## Wednesday, March 30, 2005 ... /////

### Wijnholt's topological holography

It's a sunny Wednesday and Natalia Saulina convinced me to attend a seminar of Martijn Wijnholt, a Harvard alumnus, at the M.I.T. He's been working on it with Leonardo Rastelli, also at Princeton. Their work, a topological simplified version of the AdS/CFT correspondence, relates two theories:

• the B-model on "H3 x S3" where the hyperboloid "H3" is a Euclidean version of "AdS3" (as a reader reminded me - thanks - the obvious answer why "H3" and not "AdS3" is that one needs an even number of time dimensions (0) for the complex structure to exist, so that we can twist the theory)
• a subset of the symmetric orbifold CFT, living on the boundary
Martijn motivated this research by the question whether we can check the AdS/CFT correspondence at the level of stringy loops. This has formally been achieved because in their simplified context, the loop amplitudes are uniquely determined by some recursion relations - the same recursion relations on both sides. Explicit checks have not been done.

Unfortunately, Martijn did not really have time to discuss the second theory, namely the boundary CFT, and he focused on the bulk description. However, there were some interesting points already in the bulk description. The most important one is that he argued that the twisted WZW model is equivalent to
• the bosonic (p,1) minimal model
where "p" is the flux through the "S^3". This equivalence of CFTs has been established kind of exactly although it was a bit confusing what the "(p,1)" model really was - in some sense, it does not have any operators for "q=1" - see e.g. (15.3.16) in Polchinski's book - unless you couple it to the two-dimensional gravity. (A discussion whether the gravity was needed and whether it was topological gravity or not followed - Ami Hanany, Hong Liu, me etc.) I did not quite understand where his operators eventually came from, but Martijn finally compared some operators - tachyonic ones - with the operators describing the "H3 x S3" geometry.

### Flat Earth Award

A group of kids from the "Green House Network" - the kind of children who really believe that "The Day After Tomorrow" is reality - organizes the "Flat Earth Award" to appreciate the most thoughtful and most effective "global warming denier". The 2005 nominees are

• Michael Crichton
• Rush Limbaugh
• Fred Singer
All of them are very strong and very famous candidates. Nevertheless, oil industry together with most of us who work on the right-wing conspiracy have decided that Fred Singer, an atmospheric physicist and a successful PhD student of John Wheeler, should be the winner because he has spent a lot of time with climate science and he may have a lot of things to say to these kids. Once we decided, he immediately became the frontrunner and the likely winner of the award on Friday.

And yes, he has interesting things to say - I've already read his acceptance speech. ;-)

What makes me a bit happier is that the life of these weird green kids is not such a smooth sailing. If you look at their website
you can see how the voters answer the bizarre question
• "Why do you care about the Climate Crisis?"
It is not hard to imagine what sort of answers the kids expect. However, the last few hundreds of answers were a bit different. Well, the reactions almost seem to prove a consensus. ;-) For example, the last ten comments or so look like this:

### GM to produce hydrogen cars

General Motors is planning to produce and sell a lot of hybrid cars - in which the burning gas recharges an electric motor. Today, however, GM also signed a \$88 million deal with the Department of Energy to build 40 hydrogen fuel cell vehicles and to improve the technology. Shell Hydrogen LLC will provide them with five Hydrogen gas stations across the U.S.

Note that the hydrogen motors are based on this fascinating chemical reaction:
• 2 H_2 + O_2 -> 2 H_2 O
An amazing feature of this reaction is that it does not involve carbon - the element that has recently been identified by the "progressives" as the ultimate source of evil (such as the so-called global warming as well as life itself). The hydrogen fuel cells have been used by the astronauts from the very beginnings of the space program in the 1960s, and the barriers that have always prevented this technology from spreading to the car industry and elsewhere were always economical in character. It is about 4 times as expensive to produce hydrogen. My friend George has a rather informative description of the situation at the web page of his house:

### David Tong's vortices

David Tong who is now a professor in the original Cambridge is visiting us - his friends in the new Cambridge (David returned back to home; he spent a few years at the M.I.T.) - and yesterday he spoke about his work about

• The Vortices in non-Abelian Yang-Mills
He also told me about some additional interesting ideas, but I feel I can't tell you about this private discussion. In the private discussion, he worked with an N=2, d=4 U(N) gauge theory with N flavors in the fundamental representation (yes, the number of flavors equals the number of colors, but the number of supersymmetries "N" is a different number haha). In the talk, there was no supersymmetry (this sentence was added later because David has pointed out my error in the comments, so don't get confused).

Normally, one can find cosmic strings in Abelian Higgs models - i.e. a spontaneously broken U(1) gauge theory - which are vortices: the Higgs field has minima on a circle, and this circle is identified with a circle surrounding a vortex. You might think that if you work with U(N), only the U(1) part will participate in the solution. Well, while it's true that it's only the U(1) part that is responsible for the existence of the vortex solution, the SU(N) part is important for detailed properties of the solutions.

David Tong has constructed a whole zoo of various objects - domain walls and cosmic strings of different types stretched between them; the types are determined by the U(1) that has a non-zero magnetic flux through the tube. On the cosmic strings, one can place a 't Hooft-Polyakov monopole that is able to change the type of the string. Normally, a 't Hooft-Polyakov monopole would carry no "Dirac strings", but because David works with U(2) and not SU(2), there are two different "Dirac strings" attached to this monopole.

The most intense discussions, especially between David Tong, Nima Arkani-Hamed, and partially me and others were about David's statement that the following widely believed statement is not true:
• The probability that two field-theoretical cosmic strings intercommute is always essentially one.
Note that this is usually used as a criterion to distinguish "ordinary" field-theoretical cosmic strings, whose probability should be one, from "cosmic superstrings" that intercommute with probability proportional to "g_{string}^2".

## Monday, March 28, 2005 ... /////

### Superhorizon fluctuations and accelerating Universe

Several physicists and bloggers, e.g. Jacques Distler, Peter Woit and especially Sean Carroll who may be considered a true expert in these questions and who added a very new article after this article of mine was published, recently noticed a paper that claimed that the cosmological constant was not needed. Instead, the accelerating expansion was conjectured to be a consequence of fluctuations of a scalar field (and the associated stress energy tensor) whose wavelength was longer than the Hubble radius i.e. the size of the visible Universe, roughly speaking.

