Short Items

  • Erica Klarreich at Quanta magazine has a wonderful profile of Peter Scholze. Scholze has been busy revolutionizing various parts of arithmetic geometry in recent years, and the article does a good job of giving some of the flavor of this. I noticed this morning that Scholze has a new preprint out, about a q-deformation of de Rham cohomology, so that may be the latest, hottest news in the subject.

    The new paper was written for the occasion of his acceptance of the 2015 Fermat Prize. Another Quanta piece makes the obvious point that we already know who one winner of the 2018 Fields Medal will be. While Scholze has been awarded a fair number of prizes already, it’s interesting that he’s not universally in favor of the prize phenomenon: see here for some discussion of his decision last year to turn down one of the 2016 Breakthrough Prizes.

  • In addition to being a great mathematician, Scholze also seems to be a fine human being. The AMS Notices this week has an interview with another such mathematician, Robert Bryant, who is now the AMS President, recently head of MSRI. Unlike Scholze, I’ve had the pleasure of getting to know Bryant a little bit, since he was a visitor one semester here at Columbia. The Notices article explains his interesting background, which is somewhat unusual for an academic mathematician. The math community is lucky to have leading figures like him combining mathematical talent and excellent personal qualities.

    I first heard about him back when I was a post-doc at Stony Brook, trying to learn more about mathematics and the math community. At some point I asked Claude LeBrun (a young geometer then, now an older one, with a conference in his honor next week in Montreal) who he thought the best young geometers were. He told me about Robert Bryant, and when I asked “why him?”, his answer was “He’s read and understood all of Cartan”. I wasn’t sure whether to take that seriously, but from the AMS interview, he was quite right about that.

  • For one last piece of mathematics news, fans of geometric Langlands may want to take a look at the new preprint by David Ben-Zvi and David Nadler on a Betti form of geometric Langlands.
  • Turning to physics, last week UCLA announced a $11 million donation to fund a Mani L. Bhaumik Institute for Theoretical Physics at UCLA. As NSF funding for theoretical physics stays flat or declines, at least in the US it is private funding like this that is becoming much more important.
  • At CERN the LHC has reached design luminosity, and is breaking records with a fast pace of new collisions. This may have something to do with the report that the LHC is also about to tear open a portal to another dimension. Not clear why people are worrying about the 750 GeV state with this going on.

Soon heading North for a week-long vacation, blogging likely slim to non-existent.

: For geometric Langlands fans, this and this on the arXiv from Dennis Gaitsgory tonight.

Posted in Uncategorized | 4 Comments

Some Ancient History

A couple months ago there was a session at an APS meeting with the topic Sidney Coleman Remembered. Slides are available for talks by Coleman’s student Erick Weinberg and colleague Howard Georgi. Georgi has recently posted a written version of the talk here. He also a few years ago wrote this biographical memoir about Coleman for the National Academy of Sciences.

David Derbes and collaborators [see comment section for details] are putting together a book version of Coleman’s famous lectures on quantum field theory, hope to be finished with this by the end of the summer. I’ve helped out in a very small way by sending them a scan of my notes from when I took Coleman’s course very long ago.

This will be a great resource for anyone learning QFT and, in the meantime, if you don’t have a copy of Coleman’s Erice lectures, Aspects of Symmetry, you should get one. The period of these lectures spans the late sixties and seventies, and at the time they were required reading for everyone, giving every couple years a lucid explanation of the most important new ideas in the field. The last (1979) lectures are about the 1/N expansion, and I notice that Coleman extensively credits Witten, who was a postdoc at Harvard at the time. A couple years later, Witten in some sense took over from Coleman, lecturing about supersymmetry (a topic Coleman never warmed to) at Erice in 1981.

Last Friday at CERN there was an event devoted to the 40th anniversary of supergravity. Coleman makes a couple appearances, with Sergio Ferrara claiming he was responsible for the name “gravitino” and Peter van Nieuwenhuizen quoting him as saying

I am uninterested in gravity, and superuninterested in supergravity.

One reason for this was surely the ferociously technical difficulties of constructing supergravity, with Coleman not interested in difficult calculations. Another was likely a lack of interest in topics with no known relation to experiment, which likely had to do with his comments about both gravity and supergravity. At the CERN event, Albert De Roecke’s presentation, Desperately Seeking SUSY, reviews the long story of the failure of SUSY and supergravity to make contact with experiment, including a New York Times 1993 article about the failure to find SUSY at the Tevatron. It has extensive detail about the unsuccessful searches at the LHC.

