Spinning the Superweb

Oswaldo Zapata is a young string theorist who recently got his Ph.D. in the subject in Rome. He recently wrote to me to tell me about some essays on the history of superstring theory that he has written, which he is starting to put up on a web-site he calls Spinning the Superweb. I’ll be interested to follow the rest of the essays. He has also posted the first of these on the arXiv.

Zapata’s history is largely concerned with the question of how string theory has achieved acceptance in certain circles despite its failure to satisfy the conventional criteria normally demanded of a successful scientific theory. Reading him, you might initially get the idea he is a string theory skeptic unhappy with what has happened:

From the previous examples we have learnt some important things about the development of string theory. Firstly, as research progresses in a given topic, an explicit reference to the unsolved problem tends to disappear from the literature. For instance, we saw how the quantization of gravity is considered by string theorists to be an accomplished task that does not deserve further study, or even a mention. Secondly, while research advances, the initial problem changes in such a way that it becomes increasingly difficult to unravel the convoluted relationship connecting the final problem to the original one. This was illustrated by our second example concerning string theory and the unification of the forces. Originally the idea was to extract the standard model from superstring theory, an investigation encouraged during the second half of the eighties by the promising results obtained from the heterotic string. Then, by the mid-nineties, the goal was to determine the unique vacuum of the mother of all the theories, the M-Theory. And, more recently, the focus was on the right “environment” of the anthropic solution. Things have changed, but the fundamental query remains unsolved: how do we get the standard model from string theory? With these examples we have learnt something else: this occurs while an “outward” discourse (from the “inside” to the “outside” of the professional community) proclaims that the theory has solved such problems. Indeed, in this movement disadvantages have been transmuted into virtues…

At first, a hypothesis is made, explaining openly its significance as well as its difficulties. At this stage no one is sure of the real value of the conjecture, however, it is interesting enough to drive a significant part of the physics community to devote itself to its development. Step by step “evidence” accumulates and after a while the string theory fact emerges. String theorists have created in this way their own nature: a supersymmetric world, a big bang with all the fundamental forces combined, a multi-dimensional universe, and so forth.

Zapata appears to be claiming there is such a thing as a “string theory fact”, which is somehow different than the usual scientific notion of “fact”, one that requires experimental confirmation.

Among the other unusual aspects of the string theory story that Zapata recognizes is one that has often struck me. This is a subject so complicated that very few people actually understand what is going on, including many of the people working on it. As a result, overhyped claims in the popular media play a big role, with few people able to evaluate them properly:

In fact, string theory is so complex that experts are neither able to understand entirely the main developments nor to follow its rapid growth. In general, practitioners feel confident only in a specific subfield. People working on the AdS/CFT correspondence or twistor theory, for example, do not comprehend the whole area, even though they can be extremely competent when tackling the particular problems of the subfield. Because of this, paradoxically, those that have provided the evidence in support of superstrings do not fully grasp it. Many do not understand the AdS/CFT correspondence completely but they believe in it; it is a matter of fact. A fact in string theory is a shared belief that something is unquestionably true. What I will try to show here is that string theorists often base their beliefs on what they have seen proclaimed everywhere. This ubiquitous discourse includes technical seminars and articles, which I will call the in-in discourse, as well as popular speeches and books, the out-in discourse. Furthermore, I will try to convince the reader that string theorists start to internalize the rules of the game long before they become experts; by means of a discourse that embraces the whole society. I will dub this the out-out discourse when the information comes from non-experts, and the in-out discourse when it comes from professional physicists.

Zapata goes on to give a truly remarkable description of the sociology and psychology of how people get into string theory. Remember, this is coming from a young string theorist:

