Monday, October 31, 2005 ... Deutsch/Español/Related posts from blogosphere

Doubly special relativity in 3D

Nima who just returned from the Perimeter Institute was excited about very reasonable discussions with Laurent Freidel who is a loop quantum gravity person.

Laurent has shown that the so-called DSR (double or deformed special relativity) may arise naturally in 3 dimensions.

The Harvard interpretation is that 3 dimensions are special; there are no gravitons; and moreover, there is an invariant mass scale - the maximal mass you can have to avoid a closure of space (deficit angles exceeding 2 pi) - and these things won't hold in 4 dimensions or above four.

Nevertheless, the basic story of Laurent is quite interesting. Take 3D gravity coupled to a scalar field PHI with a cubic coupling, and integrate out the gravitational field. What you obtain is an action for PHI only; it differs from the original PHI-part of the action by having a new kind of a "star product" instead of the original one. However, it is not a Moyal product but rather a new kind of product relevant for addition of momenta in DSR.

The rule is

  • exp(iPx) * exp (iQx) = exp(iRx)
  • R = P sqrt(1-L^2.P^2) + Q sqrt(1-L^2.Q^2) + L P x Q
where "x" is the cross product in three dimensions, involving an epsilon, and L is the Planck length, more or less. As you can see, the last term in "R" makes it very noncommutative but differently than in noncommutative geometry as we know it.

Saturday, October 29, 2005 ... Deutsch/Español/Related posts from blogosphere

Snow is back

Snow is back here in Cambridge. So far it is lighter than in January, but we will see where it goes. The temperature for tomorrow is forecast to be 22 Fahrenheit above the temperatures today. Many of us already have a lot of fun with the snow.

Don't forget that weather is local in time as well as in space. Our friends in Central America have a tropical opportunity to learn the Greek alphabet properly. :-) Now they're learning (hurricane) Beta.

Also, don't forget the proverb "spring forward, fall back". It's the last full weekend of October, and therefore the daylight saving time is over! If you did something wrong in the last hour and you wish it would have never happened between X:00 PM and (X+1):00 PM, just return your watch back by one hour, and repeat the hour without the error.

Friday, October 28, 2005 ... Deutsch/Español/Related posts from blogosphere

Israel and the president of Iran

The Reference Frame has repeatedly criticized the new policies of appeacement and an insufficient support of Israel from Europe and other regions, for example in the article "Disengagement is a mistake". For example, I argued

  • ... And I don't think it is quite reasonable to expect that all the Arab [sic: I meant Muslim] states are going to like the idea of the Jewish "spot" in the middle of "their" region for decades or indefinitely. ...
Unfortunately, the newest events start to confirm these worries in detail. The current president of Iran - representing the political party called "Islamic Society of Engineers" (what a strange kind of thinking for an engineer) - has called the "wise" Palestinians to "wipe off this disgraceful blot [Israel] from the face of the Islamic world". He has expressed the very same plan in many similar sentences.

You can see that my prediction was not accurate. I predicted the word "spot" while Ahmadinejab used the word "blot". Please accept my apologies for the inaccuracy. If you want to see that all good people in the world agree with the upgef**ked Mahmoud, read his newspaper.

The European Union, the United Nations, even some Arab analyticians have protested. Israel has officially asked the U.N. to cancel Iran's membership in the world's organization. Some other Iranian politicians attempted to soften the president's remarks. Nevertheless, the president of Iran has re-confirmed his statements today on a demonstration of thousands of empty heads.

The ministers of defense of all potent democratic countries in the world - which of course means primarily Donald Rumsfeld - should refresh their strategic plans for a conflict, including nuclear war, with Iran because unfortunately, the probability that such plans will be needed soon has just increased by an order of magnitude. It would be irresponsible to assume that we will never need nuclear weapons.

The Reference Frame finds it inappropriate for the politicians in civilized countries to tollerate statements such as the recent statements by Ahmadinejab and to do things that increase their self-confidence, and I personally find it inappropriate to keep this creature alive.

Gary Horowitz's bubbles

Yesterday, Gary Horowitz was explaining, in a very interesting talk, that the black holes can catalyze the creation of bubbles of nothing in the context of closed string tachyon condensation studied by Allan Adams et al.

Recall that in the Scherk compactifications with antiperiodic fermions around a circle, a single wound closed string has a ground state that becomes tachyonic if the radius of the circle is small enough. Its condensation is a perturbative addition to Witten's non-perturbative nucleation of "bubble of nothing" - a process obtained by an analytical continuation of the Euclidean Schwarzschild black hole.

Gary showed several bubble solutions that may be connected to black hole solutions via non-supersymmetric counterparts of geometric transitions, and he conjectured that this novel process may even describe final stages of black hole evaporation. These mechanisms to resolve singularities are somewhat analogous to the picture envisioned by Eva and John.

He also mentioned a paper of Simon Ross that argues that similar bubbles may even arise in asymptotically supersymmetric background in the presence of rotating charged black holes. The possibility that these bizarre processes occur even in the stable, supersymmetric context make them even more interesting.

Thursday, October 27, 2005 ... Deutsch/Español/Related posts from blogosphere

Lawrence Krauss: Hiding in the mirror

I found this book to be particularly weak among the recent books about theoretical physics in general and extra dimensions in particular. The main problem is that Krauss does not distinguish random stories and fiction from physical theories. He mixes aliens hidden in extra dimensions with QCD, Picasso, Plato, Flatland, M-theory, and many other things.

Krauss' book is a classical example of politicization of science. He tries to present extra dimensions as a form of religion; it's the main agenda behind this book to put modern physics in the context of some old unscientific fairy-tales. Of course that when we talk about some physical theories or conjectures involving extra dimensions seriously, there is no room for religious or anti-religious arguments. But Krauss prefers the non-serious approach. Unlike Krauss, I personally have no a priori positive or negative feelings about extra dimensions whatsoever. Extra dimensions is something that it forced upon us by the rules of mathematics. If physical arguments implied that elementary particles had to be 3D Platonic polyhedra, I would view this derivation equally seriously. Krauss prefers pre-conceptions and his atheism - that he incorrectly believes to be correlated with 3+1 dimensions - is one of them.

Hockey sticks: round 29

When some people claim that the human activity has warmed up the climate much more drastically than Nature could do Herself, their most convincing argument for their statement is the reconstruction of global temperatures in the last 1000 years. Although people used to think that the variations were large and there was a strong Medieval Warm Period as well as Little Ice Age afterwards, things suddenly changed in 1998 and 1999. Mann, Bradley, and Hughes published papers that argued that the temperature was essentially constant between 1000 and 1900 (the shaft of the hockey stick) and then it abruptly grew since 1900 (the blade).

Even though the hockey stick contradicted most of the folklore people used to believe, it was instantly accepted by most of the climate community. In 2001, it became the key graph on the final page of the climate report made by the United Nations (IPCC). For five years or so, no one tried to reproduce the graph. Ross McKitrick and Steve McIntyre became the pioneers. They attempted to reproduce the graph but nothing worked. After intense research, they discovered that Mann et al. used a mathematical step that essentially generated hockey sticks out of random input.

...This is probably an old unfinished posting. ...

Wednesday, October 26, 2005 ... Deutsch/Español/Related posts from blogosphere


An example of policy issues discussed at Harvard right now: on Monday, we had a physics faculty meeting. Gary Feldman explained that someone at FAS wanted to cancel the joint concentrations. In the case of physics, the joint concentrations are moderately important, especially for the students focusing on Physics/Mathematics and Physics/Astronomy. The FAS plan was to replace the joint concentrations by "secondary fields" that would not appear on the diplomas.

This topic is not going to destroy the civilization but still: cancellation of the joint Physics/Mathematics and Physics/Astronomy programs at America's most well-known college is not a completely irrelevant detail.

On Monday, Gary explained these things to us. Bert Halperin wanted to hear the arguments of the proponents first. Gary argued that they seem to have no arguments; at least none of them were mentioned in the document that proposed it. This statement of Gary seems to be supported by all other sources that I have seen and heard so far. We exchanged a few more words and then voted: everyone (in the physics department who participated) voted that the proposal should be re-considered.

Yesterday, the proposal for the new system was presented by EPC at the FAS faculty meeting, and Gary was not the only one who responded negatively although the negative replies used somewhat contradictory arguments (which is not a real contradiction because different departments and fields may require different things).

As The Crimson reports, the proposal was presented by David Laibson, a very reasonable economist who was incidentally one of the driving forces behind the petition supporting Summers against hysterical attacks of the feminists and their allies.

Nevertheless, I don't believe that EPC understands the logic and situation in sciences well enough to make constructive recommendations. This suggestion opens several questions: How important it is to allow joint concentrations? How much coursework should be required for one field or another? Is it too much, is it too little, is it too much more than in other fields, is it enough for the student to get familiar with everything that is important in her or his field? Is there enough time left for the student to think about the world independently? Is the joint program difficult enough so that it won't become just a way to simplify one's life? Does the student have enough opportunity to choose the field that he or she would find important at the end?

I can imagine that a very enlightened leader who understands sciences etc. could make a reasonable decision that takes all of these questions into account. But I am much more skeptical that a committee of non-scientists should be expected to make a good decision. Such decisions affect the work of the departments such as the Physics Department, and this is the level where these relatively technical decisions should be made.

Decisions that affect the relative growth of different fields etc. should almost certainly be done centrally, at least to some extent; but the decisions about the "details" which things should be taught and required and how should be left to the "local experts", I think. If a professor of Latin American studies argues that it is very important for a student to travel to all possible continents or participate in an international experience, one must say that he has no idea what it means to study other fields except for his own.

