Brane Damage at Fermilab

Last week Shamit Kachru gave a colloquium at Fermilab with the title String Theory and Cosmology. The scariest part was the beginning when he noted that what he would be talking about was work due to 500-1000 theorists and he put up a couple slides listing many of them.

He spent the first part of his talk laying out the “Landscape” story, somehow neglecting to mention that it was ugly, completely unpredictive, and told us nothing at all about the properties of the world today. He then moved on to discuss branes and cosmology, not making clear that branes explain absolutely nothing about the early universe or cosmology, although they do give you a new slogan he has come up with:

“Big bang as brane damage”

There were a couple questions at the end, with no one standing up and asking if this was a bad joke or something. I’m curious if anyone from Fermilab can explain to me what a typical experimentalist’s reaction is to this kind of talk:

1. Are they impressed by this stuff and don’t realize they’ve been fed a load of pointless nonsense for an hour?

2. Are they smart enough to realize they’ve just sat through an hour of pointless nonsense, but are too polite to say anything about this at the end of the talk?

3. Are they so smart they know in advance this will be an hour of pointless nonsense, so don’t even attend, and are off somewhere else getting real work done?

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44 Responses to Brane Damage at Fermilab

  1. Juan R. says:

    Ok there is a problem with “less than sign”.

    I rewrite as Y > X.

  2. Juan R. says:

    Chris,

    I forgoot the name and the second postulate that read X

  3. steve says:

    Edward Witten, Five-branes and M-Theory on an orbifold, preprint
    available as hep-th/9512219. (1996)

    the M stands for “magic”, “mystery”,or “membrane”, according to taste.From a mathematical viewpoint a better term might be “murky”, since apparently everything known about M-theory is indirect and
    circumstantial, except for the classical limit, in which it seems to act as a theory of 2-branes and 5-branes, where an “n-brane” is an
    n-dimensional analog of a membrane or surface.

  4. Chris Oakley says:

    Well, anonymous humorist, unfortunately it looks as though Weisskopf (Kon. Dan. Vid. Sel., Mat.-fys. Medd. XIV #6 (1936)) has beaten you to it. Inventing a new form of mathematics that allows physicists to “calculate” without having to worry about the consistency and logicality demanded by spoilsport mathematicians.

  5. Anonymous says:

    According to the usual bizarre model of research on string theory, I propose the following theory of everything without the difficulties of compactification and saving both string theory and the scientific method.
    The I-theory is very sImple, since is based in four postulates; moreover, it is “background Independent” and explains the mysterious value of the cosmologIcal constant without the appeal to anthropIc principles!
    Postulates of I-theory, being X and Y physical observables:
    1) X > Y
    2) X

  6. Kyle says:

    Those poor “working class” steelworkers. I mean, metallurgical engineers only make 60-80k a year. I bet most theoretical physicists would spit on such a dismal, blue collar salary.

    More importantly, being involved with massive factories that use machines to produce steel makes people stupid and policitally uninvolved. That’s why the government is frightened of string physicists and keeps them under tabs. University academians are far more dangerous than workplace engineers who have a couple of years less schooling.

    Right?

  7. J.F. Moore says:

    Sorry, that was me below. Public machine, didn’t change name.

  8. loser says:

    quantoken: well, my point was that hamburger makers _are_ pretty much replaceable. But in general I agree with your comments. Not too many people in society were crying when SSC was cancelled.

    I think it is important to be a little careful in arming the enemies of science funding with caustic and public criticism of sub-fields. Scientists generally lose when they compete for funding at the policy level with other scientists. Keeping the arguments “within the family” is wise. This blog is a good example of doing that.

  9. Arun says:

    I am sure we can show high correlation between economic growth of a country and the presence/absence of string theorists. This, in a Larry Summers way, proves the value of string theorists.

  10. Alejandro says:

    Perhaps it is shown in the Spanish Civil War and in the previous experience with the Escuela Moderna (anarchistic, at Barcelona) and the Instituto Libre de Enseñanaza (sort of socialistic, at Madrid), that the real danger is when both steel workers and science works start to develop links.

    Os to put it in a riddle, it is perhaps no coincidental the source from where [the money of] the Nobel prize come.