De Roeck also includes a copy of David Gross’s 1994 bet with Ken Lane that SUSY will appear at the LHC (when at least 50 inverse fb have been accumulated). Gross will likely have to pay this off next year, but another such bet just came due on June 16th, so a group of theorists should by now be buying expensive cognac for their more prescient colleagues.

Posted in Uncategorized | 24 Comments

Rumor Mongering

Since I don’t see why Resonaances should have all the fun, I guess I’ll post something here about the big upcoming news of the summer: is the 750 GeV diphoton bump still there in the 2016 LHC data? We’re very soon about to hit a major fork in the road for high energy physics: if the bump is there, the field will be revolutionized and dominated by this for years, ft it’s not, we’re back to the usual frustrating grind.

Last year’s tentative signal was based upon 3.2 inverse fb of 2015 data, and as of today the experiments have over 6 inverse fb of new 2016 data. One can guess that within ATLAS and CMS, plots have started to circulate of preliminary analyses of some sizable fraction of the new data, and some number of people now know which fork we’re headed down, a number that will grow to 6000 or so in coming weeks.

If you’re not one of those, you could try accessing this data indirectly, using a model of how the CERN administration works. According to this presentation at LHCP this past weekend

the next major update of physics results from the LHC is at the ICHEP 2016 Conference, August 2016, Chicago


CERN management is in regular contacts with the experiments’ Spokespersons. It is agreed that any significant (i.e. discovery-like) result (such as the 750 GeV bump becoming a signal or other) has first to be announced in a seminar at CERN.

No detailed schedule yet for ICHEP, but the first day of plenary talks there is scheduled for Monday August 8. My CERN-modeling suggests that the two forks in the road will correspond to the following two possibilities

  • A “special seminar” in Geneva mid to late July, where a “discovery-like result” will be announced jointly by the CERN DG and the two experiments.
  • A pair of seminars in Chicago on August 8 or shortly thereafter showing off bump-less plots. Much of the drama will be gone by then, since not all 6000 physicists will have kept quiet, and everyone will realize that if “discovery-like” was going to happen, it would have happened earlier.

It may become clear which fork we’re taking relatively soon, since the “special seminar” route takes some planning and will get announced in advance. If there’s no such news by mid-July I think it will be clear we’re headed down the boring fork in the road.

Unfortunately, life being what it is, that’s the most likely one anyway. To supplement this CERN-administration-modeling, you can watch the comment section at Resonaances, where rumors of no bump have already started to appear…

Update: Now, it’s an official rumor (since it’s on Twitter). I can add to this that, of the rumors I have heard, there have been no rumors that this official rumor is not an accurate rumor.

Posted in Experimental HEP News | 39 Comments

String Sociology

If you’re interested in the various sorts of internal divisions these days among people doing what gets called “string theory”, you might want to take a look at this blog entry and the discussion there with string phenomenologist Joseph Conlon.

Back in 2002 or so when I started writing my popular book, it was a lot clearer what the term “string theory” meant and who counted as a “string theorist”. If I were writing about this today, there would be a much more confusing situation to try and explain. There’s still a conventional “string theory” story about a supposed theory of everything based on quantized strings often told to the public, but it no longer corresponds much to what researchers who call themselves “string theorists” are actually doing.

To get some better picture of this, it might be a good idea to take a look at the big string theory summer conferences. The biggest is Strings XXXX, this year in Beijing, about six weeks away. No talk titles available yet, but in recent years one clear pattern has been that most of the talks have little if anything to do with the “string theory” of the textbooks (4gravitons tries to categorize things here) . These conferences have been going on for over 20 years.

Since 2002, there has been a breakaway conference, String Phenomenology 20XX, which I think Conlon characterizes accurately as follows:

one reason the String Pheno conference was founded was because people working on pheno topics weren’t getting a look-in at the Strings conference and so set up their own conference. I think the Strings conference is most accurately regarded as the Princeton view of the world (broadly, every year it reflects subjects popular at the IAS and a couple of other similar places).

