John Baez has a new issue of This Week’s Finds. He has a lot of interesting things to say about Euler characteristics and how you measure sizes in a category. Among many things I learned from Graeme Segal when he was here last semester was the idea of thinking of the Faddeev-Popov prescription in the path integral approach to gauge theory as reflecting the fact that one should think of gauge fields as a category. The category is the category whose objects are bundles with connection, and gauge transformations are the automorphisms of these objects. The general principle that when you count objects in a category you need to divide by the number of automorphisms provides a sort of motivation of the Faddeev-Popov calculation.

The US FY 2007 budget situation for math and science, which was looking very bad just recently, has taken a huge turn for the better as the House has voted to increase funding for the DOE Office of Science and the NSF. More information about this here, here, here, and here. Looks like Fermilab and RHIC will emerge from the budget process unscathed. Soon the president’s FY 2008 budget proposal will be unveiled, and we’ll see what the new Democratic majority will do about science funding.

This week’s press release announcing a “test of string theory” is from the University of Wisconsin (also here, here, and undoubtedly elsewhere). It’s no competition at all for last week’s spectacular press releases about “string theory tests”, but like the many other examples of the genre it is designed to make claims about string theory highly likely to mislead unsuspecting readers. I made some comments about this here. It’s not really that hard to come up with these “tests of string theory”, since “string theory” now has been invoked to justify studying a huge variety of different kinds of models, and is compatible with just about anything. All you have to do is find one, no matter how complicated, obscure and lacking any evidence or motivation, where you can choose the parameters so as to create effects not visible to current experiments, but perhaps visible to potential experiments, even ones many decades down the road. Without too much trouble you should be able to get a paper about this published, and at that time your university press office will surely be happy to put out a press release for you announcing that “Researcher(s) at University X have discovered a way to test string theory.” This has been going on for years, and people seem to never tire of it.

Sean Carroll seems to find it amusing that many articles on the arXiv can now be thought of as a new form of performance art. John Horgan, who got a lot of grief years ago for accusing physicists of engaging in “ironic science”, should really enjoy this.

**Update**: The Distler et. al. media juggernaut rolls on, informing the world that : The LHC, due to be finished by and running by the end of the year, may rule out the string theory, as well as the work by Distler and his colleagues offers something profound – a way to actually test string theory, and that if Distler’s bounds are satisfied, it would provide a weak support for string theory. The last article quotes Distler to the effect that string theory is just an “effective theory”, which I’m sure will clarify this for the public.

**Update**: The Shiu et. al. “test of string theory” press release has also led to lots of misleading stories. For an example check out Physicists devise test for string theory, where you’ll learn that “the University of Wisconsin theorists predict that upcoming experiments on the European Space Agency’s Planck satellite will have the sensitivity needed to prove the case for string theory.” Somehow I suspect string theorists will not give up on string theory if the Planck data doesn’t work out, and there won’t be any press releases…

I do find it amusing, although (of course) it has nothing to do with “many,” or “now,” or irony, etc etc.

FaDDeev

It would be great if you have a chance to report more on Segal’s Eilenberg lectures.

Sean Carroll actually wrote about arXiv “Poetry” as opposed to “many articles on the arXiv can now be thought of as a new form of performance art” as summarized.

Here’s the difference: the paper (whether on the page or electronically published) can be poetry. The presentation at a conference (and on digitized video) can be performance art. Some physicists write great papers but give boring, confusing lectures. Some write trivial papers but give exciting oral presentations. A handfull (again, I’m a protege of Feynman, and coauthored poetry with him) can do both outstandingly well.

Over in the Math world (but he also did Physics) Sato won the Wolf prise, but was famously bad at presentations, so that his work was essentially ignored for many years, despite his time at the Institute for Advanced Study.

Peter

It is good that mathematicians are thinking about

how to study gauge-orbit space, via stacks or

category theory, or whatever they think is

useful. Having said that, the best progress on

this front (in the last ten years), has been made

by physicists.

There are ways to parametrize orbit space which are

more effective than the old methods – Karabali and

Nair deserve some credit for this, and I will claim some

for myself as well. It is now clear how to solve Gauss’s

law in axial gauge for a lattice gauge theory. So far

these techniques physicists have developed have been

applied only to 2+1-dimensional QCD, but we all thinking

hard about 3+1.

It’s always good to have new points of view, but mathematicians

working on this problem might do well to familiarize themselves

with the progress made by the small community of physicists who

still work on non-perturbative methods.

