursts?

    While we’ve kind of dropped this thread, I think there’s a lot to be said for Greg’s suggestion about math departments becoming less claustrophobic and there being more of them. I think it also makes a difference that the supply of mathematicians has expanded even more. Certainly both anecdote and AMS statistics suggest that it’s been notably harder to get a job since the late 80’s than it was in the decades before that (though at least as measured by postdoctoral unemployment rate, we’re starting to get close, but that probably indicates the presence of greater opportunities outside academia), suggesting it’s easier for departments to find qualified faculty who don’t have Serge Lang-style outbursts.

  52. I’ll just note: only 183 more comments, and we’ll be longer than the thread we were originally discussing. A victory for internet loquaciousness everywhere. (My lodger, Carl, suggests we have a party when we reach 100).

  53. Ben: I meant both, with emphasis on the former. The evidence I have is second-hand, based on what I’ve read, e.g., about the Chicago department during the Stone Age, with three of its top faculty (Stone, Weil, and Mac Lane) being very forceful and occasionally explosive personalities. [In the mid-40’s, no one but Stone had the stones to take on Weil, or so I’ve read.] Halmos too I think was known to blow his top now and then. Well, that was Chicago; I already mentioned Princeton, and based on what I’ve read I doubt these were the only instances (let’s say of the top PhD-producing schools) back in the day. I conjecture that raising one’s voice to shouting levels was just much more of an everyday thing then, and yes, people would just put up with it (or drop out).

    A little further evidence that this was considered normal: with Mac Lane, for example, you could shout right back but then be friendly again the next day. I don’t think it was necessarily the case that you had to have a certain stature to afford that kind of behavior; perhaps that kind of rough-and-tumble was even a standard device to test people’s mettle. Again, this is largely conjectural — I’d love to hear first-hand impressions from older mathematicians.

  54. Philosophy has cleaned up its act too. We don’t brandish pokers at each other these days. This suggests it’s less the subject matter of the discipline concerned, and more the understanding of the practitioners of what’s acceptable.

    I wonder if there isn’t also an effect produced by the typically much gentler upbringing of today’s academic, compared to those of our forefathers. If I had to choose a time to be an English child from some point in the last 200 years, it would be a recent one, whichever the socio-economic group.

    I can see the point about mathematicians having less to argue about, but it should only be taken so far. I have encountered many complaints that a field has moved in a wrong direction, or has been too slow to take up a new idea. Perhap blogs could act as vehicles for the constructive expression of such views, rather than appearing largely in book reviews and referee’s reports where there is no possibility of reply.

  55. “At least part of the reason for that is that a quantum anomaly is a phenomenon with maybe four different more-or-less precise definitions, the relation between which is unclear, arising in a context (QFT) ”

    Another reason is that some quantum anomalies do not arise in QFT, but only in a different context (QJT), which is substantially different from QFT. One thing that I learned from Jacques Distler, in his criticism whose constructiveness I think was involutary, was that diff anomalies do not exist in 4D within a QFT framework. Hence extensions of the diffeomorphism algebra in 4D is not QFT.

    One difference between math and physics is that in math, anything that satisfies your axioms is right, as long as these are consistent. In physics, an idea might be beautiful and consistent and still wrong, e.g. ether theory.

  56. Thomas Larsson wrote:

    not […] in QFT, but only in a different context (QJT), which is substantially different from QFT.

    Thanks, Thomas, for highlighting my point with acting as an example! ;-)

  57. If you want a flame war, start a discussion about what constitutes a proof.

    That was my job talk! Fortunately, it was to philosophers, rather than mathematicians.

  58. If anyone else out there is as behind on their RSS feeds as I am, they might not yet have noticed this post over at the n-Category Cafe, about a talk of Bertram Kostant’s titled “On Some Mathematics in Garrett Lisi’s ‘E8 Theory of Everything'”. There’s quite a lot of detail in the comments, which remain friendly and on-topic. :-)

    The worst it ever gets is:

    So the Lisi enthusiasts who seem to be hanging around here, breathlessly hoping to learn some tidbit which will “save” Lisi’s theory are going to come away a little disappointed…

  59. This quote is by Distler, and he is entirely imagining a horde of Lisi supporters, of which there is no evidence at The Cafe (except for Lisi himself). By the way, for Distler, this is a very mild rebuke.

  60. Kea,

    I counted at least one other person there who looked (to the casual observer) to be a Lisi supporter.

    And yeah, Distler was writing less caustically than usual. His level of acidity seems to be mostly proportional to the level of ignorance he’s engaging with. The man doesn’t suffer fools gladly, and unfortunately for him, half of the physics trolls* on the internet seem to regard him as one of the Enemies. That has to take a certain toll. Particularly in light of what he wanted from the physics blogosphere: high level physics discussion. What he got was mostly popular science mixed with sci.physics.

    * troll isn’t quite the right word here. What’s the slang for someone who gets passionately involved in arguing about topics which they haven’t mastered?

  61. Dear me, A.J., we shouldn’t abuse the hospitality of this blog by bringing the physics slander to it, although I’m sure that would very quickly generate 100+ comments.

  62. …and by the way, Distler’s expertise lies solely in the string camp, the physics content of which is debatable. (Heh, do I at least get an invitation to the party at Princeton?)

  63. Kea,

    I’m one of this blog’s proprietors, so I have certain freedoms that drive-by commenters might not enjoy. And I used to be a physicist, so I still take a certain interest in the development of the physics blogosphere. (I can’t say that I’m too surprised so far. The physics blogosphere needs someone as well known and energetic as Terry Tao to set the standard for research level blogging by younger physicists.) But we can basically stop here, since the only thing I have to add is that Distler, by my standards, is reasonably expert in QFT and particle physics.

    Obviously, the physics content of string theory is not an appropriate topic for this blog. I thank you for not bringing it up.

  64. Kea,
    I think all of our readers in good standing would be invited.

    Though, I have to admit, I was under the impression you were in NZ, making it quite a trip to New Jersey.

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