Friday, February 06, 2009 ... Deutsch/Español/Related posts from blogosphere

Answering a critic from a cartoon

Welcome, Abstruse Goose readers. If you click the colorful unicorn on the AG page, there is a touching story about the way how science makes unicorns extinct. I have similar feelings, too. Except that the real scientific theories are my unicorns: they're so cute.

And I am worried about the coming world of an anti-scientific propaganda that makes theories and science unnecessary for most people who seem to prefer sociological arguments and conspiracy theories. So my reply to the unicorn cartoon is fuck critics of string theory even though, let's admit, most of them are already fucked-up.

Click the picture to zoom in.

A couple of physics blogs, including, have recently posted the cartoon above. A boy is saying some very stupid things that he considers to be arguments against the validity of string theory. On the other hand, a girl who seems to be familiar with string theory reacts in the only way that actually makes any sense in this context.

A hot commercial break: See an animated GIF of the most popular Calabi-Yau manifold (click!) among most string theorists, the quintic hypersurface
The deeply flawed and brutally misinterpreted propositions made by the boy have recently been repeated by thousands of laymen as a new mantra. There are whole websites on the Internet that have been alive for years just by repeating the stupid boy's statements from the cartoon: a classic infinite loop of obsession. I can understand why people want to repeatedly watch porn: we are hard-wired for certain things.

But the people who can read these websites more than thrice - or more than for one week - must suffer from some kind of severe mental deviation or retardation, an insatiable thirst for repetitiveness that I simply cannot comprehend. They must believe that if they eat the same excrement from a cartoon 1,589 times (guess where the number comes from), it becomes a yummy pizza. ;-)

Although all these topics have been discussed hundreds of times and all the people who have seen it, who are interested in physics, and whom I consider at least partially intelligent must have understood them, let me respond to the particular line of comments made by the stupid boy from the cartoon again, realizing that in comparison with the girl's appropriate reaction, my answers will be just a waste of time:
Misunderstanding: First of all, string theory has not made a single testable prediction in over 30 years.
Reality: String theory was born in the late 1960s as a theory of strong interactions. It has made lots of predictions about the strong interactions. Many of them were correct. Many of them, made with the old version of the theory, were quickly proved wrong. First, let me jump from 1973 to 1997.

String theory was thought to be a wrong theory of strong interactions from 1973 to 1997 or so when it was realized that string theory on certain AdS backgrounds is exactly equivalent to theories similar to QCD.

This crucial discovery has revived the line of reasoning that was studied 30 years earlier and it led to many predictions - that are much more difficult in other approaches - about nuclear physics. They are not only testable but many of them have been spectacularly confirmed. This application of string theory is arguably the most active approach to the theory of strong interactions in the beginning of this century.

Press the button to play. Joe Polchinski tries to answer the difficult question "What is string theory".

If we return back in time, string theory was (not really correctly, as explained above) abandoned as a theory of strong interactions.

It became a theory of quantum gravity around 1974 when it was realized that massless spin-two excitations (gravitons) belonged to the spectrum and they inevitably follow the rules of general relativity. The theory describing strong interactions by the 1997 holographic recipe is the same theory of quantum gravity: the 1997 discovery has really proved than an underlying "gravitational explanation" is inseparable from theories similar to "QCD", and vice versa. There is no way to separate these things again: the dualities that have been established - really proven - can no longer be unproven or disestablished.

We're not talking about "two different string theories here". Once you accept the AdS/CFT dual description of gauge theories such as the N=4 theory, there is no way to deny string theory the status of a unifying theory of all forces, having 10 spacetime dimensions, that is inseparably woven to the structure of all physical field theories. See Unity of strings.

When it became clear that string theory was a theory of quantum gravity, it also became clear that it couldn't be directly tested.

The fact that quantum gravity is almost certainly untestable by direct experimental tests has been known not for 30 years but for 109 years. In 1900, Max Planck realized that physicists should be using "natural units". Today, we talk about Planck units. In the contemporary conventions, they're products of powers of the light speed "c", (reduced) Planck's constant "hbar", and Newton's gravitational constant "G". The correct product with the units of distance, the so-called Planck length "sqrt(G.hbar/c^3)", is close to 10^{-35} meters which is so short that it has been clear, since 1900, that people in a foreseeable future couldn't possibly "see" them directly.

Again, this argument has been known for 109 years. Every person who has ever begun to study quantum gravity should have been familiar with it. I was familiar with it - with the magnitude of the "natural length scale of quantum gravity" - when I was 10 years old. Every person who claims to be interested in fundamental physics but who also reveals his or her "surprise" that the effects of quantum gravity cannot be directly seen in existing experiments is simply dumb beyond imagination.