The paper has also been given a lot of attention in the media:
Everyone who is not a direct expert in these things should know that the community is highly skeptical about such a proposal - and in some cases, for example the case of Matias Zaldarriaga (a countrymate of most co-authors of that paper), stronger words than "skeptical" would be more appropriate. People seem to agree that whatever the very long wavelength fluctuations are, they are already included in the definition of the background itself. They cannot be a source of some additional local effects by locality - this very statement is, in my opinion, enough to reject the claim and more detailed calculations are unnecessary.

### A new earthquake

Less than an hour ago, namely at 11:09:37 Eastern U.S. time, a new earthquake of magnitude 8.7 (originally reported as 8.2 or 8.5) occured on the same fault line as the December 2004 earthquake of magnitude 9.0 that caused the deadly tsunami. It was centered near Sumatra, an island that belongs to Indonesia - a few hundreds of kilometers South from the place of the previous earthquake. Thai officials warned that tsunami could follow.

Incidentally, the international help for the victims of that tsunami has exceeded 10 billion USD. Twenty percent of this amount comes from the U.S. - much like the 20 percent of the global GDP. The Reference Frame hopes and predicts that the smaller magnitude of the earthquake today - and smaller depth in which the soliton is supposed to be created (it's easier to create the soliton in deep ocean) - will translate into much lower casualties...

200 minutes after the earthquake, only 50 casualties are reported.

## Friday, March 25, 2005 ... /////

### Viscosity vs. entropy density ratio

A reader has asked me to comment on the following article in New Scientist:

The content of this article has something to do with the gauge theory duals of black holes and gases of black holes. At the end, they mention the conjectured production of the "black holes" at RHIC. I have mentioned the article of Horatiu Nastase here and therefore I won't say anything new about this part of the article here.

The beginning of the article describes a rather generic observation - due to people like Buchel, Kovtun, Liu, Son, Starinets - that seems to be a nearly universal law. Let me describe this intriguing insight in the following way:
• The ratio of shear viscosity to the volume density of entropy seems to be always greater than a fixed constant "1/4.pi" (times hbar over Boltzmann's constant). The inequality is saturated for a large class of strongly coupled interacting quantum field theories - corresponding to a kind of ideal fluids - and one can explain it by the fact that they are the holographic dual of a gas of black holes in some kind of anti de Sitter space.
Two related papers for those who want to know more:

The arguments look convincing to me. I would like to emphasize that such an inequality is not just a consequence of dimensional analysis. Indeed, if we are allowed to use "hbar, c, G_{Newton}", all quantities are effectively dimensionless and may be compared with each other. Does it mean that for any pair of quantities, there is an inequality? No way.

Nevertheless, this inequality is pretty natural. Viscosity is about the lost energy - energy that has been converted to heath, complete chaos. Such a thing may always occur if there are many microstates around. If there are many microstates of "chaos" around, it's reasonable to expect that a lot of energy will be lost - viscosity will be large. But this universal law does not talk about a rough inequality only, it actually defines the precise bound (1/4.pi). It's potentially a very nice universal law and the AdS/CFT correspondence shows its muscles.

### Raphael's and Nima's talks

A small comment: a clarifying statement by Prof. Gerard 't Hooft has been added to the report about Sidneyfest.

I will describe two talks in the same text: Raphael Bousso's duality seminar he gave yesterday, and Nima's lunch seminar today.

Raphael: good and bad backgrounds in quantum gravity

Yesterday, Raphael Bousso, one of the kings of holography, discussed what the right quantum gravity observables could be and should be in different cosmological backgrounds. String theory is always smart and it carefully avoids all potential problems - for example it gives us the S-matrix in the asymptotically flat spacetimes, and closely related variables in the AdS space. But it has told us very little about the more complicated cosmological solutions.

This is both good and bad. It's good because it always reassures us that string theory is a consistent quantum theory of gravity. It's bad because despite string theory's silence, we want some answers to these questions, and we run into many problems, especially in the case of de Sitter space:

• thermal radiation that introduces noise and eventually kills us (you may kill someone with a spoon if you're patient enough)... Note added later: Raphael corrected me - the problem is not whether you're patient enough, but whether your victim is patient enough
• the existence of event horizons that prevents us from measuring the final state
• a related problem, the non-uniqueness of the vacuum
• and so forth...
Different backgrounds have various types of problems, and people usually grade the most typical FRW cosmologies as follows:
• very good: flat space (and AdS spaces) - the S-matrix exists and the problems are gone
• very good: deccelerating Universe whose future is much like in flat space, and therefore people used to say that it is essentially as good as the flat space
• very bad: the accelerating Universe with the equation state "w > -1", which are usually grouped together with the following group because of the existence of horizons
• very bad: de Sitter space - the ultimate example of the problems and subtleties we encounter in quantum gravity
Raphael presented some arguments that encourage you to regroup the four classes differently:
• very good: flat space and AdS spaces
• average: deccelerating Universes. Raphael says that this group is worse than advertised because you would always need to know an infinite amount of information about an infinite amount of matter to describe a state of this Universe
• average: accelerating Universes. Raphael argues that this category is better than its reputation because the radius of curvature grows to infinity, the temperature drops to zero, and the integrated energy from the "spoon" is actually finite
• very bad: de Sitter space
Nima - inflation is anthropically necessary

One hour ago, Nima Arkani-Hamed explained that inflation is necessary because of a reasoning analogous to Weinberg's anthropic "derivation" of the existence (and approximate size) of the cosmological constant. Much like the cosmological constant should be small for anthropic reasons, Nima says that the curvature of the spatial slices should also be small. But it may be non-zero, as far as the anthropic reasoning goes. However, Nima is afraid to predict that it should actually be nonzero - and of course, Cumrun and me were peacefully questioning whether this kind of anthropic reasoning based on "things that sound reasonable" without any chance for a quantitative definition of the word "reasonable" is still science.

## Thursday, March 24, 2005 ... /////

### False anomalies?

One of the main topic of the discussions at Harvard today is the new paper

by Mitsuo Abe and Noboru Nakanishi. Although they're Japanese, this article may be a good opportunity to thank Samsung Electronics for the 256 MB USB Flash Drive that I've finally obtained. ;-)

What is this paper about? The gentlemen claim that
• Alvarez-Gaume and Witten were sloppy in their derivation of gravitational anomalies in 1984
• the textbook of Superstring Theory by Green, Schwarz, Witten is also sloppy
• the sloppiness is based on confusion between two types of a time-ordered product
• these two time-orderings are "T" and "T*"; the former is the literal time-ordering in the Hamiltonian/operator formalism while the latter is the type of time-ordering that one naturally obtains from the covariant path-integral approach; "T" commutes with the time-derivatives while "T*" does not
• as an example, the Japanese physicists argue that what Alvarez-Gaume and Witten considered to be a gravitational anomaly in two dimensions, is actually just the difference between the expressions containing the "T" and "T*" products

### Susskind: wormholes can't work

Lenny Susskind has a new paper:

He argues that the time travellers will have to find a different technology than the traversable wormholes (TW).