An international experience plays a completely negligible role for a physicist - especially the U.S. physicist - in comparison with experience with mathematics, and it would be very bad if people who don't understand this point were deciding about the physics curriculum.

25 years of Polyakov action

In 2005, we also celebrate the 25th anniversary of the Polyakov action. Although many of us were still in kindergarden back in 1980, we just could not ignore this important contribution of the bloc of peace to string theory. The article about Fadějev-Popov ghosts in string theory seems appropriate for the week before Halloween.

Even more mysteriously, Saša Polyakov celebrates his 60th birthday, congratulations!

Polyakov - and several other people - introduced the BRST methods to string theory. BRST quantization is a powerful technology to deal with gauge invariance, especially non-Abelian gauge invariance. Some physics fans do not understand that BRST is mostly formalism - a calculational framework to deal with various unphysical states - but physics is only the very final product of the BRST quantization that could also be found by other means - for example, by light-cone and other gauge-fixed approaches.

Tuesday, October 25, 2005 ... Deutsch/Español/Related posts from blogosphere


Strange music in the background is cause by the second article older than this one. The Iraqi constitution just passed (78 percent).

One of our former undergraduate students here at Harvard, Ben Bernanke, was chosen to replace the economist. The Reference Frame thinks it's a good choice. Bernanke introduced the concept of "goldilocks" to economics: not too cold, not too hot. This applies to inflation and deflation in particular.

We hope that he realizes that things could become too hot very soon and he will raise the interest rates to something like 6-7 percent sometimes in 2006. You know, the Americans are not afraid to borrow money. They're self-confident and optimistic enough which is one of the reasons why the U.S. interest rates should be, in average, significantly higher than the interest rates in other countries where the people are shy (such as Japan, obviously, but maybe also Europe).

Monday, October 24, 2005 ... Deutsch/Español/Related posts from blogosphere

Samir Mathur's black holes

If you hear silly songs, it is because of the videoclip included in the previous text.

Today, you won't find a single gr-qc article with at least one sentence that makes sense. Guaranteed.

One hep-th article that could have appeared on gr-qc is by our friends Ghosh, Shankarayanarayanarayanarayan, and Das (sorry, I could not resist!) who confirm using the monodromy method that ln(3) is really, really not a universal feature of the quasinormal modes of generic black holes. Update: their particular paper was wrong because of using wrong topology of Stokes' lines but keep on believing the conclusion that ln(3) is not universal.

There has not been a single article on this blog about Samir Mathur's picture of the black holes. Because I find it exciting - and with probability of order 10% even correct - Samir deserves a couple of words. He has a new gospel

in which he discusses his unconventional ideas about the black hole interior. Note that according to conventional general relativity, the horizon itself can't be identified by local measurements. The black hole interior has an interesting causal structure, and whoever falls into a black hole, can never escape (until the black hole evaporates completely).

George Chapline would argue that we should not trust general relativity and its laws may completely break down at the horizon and its interior can therefore look very different from the conventional picture of general relativity. Well, George Chapline would prefer to replace GR by gossamer superconductors.

Although such a hypothesis about a drastic change near the horizon is only possible when locality is heavily violated, Samir Mathur would probably agree with it. Samir Mathur and Oleg Lunin constructed solutions with infinitely many parameters that can be identified with the microstates of a five-dimensional black hole with two charges. Their interior is "fluffy" and Samir wants to argue that it is a general feature of black holes.

Sunday, October 23, 2005 ... Deutsch/Español/Related posts from blogosphere

Scientific consensus proves zombies

Climate scientists were asked whether zombies exist. And what they think that the U.S. president drinks. The results of their cutting edge research and the new scientific consensus is summarized on the server For your convenience, we also show it here:

Originally, there was a flash directly here.

Normally, I would think that this website was funded by an oil company to show the believers in the "global warming theory" as five-year-old retarded children who don't quite distinguish fairy-tales from reality. But there is also an alternative theory - namely that those who paid for this animation actually imagine that this is how the real world works.

Incidentally, what do you think is the easiest way to get $1 million dollars for climate? Via ExxonMobil or from one of those corrupt far-left wing foundations? The website has so far tracked 800 million dollars that various environmentalists got for their "work". For example, James McDonnell was a believer in the occult, so I guess that he would agree with giving his millions to these scientists who promote zombies, vampires, and global warming. To summarize: be sure that the statement that the sceptics are corrupt is the opposite of the truth.

More seriously, America is simply ahead. The communist regimes also created various propagandistic fairy-tales attempting to convince the children that the White House was made of zombies, but none of them was so catchy as this one. I hope that Quantoken and others in the target audience will finally get convinced by this scientific animation that the global warming and vampires are for real. ;-)

But most importantly: have fun. Will you identify which zombie is your humble correspondent?

Thanks to W.S. for the tip.

Saturday, October 22, 2005 ... Deutsch/Español/Related posts from blogosphere

Greenland ice grows


The paper in science concluding that the icecap in the bulk of Greenland grows by 2.5 inches per year was published after this article was written.

Original material

Climate modeller William Connolley - the colleague who believed that the Arctic Sun could melt 30 meters of ice layer per day - has been trying to run an after school club despite the thicket of government regulations. William failed while his shy and conservative friend Ross succeeded. William thus came close to being converted to the values of entrepreneurship...

And suddenly, indeed, he realized that he did not want to have anything to do with the sourballs who generate piles of biased data whose only purpose is a political one, namely to further thicken the thicket of government and international regulations that are annoying already today. (Yes, the letters "thick" will appear many times in this text.) Their only goal is to make life unbearable for ExxonMobil, CocaCola, McDonald's, Microsoft, all other corporations, Luboš Motl, all other people who like freedom, and for William Connolley's after school club. :-)

Be sure that the degree of regulation in Great Britain is much more modest than in most places in the world! William Connolley and his famous after school club would really suffer elsewhere; William is a poor conservative and/or libertarian guy who has been intellectually and financially raped by environmental activists who forced him to change into a leftwinger.

So it may be him who started a refreshing wave of more balanced data. For example, CNN explains that the icecap of Greenland is crucial for the debates about the future catastrophes caused by global warming because once this three-kilometer-thick icecap melts, the sea level will rise by 7 meters. This will happen, as the global warming scientists argue, by Christmas 4005. Good bye, New York City, Boston, Bangkok, and other cities. Okay, we have heard this science already. ;-)

Surprisingly, CNN admitted in the article #1 in their Science & Space section that the Greenland's icecap actually grows by 5 centimeters every year; linear extrapolation puts the destruction of the New York City's Downtown to Christmas 60,000 years before Christ. You may think that I would like such an article. But it is so terribly illogical that I just can't like it. It starts by saying that there were "wide predictions of a thaw". However, five paragraphs later, it is announced that "they said that the thickening is consistent with theories of global warming".

I don't need to explain you that there could really have been no "scientific predictions" of a thaw - something that had a 50% probability to occur and something that eventually did not occur - that would deserve this label - just stupid political proclamations, worthless guesses, wishful thinking, and emotions.

You see that these two sentences about the predictions of the "consensus theories" contradict each other - unless you imagine that most of the predictions that are being made contradict the "theory of global warming" whatever this bizarre combination of words means in this context.

Obviously, many people have made wrong "predictions". It's not a disaster but it is a good enough opportunity to learn who has made the wrong predictions that the Greenland's icecap should retreat, and not to trust these people in the future.

Be sure that empty heads like those in the eco-terrorist organization called NRDC (or, using the terminology of Chrichton's book, NERF - whose boss is Nick Drake, the brother of Frank Drake whose semi-scientific equation indirectly led to "global warming") are not the only examples. Other examples include Bill Clinton - infected by Al Gore - who just told 5000 people in Canada that "The real danger is the ice cap in Greenland is melting." And yes, there are many in the scientific community.

You can't get an "A" for both contradictory types of a prediction. I am sure that many of those "predictors" had teachers who allowed them to pass the high school exams via the answers "maybe yes, maybe no, I want an A anyway", but the readers of The Reference Frame should be a bit more strict.

There are many other inconsistencies in the article. In the middle of the text, they say that the thickening could be offset by a melting of glaciers around the fringes of Greenland but no data can support this statement. Nevertheless, towards the end, they ventilate the opinion of other authors who argue that "Greenland presently makes the largest contribution to sea level rise" which seems to contradict all other justified facts mentioned in this article. I have not seen the article cited by CNN but it seems to be a work of pure fiction.

After all, Thor Karlstom from the U.S. Geological Survey predicts a new ice age in which ice will cover all of Canada. :-)

Friday, October 21, 2005 ... Deutsch/Español/Related posts from blogosphere

News on string theory in the media

How faithful picture of string theory do the media offer? Let's look at this sample from the last 48 hours or so. ;-)

  • "EinsteinFest" at the Perimeter Institute attracts 18,000 people
  • Vanishing Netgear rebate proves additional dimensions predicted by string theory
  • India Daily has another experimental proof of extra dimensions
  • India Daily had yet another article "String Theory" one day earlier
  • Brian Regan's brain exploded when he watched string theory on PBS
  • It is argued that the rest of the show "Girlfriends" looks like string theory
  • Emerson Quartet that became famous for joining Brian Greene plans to perform Mendelssohn and Mozart
  • Steel string theory is going to perform in Ohio
  • Alan Lightman thinks that artists are like scientists because they also like string theory
  • Ancient neutrinos described in a crackpot paper may prove either loop quantum gravity, string theory, or a required diet for Schrödinger's cat
  • Computer simulations indicate that type IIA vacua with orientifolds of six-tori produce one MSSM-like model per one billion of backgrounds

Poles vs. cuts

Sean Hartnoll from the old Cambridge discussed the phase structure of N=4 gauge theory and the main topic of the debates that followed was how can the apparent existence of branch cuts in field theories at weak coupling agree with the meromorphic nature of the Green's functions at strong coupling derived from the dual bulk gravitational description where the poles - e.g. the poles known from the quasinormal mode spectrum - are the only singularities.

