The January Notices of the AMS is out. Two quite interesting articles, one of which is an interview with my colleague Joan Birman. She just recently officially retired, but, at the age of 79 is still very active in research and a major presence in the department, an example to us all. The second is an article by Anatoly Vershik about the Clay Millenium Prizes. Vershik argues that these million dollar prizes are not good for mathematics, and that the story of the proof of the Poincare conjecture shows why. Top mathematicians who think they have a chance of solving one of the Clay problems are going to work on them whether or not the prize exists (the money certainly didn’t motivate Perelman). The prizes give the public a deformed view of what is important about mathematics and encourage unseemly squabbling about how “credit” for a solution will be assigned. Vershik writes:

In my opinion, all this clamor and fuss show that this method of promoting mathematics is warped and unacceptable, it does not popularize mathematics as a science, on the contrary, it only bewilders the public and leads to unhealthy interest.

There’s an excellent article about James Clerk Maxwell in the December Physics World. It’s the 175th anniversary of Maxwell’s birth this year. He lived only to age 48, dying in 1879. The author of the article speculates that “Had he not died so young, Maxwell would almost certainly have developed special relativity a decade or more before Einstein.”

For an update on the US federal budget situation for science, see this AAAS web-page. As far as I can tell, the situation is that (as often happens) the Congress has not yet passed FY2007 appropriations for most of the government, including the DOE and NSF, even though we’re now more than a couple months into the fiscal year. As a result, these agencies are operating under a continuing resolution, without access to the increased funds that were supposed to flow because of the “American Competitiveness Initiative”. The new Congress will have to deal with this after it convenes in January, and news reports I heard today said that Congressional leaders were considering not producing new appropriations bills but running the government on a continuing resolution for the rest of FY2007. Unclear to me what this means for science funding, but it doesn’t sound good. Over the next few years, if the new Democratic Congress makes a serious effort to bring the US federal budget deficit under control, science funding may be under pressure.

At the Scientific American blog, J R Minkel has a story called Comic Books Looove String Theory, about developments in the Ex Machina comic, which is about “a retired semi-super hero turned Mayor of New York City who can control machines with his mind.” In issue 10 a lunatic starts ranting

It’s not about the branes, it’s about the bulk. You were supposed to tell people… Witten is close, but we’re closer.

Minkel doesn’t mention the recent string theory themes in Zippy the Pinhead.

Witten’s new paper with Gukov mentioned here is now available. It is about 160 pages long and generalizes the earlier Kapustin-Witten paper to the ramified case. This involves constructing “surface operators” in the 4d gauge theory, operators attached to surfaces in much the same way ‘t Hooft operators are attached to curves. Unfortunately it doesn’t discuss connections to Khovanov homology that Gukov described in his Strings 2006 talk “Surface Operators in Gauge Theory and Categorification” (I’d provide a link, but the Strings 2006 site seems to be down). The authors also note that Frenkel and Gaitsgory have a “unified approach” to this ramified case, but that “Unfortunately, we make contact here neither with the use of conformal field theory nor with this unified statement. We hope, of course, to eventually understand more.” So, there’s lots more to do…

If you want to get an idea of what it costs to run a theoretical physics center, check out the report of the Michigan Center for Theoretical Physics. The interim director of the MCTP is Gordon Kane, and they will be hosting a symposium next month to celebrate his 70th birthday.

Over at Cosmic Variance, there’s a discussion of the new Martin Scorsese film String Kings, which features “a scene showing work on an extension of the New Jersey turnpike, involving string henchmen (disguised with hard hats and overalls) a large cement truck and Peter Woit.” I guess this doesn’t seem like such a great plot idea to me for some reason. Personally I’ve been thinking that the whole recent controversy over string theory would make a great comic novel. The thing to do is to somehow get David Lodge interested…

Update: The Strings 2006 site is back up, and the Gukov talk mentioned is here.

Update: More about the FY 2007 science budget situation from Science and from FYI.

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### 36 Responses to Yet More Links

1. a says:

“Had he not died so young, Maxwell would almost certainly have developed special relativity a decade or more before Einstein.”