Generally, the ratios vary with place. A small fraction do string pheno in the US, a significant number in Europe, almost none in India, quite a few in Korea…

This year’s version of this conference has just gotten underway in Greece, you can follow the talks here. One big topic this year is the possible 750 GeV diphoton excess. Around the time of Strings 2016 we should hear whether this is real or not. If it is, String Phenomenology 2017 will likely be completely dominated by the topic, if not, it will have vanished without a trace.

Finally, at the other end of the spectrum is String-Math 20XX, which has been going on since 2011, and this year starts next week in Paris. Quite a few first-rate mathematicians are involved this year. As with Strings 20XX, most of the talks don’t actually have anything at all to do with the theory of a quantized string, and this is more of a “QFT-Math” than “String-Math” conference at this point.

One can read the blog comments mentioned to get some idea of the arguments going on about “phenomenology” vs. “mathematics”. The “phenomenologists” argue that they are the ones doing physics and engaging with data, but don’t really point out that the models they work with have no known (i.e. not purely speculative) connection to any known physical phenomenon. They’re hopeful someday things will be different, but there’s no evidence at all of any progress in that direction.

Phenomenologists like Conlon do battle with their Strings 20XX brethren by accusing them of doing “mathematics”, not “physics”, of in essence really being just an offshoot of the String-Math 20XX crowd. There’s an implicit argument that such people don’t deserve jobs in a physics department, but should move to a math department. I can report though, that while much of the String-Math 20XX research is more than welcome in the math community, that’s not true of most of what goes on at Strings 20XX (a conference that very few mathematicians ever attend).

If you find the current situation confusing, rest assured that you’re not the only one…

Posted in Strings 2XXX | 8 Comments

Quick Items

  • In a couple hours, at 1:15 pm New York time, there will be a press conference at the AAS meeting where LIGO and Virgo scientists will discuss “ongoing research” (webcast here). The general assumption is that there will be observations of new gravitational wave sources announced.
  • At some other extreme in the space of science talks, the AAS meeting also featured a talk yesterday by Sean Carroll on “Normal Science in a Multiverse”. There’s some discussion of the talk here, and twitter has this. Some counterpoint from Joseph Silk here.

    It seems that Carroll was arguing that the multiverse shows that we need to change our thinking about what science is, adopting his favored “abduction” and “Bayesian reasoning” framework, getting rid of falsifiability. Using this method he arrives at a probability of the multiverse as “about 50%” (funny, but that’s the same number I’d use, as for any binary option where you know nothing). So, from the Bayesians we now have the following for multiverse probability estimates:

    1. Carroll: “About 50%”
    2. Polchinski: “94%”
    3. Rees: “Kill my dog if it’s not true”
    4. Linde: “Kill me if it’s not true”
    5. Weinberg: “Kill Linde and Rees’s dog if it’s not true”

    Not quite sure how one explains this when arguing with people convinced that science is just opinion.

  • Among the many summer conferences one might want to take a look at, there’s last week’s Workshop on String Theory and Gender, and this week’s LHCP in Lund. Wilczek will be giving the “Theory Vision” talk at the end on Saturday.
  • Today’s Wall Street Journal has an interesting article on the not so great job market for Ph.Ds (to avoid paywall, try Googling, e.g. “Job-Seeking Ph.D. Holders Look to Life Outside School”). I find the claim that the median income for Math/Physics mid-career Ph.Ds dropped 6% over the past 3 years highly remarkable (if true). Yes, US middle class incomes have been tanking, but I that number is pretty extreme, especially since this has been a period of modest economic expansion.

    One other bit of news I learned from the article was what universities (including mine) are doing to help with the situation:

    at Columbia University, Ph.D.s are taking classes in using Twitter to better communicate their work to nonacademic audiences.

Update: The LIGO news was a second black hole inspiral. I’m sure you can find good coverage of this elsewhere.

I hadn’t realized that the AAS is sponsoring a whole Multiverse Mania Fest, bringing in to promote a new definition of science not just Carroll, but Richard Dawid. Lenny Susskind this afternoon gave a talk (see here) that seems to argue that the Multiverse is a great idea, even though it won’t ever be testable. No news on what his Bayesian percentage is, or whether he’s willing to bet the lives of helpless pets. Sean Carroll made his usual straw man attack on the “Popperazi” (who, despite what he thinks, understand what indirect evidence is), see here.

Update: Another odd multiverse-related item. Laura Mersini-Houghton and collaborators have made well-publicized claims that they have testable predictions based on the string theory landscape. I’ve written about these several times here on the blog, see here, and this posting for one example that includes a response from Mersini-Houghton and Richard Holman.