My opinion is that the branch cut nature of the amplitudes is always a perturbative illusion and any background with quantum gravity actually resolves the branch cuts into a sequence of individual discrete poles. The main challenge for this "stringy" point of view is to explain how the continuum of two-particle (double-gluon) states that appear as intermediate states in gauge theory can be accounted for in the gravity picture, or why is the spectrum of the double-particle intermediate states discrete even at weak coupling.

If you have some strong or other opinions about the existence of branch cuts and their transitions at finite values of the couplings, I am curious to hear them.

Thursday, October 20, 2005 ... Deutsch/Español/Related posts from blogosphere

The illusion of gravity

All readers who like or want to read popular texts are recommended the article "Illusion of gravity" about holography in quantum gravity in the November issue of Scientific American. It is written by a person who has done the maximum to prove the concept of holography quantitatively - namely Juan Maldacena. His article offers Escher's pictures and rather detailed explanations of anti de Sitter space and other relevant concepts.

Wednesday, October 19, 2005 ... Deutsch/Español/Related posts from blogosphere

Heterotic MSSM

Burt Ovrut (UPenn) just gave a joint phenomenology seminar of the kind that I really like. This blog has discussed the heterotic standard model several times but it is impossible for me not to inform you about the talk today - especially because Burt has announced brand new results of his team that were found primarily by Volker Braun during the last weekend - namely a unique pure MSSM (minimal supersymmetric standard model) found in string theory. We will discuss this point at the end of this text.

Getting the right spectrum from string theory

It has been a long-standing question - and one of the most important questions in theoretical physics - whether string theory produces vacua that agree with everything we know about the real world. The first question is whether we can obtain the right particle spectrum. Obviously, string theory has the capacity to produce gravity, the Standard Model gauge group, and particles charged under it that include the observed quarks and leptons. But that's not good enough. We must find a model - or models - which lead exactly to the correct spectrum. No exotics i.e. unobserved particles coupled directly to the Standard Model are allowed if we claim that our favorite background of string theory describes reality and that Shelly Glashow and Peter Woit have been ultimately proved wrong.

In the context of string theory, we usually want to find an N=1 supersymmetric extension of the Standard Model, something like the MSSM.

Since the paper by Candelas, Horowitz, Strominger, and Witten in the mid 1980s that showed that SUSY GUT models naturally follow from heterotic string theory on Calabi-Yau manifolds, people have encountered a lot of technical problems in their attempts to get rid of the exotics. Burt Ovrut argues that it is a tremendously strong constraint that was only solved recently. Also, he suggests that even though some people used to conjecture that various exotics pair up and become very massive, his more explicit calculations tend to lead to the conclusions that if the exotics appear as massless particles at the string level, they just won't disappear.

Hurricane Wilma

Hurricane Katrina has been the most expensive natural disaster in the U.S. history. You may think that this should mean that it was at least the strongest hurricane of 2005.

However, then you may realize that hurricane Rita was actually stronger. So you would change your mind and argue that Katrina was the second strongest hurricane of the year.

Nevertheless, you would still be wrong. Actually, hurricane Wilma has just become the strongest hurricane of 2005 and the strongest hurricane on record, with pressure dropping as low as 882 mbar (rank 1) near the center, compared with Rita's 897 mbar (rank 4) and Katrina's 902 mbar (rank 6).

What does it mean? First of all, it means that the particular year 2005 and the particular ocean called the "Atlantic ocean" has seen very many strong tropical cyclones compared to other years and other oceans. Note that the tropical cyclones are called "typhoons" in the East Asian region, and they have other names in other parts of the world.

These other regions have seen no increased statistics of the tropical cyclones. "Hurricanes" with this particular name are a local effect. Wilma is not the strongest tropical cyclone every: it is the 10th strongest tropical cyclone ever. There have been 9 stronger typhoons, so please don't think that we live in an globally exceptional historical era. ;-)

Hurricanes prove feminists wrong

Little hierarchy problem

When you compute quantum, loop corrections to the Higgs mass, you obtain quadratically divergent graphs. Therefore, the exact value is quadratically sensitive on the cutoff scale and it is naturally predicted to be huge - unless we fine-tune the bare mass of the Higgs. On the other hand, reality forces us to believe that the Higgs is about as heavy as two W bosons. Otherwise, its quartic coupling is far too large and the effective quantum field theory breaks down.

This is called the (big) hierarchy problem. It is big because usually we want to assume that the effective theories should be valid at the GUT scale or even the Planck scale.

Some people may say that they don't care about these high scales, and they're perfectly happy with completely new - and perhaps non-field-theoretical - physics kicking in already at a few TeV. Even these people have a problem. It is the little hierarchy problem.

According to the precise measurements, the Standard Model is incredibly successful. It seems more successful than just a theory of physics below the 100 GeV scale. If you imagine that there is new physics at "M = 3 TeV" or so, it will generate new non-renormalizable terms (operators whose dimensions exceed four) in the low-energy effective action, suppressed by powers of "1/M", whose coefficients will be of order one. You can estimate the effect of these small corrections on the measured data. Indeed, you will find no effects whatsoever and the precision we have today implies that "M" must be greater than 3 TeV or something like that.

Tuesday, October 18, 2005 ... Deutsch/Español/Related posts from blogosphere

Variational method

For those who remotely study QM II, the variational approach to quantum mechanics in general and atoms and molecules in particular was added.

Iraqi constitution

The Iraqis were voting about the proposed new constitution in an unusually peaceful atmosphere. The constitution would make Shiites and Kurds stronger, and therefore the areas dominated by these two groups were expected to vote "Yes".

More generally, the constitution is another step towards the independence of Iraq because it would replace the provisional, U.S.-controlled constitutional laws, and therefore it should not be too surprising if many anti-American people voted "Yes", too.

What do the results look like? The official final results are not available so far. The turnout was high and the national count will show a convincing "Yes" vote. However, there is a rule that if in at least 3 out of 18 provinces more than two thirds of the voters vote "No", the constitution is rejected.

The "No" vote was expected in the provinces where the Sunni Arabs have a majority - especially Ninevah and Diyala. However, unless there has been some kind of fraud in these areas, they voted "Yes"! However, there are two provinces - western Anbar around Fallujah and central Salahuddin - which have already voted a clear "No". The question is whether a third province will join these two.

Noah Feldman

If the constitution passes, it will be most importantly a victory for the Iraqi people. Second of all, it will be a victory for people like Noah Feldman. Noah - a full professor of law at N.Y.U. - who is now generally accepted to be a rising legal star was a Junior Fellow in the Society of Fellows until 2003 and was chosen by the Bush administration to be the main U.S. brain behind the creation of the new Iraqi constitution. My understanding is that Noah is actually a de facto author of the current provisional laws only, but I guess that he will feel happy if his laws are superseded by a more authentic constitution.

Imagine: Noah who is an American Jew and a Democrat is sent by the G.O.P. administration to Iraq where he had to work with the Iraqis and more or less dictate them how their new crucial document should look like. I must say that I am impressed already by the very fact that they have not killed him (and also grateful, of course). Noah believes that democracy is compatible with Islam, he wrote a book based on this (controversial) basic idea, and it was one of the reasons why he was viewed as an authority. The developments in Iraq have so far been less encouraging than what I have hoped for (and what Noah has hoped for, I think), but all these things may improve substantially in the very near future.

Monday, October 17, 2005 ... Deutsch/Español/Related posts from blogosphere

Google physics ads

I've added a GoogleAds rectangle on the right side of the blog (plus another rectangle with the Google search). Be sure that I won't get rich; in fact, it does not generate a single penny, it seems.

Nevertheless, it's fun and you may try to click at some of these ads. Some links offer free copies of Anthony Zee's textbook on Quantum Field Theory. Other links promote a book that allows you to create reality using the holographic principle. Not surprisingly, the crackpot McCutcheon with his book The Final Theory is among the links being offered, much like John Hagelin.

More serious advertisements offer you particle counters, plasma physics magazines, courses on quantum theory, and many other things. The physics ads market is not terribly advanced so far, but some diversity is already out there. If you happen to see some very interesting ads, you may share your excitement. ;-)

CSW rules from YM light cone gauge

Gorsky and Rosly have a very interesting twistor paper today,

They consider Yang-Mills theory in the light-cone gauge and identify a non-local change of variables that implies, in a pretty straightforward fashion, the Cachazo-Svrček-Witten (CSW) "disconnected" rules for the Yang-Mills scattering amplitudes. Such an understanding of the problem allows them to conjecture that there should be a natural one-loop correction to the CSW Lagrangian, arising from the Jacobian of their field redefinition, and no higher-loop corrections.

Their method shows that the twistor techniques are not merely mysterious bricks included in the third road of quantum gravity - bricks that only magicians like Penrose can comprehend - but instead, they are components of the standard light-cone gauge and spinorial procedures used to work with the usual degrees of freedom.

They start with the Yang-Mills light-cone gauge which means

  • A+ = 0

and express the physical components of the Yang-Mills field

  • Ax +- i Ay
as "x+"-derivative or inverse derivative of two new scalar fields "phi+-", respectively. The Yang-Mills action then reduces to an action written entirely in terms of "phi+-". Moreover, we really want to set "phi-" equal to zero. It must be done together with a new field redefinition for "phi+" done in such a way that the (++-) vertex absent in the CSW action disappears.