  11. quantoken says:

    J.F.Moore: Yes I appologize for my comments on steel workers. I did not mean to put down steel workers, McDonald workers, or any people of work classes. They are an inseparable part of the whole society and contribute values that’s irreplaceable. On the other hand, I agree with you that I do not see any value (other than public entertainments) that string theoretists are contributing to the society, until the day they can some what make some association between their theories and the reality world, it’s not even clear whether such a day will ever come.

    Quantoken

  12. J.F. Moore says:

    Quantoken, your glib comment regarding steelworkers isn’t really warranted. They make much more than someone working at McDonalds, and rightly so, since they produce something of substantially more value, with more risk, and more skill involved. It is not beneficial to society or that person to have them underemployed. On the other hand, it’s not really clear what society has lost if it is no longer supporting a string theorist.

  13. quantoken says:

    Surely jobless academics are much more dangerous than jobless steel workers. A steel worker who loses his job can just turn around and find a job at a street corner McDonald’s before he was able to go home and report the unfortunate news to his wife.

    But what if a string theorist loses his job? A string theorist who have to go through decades of training, maybe some brain washing as well, before he could grasp all the math tools and be able to talk fluently in the vacuous stringy language. I do not know what these people can do if one day it is announced that string theory is a dead end and no more “research” in string theory is going to be founded by public money. Not only is it a total disater to these people personally, but it is also a disaster to the public’s confidence of the general science research community.

    I do not think any one wants that to happen. A more likely scenary is the old people will continue to be supported until they die out and fade away. Meanwhile young generations should be discouraged from going into the field, with full and honest disclosures that this field has been fruitless in the past decades and could remain so for the foreseeable future.

    Currently CERN feeds half of all the world’s scientists conducting research in particle physics and fundamental physics theory. Everybody is talking about the prospective of what to expect once the LHC starts to operate in 2007.

    But no body is talking about the prospect that the whole LHC could be killed or left bleeding to death, before it even begin to operate. Or that upon completion, this thing is unable to operate in the way it is designed. That’s completely plausible. So why no one talks about THAT discouraging possibility?

    http://www.theglobeandmail.com/servlet/story/RTGAM.20050307.wphysics0307/BNStory/specialScienceandHealth/

    To me, the listed budget figure of merely $1.8 billion US dollars for the whole LHC budget, sounds very suspiciously LOW to me, for an undertake of this scale and this technological challenge. Digging a hole 27 km long underground would have costed far more than that. I know they already have the old tunnel to use, but constructing a new vacuum chamber 27 km long would have cost more than $1.8 billion already. Compare that with space shuttle launch. That’s merely a feat of accelating a 90 ton sealed pressurize chamber containing some computers and electronics to 7.9km/second, which is certainly much easier than maintaining a high vacuum in a 27 km chamber and accelerate protons to 14 trillion eV.

    So I do not know where that $1.8 billion figure came from, or has scientists been totally honest about how much it could actually cost. If it ends up costing $18 billion, or even $180 billion, instead of $1.8 billion. It could well be killed by the budget committee half way through construction. Remember the SSC?

  14. Wolfgang says:

    The “patrons” might be smarter than you think.
    I assume that one reason to lock academics in their ivory towers is to ensure that they do not cause trouble in the real world.
    In the case of Russian physicists after 1989 this was explicitly stated as one reason.
    And jobless academics are much more dangerous to politicians than jobless stellworkers etc.

    Just my 2c

  15. Alejandro, again says:

    “by patrons who have no idea what the issues are”

    I’d not be so sure of this neither. Back to the Aristotelian nonsense, a lot of people was being paid by patrons who know very exactly that the issue was “not having issue”. To keep status quo, a class of educated priests, a determinate shape of society, etc… Small barons paying other researchers for practical reasons (ballistic and fortress theory, in the case of Galileo) caused havoc in the status quo. Which, on the other hand, was the real issue of these barons too.

  16. Alejandro Rivero says:

    Doug, I would not say it is unprecedented, I am sure we can find someone. For sure, all the Aristotelian blah blah before Galileo, Pascal and Kepler. A bit later, Cartesiasism, ie, the vortical theory of the universe, could qualify for a predecessor of strings, in the “not even wrong” sense.It could be interesting also to check what theories were being “investigated” in Cambridge when it happened that Cavendish left his appointment as teacher to keep researching privately (he come back to Cambridge later). Also, and relating to Bethe thread, I wonder where had particle physics gone in the mid XXth century were not by the Lamb shift anomaly and its almost instantaneous calculation by Hans et al.