That article states:

“A velocity appeared in his theory also, but with a different numerical value that had no obvious physical meaning. Maxwell plugged Weber’s force ratio into his equations and discovered to his utter astonishment that the velocity exactly equalled the speed of light, which was then known experimentally to an accuracy of 1%. With excitement manifest in italics, he wrote, “We can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.”

This isn’t true, (1) the ONLY numerical value by dimensional analysis using the electric and magnetic constants is was 300,000 km/s, (2) Maxwell did not predict c.

Dr Alan F. Chalmers’ article, ‘Maxwell and the Displacement Current’ (Physics Education, vol. 10, 1975, pp. 45-9). Chalmers states that Orwell’s novel 1984 helps to illustrate how the tale was fabricated:

‘… history was constantly rewritten in such a way that it invariably appeared consistent with the reigning ideology.’

Maxwell tried to fix his original calculation deliberately in order to obtain the anticipated value for the speed of light, proven by Part 3 of his paper, ‘On Physical Lines of Force’ (January 1862), as Chalmers explains:

‘Maxwell’s derivation contains an error, due to a faulty application of elasticity theory. If this error is corrected, we find that Maxwell’s model in fact yields a velocity of propagation in the electromagnetic medium which is a factor of [root 2] smaller than the velocity of light.’

It took three years for Maxwell to finally force-fit his ‘displacement current’ theory to take the form which allows it to give the already-known speed of light without the 41% error. Chalmers noted: ‘the change was not explicitly acknowledged by Maxwell.’

Weber, not Maxwell, was the first to notice that, by dimensional analysis (which Maxwell popularised), 1/(square root of product of magnetic force permeability and electric force permittivity) = light speed.

The whole story is an insult to any physicist of integrity. Fairy tales distorted from historical facts don’t have a place in physics.

Maxwell never wrote the Maxwell equations in vector calculus. He had 20 differential equations and never summarized 4 or 5 key equations, which were written by Heaviside. Hence the doubtfulness of the popular claim made http://www.mathpages.com/home/kmath103/kmath103.htm that Maxwell considered the need for a divergentless field using vector calculus and was led to his discovery in the same way Einstein invented general relativity:

‘Just as the inclusion of the “displacement current” in Ampere’s formula was the key to a Maxwell’s self-consistent field theory of electrodynamics, so the inclusion of the “trace stress-energy” in the expression for the Ricci tensor was the key to Einstein’s self-consistent field theory of gravitation. In both cases, the extra term was added in order to give a divergenceless field.’

The most important thing Maxwell did do, which he isn’t given credit for, is predicting the electron in the 3rd ed of his Treatise on Electricity and Magnetism. (J.J. Thomson, editor of Maxwell’s Treatise, is given credit for discovering the electron when he just measured the charge to mass ratio.)

2. D R Lunsford says:

The claim that Maxwell would have discovered relativity is utter nonsense. There is nothing in Maxwell’s work that even discusses these issues, and with good reason – there were too many other basic problems to work on (and not just in electromagnetism) and no experimental evidence at all for the relativity of simultaneity. And just because Maxwell discovered that light is an electromagnetic phenomenon, this in no way “points forward to Einstein and relativity”. If anything, it points forward to Lorentz. But even that is a stretch. What it does it to point into the mirror – at Maxwell himself, who needs no context other than the one he provided himself.

-drl

3. Daniel Biss says:

I have to say that I don’t really understand Vershik’s argument. The prize had nothing at all to do with stimulating mathematics research in the short term, which he essentially admits in various points in the article; thus, explaining that Perleman didn’t do what he did because of the prize is totally irrelevant.

What the prize did do was to generate a ton of media attention for topology and Poincare. Vershik also addresses this and manages to conclude that it’s a bad thing, mostly by inexplicably trying to blame the prize for the bad behavior of various mathematicians. Um, I guess that’s possible, but I don’t really see it.