Eli,

Thanks, fixed.

Sean,

Sorry for any misrepresentation of your views. Maybe I’m just in a lousy mood today, but the kind of thing you are finding amusing here I find depressing.

“Performance art” or “ironic science” are nothing but euphemisms for fraud. If one does not believe in the scientific merit of one’s projects one is committing fraud whenever one applies for funding and whenever one delivers a report on these projects. That is not a question of personal opinion. Any judge is well aware of this.

Fundamental physics is not merely in a crisis, it has ceased to exist. At some point it will need to be completely rebuilt on an entirely new foundation. But can do that when the entire field has been taken over by frauds, conmen, Witten adulators and Einstein heir wanna-bes? Everything is suffocated by an atmosphere of dishonesty, fundamentally faked convictions and the need to keep silent about the most obvious facts that rule out the b—s— to avoid losing the funding. Today, fundamental physics is nothing but lies in order to preserve funding and employment.

It never occurred to me that one day I would have to be ashamed of being a theoretical physicist.What honest physicist could let any Ph.D. candidate pass who cannot debunk 99.9% of the subject matter of today’s “research?” And if someone spells out this truth, he finds himself publicly contradictedby people of whom he knows perfectly well that, in private, they agree with him completely.If Sean had given no clue that this was in fact a real abstract, I would have assumed that it was either a joke or fake physics babble in a science fiction story. I wonder what would happen to a math paper submitted to arXiv with an abstract that read like this.

Thanks for the plug! Euler characteristic and homotopy cardinality are really cool, and I love how Leinster has begun unifying them using the notion of the Euler characteristic of a category.

I first ran into the idea of “dividing by the number of symmetries” when learning how to compute Feynman diagrams. At the time I thought it was really weird. Why should a more symmetrical thing count for less. Later I saw it made sense and was part of a big story involving groupoid cardinality and ultimately homotopy cardinality.

By the way: I don’t think Sean was trying to list abstracts that qualify as “performance art” or “ironic science”. The first one, by Jackiw and Pi, looks like good solid condensed matter physics (at first glance anyway).

John,

The counting for Feynman diagrams with symmetries is Segal’s favorite example of the principle. I was less impressed by this than the Faddeev-Popov idea, since Feynman diagrams are pretty much completely understood, whereas the non-perturbative quantization of gauge theories still seems to me to be something we haven’t gotten to the bottom of (as Peter Orland also notes).

It’s also intriguing to me that there are these generalizations of the “counting in a category” idea that seem to apply to spaces and use volumes (not just counting). I first saw this idea in the long Atiyah-Bott paper on Yang-Mills on Riemann surfaces, where they note interesting relations to Tamagawa numbers. This has always intrigued me, never known quite what to make of it…

About Sean’s posting: I just mentioned it because I was very much struck by how he was amused by and seems to think highly of something like studying brane cosmologies where the branes “zoom and twirl around like multi-dimensional figure skaters”, whereas this seems to me a typical example of what’s wrong with theoretical physics these days. Nothing against this paper in particular, but the fact that there’s a huge subject of research out there so outlandishly speculative and divorced from standard notions of scientific testability is not funny.

First, I loved John Baez’s latest posting about Euler characteristic of a category. Coincidently, I had just supplied my wife with some material on Euler characteristics for a Physics course she was teaching to university students majoring in fashion design. I supplied pages from B. Datta and A. K. Upadhyay, “Degree regular triangulations of the double torus”, Forum Mathematicum, 18(2006)6, pp.1011-1025. These are to be treated as clothing patterns to be cut from cloth and sewed with edges identified, and the genus of the 3-D finished assemblage observed; after first sewing patterns for Platonic solids, asked to fill out a table of numbers of vertices, edges, and faces, and being led to discover Euler’s formula for convex polyhedra.

Second, “If one does not believe in the scientific merit of one’s projects one is committing fraud whenever one applies for funding and whenever one delivers a report on these projects.” Fraud is defined on nolo.com as “Intentionally deceiving another person and causing her to suffer a loss. Fraud includes lies and half-truths, such as selling a lemon and claiming ‘she runs like a dream.'”