  17. Doug says:

    Lubos:There is a point that is never raised in all this discussion: that the current crises in theoretical physics is not only ludicrous, but unprecedented in all the history of science, and that such erudite discussion of esoteric knowlege is being paid for, to the tune of billions, by patrons who have no idea what the issues are, let alone why they arouse such passionate discourse amongst the learned benefactors of their largess. It’s a good thing too, because if they did, they might rise up and cut off all these high-priests who cloak themselves in the robes of the false priesthood we call academia.

  18. Alejandro says:

    The funny thing, Chris, is when the folder “reasons why the universe must be 3+1” relabels to “reasons thy the universe must compactify to 3+1”. With a postscript added by hand, “or to stay in a 4-brane”.

  19. Chris Oakley says:

    Here is an interesting thing for historians of science to contemplate. What is the value of the variable date below? I am guessing, about 1984.

    “We’ve got this great theory, but it only works in N dimensions, where N is significantly greater than four.”

    Answer (pre-date):

    Very interesting. File it in the circular file and try again.

    Answer (post-date);

    The universe must therefore be N-dimensional. Cool! Let us dedicate the rest of our lives to examining the consequences.

  20. Fyodor Uckoff says:

    Chris W said: What you’re suggesting is what quite a few string theorists have been trying to do for years.

    They have been *talking* like this for years, but surprisingly few of them have actually done much concrete work along these lines. For example Adams et al have shown that very strange things can happen to AdS orbifolds if you break enough supersymmetry. I guess that large chunks of the landscape can be shown to be internally inconsistent in such ways. As Lubos said, we don’t really understand supersymmetry breaking very well; I would not be surprised to find that when we do, a lot of candidates for cosmological models will be ruled out and the landscape will collapse. If you can point us to some [failed?] efforts along these lines it would be useful.

  21. Steve says:

    Will some very smart person please write a killer paper that finally buries the landscape dogma, thus saving both string theory and the scientific method. To date, string theory has been formulated mostly perturbatively in classical backgrounds–the strings can be quantised but the background remains rigidly classical. Until string theory is (somehow) formulated in a way that goes beyond this it can’t connect to the real universe nor can it say anything really concrete and certain about cosmology. The CC mystery is kind of like the mystery that surrounded superconductivity:when it was discovered around 1911 or 1912, superconductivity was a total mystery and all perturbative attempts to explain it failed. It was a quite a long while later that the correct (nonperturbative) explanation was finally found. I would say the situation with the CC today is something similar.

    It seems that the only known way to stabilise the moduli leads to this landscape scenario. So there are three choices:
    (a) You find an effective way to kill the landscape of string theory and reinterpret string theory (perhaps even starting the 3rd string revolution)and the theory can evolve again. From a string cosmology perspective it is also more natural to think of 3 dimensions decompactifying and 6 remaining compact (ala Brandenberger-Vafa) than compactifying down 6 large dimensions on CY space.
    (b)You finally accept that higher-dimensional spacetimes, ala KK, simply can’t actually work in physics, are not stable to perturbations and so you are forced to accept the universe is actually 4-dimensional after all.
    (c)You simply refuse to give on up the idea of extra dimensions no matter what, fix the moduli or do whatever it takes to hold onto the idea (no matter how contrived) and accept that it leads to a landscape of quadzillions upon quadzillions of superfluous and redundant vacuua. Although it predicts nothing, this is then more acceptable and believable to you than a single 4-dimensional universe (for which there is some evidence!)

    As much as I would be disappointed if there are no extra dimensions (it is a profound and beautiful idea) that might just be the way the universe really is. The KK idea has been around a long time now and has not really worked out. Nevertheless, from both a mathematical and physical perspective, there is something very special about 4-manifolds. Maybe you find 4-manifolds boring, but Kepler had to give up his cosmic system based on the Pythagorean solids and accept that planets actually just move on boring ellipses. Giving up your most deeply cherished beliefs and visions for the hard truth, no matter what it may turn out to be, is the heart of science after all.

  22. Quantoken says:

    Sorry Chris W. I did not credit you for the quote. If you had put an extra line breaker after the colon, it would have made it easiler to recognize it as what you say to Fyodor, not what Fyodor said. The style of Peter’s blog is just different from some other blogs I visit.