The large wormholes are impossible classically because they would violate the positive energy theorem. Quantum mechanically, there could be loopholes that make them possible. However, Lenny Susskind argues that
• the energy must be conserved locally, and therefore the energy eaten by the throat is exactly zero
• because we know the energy exactly, we can't know the moment in which the object jumped into the wormhole - by the energy-time uncertainty relation
• consequently, you should have the same probability to reappear from the second throat at any moment, which does not seem like if you reappear at a particular moment of the history of the Universe

### DNA backup: inheriting from grandparents

Many of us - and our computer managers - often back up their data. Something may go wrong in which case there is still a chance to avoid the worst. They just return to the previous version.

The DNA code is a natural example of a large data file. Mutations and natural selection keep on editing this file - many files, in fact. Usually it was assumed that we inherit the file from our parents only (plus some mutations). If a piece of the DNA code of both parents is damaged, then the son or daughter has bad luck. There's no way to fix it.

Or is there?

David Goss has pointed out a new fascinating discovery in genetics described in the New York Times:

The biologists at Purdue University have found that 10 percent of off-spring of a plant are able to repair a genetic problem of both parents. The only acceptable explanation that the biologists have been able to propose is the following:

• The organisms carry not only the parents' code, but also a cryptic backup of the code from the grandparents (and maybe beyond). This code is sometimes used if something goes wrong with the parents' code.

Let me philosophize a bit. If you remember your biology classes, you know that there are dominant and recessive genes. Recessive genes are those that are inconsequential in a heterozygous genotype (i.e. in which there are two copies of an allele that differ). My countrymate Gregor Mendel, the father of genetics, has described many examples of recessive genes of a plant. But I guess that he would have assumed that if both parents have an important segment of the DNA damaged, it can't get fixed. But it can.

### Maldacena in the Lineland

Joanna Karczmarek is an insider in two-dimensional string theory. She has just described Juan's recent paper with many details that are not even present in his paper:

The paper is relating two families of objects and questions:
• Infinitely long strings in two-dimensional string theory
• Non-singlet wave functions of the corresponding matrix model
Concerning the first point: the dynamics in the Lineland, which is how Brian Greene calls the (1+1)-dimensional backgrounds, may look pretty boring. (We will be discussing the bosonic string theory lineland, which contains a massless "tachyon" as the only local excitation.) When you play chess, you can't even castle. Your destiny is to look into the eyes of your neighbor forever. These eyes (namely the boundaries of line intervals) are just points and they carry no emotions. It's because there are just a few types of extended neighbors in this strange Universe:
• The ZZ brane which is a localized type of a D-brane and plays no role in this article
• The FZZT brane that is spacetime filling, but the tachyon profile goes from the maximum to the minimum in such a way that the brane continuously disappears
• The fundamental string
Concerning the fundamental string, it carries
• D-2 = 2-2 = 0
transverse sets of oscillators which is not too many. Consequently, there is no Hagedorn tower of states, just one ground state which we still call the tachyon but whose mass is actually zero in two dimensions.

## Wednesday, March 23, 2005 ... /////

### Graduate students support Summers' presidency

There were several reasons why I did not post anything here for a few days:

• The report from Sidneyfest was slightly time-consuming, and there were good reasons to keep it as the first posting of the blog for a couple of days
• On Monday morning, all physics professors at Harvard received an embarassing e-mail from an anonymous sender who was most likely located in San Diego. The sender, who was provoked by my article about the last faculty meeting, connected me with voodoo, cross-dressing (?), accused me of racism, and demonstrated that he supported very different political powers in Iraq than I do (well, he or she supported the anti-American forces)
• Would you agree that it is sick to combine the discussion about Summers with the situation in Iraq and the Middle East? It was not the first time when an e-mail indicated that Al-Qaeda is going after Summers' supporters. I was feeling threatened, embarassed, and black-mailed, and now I am only slowly regaining the feelings of freedom and self-confidence
• The physics postings were also suppressed for a couple of days after the description of Witten's talk at Sidneyfest revealed that even things such as the Weinberg-Witten theorem are controversial
Concerning our University's president, I am happy to announce that according to an official poll at Harvard's GSAS (Graduate School of Arts and Sciences),

## Saturday, March 19, 2005 ... /////

### Sidneyfest

Arthur Jaffe and Barbara Drauschke organized a magnificent conference at Harvard - informally called Sidneyfest - to thank Sidney Coleman for everything he has done and he has been for physics and the physicists. Sidney, whose health is unfortunately not as good as we would wish, partially because of the Parkinson disease, has been a great physicist, an excellent teacher with unlimited patience, an eccentric human being, and a neverending source of jokes.

He has also played the role of Wolfgang Pauli of his generation; he liked to disprove ideas, and he was also a genius in explaining things to others. We have heard numerous stories about Sidney Coleman. Unfortunately, this article can only cover a tiny fraction of the stories and comments. Many participants told me that they visit this blog, and it's not impossible to imagine that some of them will write some interesting comments.

Message for all the usual suspects who like to argue with me: try to realize that your (and our) texts are being read at least by five Nobel prize winners and several other exceptional people. ;-) I will try to appreciate this fact, too. At least sometimes.

At any rate, the conference has been an exciting testimony about the heroic period in high-energy physics - the 1960s and the 1970s, roughly speaking - in which the physicists were making much more progress than today, especially because of the intense interactions between the theory and the experiment. It was the case despite the fact that these heroes of ours were much more ignorant about quantum gravity than we are today.

Friday

John Huth, the chair of our physics department, applied some of his numerous skills and he started the whole conference. I think that it would have been more difficult for Arthur to organize everything without John's support.

Two dinners were a part of the happening, but let me also say something about the talks. On Friday, David Gross '04 started. (On the picture on the right side taken in 2004, David Gross was showing the new wing of the Kavli Institute for Theoretical Physics which has already been completed.) His talk The Future of Physics, whose original edition was presented at the KITP Santa Barbara in October 2004, was very broad and entertaining. David Gross '04 was introduced by Norman Ramsey '89.