The discussion above suggests that many string theorists have begun their careers with a biased view of the subject. How they conceive the theory during their formative years depends crucially on previous contact with materials intended for the general public and, later on, on the systematic training given by senior members of the community. We have seen how these two stages in the education of future string theorists coincide at one point: they present new subjects as confirmations of the most fundamental claims of the theory. The theory has succeeded in: quantizing gravity and unifying all the fundamental forces of nature. In addition, it explains the thermodynamics of black holes and has also demonstrated a precise gravity/particle physics correspondence. This is what is taught. Even though young string theorists can feel sometimes uncomfortable with the weakness of some arguments, the challenge usually exceeds their skills. Moreover, in such a competitive field there is no time to digress by asking fundamental questions. When finally the young researcher becomes a full member, with many more resources at hand to tackle fundamental issues, it turns out that they are probably working on a specific topic with its own problems. And, not surprisingly, all these investigations assume the validity of the basic claims of the theory. The once controversial claims are no more questioned; they have been internalized as matters of fact. Eventually, the young researcher becomes an accomplished theoretician; it is now their turn to protect the theory and contribute fervently to the in-out discourse. This final step consolidates further the scientific fact and, very importantly, guarantees the reproduction of well-trained newcomers. This long and tortuous process of internalizing the rules of the game is sociological, but unavoidably also psychological. As I said above, a fact in string theory is a deep and sincere belief, and nobody can dispute certain issues without at the same time denying their own self.

With belief in string theory based on this sort of psychology, it’s not surprising that defending it from skeptics can’t be done with the usual sort of scientific discourse, but requires propagandistic techniques:

What I’ve described in this section is an alternative strategy of validation that string theorists have persistently employed in order to preserve what they consider a worthwhile field of research. The purpose of this is to protect the theory from attacks from defenders of contending models; attacks due in part to theoretical and experimental shortcomings. It is not an exaggeration to say that string theory uses propaganda, more or less as Galileo did in his times: ‘‘He uses psychological tricks in addition to whatever intellectual reasons he has to offer. These tricks are very successful: they lead him to victory.’’

Describing a New York Times article on the Maldacena conjecture, he writes:

This article, and many others of the same sort, reinforce, willingly or not, the social belief that superstring theory is ‘‘on the right track.’’ In this case, the circle of believers is expanded thanks to the participation of non expert actors: science writers and interested readers. This sympathetic environment, which will be illustrated further in the next essays, has been vital for the development of the theory. It must be mentioned that this out-out discourse does not originate independently from professional string theorists. In general, it simply reproduces the in-out discourse of the experts. I do not mean to suggest that string theory popularizers are scientifically illiterate, I just want to highlight that the substance of what they say reflects the opinion and enthusiasm of string theory specialists. In such an abstract area, things could not be any other way. As a consequence of this discourse, a favourable disposition regarding superstrings has permeated into the public domain. The lay public’s attitude functions as a support for the internal discourse. What is more, the layman’s view of superstrings is sometimes internalized by experts on the theory and then works as a reconfirmation of the old belief. To put it differently: the out-out discourse is not only oriented to popular audiences but towards experts as well; the out-out discourse is also an out-in discourse. Consequently, “non-pure” conceptions penetrate and modify the theoretical development of the field. I will call this the in-out-in process. Notice that unlike the in-out-•••-in process explained above, the in-out-in process only concerns the movement of ideas (of course, persons are also involved here, but not in the sociological sense meant before). In this way, with contributions from the in and the out, the creeping belief in the accomplishments of superstring theory is gradually confirmed…

The effects of these kinds of comments on the theory are two-fold. On one side they create a favourable background for the theory to develop, on the other they send a clear message to string theorists that they are doing right, that nature is really as they think it is. I must confess that this hypothesis is hard to prove. However this is what the next essays try to do. Before moving on to these more detailed discussions, I would like to observe something that a string theorist would be unlike to deny: when a newspaper says that colleagues at Harvard are dancing ‘‘La Maldacena,’’ they feel more confident about their own results. Something similar occurred when David Gross was honoured with the Nobel Prize for physics in 2004. My experience was that the general mood among string theorists was very optimistic. They felt that this award was somehow recognition of their own efforts in string theory. Evidence in support of this claim is varied: from technical seminars to public speeches, and from published articles to forwarded emails.

All in all, Zapata does an excellent job of explaing why string theory has been the subject of such a long-term relentless campaign of hype and propaganda, one that continues to this day.

In his essay, he concentrates on the story of AdS/CFT, the one place that string theory has had some real success. As part of this, he engages in some propaganda himself, quoting me out of context in a misleading way. When I wrote in my book about string theory as a “failed project”, I was referring to its failure as an idea about unification, not describing AdS/CFT as a failure.

All in all, Zapata’s essay is something quite remarkable: a view from the inside of what things look like to someone who is both a true believer, as well as a clear-eyed observer of how string theory has gotten to where it is today. I suspect though that his history is already starting to be out-of-date, with the same phenomena that he describes looking very different to the rest of the world. Most physicists have begun to lose patience with the hype and propaganda surrounding string theory, and want nothing to do with a supposedly scientific subject full of true believers acting on a new and non-standard concept of what is a scientific fact and what isn’t.