Here’s something I did see, though: in the weeks surrounding the Poincare/Perleman media explosion, I had probably more than a dozen long conversations about topology and the conjecture with non-mathematicians in social situations — and I was never the one who brought it up. Sounds like the prize generated press coverage which, in turn, generated a lot of discussions about math. Which sounds like a success to me…

4. Peter Woit says:

Hi Daniel,

I have mixed feelings about it, posted about Vershik because I thought it was an interesting and not often expressed point of view. The main thing about the Clay prize that bothers me is the way it depends on picking a person to give the $1 million to, or even worse, trying to decide how to split it among several people. Great mathematical results almost always involve the efforts of more than one person, with no sane way of assigning percentages to each person’s contributions. If I had my druthers, the way it would work would be for the$1 million prize to be awarded at the point the Clay committee agrees that the problem has been solved (or maybe wait a couple years), but that the money should not go to the people who solved it (who, after all, are likely to be rewarded by the university star system with amounts adding up to over \$1 million). Instead, the comittee would give the money to some organization or organizations that could use it. In the case of Poincare, giving the money to the support of Russian mathematics research might be appropriate.

5. Chris W. says:

Almost any media phenomenon that attracts the attention of millions of people will end up leaving one with reasons to be ambivalent about its effects.

That’s inevitable in a democratic mass culture, with enormous diversity in the exposure of the audience to mathematics, not to mention the diversity of individual temperaments and talents. In the case of the Clay Millenium Prizes it seems quite reasonable that the balance might lean to the negative where the culture of mathematics is concerned, for reasons like those Peter mentioned, while leaning in the positive direction where the general public’s awareness and interest in mathematics is concerned.

Whenever I reflect on the experiences that first excited my interest in the sciences and mathematics, my positive appreciation for them is also mixed with a certain rueful appreciation for their vulgarity or superficiality, as seen in retrospect. It’s enough that one eventually attains that level of understanding and is willing to talk about how one arrived at it. From this point of view there is little point in deploring the original experiences and the ignorance and credulity that might have accompanied them. I’m therefore inclined to agree with Daniel’s apparently positive assessment, but then again I’m not a professional mathematician.

That said, it is just as well that misgivings are publicly expressed, because that can also contribute to public understanding of the practice of mathematics and the motivations for doing it. Any thoughtful person with a genuine interest in the subject can learn from the diverse viewpoints expressed in the discussion of the Millenium Prizes.

6. Turkey Royale says:

Vershik, who is a serious mathematician, articulates a viewpoint not often enough heard in The US (and western Europe?), namely that one studies mathematics or physics or whatever for the love of the thing and the interest in knowing and aesthetic reasons, and that the best mathematics/physics/etc. comes out of research so motivated rather than out of programmatic, externally directed, or practically’ motived research.

Vershik expresses himself with care and with nuance; he is not dogmatic and it was my impression that he takes seriously the motivations advanced by the Clay Institute for its prizes. He certainly does give credit to the motivation of stimulating youths with an interest in math, and he does not disparage the need for educating the general public about math (judging from his extensive professional involvements, he is well aware of the complexities of funding mathematics research). As an aside he seems to want to put on record an authoritative debunking of some of the claims made about Perelman, while still respecting Perelman’s privacy (that is not providing correct information, simply pointing out the incorrect); whether he succeeded, I don’t know, since I don’t know the true state of affairs vis-a-vis Perelman.

Vershik does not agree with Paris Hilton than any publicity is good, whereas many mathematicians in the West’ do. One might crudely summarize his critique as – perhaps amateur pornography is not the best way to promote oneself.

Vershik operates with an implicit distinction between unhealthy interest’ and healthy interest in mathematics. He also worries that placing a priori value on the solution of certain problems accords unnecessarily importance to those problems, and perhaps makes the study of non-anointed problems, or themes, more difficult. By the way, he clearly does not view mathematics as the business of solving problems already clearly posed; I suspect for Vershik the activity of researchers like Gromov or Thurston (who in some sense are anything but problem solvers) is more congenial than was the activity of Erdos, although he respects also Erdos.

His is not a simplistic mathematics for mathematics sake’, although I may have made it sound that way. On the other hand, it seems to me he is implicitly critquing the programmatic, business part of scientific research in particular in the US.

7. plank says:

“Maxwell never wrote the Maxwell equations in vector calculus. He had 20 differential equations and never summarized 4 or 5 key equations, which were written by Heaviside.”