Laughlin vs. reductionism

A review of "A different [not too elegant] Universe".

Robert Laughlin is a great physicist who has found some truly important insights about condensed matter physics in general and the fractional quantum Hall effect in particular, and he deserves his 1998 physics Nobel prize.

But his attempts to say something profound about fundamental physics and particle physics seem far less serious. Be sure that my opinion is shared not only by a huge majority of "fundamental physicists" but even by many colleagues of Laughlin in condensed matter physics. The main problem with his reasoning is that he has obviously no solutions for the problems he tries to address.

All of us agree that some important features of physical phenomena do not depend on the details of underlying physics; many of these phenomena are emergent in character; it is not too important or useful to know quarks or strings in order to study most of the crucial concepts in biology, climate, physics of water, or quantum computing. If Laughlin thinks that other physicists do not realize this fact, then he is fighting a strawman. Most physicists realize these things - and many fundamental physicists actually use very similar mathematical techniques as Laughlin does in his "emergent" approach.

Friday, October 14, 2005 ... Deutsch/Español/Related posts from blogosphere

Geometric transitions

Anke Knauf from Hamburg and Maryland has made a nice lunch presentation of the geometric transitions, especially in the context of non-Kähler compactifications.


For the non-experts, let me mention that the six-dimensional Ricci-flat Calabi-Yau manifolds used in string theory to "hide" the six additional dimensions - such as the quintic (fifth order) hypersurface in the projective space CP^4 - may be deformed in such a way that a conical singularity develops within the manifold. When this singularity is present, it is not really a manifold anymore but rather a conifold - a generalization of the concept of a manifold where some patches may be diffeomorphic not to R^6 but rather to a cone. The relevant cone for the conifold is a cone over the product of two spheres, S^2 x S^3. Both of these spheres shrink to zero size at the tip of the cone. There are two ways to obtain a smooth Calabi-Yau by changing this conifold: either resolving it or deforming it which means that either S^2 or S^3 is blown up to a finite size.

The deformed conifold with N units of flux is equivalent to the resolved conifold with N D-branes on the dual cycle. Mirror symmetry morally exchanges the deformed conifold and the resolved conifold; it also interchanges D5-branes wrapped on S^2 and D6-branes wrapped on S^3 in the previous sentence because it exchanges type IIA and type IIB string theories. The Gopakumar-Vafa results about the topological partition sum for these backgrounds - and their equality - were described.

The resolved conifold is not literally a mirror of the deformed conifold, as a reader emphasizes. The simplest way to see it is that you won't find any candidate dual 3-cycles for your original 0-cycles.

Xi Yin initiated quite a debate whether this relation between two topologies and between the D-branes and fluxes - something that holds exactly for the BPS-protected quantities - is a full-fledged duality or just something that holds for the topological subsector. We mostly concluded it was exact. If you start with no branes or fluxes, the original two branches of the moduli space are connected in the singular point (conifold point in the moduli space) where the topology may change, as discussed in chapter 13 of The Elegant Universe. ;-) Nevertheless, the branches are sharply separated.

Thursday, October 13, 2005 ... Deutsch/Español/Related posts from blogosphere

Derived categories: what Joe hears

Melanie Becker (via Katrin Becker) has pointed out an interesting talk showing what dogs hear when we tell them something - and analogously, what Joe hears when someone speaks about derived categories. ;-) Well, Joe is not quite the only person with this kind of hearing.

Incidentally, it has just become possible for loop quantum gravity to solve problems related to the Pythagorean theorem.

Loops 2005

Yesterday, Cumrun gave a talk about the swampland in the Radcliffe Institute (which used to be a college for the girls only when Harvard was a male school, but eventually they merged). I liked it although it was not too new for many of us, of course. One of the points that Cumrun chose to emphasize was the derivation of the existence of dualities from the finiteness of the moduli spaces. Without the dualities, the moduli spaces (with the same metric, determined from the action) would have an infinite volume.

This approach shows how elegant and efficient some proofs of mathematical theorems may become in the future. You conjecture that an infinite sum or integral is miraculously equal to another sum or integral. You identify these objects as two different forms of a physical observable in string theory, and prove the required duality by finiteness of a moduli space which itself follows from the holographic principle. ;-) This kind of smart connection with complex calculus or even physics agrees with some of the sophisticated modern methods that were used in maths to prove various things.

These approaches are not incontroversial and several people asked their questions and expressed their opinion that it cannot lead to new insights about high-energy physics - maybe even "by construction". :-) I understand these comments. Everyone realizes that it is not guaranteed that new approaches to uncover the new wave of discoveries in theoretical physics will succeed. And most people realize that it is not easy today to find some really new and exciting stuff.

But whenever Cumrun or someone else says a sentence that is even partially wrong, someone immediately tries to correct him. We simply can't build and don't build on wrong assumptions and wrong statements. And if an assumption is uncertain, everyone acknowledges that it is uncertain. And if the assertion is ambiguous or incomprehensible, someone asks what it means. In summary, Cumrun and several colleagues try to identify the common patterns of the known vacua of string theory in order to learn some general lessons about quantum gravity; string theory is used as an experiment to study quantum gravity. These general lessons include

  • finiteness of the volume of moduli spaces in string theory
  • a special example of the previous point is the finiteness of the volume of the parameter space of CFTs with respect to the Zamolodchikov metric
  • upper bounds on the numbers of species, possibly correlated with the cutoffs
  • lower bounds on the numbers of species in various backgrounds
  • bounds on the strength of various interactions (under construction)
I totally understand Peter Woit who can't understand why this is an attempt to build on well-established and rigorous features of string theory and to find more general and far-reaching conclusions - with negative knowledge about string theory one simply can't do better. But there are fortunately other people in the world who must try to do better.

When I looked at Robert Helling's description of Loops 2005

plus the related papers and so forth, my impression was completely different than the impression from Cumrun's visionary talk. Their conference seems as a continuous inflow of ideas that are wrong and ideas that are not even wrong. Also, it seems that I am kind of familiar with the work of nearly all the speakers, and know why each of them is kind of incorrect (except Robbert Dijkgraaf who is usually right but who did not make it to the conference at the end).

Carlo Rovelli tried to derive the graviton propagator. We discussed this paper already. First of all, a graviton propagator only makes sense once we expand the metric around a background, which is in contradiction with the very general goals of loop quantum gravity. Second of all, in loop quantum gravity, it is known from the articles of Baez and others that singular simplices dominate the path integral, while Rovelli (incorrectly) assumes that the nice simplices that look like flat space give the most important contributions.

John Baez argued that there was some interesting progress in spin foam models, contradicting his previous but recent observations that there has been no progress in quantum gravity.

Lee Smolin proposed a model how macroscopic causality emerges (the problem in LQG is, first of all, that there is ultralocality and signals can't propagate at all for simple choices of the Hamiltonian). After Lee constructed quarks from LEGO, he conjectured that this model was connected with the Pioneer anomaly and low-angular-momentum discrepancies at WMAP. Well, maybe... ;-)

John Barrett presented a well-defined new version of a spin-network-like model which admits a diagrammatic expansion. I am pretty sure that these things can't be related to gravity, but the talk, if we believe Robert Helling, made sense.

Stefan Theissen tried to explain basics of string theory as known in the 1980s to our LQG colleagues.

Fotini Markopoulou argued that quantum gravity is like a self-correcting algorithm of a quantum computer. I can't say anything intelligent about such conjectured connections because I couldn't distinguish them from tens of crackpots' ideas flowing to my mailbox every week. It is plausible that there is something interesting going on in this direction - and it is appealing - but it just makes no sense to me so far.

Olaf Dreyer, possibly inspired by Lee, proposes to solve the problems that have been solved by decoherence and conjectures that quantum mechanics is not linear and probabilistic but non-linear and deterministic.

Other talks discussed modest questions about thermodynamics of discrete systems analogous to the Ising model; speculative connections about temperature and time evolution. There are several other ideas around but eventually Robert Helling stopped his reports because there was nothing in the talks.

Thanks, Robert, anyway! And a message for Peter Woit: if you think that Cumrun's program is comparable to the weird ideas from Loops 2005 listed above, then I must say that you are [the rest of the message has been censored to preserve our usual highest standards of politeness].

Tuesday, October 11, 2005 ... Deutsch/Español/Related posts from blogosphere


Peter Ouyang just argued, during a phenomenology seminar, that pentaquarks do not exist - or, at least, they are not generic predictions of chiral soliton models. See experimental Fermilab news with the same conclusion. Peter's theoretical arguments were somewhat technical in character (well, some unconvincing pictures from the experiments definitely helped his case); some previous solutions were argued to disappear as soon as very small masses are introduced to the model and the SU(3) flavor symmetry is broken a little bit.

Pentaquarks in general

One of the interesting features of QCD is that all stable particles seem to be either 3-quark baryons, or quark-antiquark mesons. There are other ways how color-neutral states could be created, but these exotic hadrons usually seem to be absent from the spectrum of stable particles. This is why the object that decayed into a nucleon and the K-meson that contains an anti-s-quark was so interesting. Because of the anti-s-quark, there should be an anti-s-quark in the initial state. The processes are fast enough so that they must be caused by strong interactions which preserve strangeness; therefore, there had to be an anti-s-quark in the initial state, too. You may conclude that the minimal configuration in the initial state contained four quarks and one antiquark (namely anti-s-quark).