Their claims are based on two 2006 papers, see here and here. Very recently Will Kinney posted this paper on the arXiv, which has in the abstract:

we compute limits on these entanglement effects from the Planck CMB data combined with the BICEP/Keck polarization measurement, and find no evidence for observable modulations to the power spectrum from landscape entanglement, and no sourcing of observable CMB anomalies. The originally proposed model with an exponential potential is ruled out to high significance.

See the conclusions section of the paper for the details.

This isn’t particularly surprising or odd, although one wonders if the Kinney paper will get a fraction of the attention that the original claims have gotten. What is odd is that I hear that Mersini-Houghton is asking to have the paper removed from the arXiv, on grounds that have something to do with the fact that she was originally collaborating on the project with Kinney, but is not listed as an author (although he offered to put her name on it). I can’t think of another example of this kind of thing ever happening before, perhaps others are aware of similar controversies.

Update: Much more detail at Backreaction, including comments from Will Kinney explaining the issue with the arXiv.

Posted in Uncategorized | 50 Comments

Some History of Science

The period of the “String Wars” has now receded far enough into the past that it has become a topic of interest to historians of science. I learned today from Sabine Hossenfelder’s round-up of various articles addressing the history and sociology of string theory that Sophie Ritson has published an article on the 2006 “trackback” controversy. It’s a fairly straight-forward account of that story, based on publicly available sources, emphasizing the interesting issues raised about science blogging.

While the article deals with the 2006 history, what has happened since then sheds some light on the topic, for example making clear that the “active researcher” business was always a red herring. Within a couple years after 2006 I noticed that arXiv trackbacks were appearing to all sorts of sources obviously not “active researchers” (for example, Slashdot articles). I tried to find out what the new arXiv policy was, but got nowhere. At one point I decided to do some experimental work, setting up a fanboy string theory site, trashing string theory critics and enthusing over the multiverse. An arXiv moderator took a quick look, and decided the anonymous author qualified (see discussion here). I realize this was obnoxious behavior, but thought it at least had a chance of goading the arXiv moderators into revealing their current policy. No dice. Every so often I’ve tried again to contact someone associated with the arXiv to ask what their policy is, but this has never led anywhere. Sabine describes the current arXiv trackback policy as “one of the arXiv’s best-kept secrets”. If you look at recent arXiv trackbacks you’ll see that the list is dominated by links from the excellent MathOverflow site, but also includes links from a wide variety of other sources that clearly are not “active researchers” (for instance: New York Times stories, press releases on, MIT Technology Review weekly lists of arXiv papers, and Quanta magazine stories).

Besides the secret nature of the current policy, the odd way in which the “active researcher” policy came to light is rather remarkable. This all started back in August 2005 (see here) and at that point trackbacks pointing to this blog were appearing. A few months later that stopped and, wondering why, I wasted a lot of time trying to contact people associated with the arXiv to find out what was going on. I finally heard from a Cornell administrator that links to my blog were not being allowed for an undisclosed reason, and I wrote about that here. Sean Carroll picked up the story here, and a former member of the arXiv editorial board revealed the “active researcher” policy in a comment at that blog entry. This I gather forced Jacques Distler into a public discussion of the policy here, which I commented on here. The Ritson article covers this part of the story in some detail.

So, bringing 2006 history up to date, I have no idea what the current arXiv trackback policy is, other than that they’ve found some new criterion other than the “active researcher” one to justify blocking trackbacks from Not Even Wrong. I guess this will remain “one of the arXiv’s best-kept secrets”, at least until someone accidentally reveals all in a blog comment somewhere…

Posted in Uncategorized | 19 Comments

Short Items

  • String theory continues to make progress. Today the news is from Megan Fox:

    “Sometimes I just know things,” she explains. “I accidentally tap into stuff sometimes. I used to do it as a kid, and I do it as an adult. I crossed over and saw a future string.”

    String, as in string theory. Fox is into stuff like that. She’s also spiritual. On her Instagram profile, she describes herself thusly: “Child of the Cherokee Tribe … forest nymph … Lunar Leo mother goddess to 2 bohemian revolutionaries-my kamikaze free spirit & my peaceful warrior.”

    A few months ago it was Jaden Smith moving the subject forward:

    Jaden sees himself as a modern-day prophet and is working on a collection of essays,” a pal says in the new issue of Us Weekly. “They’re new takes on string theory and chaos theory, but more mystical.”