This entry was posted in Uncategorized. Bookmark the permalink.

29 Responses to Spinning the Superweb

  1. Spiny Norman says:

    “I will call this the in-out-in process. Notice that unlike the in-out-•••-in process explained above, the in-out-in process only concerns the movement of ideas (of course, persons are also involved here, but not in the sociological sense meant before).”

    You do realize, Peter, that this is a crude (but funny) joke?

  2. Peter Woit says:


    The thought has occurred to me that the whole thing is a rather fantastic joke of some kind. But I can’t figure out what kind…

  3. Peter:

    Oswaldo doesn’t seem to accept the distinction between belief in a mathematical conjecture, which may ultimately be ‘provable’ as a theorem, ‘merely’ through consistent application of ‘axiomatics’, and assurance of completeness; and ‘belief in’ a scientific conjecture (model), which requires some degree of empirical inductive support to warrant any ‘degree of belief’, and can never be ‘completely’ verified.

  4. Pingback: Belief and facts in theoretical physics « Shores of the Dirac Sea

  5. Sandro says:

    I think I’ve got to agree with Leonard Ornstein. He makes actually a good point in distinguishing the two kind of “beliefs”: indeed, in my opinion, mathematical beliefs like that homological Mirror Symmetry must be there for pairs of mirror Calabi-Yau n-folds are well worth pursuing, and of course knowing what has been done by String theorists can be quite useful. This is my mathematician’s view of the subject, though…

  6. Peter Woit says:

    Sandro and Leonard,

    The big problem with the Zapata essay is that he doesn’t distinguish between two completely different things:

    1. The AdS/CFT conjecture, which is an essentially mathematical conjecture about a relationship between two different mathematical structures, and for which there is quite a lot of evidence, with many people working on gathering more evidence and making the conjecture more precise.

    2. String theory as a 10/11d unified theory of particle physics and gravity. For this, not only is there no positive evidence, there is now a lot of evidence that this can’t work.

    Case 1. is a rather conventional story about how “belief” in a mathematical conjecture becomes stronger as it passes various tests, you understand it better and make it more precise. It is case 2. that is highly problematic, where you have lots of people “believing” in an idea about the fundamentals of physical reality. Zapata gives a good explanation of how hype, propaganda, PR, and hiding behind extreme complexity have led to this much more problematic sort of “belief”. I’m still having trouble believing myself that he has a positive view of this second situation.

  7. Peter Shor says:

    I just realized: part of the problem of string theory may be that the sociology of physics departments does not let people work on purely mathematical things like AdS/CFT without some claim that they are connected to the laws of physics.

  8. Coin says:

    So… reading Zapata’s Arxiv essay (which only seems to contain the first of Peter’s blockquotes– what are the other quotes from?) something that seems to me important is that he doesn’t seem to be judging, particularly, anything he’s writing about– taken by itself the paper seems to mostly just be describing a sociological process, a process where a conjecture becomes a fact just because everyone’s given up on trying to prove it.

    Ornstein/Sandro/Woit above raise some objections having to do with the idea that in some contexts (say mathematics vs physics) this process or something like it might be appropriate more so than others, and Zapata doesn’t really acknowledge this distinction? But it seems like the question of whether and when this process is appropriate is separate from the question this particular essay seems intended to address, which is more just whether the process is happening at all. I think this can be an interesting and valuable question by itself– is String Theory progressing with time on its central questions, or just gradually shrugging them off?

    This said the main question I’d ask about Zapata’s paper is whether the process he describes is unique to String Theory. It’s certainly not hard to come up with examples in mathematics where a very large body of work springs up around a conjecture which is proven either much later or not ever at all. Even in physics I seem to hear a lot about incidents where questions about the mathematical validity of some quantum physics procedure or other (renormalization and “integrating over the singularity” in path integrals come to mind) just got kind of dropped over time without ever really being addressed. I have a strong suspicion if you tried to take the analysis Zapata performs on string theory, of catching unsolved problems in the act of being “disappeared”, and applied this to a number of other sciences in their early stages, they would not come across very differently.