## Friday, March 18, 2005 ... /////

### Jacques' anthropic talk

Jacques Distler, our blogging string-theoretical friend, just spoke about

• The fun with random polynomials
which is a project he works on with Uday Varadarajan (Austin). The main point of the project is to generalize
to the case of arbitrary supersymmetric renormalizable (quartic) potentials for the "N" fields that play the role of the redundant anthropic superstructure. Recall that in the picture of Nima, Savas, and Shamit, there are "2^N" vacua because each quartic potential for one of the "N" scalar fields has two minima. For "N=400" or so, this is a large number of vacua. Some of them will have a realistic (i.e. very small) value of the cosmological constant and the Higgs mass, but the observation of Nima et al. is that under certain assumptions, all other parameters may have nearly constant values across the "friendly neighborhood".

Jacques considered generic cubic superpotentials of "N" chiral superfields that are constrained to preserve a "Z_4" R-symmetry under which the fields are odd, and therefore the superpotential must be an odd function. Renormalizability implies that there are linear and cubic terms only. He fixed the "GL(N,C)" symmetry in such a way that his model only differs from the superpotential of Nima et al. by an extra trilinear term
• sum_{i smaller j smaller k} b_{ijk} phi^i phi^j phi^k
with a huge number (N choose 3) of new coefficients b_{ijk}. Generically - except for sets of measure zero in the (a,b)-parameter space (where "a_i" are the coefficients of the linear terms in the superpotential) - one still obtains "2^N" different vacua. It is straightforward but tedious to calculate the average values of the superpotential, the squared potential (second moment), as well as all other conceivable polynomials of the roots (vacua) - sums over all roots (vacua); all the average values are polynomials in the variables "a,b" themselves. The vacuum energy and perhaps other physical parameters are calculated in this way.

You essentially know how to do it if you know that the coefficients in a quadratic equation are the sum and the product of the roots, respectively, and similar rules apply for higher degree polynomials, even if they are polynomials of many variables. It requires some neat linear algebra and characteristic polynomials.

This was the less controversial - the mathematical - part of the talk. The more controversial part of the talk was the physical interpretation. Jacques intended to avoid the anthropic principle, but he could not. He did not avoid it simply because he was talking about "generic values of b_{ijk}" for which some conclusions apply, and so forth. This very fact has essentially separated the room into two political parties of theoretical physics defined - more or less - by their relation to the anthropic principle:
• Jacques and Nima defended the straightforward and somewhat ad hoc procedures.
• The rest of us who participated in the discussions - which means especially Cumrun Vafa and Nati Seiberg who is visiting us because of the Sidneyfest on Friday and Saturday - were dissatisfied with the vague anthropic rules of the game.
Nati Seiberg liked the talk, as he explained us now at the dinner - and he proved it by the fact that he did not sleep. Nati Seiberg's main criticism was the apparent two-stage process in which the vacua were chosen:
• First, one talks about various distributions in the "b" space - where "b" are the coefficients of the trilinear terms in the superpotential.
• Second, one decides about some values of "b", and he talks about the "landscape" of different values of "phi's" and the distribution in this landscape assuming fixed values of "b".
Nati did not like it because in reality (i.e. in the full string theory), one should consider "b's" to be just other examples of the fields "phi" and consider all of them simultaneously and look for the allowed solutions involving all of these fields.

Cumrun complained about the vague and arbitrary sense in which the word "generic" was used in the sentence "generically, the qualitative conclusions of Nima et al. are not changed". He argued, and I agreed with him, that there are infinitely many "measures" that can decide what choice of the couplings "b" is generic and what choice is not. For example, Cumrun's "generic" choice is to choose "b" in such a way that the resulting superpotentials "W" are distributed according to any distribution we like. We believe that both of these choices are equally (un)justified.

Moreover, I was trying to convince others that generically, for a "naturally generic choice of b" one will be very *close* to one of the bad regions where the approximation breaks down and "b" imply a very different picture from the case of Nima et al. (where all "b" equal zero). More concretely, the statement that the other couplings have a small variance will fail. It's simply because there are roughly 1 million different coefficients "b" that one works with in Jacques' superpotential, and it is more or less guaranteed that at least one of them will be in some very special interval whose width is 1/100,000 of the allowed interval for values of any "b". I think that Nati was trying to convey a similar point, in a sense.

The simplified point of the anti-anthropic people is that there exists a huge number of ad hoc procedures with different outcomes, and one should use physical, not sociological, principles to select the right rules. Of course, according to Cumrun, me, and probably others, the preferred physical principles that should decide which choices are generic and natural should be based on the actual dynamics of our theory itself, as exemplified by the Hartle-Hawking wave function in Cumrun+Hiroshi+Erik's paper about the entropic principle. They should not be based on some extra external (or political correct) assumptions about "uniformity" or "democracy" of something.

Once again, the viewpoint that I share with Cumrun is, once again, that no arbitrary assumptions about the selection etc. should be added to our theory. If we know what dynamics of our theory is - something equivalent to its action - all physically meaningful predictions should be obtained simply by an appropriate mathematical manipulation with this action (or whatever it is replaced by). Dividing fields and constants to fields and constants of 1st category and 2nd category and assuming various randomly chosen and unjustified probability distributions for these variables is simply not a scientifically satisfactory approach.

## Wednesday, March 16, 2005 ... /////

### Gubser and structure formation

If you had the feeling that there were too many people today who were opening the blog, be sure that it was just a temporary effect of the no-confidence vote yesterday. The Reference Frame has had 2927 unique visitors today (the 24-hour period ending at 6 p.m.) and 6346 total visits, and I assure you that this number will decrease back to the usual values that are dominated by the physicists and the physics fans.

Steve Gubser (from Princeton) has just gave an interesting talk at the joint seminar in which he tried to convince us that structure formation (the process in which the early clumps of matter and the first galaxies were born) is a very interesting topic in cosmology, even for string theorists, in which some signs of new physics may be found if one tries to reproduce the observations.

He argued that the data behind structure formation are more exact than the data that are used to discriminate between the different models of inflation. Structure formation has been studied less intensely by string theorists than inflation (well, it's because it's closer to astrophysics and seemingly further from fundamental, extremely high-energy physics), and the comparison should become more balanced, he argued. One of the observations he was trying to explain were the more-than-expected empty voids in between the clusters of galaxies which are marginally contradicting some computer models of structure formation.