Monday, October 10, 2005 ... Deutsch/Español/Related posts from blogosphere

A briefer history of time

David Goss has informed me about an interview that promotes a new book

that Stephen Hawking wrote with Leonard Mlodinow. It is presented as the second greatest book ever; guess which one is the best book. The journalist, Emma Brockes, has apparently sent Hawking a sequence of long, chaotic, diluted, unseparated, and emotional questions - judging by Hawking's response:
  • “I want shorter, better focused, numbered questions, not a stream of consciousness.”
In the new book, many more sections than ever before are dedicated to string theory and M-theory. I have always been impressed by Hawking's ability and will to follow all the new developments in physics. Emma Brockes asked Hawking "how string theory will impact human lives if it is proved correct". Hawking - who is most likely used to this type of questions - answers
  • “When we understand string theory, we will know how the universe began. It won’t have much effect on how we live, but it is important to understand where we come from and what we can expect to find as we explore.”
Hawking was also asked about the reasons behind the small percentage of women in science, and he thinks the same thing as many of us:
  • “In the past, there was active discrimination against women in science. That has now gone, and although there are residual effects, these are not enough to account for the small numbers of women, particularly in mathematics and physics.” Twitch, bleep. “It is generally recognised that women are better than men at languages, personal relations and multi-tasking, but less good at map-reading and spatial awareness. It is therefore not unreasonable to suppose that women might be less good at mathematics and physics. Of course, these are differences between the averages only. There are wide variations about the mean.”
Emma Brockes - who, using her words, imagines cheese strings every time Hawking says "string theory" - apparently disagreed with Hawking, arguing that
  • The problem with Hawking’s voice synthesiser is that there is not much tonal variation; I assume the map-reading, spatial-awareness thing is a joke. The women-being-less-good- at-science thing is clearly not; it is a widely held but rarely admitted-to assumption that, if not itself chauvinistic, is always made so by its corollary -- that science and maths are “harder”, more rigorous and ultimately more relevant disciplines than flaky “women’s” subjects.
I assure Ms. Brockes that Stephen Hawking was not joking about map-reading and spatial awareness. D.G. has quipped that if President Summers made such an interview, it "might not only have cost Mr. Summers his gig at Harvard, but also perhaps some of his reproductive apparatus....". ;-)

Let me mention that if the journal wanted to present evidence (or at least create an impression) that Hawking is wrong, they may have wanted to choose a different journalist than Emma Brockes. :-) Nothing against her! And nothing against her interview which I found very good - although not exactly as a source of information about physics. And I appreciate that she kept the nice title although Hawking apparently did not fit too well into her preconceptions about the world.

Columbus day

Christopher Columbus realized that if he sails a few thousand miles to the West, he has to get to some of the richest countries in the world such as India, Vietnam, and North Korea. As you can see on the map, he was essentially right. It's equally important that he received some Spanish royal grants to realize his ideas. Although he only found the Americas, instead of a better trajectory to India, it may have been a pretty good investment for the queen anyway. The physicists' search for a better understanding of the Universe often resembles the stories of Columbus. There are some objectively existing structures around; we have to discover them; we have a pretty good idea about the fundamental principles; and sometimes there can be some subtle errors in our mental picture. Happy Columbus day.

Sunday, October 09, 2005 ... Deutsch/Español/Related posts from blogosphere

Powell for Harvard Corporation

There are some signs that my hottest candidate to replace Conrad Harper in the Harvard Corporation has a nonzero chance to be elected. During the last FAS faculty meeting, some people argued that the new member of the corporation should be tightly connected with the academic world - which may have been an indirect criticism against Colin Powell, proving that the discussion about him is serious.

Harvard should fight almost as much as possible to get him for this position. Is there some evidence that Colin Powell is suited for the administrative positions in the academic world? Sure. He is also being considered to become the twelfth president of Cornell University. How much is the Kremlin on the Charles able and willing to fight back?

Kyoto counter: costs and benefits

Abstract: The main point of this article is to say a few words supporting the number 150 billion dollars a year for the Kyoto protocol (Nicholas Stern wants much more, about 400 billion dollars a year, 1% of GDP) for the expected negligible 0.07 Celsius degree decrease of temperature in the next 50 years, both used in the Kyoto counter in the sidebar.
A week ago, we correctly predicted that the JunkScience Kyoto counter would show the first saved millikelvin this week. Ladies and Gentlemen, open the bottles, the moment has arrived. ;-)

Many people have doubts about these numbers. Some people may go so far that they hypothesize that no one has even attempted to calculate how much the Kyoto would cost and how much it would affect the climate. Let me say that it would be a truly bizarre idea if some bureaucrats would propose to terrorize virtually every company in this world and they would not even attempt to calculate the costs and benefits of their proposed new policy.

Saturday, October 08, 2005 ... Deutsch/Español/Related posts from blogosphere

Langlands duality

Someone has sent me an article by Edward Witten with his Stony Brook talk about the

I am using Witten's favorite word "duality" instead of "program" because it is a bit more concrete; it's puzzling why the mathematicians haven't realized that their terminology can be sharpened. I encourage everyone to respect that the official terminology has changed to a "duality" right now.

What does number theory, Wiles' proof of Fermat's last theorem, and the S-duality of N=4 Yang-Mills theory in d=4 for general groups have in common? Well, the answer is, once again, Langlands duality - a framework established in the 1960s. For a recent and brief discussion of it, see this article by Edward Frenkel.

The magic trick that transforms the Langlands duality into an umbrella that unifies the diverse insights in the list above is the fact that the duality may be formulated "above" different fields - finite fields similar to "Z_p" as well as continuous fields we know and like. The latter is the geometric Langlands duality.

Start with the N=4 theory in four dimensions and its SL(2,Z) S-duality group from which only the Z2 will be used. For U(1), the spectrum of electric charges is mapped, by S-duality, to the spectrum of magnetic charges which belong to the dual lattice, by Dirac's quantization logic. For non-Abelian groups, you expect the root lattice to be relevant. The dual lattice is typically the weight lattice, and one may hope that it is the root lattice of another group. U(N) is dual to U(N). SU(N) is dual to SU(N) (mod Z_N, to be more exact). USp(2N) is dual to O(2N+1), and you may try to figure out what's dual to O(2N), E6, E7, E8, F2, G4. Answers welcome.

Sea level

A left-wing friend has sent me a link to a "nicely written and balanced" article about the climate in Antarctica. It starts with a subtitle "predictions vary from the catastrophic to the cataclysmic" and the rest is analogous - it is about a selective choice of places (especially the Peninsula which is about 2% of Antarctica) where ice is currently melting that are useful to support either the catastrophic or the cataclysmic predictions - which are the two choices that all of us apparently have. ;-)

It is the kind of articles that make me think where could I buy an object that varies from a revolver to a rifle. ;-) I didn't want to link the article itself because it's counterproductive to make an advertisement for crackpots but eventually an anonymous author of a comment convinced me to link it anyway. And because I want to minimize such interactions, I linked the article even though I believe it is wrong to promote such crackpots who already have enough publicity anyway.

Nevertheless, the article explains that we should be afraid that all major cities may be destroyed because the sea level will possibly rise by 80 meters; this is the expected rise if all of terrestrial ice melts. Say goodbye to New York, Rio, Bangkok, Boston, and all other major cities, the author recommends.

The author however does not explain when his "prediction" is gonna be realized. So let me mention that the "catastrophic" rise of the sea level due to the phenomenon we discuss - melting glaciers - was recently 0.42 millimeters per year. This figure is the most accurate and most averaged measure of the "global warming". Since the radius of Earth is 6,378 kilometers, you need 15 billion years - more than the age of the Universe - to make the increase match the radius. ;-) Yes, the Sun will already be gone.

Another little, more serious calculation shows that for his "prediction" of the 80 meter rise to be realized, he must hope that at least the same rate of increase will continue for 200,000 years. In reality, of course, it will be reverted roughly in several decades. But let's academically assume that the rise will continue. We will have 200,000 years to move the cities elsewhere. Even the corrupt Louisiana officials now need less than 1 day to evacuate New Orleans.

This is roughly 100 million times faster than what is needed. Do you want to push the numbers in a certain direction to increase the danger? Be my guest: my argument is robust with 8 more orders of magnitude on my side.

Or are you afraid of the buildings? Most of the buildings will have to be torn down in 200 years or so, not 200,000. Assuming that our grand-to-the-power-of-10,000-children won't be complete morons, they will build cities at safe enough places according to their data which do not have to coincide with the major cities we know today. No rational calculation can justify the worries about the effect of continuously rising sea levels on the major cities.

These worries exclusively control the minds of those who don't want to concentrate and do this simple arithmetics properly. Those who have absolutely no other problems to worry about because their parents have given them everything and the state sector is currently guaranteeing that their lives are full of wealth and safety. Those who only want to use these confused speculations for political goals - or to make them more visible as journalists in order to increase their paycheck. The people who actually need to do similar calculations - such as the Dutchmen - know very well that there is nothing special going on with the sea level right now and they have completely different concerns.

As Slawomir says in the comments, nature rules. If we want to "live", we better get out of its way. We can always move uphill. Or away from the earthquake areas like Kashmir where 20,000+ people died today. Away from various risks that cause such disasters almost every week. And away from the way of thinking that tries to make us investigate non-existent problems rather than the real ones.