    (Of course, even if the kind of behavior Zapata describes is widespread within math and/or science, this wouldn’t necessarily reflect well on string theory anyway– that is, I’m not trying to suggest string theory gets an “everybody does it” pass. It seems like string theory’s unique status, that of simultaneously being widely assumed to be central in science yet performing relatively poorly in terms of contact with experiment, means we might reasonably demand higher expectations of string theory than we might some other young sciences. For example it might be that, I don’t know, the theory of motives is on just as shaky theoretical grounds as AdS/CFT due to an analagous failure to prove the underlying conjectures; but motives do not get the sort of central, “only game in town” treatment in mathematics that strings get in physics, and are in fact kind of obscure. Or it might be that the early historical stages of QFT brushed over some critical questions of consistency and finiteness, in a way similar to what string-theory based quantum gravity studies have done; but in QFT the reason why this was forgiven is that QFT was actually producing practical numerical results, in a way which I don’t think string theory QG can.)

  9. John Baez says:

    Peter Shor wrote:

    I just realized: part of the problem of string theory may be that the sociology of physics departments does not let people work on purely mathematical things like AdS/CFT without some claim that they are connected to the laws of physics.

    Yes. The mere fact that a mathematical structure is beautiful and interesting is typically not enough for physicists; it’s supposed to be related to the real world. At first glance this sounds entirely sensible, but it has a bad side-effect: even when physicists are studying a mathematical structure with no clear relation to the real world, they feel psychological pressure to act like they’re studying the real world – or even to believe that they are. This creates misleading rhetoric – or even self-deception.

    It’s not just a problem in string theory; it’s also true in loop quantum gravity.

    This is one reason I’ve quit going to quantum gravity conferences and started focusing on pure mathematics. If it’s “merely mathematics”, the need for certain kinds of rhetoric is eliminated.

  10. BigG says:

    This choice of term “real world” needs to be done away with. What does real mean? What does world mean? Is math not real? Not part of the world?

  11. Tim says:

    @Coin: I totally agree that Zapata does very carefully avoid any judgment, maybe in order to not offend anyone – seems to be done extremely clever, at least to me.

  12. Sandro says:

    “[…]even when physicists are studying a mathematical structure with no clear relation to the real world, they feel psychological pressure to act like they’re studying the real world – or even to believe that they are.”

    This is exactly the problem.

    “This is one reason I’ve quit going to quantum gravity conferences and started focusing on pure mathematics. If it’s “merely mathematics”, the need for certain kinds of rhetoric is eliminated.”

    And this is exactly the solution.

  13. Peter Shor says:

    Sandro says (quoting John Baez)

    “‘This is one reason I’ve quit going to quantum gravity conferences and started focusing on pure mathematics. If it’s “merely mathematics”, the need for certain kinds of rhetoric is eliminated.'”

    “And this is exactly the solution.”

    This is, unfortunately, not the solution for many string theorists. Mathematicians have a similar, although different, problem: to claim you’re really doing mathematics, and be accepted by most mathematicians, there has to be some pretense of mathematical rigor. Physicists don’t require mathematical rigor; historically, the connection to the real physical world has presumably been a good substitute for this. While some string theorists would fit fine in mathematics departments (and some already are), I would guess that most could not.

    For a non-string theory example, Michel Talagrand has recently proven some of the claims of the physicists using the replica method using mathematically rigorous techniques. This work is acclaimed among mathematicians, but physicists are completely unimpressed.

  14. Chris W. says:

    Following up on Peter Shor’s latest comment, there is an obvious parallel to the above in the relationship between the work of physicists and engineers. That is, a nagging and possibly fundamental issue of understanding for a physicist might be—in fact, typically will be—of little or no interest to engineers. In some cases this applies to entire subfields.

    More to the point, the kinds of shifts of attention and effort that Zapata describes can be regarded as shifts of problem formulation, in the hope of finding a better avenue for understanding and technical progress. I’ve mentioned it before in comments on this blog, but it’s worth repeating an observation of Shiing-Shen Chern. In a volume published during the Einstein Centennial (1979) there is a reminiscence by Chern about Einstein, partly based on discussions Chern had with him when he was at IAS (1943-1948). Chern observed that problems generally (always?) come to a mathematician in a reasonably well-stated form, whereas a substantial part of the task of a theoretical physicist is to arrive at a good problem formulation before attempting to apply any refined technique or method of attack. This is especially true at the frontiers. (I and others would argue that metaphysical ideas often play an essential role in arriving at these problem formulations.)