His solution was based on an extra ultralight scalar - whose inverse mass is roughly a Megaparsec (the typical size of the haloes around the galaxies). The corresponding "fifth interaction" only couples to the dark matter (dark sector) in the first approximation, and it only induces dimension six operators in the visible (baryonic) sector which is below the threshold what is observable. The equivalence principle has not been tested too well for dark matter, so such an extra fifth force is not directly falsified.

The exchange of a massive scalar gives you a Yukawa force that exponentially decreases at distances of order 1 MPc. Recall that the exchange of a scalar is attractive between sources of the same sign - much like for gravity whose spin is two, and unlike the electric forces that exchange a spin 1 gauge boson. This can be seen to help gravity to speed up the cluster formation and empty the voids more efficiently, which is good for observations, he argued.

(An example of the effect of the scalar is the scalar called the T-modulus, a radius of a circle, which will try to repel the momentum modes and the winding modes of a string because they carry the opposite sign of charges with respect to the scalar.)

This basic story sounds logical, but one could probably imagine many other ad hoc modifications that have the effect (for example, Jacques Distler proposed that the voids are actually filled by "dark galaxies" where the stars have not started yet). Instead of speculating, let me finally mention a relevant paper by Gubser, Nusser, Peebles:

Recently there have been quite a few good newspaper articles about theoretical physics and string theory in particular: informative, fair, balanced, organized. The article about "Twenty years of string theory" in The New York Times is probably the best example. Unfortunately, the text of Keay Davidson from San Francisco Chronicle does not fit the bill.

What is the main reason why I think that this article is dumb? The main reason is that the journalist was obviously completely unable to figure out who are the people who may give some qualified opinions about the subject. Consequently, the article is nearly equivalent to a poll between random people on Massachusetts Avenue or random people in the jungle, for that matter. The article is a typical example of the journalistic opinion that the truth about high energy physics may be determined by a referendum in the jungle.

If an uninformed person reads the article, she could think that the opinions about quantum gravity and high-energy physics of David Gross, John Schwarz - and also Brian Greene and Raphael Bousso - are as important as the opinions of Zlatko Tesanovič, Michio Kaku, Lawrence Krauss, Peter Woit, Philip Anderson, Bob Laughlin, and Carlo Rovelli. My apologies to those in the latter list who believe that their opinions about the current state of string theory matter - I beg to differ (with the possible exception of Michio Kaku who is described as the main proponent of the theory).

### A sad day for Harvard

March 15th, 2005 (thanks CIP for having corrected my typo) will be mentioned as a sad day in the history of Harvard University. The main point of the FAS faculty meeting in the Loeb Drama Center was a largely symbolic no-confidence vote proposed by Prof. Lorand Latory. It passed by a healthy margin 218:185; eighteen professors abstained. The less radical but equally sick resolution composed by Prof. Theda Skočpol has passed by a huge margin, too (253:137).

Figure 1 (missing): Lawrence Summers surrounded by celebrating protesters and journalists.

Because I was afraid of this result, I voted for the motion to postpone the no-confidence vote indefinitely; unfortunately, this desperate attempt of Philip Kuhn (Asian Languages) to avoid a disaster did not pass. The previous blog article with 54+ links to texts supporting Lawrence Summers was here.

This slightly surprising result has occured despite a significant number of speakers with very powerful and very diverse arguments opposing the motions - speakers whose reasoning has topped the intellectual strength of the advocates of the resolutions, as far as I can say. It was not just Steve Pinker, our star psychologist who has unsuccessfully tried to explain everyone that the statistical distributions are derived via research and papers, not by votes, and the right-wingers Ruth Wisse and Stephen Thernstrom who offered their arguments. Some economists followed, although their speeches were not quite perfect from a formal viewpoint. As another speaker has pointed out, the historians will look at the FAS faculty today as an example of another era of McCarthyism where the enemy was not in the government: it was within which is much more worrisome.

## Tuesday, March 15, 2005 ... /////

### Chapline: black holes don't exist

Dozens of readers want to see the following sentence every day: black holes don't exist.

George Chapline just gave the most provoking and most bizarre colloquium we have seen at Harvard for years. (I guess that the talk would not be bizarre enough for Quantoken and perhaps not even for Arun, and I apologize if they will be disappointed by the amount of strangeness.) Chapline used to be a T.A. for Feynman's lectures, he was awarded by various awards, but his goal right now is to revolutionize our understanding of the strong gravitational fields.

His talk was based on various papers such as

Chapline admitted that every time he was giving a talk, people would think that he had lost his mind. This was the case until 2000 or so when he met Robert Laughlin who agreed with Laughlin completely. There is a difference however: Laughlin is a Nobel prize winner who became a big shot in condensed matter physics while Chapline is a field theorist. From an outsider such as Laughlin, some comments simply may sound a bit less embarassing because everyone knows that Laughlin just tries to extend his incredible success from condensed matter physics where he has achieved everything he could to completely different fields of human activity.

(I guess that many readers of mine have heard the rumors about a similar black hole talk by Laughlin at Stanford. Lenny Susskind jumped on him and defended rigorous and established physics vehemently. Thanks, Lenny.)

## Friday, March 11, 2005 ... /////

### Quasinormal story on quasinormal modes

Technical comment: the reason nobody posted comments on this blog for quite some time is that it freaking didn't work... Just wanted to let you know that blogger.com has had some technical problems. I hope that you have written your original comments and ideas in a private file of yours and you can post them now when the blog (hopefully) works again. Thanks.

Two years ago or so, the relativistic community - or more precisely the loop quantum gravity sub-community - was excited about the quasinormal modes. I was asked to explain what was the fuss all about and also why I had anything to do with it. It's a rather interesting story - one whose original goals were doomed from the very beginning but one which may still hide some secrets of Nature - namely mysteries of quantum gravity.

What are quasinormal modes?

First of all, let me say what a quasinormal mode is. Start with quantum mechanics - a particle in the potential which confines it classically, but allows it to tunnel out quantum mechanically (like one of these toy models of alpha-decay - an alpha particle confined in the nucleus). In this case, there are "metastable" modes in which the particle sits in the "hole" for quite a long time, but eventually it escapes by quantum tunneling (the rate of the tunneling exponentially depends on the parameters, which is why the lifetime of various alpha-decays are so incredibly diverse in size).