Friday, October 07, 2005 ... Deutsch/Español/Related posts from blogosphere

Kožený detained

Viktor Kožený - who emmigrated with his parents from Czechoslovakia to Germany in 1979 - studied physics in our department of Harvard University for several months before 1989; I was told that everyone liked him here. He switched to management and earned a Bc. degree from Harvard Extension School. In 1990, after the collapse of communism, he returned to Czechoslovakia. He charmed most of the leading economists, including Václav Klaus. With his "Harvard Investment Funds" (whose name was justified by the fact that at that time, he may have been the only Czech citizen who had something to do with Harvard, at least as a student) :-), he became a superstar of the voucher privatization who transformed this event from a game for 600,000 people (who could get pretty rich) to a mass event in which a majority of Czechoslovak citizens (about 8 millions) participated. Eventually he controlled companies whose value was in hundreds of millions of dollars.

Then he left Czechoslovakia again, acquired Irish citizenship, and extended his business to the former Soviet Union where he bought some worthless oil stocks in Azerbaijan; fortunately, as some sources say, he sold them for an even greater amount of money to some Americans. When they found out what they bought, they were not happy. Many people both in the Czech Republic (some of the investors who sold him his vouchers plus anti-capitalist activists) as well as the U.S. wanted him to be arrested. (I've lost roughly 20 stocks of a glass factory because of the strange situation of his funds, but I'm not gonna hate him because of that.)

He has lived on the Bahamas and was extremely interested in various modern technologies - smart dust is an example - but also affine geometry. ;-) Three years ago or so, during his (unsuccessful) bid for the immunity from the European Parliament in which he developed an intriguing program how to transform the EU into a 25th century technologically advanced country, he offered me the post of the shadow minister of education (be sure that I have never received a penny from him), and I am proud of the offer even though - try to guess - I rejected it.

It was announced that Kožený was detained yesterday, together with two U.S. employees of him, and charged the U.S. accusations on 27 counts (and thousands of pages), mostly bribery of the former Soviet officials. He may be a "pirate of Prague" as they call him, but despite his questionable approach to moral values, I think that he is still a rather extraordinary person and it's bad that our society can't use such people more efficiently than putting them into jail.

Climate change on Mars

In the second part of the article, we discuss the climate change on Mars; see also global warming in the rest of the Solar System. But let us start with:

Dutch journalism award: Kyoto is junk

Congratulations to Marcel Crok - the author of the Dutch article whose English version is here (12 pages). He was awarded by the prestigious Dutch scientific journalism prize from the Free University of Amsterdam (VU), its Medical Center, and Hogeschool Hindesheim. The prize includes 10,000 euro and a piece of art.

Steve McIntyre proudly announced the news here. An automatic translation of the Dutch news to English is here.

Crok's article - that I remember pretty well - explains that the analysis of the "hockey stick graph" revealed that this main pillar of the "global warming theory" was nothing else than a result of flawed statistics and raised questions about the integrity of the world climate research.

His description is very detailed - he even discusses the the secret "CENSORED" directory that Michael Mann apparently used to "hide" the data that were inconvenient for their pre-determined main conclusion - namely their bold claim that the present era is exceptionally warm compared to the temperatures in the last 1000 years. More concretely, the content of this directory effectively proves that Mann knew that the "hockey stick" and "unprecedented global warming" disappears if the bristlecones are removed from their ensemble.

What about Mann and Bradley? (Let me omit Hughes who is a bit separated.) While everyone else knows that their paper was flawed, they still seem to deny and misunderstand everything.

Thursday, October 06, 2005 ... Deutsch/Español/Related posts from blogosphere

Nongeometric flux vacua

Brian Wecht has explained us - a J453 standing room only crowd at Harvard - their (Jessie Shelton, Wati Taylor, and Brian Wecht) work on

Their approach is meant to generalize the flux compactifications into a broader class that is closed under the action of T-duality. Brian first invited everyone to MIT whose physics department has a new temporary building, water cooler, and Dan Freedman. His physics talk started with a six-torus in type II that can be written as a product of three two-tori. You orbifold this six-torus by a "Z3 x Z2 x Z2" group where the "Z3" permutes the three two-tori cyclically and Z2's change the signs of the coordinates on two of the three two-tori. Brian Wecht called it "Z3 x Z2" only but he asked us to use our notation for his careful, but incorrect description of the orbifold group. :-)

So my notation for his "Z3 x Z2" is "Z3 x Z2 x Z2" even though the group he generated is really a non-Abelian, semi-direct product but at least it has 12 elements. ;-) Also, he did not care about the orbifold singularities that probably may be blown up, but he wants to ignore all the new degrees of freedom that live there.

Start with a three-torus with "N" units of H3-flux. Once you choose a B-field gauge (gauge-dependence is another source of controversy) and write the "B_{xy}" field as "N.z", you may T-dualize this to get a three-torus whose two-torus gets tilted ("tau" goes to "tau+N") if you rotate around the third circle: it's a twisted torus. The amount of twisting is considered by the authors to be a new kind of flux - it's a terminology that may be confusing especially because many of these "fluxes" are some topological, but purely geometrical invariants of their compactification manifold that they can't really define in the general case. Then they T-dualize - or mirror symmetrize - these configurations in many other ways and obtain new kind of non-geometric fluxes; the last ones are supposed to be the most surprising ones - the extremely non-geometric ones. The previous ones measure which T-duality appears as a monodromy around one of the circles, but the last ones are probably even more unusual.

Wednesday, October 05, 2005 ... Deutsch/Español/Related posts from blogosphere

Repeatability of models

Because William Connolley uses old-fashioned techniques imported from the Soviet Union to censor everything that is not convenient for his goals - for example he erases every comment that tries to put the questions about repeatability on firm ground - I must write a reply to his rather weird ideas (dominated by childish personal attacks against Steve Milloy) about repeatability of climate models on my blog.

In science, it is essential that discoveries are repeatable. It means, for example, that if you think that your new drug can improve the chances of the cancer patients to survive because you apparently observe that the survival rate increased a bit in your group, your statement is not yet established science. If your statement about the positive effect of your drug is scientifically true, anyone else must be able to get the same conclusion.

If you make a calculation whose outcome is the muon/electron mass ratio around 206.8, it will only become a part of science if others can repeat the same calculation.

Open heterotic strings

The strings must satisfy some boundary conditions at their boundaries in order to cancel the boundary terms in the variation of the worldsheet action. The Neumann boundary conditions,

  • partial/partial sigma (X) = 0,

were thought to be the only meaningful boundary conditions for the open strings until several smart people, most notably Joe Polchinski, pointed out that the Dirichlet boundary conditions are equally important, consistent, and related to Neumann boundary conditions by T-duality. Moreover, they lead to all D-branes and all this wonderful stuff.

One of the trivial consequences of this reasoning is that the heterotic strings can't be open: the boundary conditions relate the left-moving and right-moving degrees of freedom but the heterotic strings have a different number of degrees of freedom on their two sides. Setting the "extra" ones equal to zero at the boundary is far too constraining; it would allow no nontrivial solutions.

Let me summarize. There seem to be no open heterotic strings and consequently no heterotic D-branes which was the main paradox discussed in

Now another physicist whose name is again Joe Polchinski, and you may speculate that it is not a coincidence :-), writes a note that there exist

after all. More precisely, he argues that they only exist in the case of the SO(32) heterotic string theory (HO) and not E8 x E8 heterotic string theory (HE). The previous sentence may sound particularly bizarre because these two heterotic string theories are related by T-duality, as you can learn in a textbook written by another Gentleman whose name is also Joe Polchinski.

An Eot Wash talk

Claire Cramer just spoke about their experiments in the Eot Wash group in Seattle. (The U.S. English name "Eot Wash" is a deliberately misspelled version of the name of the guy who did the first tests of the equivalence principle.) Everyone seems to admire the group at the University of Washington as the clear leaders in the field of all similar experiments such as the torsion balance tests of sub-millimeter gravitational forces and the Lorentz and CPT violation.

I am probably far too conservative for the physical idea that the Lorentz symmetry or the CPT symmetry are violated in a new, yet unknown way; for me, these questions were settled 100 years ago. Of course, this does not quite include the fifth force etc. - very large extra dimensions, new light scalar fields and so on - although I still believe that the probability that gravity gets modified at the multi-micron scale is vastly smaller than 50 percent.

Tuesday, October 04, 2005 ... Deutsch/Español/Related posts from blogosphere

Half of Nobel "stays" at Harvard

The 2005 physics Nobel prize has been divided between three people. One of them who wins half a prize - Roy Glauber - is our colleague at Harvard. Congratulations! He already has a lot of experience with the Nobel prizes (sorry but it's just difficult for me to get the voice out of my nose!); see the first photograph here. (Also, he grew up in the same apartment building as the Kadanoffs and a block away from Sheldon Glashow.)

The press conference started at 11:00 am here in the physics library at Harvard; the reception began at 4:00 pm in the same library. John Huth and others said some entertaining and nice stories about Roy, who spoke himself, much like dean Kirby and Larry Summers. After some wise Jewish proverbs and other nice words, Larry also admitted that while he was the secretary of treasury under Clinton, he made the Nobel prize taxable! :-) Of course that he would have avoided the mistake if he knew about the award today. This was the tenth physics Nobel prize for Harvard - and the winners number #11-#15 were probably in the room already. :-)

Roy Glauber was born in 1925, more or less much like quantum mechanics, and you can guess that it is no coincidence. Although his name does not occur too often in textbooks, his contributions are very important. Especially the contributions to detailed balance (his special stochastic matrices that satisfy it) and quantum optical coherence for which he was awarded. See some of his other articles at Google.

The fact that absolutely no one has figured out that the winners could be candidates - not even The Reference Frame - does not mean that they don't deserve it!