————

actually I think he did manage to summarize the equations using a quaternionic formalism. It’s been quite a while since I’ve read this so I could be wrong.

8. On page 29 of this I expressed similar sentiments to Vershik’s. If the prizes have any effect on mathematicians, it won’t be towards the greater openness to which we aspire at the n-category café.

9. D R Lunsford says:

plank – That is right – that’s what really annoyed me about the relativity statement – it ignored Heaviside, Gibbs, Lorentz, Hertz, Roentgen, and on and on, all the people who discovered the phenomena and developed the theory before Einstein came along and put it all right.

For the record, Maxwell had his own phrases for div grad and curl (convergence, slope, and twirl) and did in fact apply quaternions to his theory, sometime in the early 1870s before his book was published. I don’t recall if it is in the book but I think it is at least mentioned.

However he did not have grad – i d/dt, which you need to really do his theory with quaternions. Had he had that, THEN he would have been one step away from the Lorentz transformation.

-drl

10. Peter Shor says:

Of course, a novel about the string theory controversy (if it’s not one of those postmodern novels) requires some kind of ending. Here are some possibilities.
(1) The string theorists are unexpectedly vindicated by LHC. (Many string theorists clearly are hoping for this ending, even though it seems rather unlikely.)
(2) The hero has a mental breakdown, quits theoretical physics, and writes a semi-autobiographical best-selling novel. (Also unlikely.)
(3) Finer examination of the cosmic microwave background reveals a message from God, in which He reveals the true workings of the universe. None of the competing theories come even close to the right answer. (I’m not betting on this outcome either.)

11. Chris W. says:

At risk of beating a dying horse, I’ll ask yet again what “vindication” of string theory by results from the LHC is supposed to mean, in light of the string theory Landscape, which seems capable of “vindication” by just about any result one pleases.

Is this not the case? If so, why not? My assumption is that the current efforts to statistically survey the structure of the Landscape represent fairly desperate and ever more unpromising attempts to answer these questions. Without such answers the above-mentioned hopes of many string theorists would seem to be simple delusions, regardless of what the LHC reveals.

(All this reminds me of undergraduate attempts to prove some mathematical assertion in the wee hours of the morning, which end pathetically in “establishing” some tautology.)

12. Is there really a Physics equivalent of this?

By definition, a [first order] Celebrity is someone who is famous for being famous. Paris Hilton is a second order Celebrity: someone who is famous for being unjustifiably a first order Celebrity. More and more, morning major network “news” programs feature interviews with second order Celebrities who have appeared on some “reality TV” show on the same network as the “news” program.

Although there have been Physicists who became first order celebrities, although treated as second order, such as Einstein, Sagan, and Hawking, I am not aware of any true second order Celebrity Physicists, aside from TV personality engineers masquerading as scientists, such as Bill Nye Science Guy, and the debate raging about String Theory. Am I wrong?

13. Arun says:

Maxwell’s treatise on electricity and magnetism is viewable on books.google.com

14. Lame says:

Peter:

We are begging, BEGGING you to give us an actual technical argument here; why do you ALWAYS rely on authority when any physics issue comes up? Much easier playing pretend physicist on your blog huh? Sure impresses all your fans, particularly convenient that it requires NO INTELLECTUAL EFFORT OR SKILL on your part! Nice deal.

You remind me of those annoying undergraduates who talk a big game but don’t actually KNOW anything. How about backing up your words with some content for once? Can you do that without running away to Mommy/Daddy/d’Hoker and Phong to bail you out when the discussion requires actual knowledge? Tell us what is wrong with AMS with an argument other than “people who know tell me there is something wrong with AMS”.

Lousy science journalists will fall for your act Peter, but you don’t fool a single decent theorist.

15. Jonathan says:

The files from the strings 2006 talks still seem to be online and at least here in China I can access them.
http://strings06.itp.ac.cn/?id=agenda_arr

If you really can’t see them from the US then e-mail me and I can speak to those in charge of the site.

J

16. Peter Woit says:

Jonathan,

Thanks! The site seems to have just been temporarily down. I’ll add the link to the Gukov paper.