    Quantoken

  23. Chris W. says:

    That quote was in my reply to Fyodor, not in his own comment.

  24. quantoken says:

    Fyodor said: The oft-repeated refrain that “the theory is smarter than we are” is being invoked in this context.

    I read the above sentence in the logically equivalent form that string theoretists admit “we are more stupid than the theory we invent, (which is a useless theory)” 🙂 Which is the unfortunate fact.

    Peter said: “The scariest part was the beginning when he noted that what he would be talking about was work due to 500-1000 theorists and he put up a couple slides listing many of them.”

    What is scary is NOT that his talk is backed up by very solid scientific works of 500-1000 people. But rather the fact that such a vacuous thing is all that they can show us, after decades of work by 500-1000 of the most sophisticated theoretists. It’s 10^120 more vacuous than the cosmological constant itself:-).

    Quantoken

  25. Chris W. says:

    Fyodor: What you’re suggesting is what quite a few string theorists have been trying to do for years. So far they haven’t had much success. Susskind (at al) recommends that they stop worrying and learn to love the Landscape, while brushing aside concerns about testability as manifestations of an obsolete viewpoint on the philosophy of physics (and science) that has been transcended by the theory. The oft-repeated refrain that “the theory is smarter than we are” is being invoked in this context.

  26. Fyodor says:

    Well, with reservations I agree with both Peter and Lubos. I thought that Peter was just complaining about the evident bizarrerie of what Shamit K was talking about. For Lubos: it seems to me that what you should be doing is to look at cosmological models coming out of or inspired by string theory, and try to show that nearly all of them are somehow unstable or internally inconsistent. There are lots of examples of backgrounds in string theory that look ok until you consider some non-perturbative effect, and then they die or [AdamsPolchinskiSilverstein] get turned into something completely different. Maybe one can cut that 10^500 down to 10^1? Or 10^0 ?

  27. Luboš Motl says:

    Shamit is a nice and extremely smart and technically powerful guy – which of course makes it slightly more difficult for me to say that I essentially agree with Peter.

    The level of anthropicity of this thinking has been increasing in the past few years. A couple of years ago, Shamit would tell me things like “you don’t need to believe the anthropic principle; this is a question we should understsand anyway”. This kind of disclaimer has been disappearing.

    It seems that now it is expected that one believes the anthropic thinking as the ultimate answer we can have about nature. It is the motivation for this kind of research as well as the broad framework in which the research is done. I just can’t imagine how could I ever be convinced that a theory of this kind is a correct one because it lacks quantitative predictability.

    Some people really seem to be excited by the very fact that they can embed a relatively convincing framework into string theory whose conclusion is that we can’t predict anything – or perhaps, we can even choose which things can’t be predicted and which things can be predicted, even though we can’t actually make these predictions.

    This opinion is contrary to everything I believe about constructing theories and determining their value. String theory is valuable only because it can naturally predict the right spectrum of particles and interactions (including gravity), at least qualitatively, from a starting point that has many less assumptions. The anthropic framework may be describe by the opposite words.

    It has always been trivial to construct a theory that can’t predict. The Bible, via the power of God and His Son, has also an “explanation” for everything – God wants it this way. The landscape of all possible field theories is another example.

    The main difference between the anthropic explanation and the God explanation is that the Christians are often right-wing and prefer the church and family, while the anthropic people are mostly left-wing and better in calculating quantum field theory. But as far as the explanation goes, it seems on equal footing.

    A theory can only become a convincing scientific theory if it explains more data than what is inserted, and this is a dogma for me, if you wish. Otherwise it’s just a story, fairy-tale, mnemotechnical bookkeeping device at best. In effective QFT, we must insert a rather small value of the C.C. But if we create whole untestable God stories with 500 fields and complicated potentials etc. just in order to get one number, I just can’t imagine that this approach can ever be promoted to science.

    Equivalently, the probability that (assuming that there is a complicated mechanism that only generates the C.C.) we would guess the right mechanism behind the C.C. – just by looking at the single number and the plethora of tools that string theory gives us – is something like 10^{-200} and I see no point in trying to find the “right” mechanism.