Bringing funding into the picture allows one to determine a specific dollar figure for damages. But who has “standing” to sue? Whose ox is gored? A friend of mine was several consecutive years denied funding for an astronautical engineering concept he’d presented at conferences, then on his web site, and finally as an award-winning refereed paper in an engineering journal. The next year, another person (PhD in Physics) won exactly the Federal grant in question, for substantially the same material, even using the keyword which my friend had in fact coined and first published. The grant-winner (as I witnessed) both admitted and denied having read my friends’s earlier work, could not explain where he got the keyword for the title of his grant application, and has been extremely hostile my friend and me subsequently. The grant in question was $75,000. My friend hired an attorney, who cocluded that proving fraudielent intent was allmost impossible, that intellectual property rightd were diminshed by open online and journal publication, and that the matter was not worth pursuing in court. My conclusion: the well-publicized frauds in science are about faked research data. The less-publicized but more common are about “lies and half-truths” and theft of intellectual property, but that these are diffult to pursue in court.

Remember the Math teacher who sued McDonalds, disputing how many billions of burgers had been sold? The judge agreed with the arithmetical argument, but denied that the teacher had been injured through the lies or half-truths, and thus had no standing to sue or prevail.

For string Theory, to use the Talmudic formulation, “whose ox is gored?” How can a Physicist hope to prove in court that he or she has been actually damaged by being denied hiring, promotion, tenure, or grants?

The damaged parties are the federal government as represented by the funding agencies like the NSF and the DoE. I don’t see how it is much different from, say, welfare benefit fraud or tax fraud.

“The Distler et. al. media juggernaut rolls on, informing the world that : The LHC, due to be finished by and running by the end of the year, may rule out the string theory, … the work by Distler and his colleagues offers something profound – a way to actually test string theory”.

So if this is true, a genuine test as advertised, then if it comes out negative, presumably Distler, Green, Greene, Motl, Johnson, et al. will all give up string theory and do something else.

Does anyone believe that??? Not likely!

String theory would make a strategic retreat to higher energies…

When theories retreat to higher and higher energies when confronted with experiment, they are probably wrong. Or not even wrong.

Why are you in such a lousy mood, Peter? Did your research suffer a setback?

Michael,

Nope, research is fine, but progress is slow. I’m spending a lot of time working on the graduate course in representation theory that I’m teaching. It’s time well spent since it is giving me new ideas and deepening my understanding of the subject. Always a pleasure to hear from charming anonymous string theorists such as yourself…

The Feb 5 issue of Time magazine includes a full-page article under the banner

“The Geometry of Music: A composer has taken equations from string theory to explain why Bach and Bebop aren’t so different”.Tymoczko has gotten a lot of coverage in the press over the past few months (for reasons that aren’t obvious to me), but I’m just now noticing how prominently the “string theory” angle is being played. According to Time,“Borrowing some of the mathematics that string theorists invented to plumb the secrets of the physical universe, he has found a way to represent the universe of all possible musical chords in graphic form”.They note that Tymoczko, a composer from Princeton University, is the first music theorist to have a paper published in the journal

Science. His idea, for those who have somehow not heard about it yet, is that the universe of chords consists of “weird multi-dimensional spaces known as orbifolds”. The simplest chords, consisting of just two notes, reside in a space like a Mobius strip. More complex chords“inhabit spaces that are as hard to visualize as the multi-dimensional universes of string theory”.Harvard Magazine reports that

“Tymoczko spends time with scientists and it was a physicist who suggested the orbifold upon hearing his description of the musical map’s properties. Tymoczko notes that physicists are forever using music as a metaphor for their work; now, he says, music can reciprocate.”This article goes on to say Noam Elkies helped Tymoczko with the math.It occurs to me that this might be bigger news than people have realized. For years, string theorists have lamented the fact that “we don’t really know yet what string theory is about”. Maybe now we know. It isn’t a theory of physics at all… It’s about music! Or more specifically, it’s a way of encoding traditional musical styles and pleasing chord progressions. But seriously, to the extent that “orbifolds” (in the sense used by Tymoczko) were invented by string theorists, this seems consistent with my impression that the mathematical machinery of string theory is actually a giant curve-fitting framework of almost limitless flexibility that can be fit to almost any subject. Does this marvelous applicability of mathematical techniques to music theory imply that this is the true final theory of music? Or is it a case of “When you have a hammer, every looks like a nail”? Interestingly, though, Tymoczko acknowledges that his theory won’t really help anyone write better music. It essentially is just an attempt to represent formally some of the knowledge that composers have always known intuitively. Oddly enough, all the articles talk about chords, but none of them talk about rhythm, timbre, or any of the other aspects of music.