Lame,

Thanks for the hilarious parody of the behavior of Jacques, Clifford, Lubos and various of their anonymous allies over at Asymptotia. Very, very funny!

17. D R Lunsford says:

Arun – that is very nice – I see he does mention quaternions in passing but does not attempt a systematic development (articles 618 and 619 in ch IX). That is good because none was possible. It does make one wonder if he had considered adjoining d/dt to grad.

-r

18. Ari Heikkinen says:

“Vershik argues that these million dollar prizes are not good for mathematics”

I couldn’t disagree more. I mean, if there’s a million dollar prize, it’ll make the brightest minds pursue those ideas worth the prize.

I think the most useful problems to the human kind should have prizes worth even more.

Surely, even Peter, as a mathematician, would gladly work on something worth a million dollars prize, if that’s something he’d have a good intuition to work on.

19. Ari Heikkinen says:

And my only hope is that Peter Woit and Brian Greene can go have beers and disagree with respect.. 😉

If they can’t, then science isn’t probably worth any funding from the government’s perspective..

20. Peter Woit says:

Ari,

I’m not so sure the million dollars makes much difference on whether people work on these famous, high-profile mathematics problems. If I thought I had a good idea about how to solve one of them, I’d work on it, even if it didn’t have the million dollars attached. Unfortunately I don’t have any promising ideas about any of those problems, so it’s not an issue….

And don’t worry, I and Brian have never had a problem disagreeing respectfully, and this is true of just about all the string theorists I know. The weird unprofessional behavior of a small number of them in response to scientific disagreements has very much surprised me in recent years.

I’ve posted here several times, because I hang out here quite a bit; because I appreciate whatever it is that I appreciate about it…

But, for whatever reason, it seems appropriate at this juncture to say that as far as I am concerned NEW is well worth the effort and not *just* because I have similar dispositions to concerns in, for a complete lack of anything better to call it, the philosophy/economics/policies of today’s physics but because I find this blog to consistently be a collection of excellent / affordable / cogent pieces of writing about topics I find fascinating. It’s damn good blogging… is what I’m saying!

But, I think it speaks volumes that unnecessarily aggressive posts repeatedly appear here. Not that authors shouldn’t think twice about their statements: This is the internet afterall and we all speak freely here. Instead, the record speaks for itself.

22. Neville says:

In my experience, much of the general population views mathematics as a dead subject, which reached its zenith with the discovery of long division. Many scientists and engineers of my acquaintance seem to think mathematical discovery was finished in the 19th century. The Clay Millenium Prizes publicize mathematics as a living subject. Perhaps some youngsters will find inspiration in the notion that mathematical mysteries abound.

23. mathjunkie says:

The author of the article speculates that “Had he not died so young, Maxwell would almost certainly have developed special relativity a decade or more before Einstein.”

What is the basis of saying that?

24. The January AMS Notices now has online a letter from Birman on the Yau-vs.-New-Yorker controversy.

25. I Care says:

The entire academic community needs to police itself (field by field) to ensure that the same (more or less) review process be applied to every paper submitted to a particular journal, regardless of how influential/famous/well-established its author(s) or editor(s) may be. That may sound a bit idealistic, but if one is not, one shouldn’t be working in the ivory tower anyway. Academic politics is oxymoronic to me, if the area one studies is indeed objective and rigourous.

26. Peter Orland says:

I Care:

If large communities of people police themselves, they will
soon become victims of police brutality. Academic freedom
has drawbacks; nastiness, unfairness, etc. But policing academic
communities (even self-policing) will have ten times as much
how it would be with acedemic aristocracy.

27. Moeen says:

Peter,

I’m not sure how you come to your conclusion. What’s wrong with setting ethical standards in academic communities and making sure there are consequences for people that violate those standards regardless of their fame or influence? I don’t see how this would create an “academic aristocracy”, this is about ethics, not politics, and with few people outside academic communities with an interest in policing them, self-policing seems like a pretty good idea.

28. Peter Orland says:

Moeen,

There are such ethics. There are consequences. I know
pesonally of cases where famous people have had their
papers rejected because they did not meet certain standards (unfortunately, I can’t tell you who who). There is peer
review. Sure, the system isn’t perfect. But yes, it IS about
politics.