    It seems more appropriate to say that we don’t understand one number, we won’t know the right explanation of the C.C. (we only have real problems with the C.C. after SUSY breaking, and therefore the ignorance is because we don’t understand SUSY breaking) until the complete theory of everything – which includes string theory in the cosmological context – is understood – and we should focus on places where we have a lot of data to unify into one theoretical description. (Well, we don’t have too much data right now even beyond the C.C. but that’s a different topic.)

    Also, in some sense, the landscape business is “politically correct”. For example, treating all conceivable vacua as equal is the ultimate example of egalitarianism and political correctness (and I would also add stupidity).

  28. Peter says:

    I don’t object to Kachru’s work because it’s hard to believe or weird, I object because it’s not science. It not only doesn’t predict anything about anything, it inherently is a framework that can never predict anything about anything. To see leading figures in particle theory giving pretentious talks like this that are not science in any sense of the term is outrageous, disgraceful, and someone should call them on it.

    No, Kachru doesn’t “predict” the CC, he sets up a framework in which you can’t predict the CC, and thinks that is a great achievement. I have no idea whether the CC will be computable in an ultimate theory. Right now we don’t have a convincing unified quantum theory of particle physics and gravity. When we do, maybe the CC will be computable within it. But the problems with string theory go way beyond the CC. If Kachru’s framework allowed one to calculate something, but not the CC, one could take it seriously. But it doesn’t allow you to calculate anything. Not one single thing, nada, zip.

  29. Fyodor Uckoff says:

    Basically what you are saying, Peter, is that you find the work of Kachru et al hard to believe. And I agree — I think we should try our best to explain things within one Universe. And I’m pretty sure that Shamit would agree that such efforts should [also] be pursued. But what I find puzzling is this: you find this stuff hard to believe. But the observed fact that the cosmological constant is non-zero and small is utterly, completely mind-boggling from *any* conventional point of view. So when somebody comes along with a correct theory of all this stuff, it is *guaranteed* that it is going to be something extremely weird. I’m sure you don’t expect someone to do a conventional quantum field theory calculation, however clever, and have the value of the CC fall out at the end. So the mere fact that Kachru’s colliding branes in higher dimensions *looks* utterly incredible means nothing. The *correct* theory will probably look weirder still, no? So what’s your problem with weird theories?

  30. Peter says:

    I didn’t attend the Kachru talk in person, just looked at his slides online and watched some of it on the online video. When I have personally attended talks like this I have generally at the end stood up and asked a question along the lines of “From what you have said, isn’t it true that this is a theory that can never predict anything” (most notably when Susskind gave a colloquium here, and when Douglas gave one at City College a while back). No I don’t enjoy publicly confronting people like this, but I think it’s outrageous that they give this kind of talk, then no one says anything.

    I did attend Smolin’s talk, don’t remember why I didn’t write anything about it. He basically went over his recent paper in which he argues that any quantum gravity theory based on connection variables implies “doubly special relativity” effects, effects that he was claiming have implications for the AUGER and GLAST experiments.

  31. Thomas Larsson says:

    In a way, all this reminds me of the contrast between Lorentz’s and Einstein’s explanations of the null result of the Michelson-Morley experiment.

    We live in a region of the Landscape where the aether wind is very small, because a large aether wind is not compatible with human life.

  32. Chris W. says:

    In a way, all this reminds me of the contrast between Lorentz’s and Einstein’s explanations of the null result of the Michelson-Morley experiment. The fact to be explained had a stark simplicity about it, whose full significance Einstein grasped and Lorentz couldn’t quite perceive, in spite of his gifts as a theoretician and mastery of the subject.

    Of course, it has become clear that for Einstein the Michelson-Morley result was expected and almost trivial; he was led to the underlying principles by thinking about Maxwell’s electrodynamics and certain observations which by themselves had not heretofore appeared to be problematic.

    In contrast, string theory’s birth was oddly accidental. The hope has been maintained for 25 years that its underlying physical principles would eventually become clear. Instead, it has begun to seem like a mockery of the very idea of physical explanation — a massive virtuoso exercise in mathematical modeling, supported by the “accursed fertility” of differential geometry (to use Kant’s phrase*). As Kachru says without apparent irony:

    “In studying any of these issues in depth, [the] most striking feature is the diverse array of possibilities the theory encompasses.”

    Again, why is this diversity supposed to be a virtue, when there is so little empirical basis for believing that most of these possibilities are actually realized, and so little real insight offered to account for their absence?