    Of course, the central issue and recurring theme on this blog has been whether this process of redefining the problem—in physics and science generally—should be allowed to extend so far as to undercut the very possibility of refutation by observation of the proposed solutions.

  15. Chris W. says:

    PS: I’m pretty sure the book I have in mind is Some Strangeness in the Proportion: Centennial Symposium to Celebrate the Achievements of Albert Einstein, edited by Harry Woolf (Addison-Wesley, 1981). It’s listed on Amazon.

  16. Sandro says:

    @Peter Shor,

    sorry about the misunderstanding: I wasn’t referring to a common string theorist, but to “physicists (who) are studying a mathematical structure with no clear relation to the real world”. In most cases these people have the necessary rigor to be called mathematicians (unless you define a mathematician to be someone that can’t read physics papers), and there’s just a psycological barrier, as John says. I agree with you that many sting theorists would struggle in a maths department.

  17. Peter Shor says:

    Hi Sandro,

    Sorry to have misunderstood you. I agree that most of the quantum information theorists (for example) in physics departments are working with sufficient mathematical rigor to be accepted by mathematicians.

    On the other hand, the replica method in statistical mechanics is completely non-rigorous, and it has led to some amazing mathematical results which I don’t think could have been found if the theorems hadn’t been discovered first by the replica method, and then proved rigorously by mathematicians. Some of the physicists using it are studying statistical mechanics systems which have nothing to do with actual physics, but which arise in computer science, and I don’t think they’ve suffered any adverse consequences. Of course, the replica method is also very useful for systems which arise in the real physical world, so there’s no need to justify the whole field.

  18. Sandro says:

    Hi Peter Shor,

    I completely agree with you. The situation I’ve in mind is that of a physicist who realizes at certain point that he’s actually a working mathematician, with prevalent interests being on the maths, and decides to go for pure maths. Of course, his background in physics will allow him to realize that some results in physics, like those implied by the replica model in statistical mechanics you mention, can have an impact also on mathematics, or at least constitute results which are worth investigating from a mathematical point of view. In an ideal world, such a person should not have any problem fitting in a good mathematics department, but I’m not sure if this is always the case…

  19. davetweed says:

    I think the discussion between Sandro and Peter Shor slightly misses the point. Isn’t the problem not that people who want to switch from physics to mathematics can’t, but that it’s very difficult for a physicist to say “I think this mathematical structure may be useful in modeling some physics, but I can’t demonstrate this yet. I want to keep studying this IN THE HOPE IT WILL LEAD TO PHYSICS rather than purely for its own sake (ie, mathematically), but it’s not successful physics yet”. It’s a version of the problem in many disciplines that there’s arguably a bit too much short-term-ism you can’t really get the time to “build up some conceptual tools for discipline X (that aren’t yet convincing)” within the X department itself.

  20. H-I-G-G-S says:

    This supposed history of AdS/CFT omits one of the three foundational papers on the subject (hint: the paper appeared about a week before the Witten paper he discusses at length). He also seems ignorant of many of the ideas and results that led up to Maldecena’s conjecture. A clear-eyed observer? Looks to me more like one eye only partially open.

  21. Joao Leao says:

    Peter,Leonard,Sandro, etc..

    I am afraid you are splitting hairs you don’t have! A conjecture, in either math or physics, may be more or less plausible as it is supported by more or less plausible arguments. But it is not a fact until it meets the standard of a mathematical proof or a modicum of empirical data in its favor. What Oswaldo points out is that this is no longer the case as far as the Maldacena correspondence is concerned and even your reaction to his observation supports him! Since BMN asserted it as such the AdS/CFT correspondence is an undisputed fact and no one holds any doubts about it, including yourselves! This in spite of the fact that there is no mathematical proof of it or any real world experimental results to support it. No one in his right mind would even spend time trying to find a proof or, more crucially, the likely limits of its applicability. Funny that BMN are still kind of cautious about it obtaining in the non-supersymmetric gauge theory case but who doubts that today after all the great heavy-ion collision “duality predictions”? 3,000 papers could not be wrong, could they?

    It seems to me that OZM is hardly making a joke but instead an insightful and judicious analysis about something he has directly witnessed: the production of “string theoretical facts” by a mix of social pressure, dogmatism, popular hype, PR, and tabloid level journalism. I think what he is saying deserves better attention than you seem willing to give it.