    After all, he’s getting an out-of-this-world assist with the tome. Explains the source, “Jaden thinks he has spiritual ties to people in other dimensions and galaxies, and they are helping him write.”

  • At some sort of other extreme, Sabine Hossenfelder has very sensible things to say about the string theory phenomenon here.
  • If you read Physical Review Letters or the Financial Times you might think that a “key to an unseen portion of the universe” had been found. Luckily for you, Natalie Wolchover is on the case, uncovering the story of why you might not want to take that new fifth force seriously quite yet.
  • If you’re interested at all in the story of the superluminal neutrinos, you might want to read Gianfranco D’Anna’s fictionalized account of the story, 60.7 Nanoseconds, which has just appeared in English

Update: This string theory story is so bizarre I don’t know what to make of it:

While working on String Theory, Kaku, discovered what he sees as evidence that the universe is created by an intelligence, rather than merely formed by random forces. He suggests he can explain it by what he calls, “primitive semi-radius tachyons.” We do not yet have a succinct explanation of this idea from Kaku, other than he’s referring to tachyons, which are theoretical particles that unbind particles from one another.

Without getting into physics itself, Kaku concludes that we live in a Matrix-style universe, created by an intelligence.

“I have concluded that we are in a world made by rules created by an intelligence”, he said. “Believe me, everything that we call chance today won’t make sense anymore. To me it is clear that we exists in a plan which is governed by rules that were created, shaped by a universal intelligence and not by chance.”

Posted in Uncategorized | 39 Comments

This Week’s Hype

One possible reaction to the phenomenon of hype in fundamental physics is to not worry much, figuring that it should be a self-limiting process. While there’s a huge appetite in the media and elsewhere for the “exciting new idea”, overhyped “new” ideas sooner or later should pass into the category of no longer “new”, and less capable of producing “excitement”. The problem is that this doesn’t seem to be happening: favored physics hype keeps getting promoted as “new” and “exciting”, no matter how old it is.

In the case of multiverse hype, Andrei Linde was promoting the idea 34 years ago, back in 1982. That hasn’t stopped many people from heavily promoting it as “new” for quite a few years now. Taking this to a new level, a talk by Martin Rees this past week at the Hay Festival advertised the multiverse as not just exciting, but so new as to be one of the main developments in physics of the past year:

The astronomer will share his excitement about recent cosmic ideas and discoveries. Since last festival there have been new searches for life (even intelligent life) in space. One of Einstein’s greatest predictions has been confirmed with the detection of gravitational waves from colliding back holes. Images of Pluto have surprised us, and astronomers have discovered thousands of planets orbiting other stars, some resembling Earth. And there is speculation that physical reality encompasses more than the aftermath of our big bang: we may inhabit a multiverse.

Lord Rees explains in more detail in the Telegraph how exciting this is. It seems that he has been excited about this for more than a quarter century, with a book on the subject back in 1989. Since at least 2003 and a Templeton-funded Stanford conference on the multiverse, he has been publicly expressing willingness to bet his dog’s life on the existence of the multiverse, and he repeats that in the Telegraph article (should someone contact the RSPCA?). Luckily for the Rees family pets, there’s no way to ever resolve this issue, so the last couple generations have survived, and so will further ones.

Update: Also this past week, in the category of hype that will never die, Scientific American has Gravitational Waves Could Finally Help Us Prove String Theory. This particular hype campaign goes back at least a dozen years. See here for a 2004 blog post about a UCSB press release featuring claims that LIGO might produce evidence for string theory in 2005 or 2006.

Posted in Multiverse Mania, This Week's Hype | 9 Comments

Summing It Up

There’s a new popular book out about number theory by the team of Avner Ash and Robert Gross, entitled Summing It Up: From one plus one to modern number theory. This is the third such book that they have written, and I’m embarrassed that it seems that I never reviewed the other two here. All three are highly recommended for anyone who wants a popular book-level introduction to some of the central topics of modern number theory.

  • Summing It Up is the latest of the three, but it’s also the most elementary. It’s an introduction to the subject of modular forms, starting at the very beginning. The first half of the book covers in detail some basic ideas about number theory that can be understood in elementary terms, including things like the problems of counting the ways an integer can be a sum of squares or higher powers, or partitioned as a sum of smaller integers. The second half of the book tries to explain in as simple and concrete terms as possible what a “modular form” is, and what some of the properties of such objects are.