    * from the following remark, as quoted by Karl Popper:

    “Concerning metaphysics in general, and the views I have expressed on their value, I admit that my formulations may here or there have been insufficiently conditional and cautious. Yet I do not wish to hide the fact
    that I can only look with repugnance and even with something like hate upon the puffed-up pretentiousness of all these volumes filled with wisdom, such as are fashionable nowadays. For I am fully satisfied that the wrong way has been chosen; that the accepted methods must endlessly increase these follies and blunders; and that even the complete annihilation of all these
    fanciful achievements could not possibly be as harmful as this fictitious science with its accursed fertility.”

  33. Anonymous says:

    I heard Lee Smolin, the LQG guy, spoke at the string group at Columbia recently. Did you attend? If so why no comment?

  34. Jean-Paul says:

    Well, Shamit is an exceptional case, in a way similar to Douglas. Unlike most landcape loonies, they are respected string theorists so they deserve some attention.
    Now they want to establish themselves as “phenomenologists”, talk to experimentalists, give public lectures etc. Unfortunately, this leads to ridicule. The line “big bang as brane damage” joins “solution of unification by nullification”,
    “out of this world solution of the hierarchy problem”, “little Higgs” and other absurd one-liners that dominate the infamous “physics beyond the standard model”.
    I remember one Witten’s colloquium on unification: he started from experimental data and after 10 minutes he was deep into linear bundles. Fortunately, he didn’t try jokes, so he avoided ridicule — it was just another weird talk…
    Jean-Paul

  35. anonymous says:

    Peter, I take it from “and told us nothing at all about the properties of the world today” that you were there for the talk. If so, then why didn’t you make this comment? Is it easier to be brave online?

  36. Peter says:

    The same thought had occurred to me….

  37. Anonymous says:

    I’m guessing that if one compared “stephen”‘s IP to “plato”‘s one might notice a pattern.

  38. stephen says:

    Not sure why you’re quoting this press release (which doesn’t have anything to do with Kachru’s talk).

    I was aware of the cyclical universe idea and brane collisions, and watched the cosmic string develope from supersymmetrical valuations.

    Please be patient.

    One would have to know how to get there and “if,” from early comsological idea of a early universe, and we assume it is cyclical, something had to exist before the strings?

    I used the whole example of Dvali’s analogy as a comparison to all the dimensions (yes I am listenng to you), in context of the fermions on the brane(what is held to it?) the water(represents the dimensions), and the idea of bosonic production off the brane, concealed as gravitational wave production.

    If the torus existed from the genus figure collapse, how would rejuvenation take place? Anti-gravity production indicated by the jets? Swiss cheese universe?

    Do you not feel such geometries/topologies can be comparative to cosmological associations Peter?

  39. Anonymous says:

    “Big bang as brane damage”??
    I think I will go off and read some of Bethe’s old papers instead…

  40. An experimentalist (Monad) says:

    Years ago, I went to one general ST talk by Brian Green. My (very) crude grasp of it was that even when they get it right and the masses of all the quarks and leptons roll out of an ab initio calculation, they will have exchanged the 20 or so free parameters of the SM for the free parameters of the topology of thier multi-dimensional space.

    When (if) they get that far, I’ll take another look. But for now, yes, I stay in my lab.

  41. Peter says:

    Not sure why you’re quoting this press release (which doesn’t have anything to do with Kachru’s talk).

    Dvali’s extra dimension nonsense doesn’t predict anything about anything (he has no idea how many extra dimensions there are, their sizes or properties). This isn’t science in any reasonable sense of the term.

  42. stephen says:

    I am sorry, I just realize the mistake I might of made.

    I compared the metal plate Dvali hits, to a brane?

  43. stephen says:

    If gravity is modified at large distances, it’s modified everywhere. That would make it possible to verify modified gravity by measuring the orbit of the moon to within one millimeter

    http://www.eurekalert.org/pub_releases/2005-02/uoc-sma021405.php

    So would Arkani-Hamed, Sava Dimopoulos, and Gia Dvali doing extra dimensions… and the attempts to explain these dimensions, be a fruitless and not worth finding experimental opportunities?

  44. Anonymous says:

    They probably showed up to hear professor Kaku talk about alien visitations and were sorely disappointed.

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