What do I mean? Consider the Hilbert space for the harmonic oscillator. You often write down the state |0> (thanks to Quantoken for telling me that every child remembers that the vertical line is written as "ampersand hashmark seven c semicolon"), but you may also want to consider the "coherent" states |z> that are the eigenstates of the annihilation operator "a":

  • a|z> = z|z>
In the phase space, this coherent state |z> looks just like the ground state, but it is shifted by some amount both in the position and the momentum directions. Glauber studied these states in various contexts that are described by the harmonic oscillator - which includes the electromagnetic field itself as well as other fields. He understood that this very right combination of states with different numbers of particles - one that can also be written as "exp(z a+)|0>" - has the effect of shifting the classical value.

All of us use these fundamental insights in quantum mechanics, including string theory. In string theory, the coherent states are used, among many other things, to explain that all vacua in the same moduli space may be obtained from each other and lead to an equivalent theory. There is only one string theory although it has many states in its Hilbert space.

Glauber also figured out some essential features of the squeezed states and other states. This text is not supposed to cover everything he did.

The other half

The other half of the Nobel prize is divided to John Hall from Boulder, Colorado, and Theodor Hänsch from Munich, Germany for their work on laser-based precision spectroscopy, including the optical frequency comb technique which was - unlike the coherent states - discovered very recently. It involves femtosecond lasers. It may be the first time I hear the names of the two Gentlemen, and it may be better to leave qualified comments to some atomic/molecular/optical physics bloggers (thanks to Dave - I really did not mean condensed matter physics) if one exists.

The "comb" of course means that an equally spaced set of frequencies can be localized using the laser; this technology allows one to improve the measurements of length by three orders of magnitude, among other things.

You can see that the fraction of the Nobel prizes going to the U.S. still safely exceeds the proportion of the carbon dioxide created in the same country. Also, in this particular competition, it is not Princeton that competes with Harvard: it's Stanford. Harvard will actually have to receive a few more physics Nobel prizes to catch up with Stanford.

The lightbulb

When I read the self-congratulatory article of the climate competitors of this blog who just achieved - thanks to lots of fervent global warming believers in various journals - 500,000 visits much like The Reference Frame (the counter on the right side counts the daily unique visitors), it's hard to avoid the feelings of compassion for them. And a well-known joke about the lightbulb comes to mind if you think about their collective efforts.

Do you know how many climate scientists does it take to exchange a lightbulb? Ten.

Mann and Bradley are afraid that the broken lightbulb may be too hot and want to cool it down by a broken hockey stick. Connolley calculates that they need 1000 bottles of ice to cool it down and Steig makes sure that this calculation becomes a part of the consensus in the ice community. Ammann helps Connolley and Mann to attack the people who say that they should try to turn the lightbulb around.

Schmidt calls the aliens via his friends in NASA who could help them to locate the greenhouse that is apparently making the lightbulb so hot. Rahmstorf adds the general relativistic corrections to the heat contribution of the carbon dioxide to the temperature of the lightbulb. Benestad is present to guarantee that there will be 10 people in the team, exactly as predicted by the climate models.

Archer tries not to exhale so that the concentration of CO2 inside the lightbulb does not grow too much. Finally, De Garidel writes the grant applications for them to have money to buy a brand new palace in Kyoto, Japan with a new lightbulb in it. He explains that the more members their lightbulb change team will have, the more scientific their approach will become. And the sponsors agree.

Disclaimer: This joke does not apply to all mainstream climate scientists. If you want to read a new intelligent essay by von Storch and Stehr, one that explains that plans for adaptation must replace attempts for moderation (such as Kyoto), visit this page on Prometheus.

LIGO: still nothing

The LIGO team - or after you look at page 1, you may want to call them the LIGO nation - has searched through 2 weeks of their data for gravitational waves from black hole binaries and so far they found nothing. But it's not yet a reason to conclude that LIGO won't work or even that the gravity waves don't exist!

Monday, October 03, 2005 ... Deutsch/Español/Related posts from blogosphere

Angular momentum

Those who remotely study Quantum Mechanics II ;-) should notice that after the insights about the identical particles, we now discuss the angular momentum. See Fall2005-Lectures here.

Seriously about Bogdanoffs II

A fascinating book on the Bogdanoff affair and the rest of physics: click and buy
I was just asked to give my opinion about the Bogdanoff paper(s) on Wikipedia, so I replied with a neutral comment. It is surprising that some people who otherwise propose that everyone should study alternatives to string theory - such as Peter Woit - are so incredibly negative about the Bogdanoff paper(s).

Why? Because the Bogdanoff brothers are proposing something that has, speculatively, the potential to be an alternative story about quantum gravity. As a string theory believer, I would say "a new dual description of quantum gravity i.e. string/M-theory". What they are proposing is a potential new calculational framework for gravity. I find it unlikely that these things will work - but it is probably more likely than loop quantum gravity and other discrete approaches whose lethal problems have already been identified in detail.

In the previous article I focused on the creation of myths and their idea about the fluctuating spacetime signature. But let me now ask you about the following proposal that is included among their refreshing speculative ideas.

Usually we assume that the geometry completely breaks down at the sub-Planckian distances, together with the spacetime topology and all other things. It's because the excited string states and other states appear together with infinitely many higher-derivative corrections. But let us now believe that geometry is a useful picture despite all these effects.

Imagine that you start with a generic gravity action whose pure gravitational part has terms like
  • L = R / (16.pi.G) + alpha. R (wedge) R + beta . R^2 + gamma . R^3 ...

and so on. The topological term "R (wedge) R" would have to be replaced by something else in higher dimensions. At long distances, the first, Einstein-Hilbert term is important (after the vacuum energy, of course). At short distances, we usually assume that the infinite tower of higher-derivative terms takes over and we can't say anything; the metric is not a relevant degree of freedom anymore because we must really add a whole tower of new, equally important states predicted by string theory.

Helicobacter pylori

The first Nobel prize - one for medicine - goes to Barry Marshall and his collaborator Robin Warren from Australia for their discovery of Helicobacter pylori, the cause of most ulcers, in 1982. Because I happened to have studied this spiral-shaped bacteria for certain personal reasons roughly 8 years ago, I may say that these guys definitely deserve their award.

Don't panic: having Helicobacter pylori is by itself no big deal: one third of the people on the planet have it.

How can you say that their discovery was revolutionary? It's mainly because in their case, much like in lots of other examples in science, the Helicobacter pylori theory was ridiculed by the so-called "scientific consensus" promoted by scientists as well as doctors. The scientific consensus believed that no bacteria could live in the acidic stomach and the ulcers were always caused by stress, spicy food, and too much acid.

The following paragraph is brutal and should not be read by children.

What could Barry Marshall do to force the people to pay attention to their theory? Well, he drank a test tube of the bacteria and swiftly developed gastric ulcers, which he then cured by antibiotics. It was obviously very difficult to convince anyone. Fortunately, the times are changing, the people behind the "scientific consensus" are nowadays identified as a sort of anonymous morons, and Marshall and Warren may share their well-deserved one million of US dollars. And they became, of course, mainstream scientists.

Human stupidity repeats its mistakes all the time. This was not the first time when a microorganism was known to cause a disease but virtually all scientists humiliated the idea without having a good reason to do so. (And believe me that there are many examples in science that are not about microorganisms causing diseases.) In 1795, Alexander Gordon of Aberdeen figured out that the fever after the childbirth was probably an infectious disease that he could cure. The consensus said no. In 1843, Oliver Wendell Holmes presented convincing evidence that puerpetal fever was contagious. No. In 1849 Semmelweiss virtually eliminated the fever from his hospitals by better sanitary procedures. The consensus said that he was Jew and they even fired him. Only in the early 20th century, i.e. 150 years after the first discovery, people started to agree that the fever was infectious.

Sunday, October 02, 2005 ... Deutsch/Español/Related posts from blogosphere

Brian and E=mc^2

Brian Greene had an

  • op-ed in the New York Times

on Saturday about Einstein's famous equation E=mc2. You may recall some of the important developments in the history of physics that took place almost exactly 100 years ago, and some interesting examples showing why this equation is important.

For example, Brian calculates - and you can check it - that if you were able to use the New York Times more efficiently - which means that instead of reading it, you would annihilate it - one copy would give you enough energy for the New York City for one month. :-)

The Times have introduced a funny typo in another article about Einstein on Friday that was corrected on Sunday i.e. two days later. The Lorentz factor was originally written not as

  • sqrt (1 - v2/c2)

but with a sign error. That's pretty entertaining. As far as I understand, it was neither Brian's fault nor the fault of the humble correspondents who were supposed to check his article before it got published. ;-)

It reminds me of the elementary school where I had a bizarre theory. I obviously misunderstood special relativity for quite some time. The best thing I could imagine was - using the current language - a Euclidean spacetime whose signature was (++++). An even more bizarre feature of the model was that the worldlines of light were not tilted lines "x=ct" but rather "x=ctP" where tP was the proper time, namely sqrt(t2 + x2/c2). Whatever the general confused rules were, it meant that the light-like rays were actually horizontal.

How did I add up the velocities? Obviously, as angles in the Euclidean space. And because the speed of light was connected with the angle 90 degrees, you got something like "pi/2+v/c" if you combined the speed of light with another velocity "v" whose angle is "v/c". The sin of this combined angle is still equal to one, up to the second order terms, which - I thought - was enough to explain the negative result of Morley-Michelson aether experiments.