Mathematically, one can find an associated exact formal solution of the Schrodinger equation with a complex value of energy. The constraint is that at infinity, the particle's wave function is "purely outgoing". The exponentially growing (with x) and oscillating component of the solution at infinity is allowed, but the second linearly independent solution of the equation, the exponentially decreasing and oscillating function, is not allowed. Such a condition is kind of "opposite" but equally constraining as the condition for convergence (decrease at infinity) of the normalizable wave functions of the bound states, and it only has discrete solutions that are called the quasistationary states. Much like the bound states, they describe poles in the transmission amplitude.

## Wednesday, March 09, 2005 ... /////

### WMAP and cosmic strings

Quantoken asked what's new with the observed cosmic strings - his or her personal theory is that CSL-1 "was really just bird shit causing the original telescope to record a slightly distorted image".

The next debater immediately pointed out a new article astro-ph/0503120:

The article first of all confirms that there are no cosmic strings seen in the microwave background whose tension would exceed a certain bound and whose velocity is smaller than 0.7c or so. Then they focus on the neighborhood of CSL-1, the double galaxy conjectured to be a result of gravitational lensing by a cosmic string. Yes, they use the same coordinates from Mark Jackson that I published in the previous blog article.

The result?
• They observe the discontinuity of the microwave background temperature near the cosmic string with *2 sigma* significance which may or may not be a sign of the cosmic string. The whole CSL-1 double galaxy fits into one pixel of or so, so they have to use 4 pixels around, and the precision is not great. PLANCK is expected to be twice as sensitive. The cosmic string would have to move by velocity higher than 0.94c to fit the data.
Henry Tye at Harvard

On Thursday, Henry Tye was giving a nice talk at the Duality Seminar about the cosmic strings. It included a lot of new interesting information about the simulation of cosmic string networks, about the WMAP - cosmic string relation described above, and so forth. He also said that the number of cosmic strings from an Abelian i.e. U(1) Higgs model in the visible Universe should be 40 plus minus a few. If it's not fourty, the strings must be strings from string theory, some people say! ;-)

## Tuesday, March 08, 2005 ... /////

### Littlest Higgs model & deconstruction

The main article about Nima Arkani-Hamed on this blog: click at his name...
This note is gonna be about the concept of and its different applications. Itay Yavin, a grad student from Harvard, just spoke about their littlest Higgs model, and I will mention some features of their model at the end of the paper.

What is deconstruction?

In philosophy, deconstruction is one of the characteristic methods associated with postmodernism and with the name of Jacques Derrida. Deconstruction is not attempting to read a text and judge it by the content; instead, it tries to interpret every sentence as a result of social and political conflicts between the author and her or his cultural environment. This goal of this kind of "critical" thinking is to show that the content does not make any sense that could be permanent; the categories and terms are neither objectively well-defined nor separable and they only exist within the given context.

Those who are interested in Feynman and deconstruction (in philosophy) may want to open a very recent article at Mormon Philosophy and Theology. My father and sister were baptized by mormons several years ago ;-) although their current "mormonity" is very limited - but nevertheless I hope that the link is not inappropriate.

Because The Reference Frame does not believe that all methods how to use the human brain are equally valuable, the paragraph above is everything we're gonna say about deconstruction in philosophy which we're gonna interpret as a generic example of flawed thinking from now on. We're going to use the term "deconstruction" in the particle physics sense. ;-) In this context, deconstruction is a particular method to construct new physical theories. It was pioneered by the following influential paper
Because Andrew Cohen is from Boston University, Sheldon Glashow rightfully identified deconstruction as an important contribution of Boston University to particle physics in the last 5 years - and an argument that Boston University's approach to theoretical particle physics may be superior to Harvard University's approach. That's an excellent argument - because deconstruction is definitely one of the most influential ideas in phenomenology in the last 5 years - except that Andrew did the work with Nima Arkani-Hamed from Harvard and Howard Georgi from Harvard while he was a visiting scholar at Harvard. ;-)

### Docket items

Next Tuesday, there will be two anti-Summers moves at the FAS faculty meeting at Harvard. J. Lorand Matory wants the faculty to state that it lacks confidence in Summers. This is the more radical of the two docket items.

Theda Skočpol, the wife of William Skočpol, an experimental physicist from B.U., wants the professors to regret 's statements and style, as explained in Skočpol's recent confusing speeches, and express their appreciation for the continuing self-humiliation of our president.

Both colleagues of ours - Matory and Skočpol - have spoken about the issues at recent faculty meetings, and both of them are misguided. It seems that the critics of Lawrence Summers prefer sociological arguments over science - so let me propose 54 sociological arguments that they are not right: recent articles about the brouhaha. The articles support Summers and they were collected kind of randomly, and I apologize if an interesting article is missing in this list.

### Hans Bethe died at 98

Hans Bethe, the physicist who explained and applied the nuclear and thermonuclear reactions both in the stars (carbon cycle) as well as in the bombs (Manhattan project), died in Ithaca at the age of 98... It's sad but many of us would be happy to live for ninety-eight years.

Hans Bethe was also the left-wing counterpart of the right-wing Edward Teller (*1908 Budapest - +2003 U.S.)

### Klaus is visiting Bush

Figure 1: Czech president Václav Klaus in a commercial: "You can do anything after graduating - go for the best!"

President to Welcome Czech Republic President Klaus to Washington

• President Bush will welcome President Václav Klaus of the Czech Republic to the White House on March 8. The Czech Republic is a close friend and ally of the United States. It remains a staunch member of the Coalition that brought freedom to Iraq and Afghanistan, and a strong NATO ally. The President and President Klaus will discuss transatlantic priorities, Iraq, the advance of democracy in Eastern Europe and the broader Middle East, and other key global issues during their meeting.

That was news from the White House; see also the picture of Klaus and Bush in Brussels. Václav Klaus is the father of the Czechoslovak economic reforms after 1989. Klaus is a soulmate of Margaret Thatcher and Milton Friedman. In the domestic context, he has been the most visible Czech and Czechoslovak politician after the Velvet Revolution. He is considered to be one of the brightest European politicians of the current era and is known as an outspoken Eurosceptic. Today in Dallas, Klaus released his new book

Although the Czech Republic was a part of the anti-Saddam coalition and provided the coalition with a few troops, Klaus himself did not support the war. The most problematic was Klaus's debate with the U.S. ambassador Craig Stapleton at a March 28, 2003 meeting. According to some sources, Klaus speculated that if the weapons of mass destruction would be found in Iraq, he would believe they were planted. Stapleton was probably upset. But Klaus argues that all this tension has already evaporated.