  22. David B. says:

    Dear Joao:

    Few of the experts believe the correspondence is a fact in the mathematical sense of having a proof. If you want a real explanation of why a great part of the field has moved on, read the post I made on my blog. Calling something a fact has more than one meaning.

    There are also plenty of people trying to find a proof of it, all of them rather respectable physicists.

  23. Joao Leao says:

    Dear David,

    Thank you for your kind response and for pointing me to your blog entry. I read the very interesting exchanges and marveled at your clever “bayesian belief argument”. Unfortunately I have the same qualms with it that other people well expressed on your blog. But I do not think that you have to believe a conjecture to be true to do relevant work on it. Think of the Artin and Langlands conjectures or, more gloriously, of the Riemann Hypothesis. And, mind you, I fully recognize that there is considerable heuristic support for some form of a gauge/gravity duality. I only object to this compulsion to state as established fact something that you know it is not quite yet so! In this I have to concur with Oswaldo and point to this as a form of bad faith that has regrettably become the norm in and around the string community.

    I am glad to know that there are people still hunting for the proof, though. If it is not asking too much maybe you can point us out one or two, no? Thanks in advance.

  24. David B. says:

    Hi Joao:

    For recent work, there is a huge community that is using the hypothesis of integrability to try to bootstrap the AdS/CFT correspondence for the maximally supersymmetric case. Some of the main proponents and characters are Beisert, Dorey, Kazakov, Minahan, Staudacher, Tseytlin, Zarembo (but there are many more). The discussion is rather technical at this point, but the aim has always been to prove in a rigorous way various key aspects of the AdS/CFT correspondence.

    For other setups, Gopakumar et al. have been studying how to rewrite Feynman diagrams in four dimensions so that the AdS geometry becomes more manifest.

    Maldacena and collaborators have found a huge number of the pieces of the AdS/CFT dictionary.

    Berkovits and Vafa have a different starting point from string actions.

    I am also aware of various puzzles that have been raised by Giddings regarding locality on sub-AdS scales, and Polchinski has been studying various problems related to understanding black holes and the problem of information loss (even if at the level of toy models). One of the key missing links that people really want to get their hands on is deducing the flat space S-matrix of string theory from SYM (recovering the Veneziano amplitude of flat space).

    My own work in the last few years has been on starting from field theory and trying to deduce everything else.

    Don’t be deceived by outward appearances: people in the field are very aware that this is a conjecture. People take it to be true in the same spirit as the Riemann hypothesis, and as such there are a lot of applications that spring forward from the equality of two apparently different formalisms.

    A lot of the work assumes it is correct to make deductions about situations where there are no other computations one can do. Because in some situations one really does not know what quantum gravity is, many papers assume that the definition of quantum gravity in AdS spaces is exactly via a QFT in fewer dimensions. This would sound as a tautology, but there is still the burden of showing that the semiclassical intuitions about quantum gravity are indeed correct in the appropriate limits.

    No matter how one looks at it, if one really wants something close to a proof (real understanding of what’s going on), one has to solve problems at strong coupling in one way or another. This is just extremely hard in general, but the community of people looking into this issues is huge. Although sometimes it is hard to tell what is going on from the way that the papers are worded if you are not working on the field itself.

  25. Joao Leao says:

    Hi David,

    Thanks so much for the references. You provide a very detailed guidebook. I will withhold judgement until I can read through some of the work you point out. I am aware this is hard work and that it can no longer be considered as part of sting theory apologetics since it aims to set a general context for strong coupling regimes in general. Still I maintain that that is precisely why one needs to be extra careful in separate facts from fictions of convenience.

    Thanks again for indulging me,

  26. Amir says:

    Hi Peter
    I was wondering where you got the quotes that you’ve put on your blog here. I’m going through the arXiv paper and can’t find any reference to for example this sentence:

    “Even though young string theorists can feel sometimes uncomfortable with the weakness of some arguments, the challenge usually exceeds their skills. Moreover, in such a competitive field there is no time to digress by asking fundamental questions.”

    The above quote is also nowhere to be found on the author’s blog.

    Best, Amir

  27. Peter Woit says:


    The quoted material is in the fourth paragraph from the bottom of this page of the author’s blog


  28. Amir says:

    Thanks, Amir

  29. Pingback: The Music of the Superstrings « Not Even Wrong

Comments are closed.