    I’ve just finished teaching a graduate course on representation theory, and ended up the course with a short discussion of the representations of the group SL(2,R) (two by two real matrices of determinant one), and what this had to do with modular forms. The relation of modular forms to representation theory (not discussed in the book) is roughly the following. The action of SL(2,R) on itself by left multiplication induces an action on functions on the quotient space SL(2,R)/SL(2,Z) (elements of SL(2,Z) are matrices with integer entries) and one can ask how this representation decomposes into irreducible representations, with modular forms providing part of the answer. How this works is quite basic to our modern understanding of how representation theory and number theory are related.

    In the last few chapters the authors try to explain how modular forms answer concrete counting questions raised in the first half of the book. A problem with trying to do this kind of thing is that while the questions may be straightforward to state, and the basic definitions of modular forms relatively accessible, connecting the two requires invoking some subtleties (half-integral modular forms). The authors several times apologize for not being able to explain exactly what is going on. I’ve always been quite fascinated by these particular subtleties, since they appear in the basic relationship of representation theory and quantum mechanics. The half-integrality here is related to the half-integer that appears in the ground-state energy of the harmonic oscillator. For quite a bit about how this is related to representation theory, see the book I’ve been working on. I’d love some day to write about the relationship of the ideas that appear in quantum mechanics to the ones that appear in modular forms, but first of all I need to understand myself much better what is going on.

  • The first of the three books by Ash and Gross was Fearless Symmetry: Exposing the Hidden Patterns of Numbers, published in 2006. It’s perhaps the best place to start for a popular introduction to the Langlands program and what it says about the relationship of number theory and representation theory. Modular forms make a brief appearance in that book, where an explanation of them had to be skipped over due to a lack of space. The newest book makes up for that omission.
  • The second of the three books was the 2012 Elliptic Tales: Curves, Counting, and Number Theory. It covers in detail the topic of elliptic curves and their role in number theory, aiming at a description of one of the main open problems of the subject, the conjecture due to Birch and Swinnerton-Dyer. This is a very active subject of current research, with significant progress being made. If one had to guess which of the Millenium Problems will be the next to fall, this might be a good bet.

While there’s a long tradition of popular books about number theory, these typically emphasize elementary methods for solving problems, ones that can be understood without a lot of the modern machinery. The first two Ash-Gross books do a good job of trying to give some insight into this modern machinery, even though a popular book can only do this in a very limited way (just as popular physics books can only give a very limited explanation of quantum field theory). The new one is different in that it makes a serious effort to explain exactly what is really going on, although following this path means that the book can only cover the first steps in the direction of modern techniques for understanding number theory.

Posted in Book Reviews | 13 Comments

Killer Asteroids

During my recent vacation I visited my old friend Nathan Myhrvold, and got a tour of his company’s lab near Bellevue. At that time he told me about what he had been working on recently, which has now appeared on the arXiv here, and is the subject of news stories today at the New York Times and Science magazine.

I confess I’ve never worried much about killer asteroids, but am glad that someone is doing this. Nathan has always pursued a wide range of different interests, and killer asteroids has evidently been one of them. I first heard from him a year or two ago about how he had gotten interested in the question of how to model the observability of such objects. Such modeling affects choices to be made about how to optimally search for these things (space-based or earth-based telescopes? what kind?). He wrote a paper last year about this, which was published in March.

What Nathan told me when I saw him was that he had found significant problems with the modeling done by the NEOWISE/WISE group at NASA, and you can now judge for yourself by reading his paper. I’m very far from being able to understand the details of this story well enough to judge who’s right here. I do know Nathan well enough to know that his work on this deserves to be taken very seriously, and would bet that he has identified real problems. As noted in the comments there, the reaction from one of the NASA WISE people quoted at the end of the Science article wasn’t exactly confidence inspiring.

Update: There’s a press release about this out from NASA today, pretty much devoted to attacking Nathan’s work.

Update: For some specific criticisms of Nathan’s work, see the comment thread here. For a response to some of this from Nathan, see here.

Update: Scientific American has an article about this here.

: As pointed out by Wayt Gibbs in a comment, those interested in some discussion of the main point at issue might want to read the exchange here.

Posted in Uncategorized | 74 Comments