## Sunday, March 06, 2005 ... /////

### KITP: Gross as actor, Feynman inventing Hawking radiation

As many of you, I am receiving hundreds of nonsensical e-mails from not terribly reliable sources but this one is pretty interesting because it authentically describes the atmosphere in Santa Barbara which hosts Science, Theater, Audience, Reader, an activity attempting to combine physics and literature:

• I am driving back to San Francisco from Santa Barbara in a few minutes but I want to get this down while it's fresh in my mind. I just had breakfast with Alan Lightman, a delightful Southern intellectual, and equally delightful Marcia Bartusiak (both from MIT). We were discussing Phil Morrison, Bethe, Salpeter - old days at Cornell. It got around to Hawking and what he will be remembered for. Then Alan Lightman, author of "Einstein's Dreams" told us the following "narrative" which was a big theme at Kavli meeting hosted by David Gross, who actually is a GOOD ACTOR. He did a scene as Feynman in QED - good job.

It is not hard to imagine as an actor - won't they put the video of this Feynmanian scene on-line? ;-) Note that Alan Alda is among the previous actors who were playing the role of Feynman, and therefore David Gross is in a good company even though Alda received the Nobel prize neither for the strong interaction nor for liquid nitrogen. OK, now the "narrative":
• In 1972 before Hawking came out with the Hawking radiation formula. Feynman was meeting with Kip Thorne's grad students, Bill Press, Saul Teukolsky & Lightman. They discussed a recent calculation of shining light on a rotating black hole and getting more energy out then in at expense of decreasing rotational energy of the hole. They all went back to Lightman's office. Feynman said: "Hey this is like stimulated emission. So he went to black board and did a A & B coefficient model and then when angular momentum J of the black hole J -> 0 there was still "A" spontaneous emission and it was the later Hawking formula!
Well, let me admit that I don't quite understand how the formulae from stimulated emission are useful for deriving the "Hawking formula", whatever it is. It could be interesting to try to reconstruct Feynman's blackboard.
• A maid erased the board that night before Lightman and the others realized they should have written down what Feynman wrote. Not even Feynman thought it was important enough to write a paper about apparently.
Well, the idea that Feynman derived Hawking's results before Hawking certainly sounds entertaining, but the details so far don't seem to be completely solid. Well, let me admit that my source is closely associated with extraterrestrial civilizations. He "shared a woman with Feynman" (different years) and an extraordinary photograph of Feynman with not-too-dressed women may be found in his book. Bizarre. ;-)

## Saturday, March 05, 2005 ... /////

### Richard Feynman

Sean Carroll has decided, using the words of TripleIntegral, to re-evaluate the actual achievements of Richard Feynman according to the contemporary criteria of political correctness. Sean is perhaps the first person who has applied this methodology of "humanities" to hard sciences (with a possible exception of Lysenkoists). He wrote about the "counter role model", as he describes Feynman, that
• "[Feynman] didn't have wide-ranging intellectual interests outside of science ... He was a pretty narrow guy ... But [having broad interests] might make [him a] better human being[s]."

I happen to think that Feynman was not only one of five most original and important physicists of the 20th century, but he has also been an extraordinary human being. He was not only the father of the path integral approach to quantum mechanics and QED in particular, the originator of the Feynman diagrams, and theory of superfluids - but also the author of many other concepts such as nanotechnology and quantum computing (the breadth of these contributions already kind of ridicules the breadth of the contributions of other scientists mentioned in Sean's article).

But Feynman's virtues are not confined in science. Those of us who have read Feynman's books - and not only the subset that prefers Feynman's name as a part of their e-mail address - also know that he was a great teacher, a loving boyfriend, husband, and father, and a very successful writer with an extraordinary sense of humor. He was good at playing drums, painting, picking locks, and spotting errors and tricks. Feynman has decoded Mayan calendars, Mexican hieroglyphs, and he may be labeled as a social anthropologist focusing on cultures and languages of Japan, Brazil, Las Vegas, and Tuva (thanks to CIP for reminding me).

And he was a very honest person and a prototype of scientific integrity and independence; a curious, emotional, straightforward guy whose thinking was rooted in common sense. A person who believed that the people should be what they are, and they should not pretend that they're something else - and a man who lived in this way. He loved freedom - and freedom was one of the values that has made his life happy. And yes, he was also a man who was able to get very angry. ;-) He was also a guy who understood the modern world, including the world of politics and economy. A universal scientist that has mastered virtually all fundamental issues related to physics, biology, evolution, sociology, and technology. A thinker who always preferred to see how the things work, instead of learning what other people say.

## Thursday, March 03, 2005 ... /////

### Gravitons as squared gluons & twistors

In December 2003, Edward Witten has started a new industry - the application of Penrose's idea of twistors to the scattering amplitudes of four-dimensional gauge theory. What is the status of this field more than one year later?

Witten's twistors 1 year later

The gauge-theoretical amplitudes at the tree level - the objects that have a very simple form in the twistorial variables - have been kind of understood; various prescriptions (disconnected and connected) have been found and relations between them have been identified; recursion relations have been proved, and so forth. I feel it's fair to say that at the classical level, the power of the twistor formalism has been almost fully revealed. The quantum loops in gauge theory are much more difficult, and the original prescription using topological string theory has not been terribly useful, as far as I can say - and the same is probably true about other stringy incarnations of the formulae. The unwanted conformal gravity states appear in the loops and give undesired contributions, but it does not seem to be the only problem. However, we can ask a simple question:

There exists one fundamental reason why the twistor methods should be more natural in the case of gravity, namely:

• The scattering amplitudes in gauge theory are not terribly natural objects; we prefer the off-shell correlators of gauge-invariant operators - the latter are the quantities relevant for the AdS/CFT correspondence and other applications
• On the other hand, gravity is naturally defined on-shell - the scattering amplitudes are naturally the only simple gauge-invariant quantities, and because it's only the scattering amplitudes that the twistors give us, the twistor language may seem efficient and sufficient
However, there is one elementary theoretical counter-argument and one experimental argument that show that the twistorial gravity math class is tough:
• The real power of twistors emerges when the twistors are applied to scale-invariant or conformal physical systems such as the N=4 gauge theory in d=4. Gravity is not conformal - it has a priviliged distance scale (the Planck length). The only gravity that is conformal is conformal gravity ;-), whose Lagrangian is essentially the squared Weyl tensor - and conformal gravity is not a physically appealing theory because of the ghosts and other defects
• The LHC will be measuring the scattering amplitudes involving up to 8 gluons or so and therefore there is an experimental motivation to learn new efficient methods to calculate and new patterns underlying multi-gluon scattering; on the other hand, an experimental observation of multi-graviton scattering belongs to science fiction, and the experimental motivation to study complicated gravitons' amplitudes does not exist
These are the reasons why the marriage of gravity and twistors should be happy as well as unhappy. But what do the twistors actually tell us about gravity? How do the gravitational scattering amplitudes look like in the twistorial variables? You should look at an up-to-date paper, for example the paper by Cachazo and Svrček
This paper derives some recursion relations for the gravity amplitudes in four dimensions - relations analogous to the recursion relations mentioned (and linked) at the beginning of the article. Such recursion relations may eventually be useful to prove a new full twistorial prescription for the amplitudes. What do the amplitudes look like?