I am the writer of one of the last articles quoted and I have a few issues that I would like to see clarified.

Firstly, Distler’s meaning is not correctly interpreted in this quotation. I quote from the article directly:

– “Distler said that a successful outcome in the experiment, however, should not be seen as anything more than a weak support for string theory. The results of the experiment can effectively rule out certain quantum field theories but not serve as verification.”

The full quote speaks for itself.

Secondly, an “Effective Field Theory” is not simply a field theory that is ‘effective’. The reason why the article specifically placed these words in quotations is because it is a specific term referring to an approximate theory describing physical phenomena. I would hope the authors do their research adequately before quoting in a manner meant to misconstrue others’ opinion.

Thank you.

Amos,

I stipulate that absolutely nothing of any denotative content about string theory (which is not a theory) has ever been or could be conveyed to anyone who is not a physicist or a mathematician (or graduate student therein). There is absolutely no shortcut around the shift in the conception of physical reality of 1926 (and the less drastical ones between then and 1974). The physics illiteracy of the general public is a necessary condition for the rise of propagators of patent nonsense to the echelons of academia. People not just don’t know anything about it, they don’t even know enough to be aware that they don’t know anything. (That includes anyone who doesn’t know about Lagrangian and Hamiltonian mechanics.) And this won’t change until it is acknowledged.

String theory is the tantrum that spoiled rotten brats throw because they had to face the reality that they are not the

Übermenschenthat their inferiority complexes compell them to see themselves as.You have all heard of NURBS: nonuniform rational B-strings.

Jun Xian,

Seeing WW scattering that satisfies unitarity, Lorentz invariance and analyticity would not in any sense provide weak support for string theory. It would say nothing at all about string theory one way or another, and Distler’s claim otherwise is just dishonest and intentionally misleading.

I know what an “effective field theory” is. Your text contains several inaccuracies about the relation between string theory and quantum field theory. It is not true that “String theory is the most successful of various quantum field theories..”, string theory is not a quantum field theory. It is also not an “effective field theory”. It’s not surprising that you’re confused about the relation between QFT and string theory, given that Distler et. al. have been on a campaign to try and confuse the issues in this case (their results apply to QFT, have nothing to do with string theory).

Instead of repeating unskeptically misleading claims about the significance of his work by a scientist, it would have been a good idea in your reporting to consult some other particle theorists than the authors of this paper, in order to see see if the author’s claims are supported by their colleagues in this field.

Some further details on “dividing by the number of symmetries”… The “general principle” mentioned by Peter and John sounds a lot like old-fashioned Polya-Burnside enumeration. (See John’s “Week 147.”) The “big story” paper mentioned by John is “Categorified Algebra and Quantum Mechanics, by Jeffrey Morton, which cites two papers by Joyal dealing with the combinatorics of “structure types” (as does John’s “Week 185”). For details of the connection between old-fashioned Polya-Burnside enumeration and Joyal’s structure types, see a 1999 dissertation, “Graphical Enumeration: A Species-Theoretic Approach,” by Leopold Travis. The Travis paper is pure mathematics rather than physics, and so may appeal to a wider audience than the “big story” paper.

Well, if you understood what an effective field theory is, perhaps you should not have stated “The last article quotes Distler to the effect that string theory is just an “effective theory”, which I’m sure will clarify this for the public.”, which is a rather overt attempt of yours to mislead the public, in my opinion.

Not to mention that I clearly stated in my article that Distler’s words were to the effect that it could ONLY serve as a refutation if the WW scattering did NOT satisfy the bounds. Looked at from a different angle, failure to disprove can be taken as an extremely weak support.

I admit to making some technical mistakes in the article, which have since been corrected. However, I do not appreciate the exploitation of my personal failure at understanding as a method to attack Distler’s work.

I have nothing for or against either side of the issue. As such I have no quarrel with you concerning the truth of his theory or otherwise. I simply would not like my article to be misquoted and hence cause undue misrepresentation of Distler’s work, no matter it’s value.

Thank you.

Jun Xian,

My quotes from your article were accurate, and included a link to the actual article so that anyone who wanted to could see them in context.

Now you’ve turned the “weak support” from your article into “very weak support’. Again, the accurate statement is that if these bounds are satisfied, this has nothing to do with string theory. It would not provide “weak support” or “very weak support”, it would have nothing to say at all about the subject.

I don’t blame you for technical mistakes. This is a difficult subject and non-experts are going to have trouble understanding it. The inaccurate statements in your article seem to me to be the direct result of Distler’s misleading you about the significance of his work.