Well, it took several weeks of months before I understood that the spacetime actually is a diagram of the actual events that gives you space at time "t" if you slice it. Such an experience with my own silliness gives one a certain understanding for the reason why many people may have problems to understand relatively simple things - although the understanding is not perfect because if someone had told me how the relativistic spacetime really worked, the confusion could have disappeared instantly, instead of disappearing after long weeks of being lost in the darkness. And maybe not. ;-)

Drake equation - 2005 edition

Where are they? Because I happen to believe that the number of extraterrestrial civilizations that can communicate with us is not too large, let me update the famous formula due to Drake.

The expectation value of the number of extraterrestrial TV programs that we will watch by the year 3000 is again a product of many comparably unknown quantities n_i. They count various necessary assumptions for such a TV program to be aired. Most of them are various probabilities and you can imagine that they are close to one or smaller than one by several or many orders of magnitude. By choosing the numbers according to your beliefs, you may obtain estimates that may imply that we should be watching aliens' TV programs every day - which seems ruled out - or, on the contrary, that we are almost certainly the only technologically advanced humans in the visible Universe; and in the most "pessimistic" case, even the only ones in the Landscape (where it becomes more difficult to count the number of galaxies per background). ;-)

The number of TV shows is approximately a product of

  • the number of galaxies in the visible Universe
  • the number of stars or, more speculatively, their equivalents per galaxy
  • the percentage of stars that have planets
  • the percentage of planets that have an acceptable temperature
  • the percentage of planets that have an acceptable concentration of carbon
  • the percentage of planets that have an acceptable concentration of oxygen (if you believe that life can be based on a completely different chemistry, sum over all possibilities)
  • the percentage of planets that have an acceptable value of their spin

  • the percentage of planets with rocky enough terrain to admit life
  • the percentage of such planets with a good enough value of the gravitational field
  • the percentage of planets that have viable enough system of plane tectonics that may be needed
  • the percentage of planets that have a Jupiter in their solar system if it is necessary; otherwise substitute one
  • the percentage of planets that have a good enough Moon if it is necessary; otherwise substitute one
  • the probability of all collisions and other interactions that may be needed to create a viable Earth at the beginning
  • the probability of all other physical and chemical assumptions that may be needed for early life but are not listed here or are not even known
  • the probability that some critical amino acids are produced after the planet is created - which probably requires some thunderstorms and other events
  • the probability that the first protein-like or RNA-like molecule - a molecule able to self-replicate and carry information - is created in a short enough time
  • the probability that this RNA won't be the final stage of development of life
  • the probability that a DNA-like molecule appears
  • the probability that the non-trivial transition from prokaryotes to eukaryotes occurs successfully (these things may occur pretty quickly and likely if the environment is good enough - as shown by the fact that these things happened pretty quickly, relatively to the lifetime of the solar system, on Earth)
  • the probability that one of the equivalents of evolution from the primitive multi-cellular organisms to the equivalent of mammals occurs successfully
  • the probability that the equivalents of primates are created
  • the probability that their monkeys actually start to control their environment in a slightly intelligent way
  • the probability that they invent agriculture and/or organized hunting to have enough food so that they don't have to spend the whole days by looking for food
  • the probability that they have big and powerful enough brains to start to develop some actual tools
  • the probability that they actually start to do it and start to dominate the environment because of their intelligence as opposed to brute force
  • the probability that their brute force is big enough so that the intelligence won't be defeated by brute force of other animals; sum the probabilities over all animals that are candidates for creating an advanced civilization
  • the probability that their brute force is small enough so that they are actually forced to think instead of just eating the other animals forever; note that there is a marginal tension of this item with the previous item which may require a lot of fine-tuning
  • the probability that their environment is challenging enough so that they must try to get better and smarter, instead of just eating bananas all the time
  • the probability that their environment makes their life sufficiently easy - including pleasant enough climate - so that they can do everything necessary for their survival and other things, too
  • the probability that they invent a language as a tool for communication - one that has the potential to be improved
  • the probability that they successfully, compassionately, but resolutely kill a sufficient percentage of the primordial environmentalists 8,000 years before Christ who argued that it was immoral to cut the trees
  • the probability that some of them become fascinated by the patterns in nature and start to develop the first ancient forms of science, arts, astronomy, and religion
  • the probability that they establish big enough empires in which culture and science may be produced in a systematic fashion
  • the probability that they invent trade and other things that are necessary for the accumulation of capital
  • the probability that a sufficiently powerful religion that is able to force many people to memorize things and to focus on the big questions takes over, even if the actual answers at the beginning are wrong
  • the probability that their Catholic Church won't convince everyone forever that the Holy Scripture contains the ultimate answers to everything that humans need to know
  • the probability that they systematically develop the scientific method as a way to separate correct conjectures from the wrong ones regardless of the initial beliefs and independently of short-term interests
  • the probability that they start to realize the ideas of enlightenment and the creative power of freedom; it includes the assumption that they will appreciate that the truth as they learned it does not have to be the final answer to everything
  • the probability that the fate of their heretics will be difficult enough so that they're forced by the brute force of their Catholic Church to be good enough, but sufficiently simple so that some of these heretics survive for the critical time that is needed to make a real progress (note the analogy with the animals above; a similar theme occurs many times in this history)
  • the probability that they actually develop a necessary set of scientific and technological discoveries
  • the probability that they invent a social and political system analogous to democracy in which the leaders that become counter-productive may be replaced by the statistically more promising ones without involving a civil war and losses in each case
  • the probability that their Great October Revolution won't swallow the whole world and that the communists (and similar groups) won't convince nearly everyone that they know what the ultimate model of the society should look like forever
  • the probability that their civilization won't kill or otherwise neutralize a too significant part of their good and wise people because of some racial or political prejudices
  • the probability that they won't exterminate themselves within a few years after they develop their weapons of mass destruction

We are obviously getting to the future, but we may continue...

  • the probability that they will escape from various tempting ideas of socialism, communism, political correctness, NGOism, environmentalism, and new "atheist" religions - all of which have the power to stop or even revert the social, economic, scientific, and technological progress
  • because of the importance of this assumption, let me add another related factor - the probability that the creatures will be rational enough not to be scared by various alarmist scenarios like the judgement day according to Jehovah's Witnesses or the Global Warming alarmists
  • the probability that they will identify the effects of their civilization that actually have the power to cause significant problems or even instant destruction, and that they will be able to avoid the bad influence
  • the probability that they will defeat all other dangerous anti-civilizational tendencies such as their counterpart of islamic fundamentalism that intends to return their worlds by millenia into the past
  • the probability that a significant percentage of these beings will actually work on material and meaningful intellectual problems (such as industry, real science, and technology) relevant for making their life and civilization better, as opposed to huge social engineering programs, postmodern pseudoscience, and speculating with "higher order derivatives" and funds of hedge funds - i.e. the probability that the work of the people and the commodities sold on the market will keep its essence and won't become just a silly game with money and pseudoscientific ideas
  • the probability that the life of the people who generate some kind of progress will be enough fun so that they won't start to disappear
  • the probability that they will find a satisfactory source of energy that allows them to think about the ambitious goals and transcending the boundaries of their planets (and solar systems), including the probability that they will be able to defend this source of energy politically
  • the probability that after all this difficult history, they will be still willing to communicate at all
  • the probability that they realize and we realize that communication has two sides, and it is not enough just to listen, and it is not enough just to broadcast
  • the probability that there will still be enough concentration of the capital, power, and curiosity so that they will be thinking about big scientific programs such as the GUT scale accelerators or intergalactic journeys
  • the probability that the powerful ones will still be interested in these big scientific goals, as opposed to continued life with no new progress
  • the probability that they will have powerful enough signal to broadcast intergalactically because the number of lines above make it likely (together with our direct observation of our Galaxy) that two such civilizations probably won't appear in the same galaxy
  • for dimensional analysis, I must include the total number of TV programs that they will broadcast to the direction of Earth as a factor
  • the probability that we have a good enough sensitivity to detect these signals
  • the probability that we are using a compatible method of coding - and mathematics and information in general - so that we will distinguish their programs from noise
  • the probability that we will actually decode their particular TV programs
  • the probability that we're not the first civilization that has a chance to realize all the ambitions above
  • the probability that we will realize that they are aliens even though we used to call them Albanians, for example
  • the probability that we realize our relation to the aliens if there are any relations to be learned
  • the probability that we will be here and care about science around the year 2500
  • the probability that they will still think it's an interesting project to try to communicate with other civilizations even if the Alien's Reference Frame convinces them that the success is unlikely
  • the probability that there exists no principle in science that makes the Earth physically special, equivalently to the Bible, after all ;-)

You see that there are many concerns. Even if the geometric average of the probabilities above is as large as exp(-1), you still obtain a product of order exp(-60)=10^(-26) and a very small number of candidates - probably less than one hopeful star per visible Universe.

There are simply many points at which the progress could have stopped - and the rest of the history could have been dictated by RNA dominance, prokaryotes, Catholic dogmas, environmentalism, communism, and other things whose very basic essence is to stop any further progress beyond their final vision of the planet; this includes ideologies labeled with the funny adjective "progressive".

Most of the steps in which the life on Earth was developing occured quickly; but it does not mean that they were guaranteed. Events can be fast once they occur, but they can still be unlikely. There were also many steps that required some kind of fine-tuning - the humans could have been neither too strong nor too weak, otherwise they could never develop the advanced civilization. And the same theme repeated itself many times...

You can also say that all these percentages and probabilities are really almost one - the events were nearly inevitable - and we should be seeing a lot of aliens around. With the current knowledge, I am afraid that this uncertainty can't be settled scientifically. The experimental state-of-the-art is that we don't seem to see any aliens, which makes the theory that we are unique more justified than the theory that the aliens are generic.

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