KLT relations: squaring the amplitudes

I believe that the most powerful relations are the Kawai-Lewellen-Tye (KLT) relations from 1986 that essentially say
• Closed string (or gravity) amplitude equals open string (or gluon) amplitude squared
That was too rough, was not it? We should be a little bit more concrete. The gravitational scattering amplitudes are the low-energy limit of a special type of scattering amplitudes for the closed string. At the tree level, the relevant stringy diagram is a sphere. On the other hand, the gluon scattering is the low-energy limit of a special type of open string scattering amplitudes that arise from the disk diagram at the tree level. (Similar relations for the loop amplitudes can't be derived easily because of the complexities of the closed string moduli of Riemann surfaces.)

## Wednesday, March 02, 2005 ... /////

### Maxwell's son knighted

Our students' former classmate and the son of Mary Maxwell - one of the famous women who gave their names to the Maxwell-Dworkin building at Harvard (is she related to James Clerk Maxwell?) was knighted by the British queen.

He can put KBE - Knight Commander of the British Empire - after his name. However, her majesty did not allow Bill to use "Sir" before his name because he's one of the rebel "Americans" who stole a colony from the British empire. Congratulations anyway! Also, Microsoft Windows may now be called Windows KBE, not to be confused with KDE. ;-)

### Europe and America: united in cold

Five weeks ago, we enjoyed the Great Blizzard 2005 in Boston. In February, we have had an ordinary snowstorm every other day. The last one that started about 3 days ago brought us about one foot of snow. The snow record books will probably have to be updated in Michigan and Ontario, too. Ski resorts in the New York state are booming.

Some people enjoy this weather - is not the white snow blanket that covers the whole cities beautiful? Some people think that it has been too much of a good thing. Some other people just hate it.

The latter category may feel happier that Europe has been much colder than the East Coast recently:

Temperatures in Germany fell to a 100 year low (while the unemployment is at 75 year high - 5.2 million). The mass of snow covering the Czech Republic was probably the largest in 40 years. (It's believed that the floods won't follow because they usually require a lot of rain in the country.) Today in the morning, the average temperature in Western Bohemia was -20 Celsius degrees. Record low temperature have also been recorded in France, Spain, Croatia, Switzerland, Netherlands (record since 1845), the United Kingdom, and elsewhere.

The climate models have been improved so that they predict chilly Februaries in Europe whenever the year is a multiple of 401 - it's the freezing effect of the 401k U.S. retirement plans. Incidentally, the climate models completely fail to reproduce the strong and obvious local correlations between the temperature trends and industrialization - an indication that most of the observed trends will be due to the heat island effect (i.e. local warming) after all. By the way, I am absolutely certain that some believers won't resist and they will add a comment under this article arguing that a cold winter, hot winter, a lot of snow, little snow - all of these things are holy signs of global warming. Why I am so certain? Because global warming is an uncurable disease - something like fundamentalist islam. ;-)

That's the East Coast and Europe. What about the other continents, for example Asia? Ten days ago, they also experienced a record snow in India that froze life in Srinagar. In Taiwan, the cold will get even worse. At about the same time in Australia, they complained about an unusually cool and wet February; many believe that the month was just a chilly exception. And it's plausible that the cold was localized in Victoria and NSW while the rest of Australia was warm.

As you can see, it's easy to get convinced that we're entering a new Ice Age. That would be a hasty conclusion. The weather in Indiana and Wisconsin is warmer than usual.

### Gia Dvali solves 1/2 of the C.C. problem?

My friend Oldřich Klimánek who is currently translating "The Fabric of the Cosmos" by Brian Greene to Czech has pointed out the following popular article to me:

What does he say about the cosmological constant? Well, it does not exist. The accelerating expansion of the Universe is, Dvali argues, due to a "leak of gravitational force" into extra dimensions that only appears at very long distances.

So far I don't exactly understand how Gia's picture works. But definitely, it's one of the proposals to modify gravity in the extreme infrared - he talks about the Yukawa-Newton potential (arising from massive gravity). Dvali predicts new modifications of the motion of the Moon and the planets. In the case of the Moon, it should be testable because of the mirrors on the lunar surface that have been installed by Apollo 11 (and terrestrial lasers).

## Tuesday, March 01, 2005 ... /////

### Matthias Ihl

Matthias Ihl, a German theoretical physicist from Austin, started his own blog.

Don't be discouraged by the German language - some of the important postings are written in English. The main reason why I promote his blog is its excellent design. Don't you think that the colors, fonts, texts, and icons of his blog are perfectly balanced and beautiful? Jawohl! :-) What a beautiful blog.

### Melting crystals and quantum foam

The patient readers may learn something about the discrete structure of spacetime at very short distances.

...

Yesterday Cumrun Vafa gave a cute colloquium at Harvard. The relevant papers are

Shiraz Minwalla introduced Cumrun as a new category of a physicist. Most theoretical physicists Shiraz knows may be classified either as mathematically oriented people; or as physically oriented people. Cumrun belongs to a third category: he is a magician because he sees the truth directly, Shiraz explained.

Cumrun worked with a PowerPoint presentation that included a lot of animated pictures. As a true artist, he drew mathematics (for example, the integral signs) by hand. Well, we will have to fix this imperfection. ;-) Cumrun described Isaac Newton, apples, Albert Einstein, general relativity, and so forth. I assume that most readers don't need to hear this part. As an anonymous pal below has pointed out, Cumrun Vafa has also shown photographs of string-theoretical experiments taken at Harvard, including the pants diagram encoding the stringy interactions. :-)