Amos Dettonville,

Tymoczko’s father was a sort of logician/philosopher of mathematics and his sister is an assistant prof in math at Michigan. This might be the simplest explanation for any affinity he might have for mathematical ideas.

I know this is a bit off the topic, but your title is Odds and Ends and I could not resist…

Is this what Lubos is driving these days?

http://www.toyota.com/vehicles/2007/matrix/m_theory.html

the add says ” a theory you can’t wait to put to test! ”

Has anyone studies the impact of string theory on consumer products yet, or vice-versa?

Hesitated to mention Tymoczko’s paper because it leads to such an obvious swamp of pseudoscience. The ultimate end point is Keely’s Sympathetic Vibratory Physics:

http://www.svpvril.com/musicuni.html#TOP%20musicuni

And of course Bruce Cathie’s series of ufology books, including “The Harmonic Conquest Of Space” (1998):

http://www.amazon.ca/s?ie=UTF8&rh=n%3A952076&page=15

Tymoczko’s twaddle is such obviously vacuous pseudoscience it requires little discussion. But the fact that Tymoczko saw fit to trumpet some alleged connection with string theory seems ominous. It suggests the thin membrane (or should I say “brane”?) which separates mathematically valid but entirely speculative science from “that Serbonian bog,” as John Clerk Mawell remarked in his Rede Lecture of 1876, “which has swallowed whole armies of scientific music-makers and musical men of science.”

I suppose we must draw a distinction twixt speculative untestable nonsense which is nonetheless based on known laws of physics and contains valid mathematical procedures (though never leading to a testable calculation) and the outright gibberish purveyed by the John Keelys and Hans Keysers and Bruce Cathies of the world. But frankly, if you can’t test any of it, I don’t care for such fine distinctions.

Incidentially, there’s a veritable Himalayan mountain of musical pseudoscience dealing with harmonics and eigenfucntions and various and sundry crackpottery. Tymoczko is just the tip of the iceberg.

http://www.altered-states.net/barry/update95/index.htm

http://www.sacred-texts.com/eso/sta/sta19.htm

http://www.sacredscience.com/archive/Kayser.htm

And so on. A tidal-wave-sized sewage spill of superstition masquerading as a mathematico-musical “theory of harmonics.” Classic neo-Platonic number mysticism, acoustical gematria pure and simple. Perhaps string theory could be renamed “cosmological gematria”…?

I suppose you need a compact vehicle to navigate the compact dimensions. And you would need pretty good cornering to handle the 10^-35 m (or thereabouts) radius. No doubt Toyota have thought of all of that.

King Ray Says:

February 5th, 2007 at 4:26 pm

“When theories retreat to higher and higher energies when confronted with experiment, they are probably wrong. Or not even wrong.”

Strictly speaking, the alchemists were NOT WRONG, even if they never did find the Philosopher’s Stone

– Lead CAN transmute to Gold.

Upon discovering thorium changing to radium, Rutherford said to his assistant.

“For Christ’s sake, Soddy, don’t call it transmutation. They’ll have our heads off as alchemists.”

About 60 years later, Gold was produced in reactors. Without a handy Supernova, you’ll never make a living at it though.

Has anyone studies the impact of string theory on consumer products yet, or vice-versa?It is not yet as successful as cold fusion.

I’ve been aware of the connections between music and mathematics for a long time. Back in 1999 I was walking through a university book store and saw a book on harmonic analysis in the music section. I already owned the book, so I put it in the mathematics section. The next day, it was back in the music section. I returned it to the math section. The next day, it was back in music at which point I gave up.

Thomas Love,

You should have affixed a Post-It Note (or something) that sarcastically suggested to the bookstore staff that they open the book and flip through a few pages before jumping to conclusions about the subject matter. Then again, it probably wouldn’t have helped……

It seems that in the minds of many people, including many journalists (and even, I suspect, more than a few mathematicians) that theoretical physics and mathematics have become an undifferentiated mush.

An interesting question: How does one explain to somebody that applying an aspect of a physical theory’s

formalismto a problem in an otherwise unrelated field is not the same as applying the theory to said field, and that identifying and characterizing the abstract structures underlying such cross-applicable formalisms is what mathematics—as opposed to the natural sciences that employ mathematical formulations in their theories—is all about.[By the way, Dmitri Tymoczko evidently has a sister who is a mathematician (Michigan).]

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