In free academic communities, just as in free societies,
people often get away with unethical behavior. This problem
won’t be cured by imposing more control. A “self-policed” academia is inevitably going to be policed by some selves
and not by other selves.

What people who advocate more control on any
society overlook; in a more rigorously-policed society, just
as in a self-policed state, MORE people get away with WORSE unethical behavior. Rigorously-policed societies have more corruption, not less.

29. Moeen says:

Peter,

I’m not sure what you had in mind by self-policing, but all I was aiming for was merely setting higher ethical standards for the entire community. It won’t help if only some parts of the community impose higher standards an others don’t, there has to be a consensus.

It is because the mathematics community failed to uphold better standards for themselves that, as Joan Birman said, “the entire profession has received a very public and very bad mark.” If academic communities fail to do so in the future, the loss is their own.

I don’t think the analogy to police-states is a good one since the only examples of such governments I’m aware of are usually responsible for various human rights violations. Regardless, I was not trying to promote the academic equivalent of a police-state, as that would have just been silly.

30. Maroc says:

Of course, a novel about the string theory controversy (if it’s not one of those postmodern novels) requires some kind of ending. Here are some possibilities.
(1) The string theorists are unexpectedly vindicated by LHC. (Many string theorists clearly are hoping for this ending, even though it seems rather unlikely.)
(2) The hero has a mental breakdown, quits theoretical physics, and writes a semi-autobiographical best-selling novel. (Also unlikely.)
(3) Finer examination of the cosmic microwave background reveals a message from God, in which He reveals the true workings of the universe. None of the competing theories come even close to the right answer. (I’m not betting on this outcome either.)

31. Peter Orland says:

Moeen,

How can the community impose (your word, not mine) higher standards without leading to abuse of authority? My point is
that the current system is flawed, but it does work. As long
as journal editors, referees and reviewers are human, there
will be mistakes and abuses. Do you really think this can be
resolved by some new system of authority?

The consequence of imposing good science is bad science,
just as the consequence of imposing good art is bad art.

32. Moeen says:

Peter,

I still do not see how if the community as a whole decides to set higher standards for everyone, then that would lead to an abuse of authority. All this means is that no matter how much influence you have, you’re still subject to the same rules as everyone else. Sure the system works, but that doesn’t mean it can’t be better. There doesn’t have to be a new system of authority just an improved one.

The analogy to art doesn’t work because what makes “good” art different from “bad” art can be pretty subjective, whereas in science, and certainly math, there’s a very clear difference: good science is accurate, bad science isn’t.

In any case, as far the events that Birman was referring to, Yau violated the normal peer review process by pushing the Cao-Zhu paper into the AJM journal by bypassing the editors, and no one called him on it. As a result, they seemed to be implying that they were okay with this kind of behavior, damaging the integrity of the profession. Seems like Yau is the one responsible for an abuse of power here, not anyone else.

33. Peter Orland says:

Moeen,

I don’t think we are going to agree on this, so this is my last
effort against more stringent control of science, though I am

How is this the system of authority going to be improved? I don’t
see how to do it reasonably. The final authority is the scientific community. As long as the main goal of people in that community
is the truth, that is the best authority. Changing the power structure
will make things worse, not better.

I still think my anology with art is a pretty good analogy.
Consider how poor the general quality of science, as well as art
has been under totalitarian regimes (they both fare somewhat
better under authoritarian regimes, but not well).

It seems to me that the system worked very well on the
Poincare-conjecture affair. The Cao-Zhu paper was published, as
you say, but the reaction of the math community is clear. This
is a simple matter of democracy in action.

34. Jeff Holtz says:

Peter,

I agree. The math community has responded quite effectively to the manner in which the Cao/Zhu article was published. But, I don’t think it has responded very effectively to the downright plagiarism of Lemma 7.1.2 .

This document clearly shows that it was not just a accidental side step, but deliberate copying from Kleiner and Lott. I’d be interest to hear opinions on why there has been such a tempered response.
See this file:
http://www.cds.caltech.edu/%7Enair/pdfs/CaoZhu_plagiarism.pdf