Is quantum gravity directly relevant for people's everyday lives? No. Was it ever argued to be relevant? No. Is it a new situation that most people don't really care about fundamental physics or any other theory-loaded science? No. Did the people on the street in the 1930s say that they gave a damn? No? That's because they didn't. ;-)

Despite this apparent separation of the scales, hundreds of exceptional physicists - really many of the smartest people on this planet - decided that it was the right time to study physics at the fundamental scale. All of them have always known that these effects couldn't be directly seen because they're associated with extremely short distances and durations and extremely high temperatures. And indeed, it became possible to unequivocally say a lot of statements about the nature of phenomena that are crucial near the Planck length.

The topology of space can change; the total number of dimensions visible at this scale must be 10 or 11 whenever all other "obscure" degrees of freedom are geometrized; black holes preserve the information, even during the evaporation; strings, branes, and various topological defects are parts of the spectrum whenever certain moduli approach the asymptotic regimes. I could write thousands of pages of much more specific and quantitative predictions of string theory: see Top twelve results of string theory for a summary. Generating predictions is what string theorists are doing all the time.

The fact that these predictions cannot be tested in your basement is not a flaw of string theory but an obvious consequence of the very choice of the questions: we want to study quantum gravity, the processes at the "natural scale". These processes simply can't be testable in your basement, because of a simple calculation that even kids should be able to understand. This has nothing to do with string theory per se: it is a property of the very questions we are asking.

The argument that quantum gravity is inherently untestable could have been made more than 100 years ago. But if someone had used it to suppress all research of the subject in 1909 or so, he would have killed hundreds of amazing insights that came out of this research. Many of them tell us seemingly "divine" answers to difficult questions about quantum gravity while others tell us answers to completely different questions - like those about the collisions of gold ions - that turned out to be connected with quantum gravity.

The people who are trying to suppress the research of string theory today are surely trying to eliminate many discoveries that will be made in the future.

Paradoxically enough, it was string theory that has also found a possible flaw in Planck's estimate - i.e. in his argument showing that the fundamental scale had to be extremely tiny and inaccessible. When we add the extra dimensions into our considerations and analyze their possible radii, multiplicities, and general shapes, we find out that it is conceivable that the "higher-dimensional natural scale" can actually be much closer - and perhaps even accessible to the LHC - because it may be close to 10^{-18} meters if some additional dimensions are large or curved enough. And the extra dimensions themselves may still be a few microns in size.

Such options are considered unlikely - I quantified the probability of such scenarios to be around 1% - but they show that effects that used to be considered inaccessible to science may often become accessible, and quantum gravity might be just another example following hundreds of other examples.

A reduced Planck scale is the "phenomenological way" how string theory unexpectedly allows seemingly untestable questions to be tested. Predictions of low-energy physics that follow from the high-energy starting point are the "theoretical way" that connects the observations with the mysterious fundamental scale.

String theory reproduces all of physical quantities of low-energy gauge theories coupled to Dirac fermions (including all loop effects, non-perturbative effects, renormalization rules, confinement, Higgs mechanism, etc.). It parameterizes the low-energy parameters differently than QFT - in terms of discrete data (instead of continuous data) which might perhaps be viewed as "less convenient" ones but they are equally consistent. String theory is as correct a description of these non-gravitational observations as quantum field theories are. You can't really say that it is "empirically worse off" than quantum field theories. And its theoretical status is surely better off than in quantum field theories: it incorporates gravity including loops and other quantum effects!

And string theory is actually linked with pretty much all interesting directions in phenomenological "particle physics beyond the Standard Model", including supersymmetry, GUTs, deconstruction, and others.
Misunderstanding: By making string theory ridiculously malleable with your 10^{500} ways to compactify the extra dimensions, you essentially put the theory beyond the reach of any conceivable experimental test.
Reality: String theory is absolutely robust. It can be demonstrated that there exists no consistent way to deform it or "slightly modify" its rules of the game. It is the first theory known to the mankind that has no adjustable dimensionless non-dynamical parameters whatsoever. The adjective "malleable" associated with string theory is completely absurd.

On the other hand, much like other theories in science, string theory predicts many solutions - many potential "vacua" - where physical phenomena might in principle take place. Let me emphasize the difference again: we have entirely fixed rules but there exist many ways how to live according to these rules. But the number of predicted solutions, whether it is larger or smaller than you expected, can never be used as an argument for or against the validity of a theory. It is simply a feature of the theory and one needs actual further tests to decide whether the feature - or the prediction, if you wish - is valid or not. At this point, we don't have empirical data about these issues.

Genetics is arguably disappointing because it doesn't show that the human DNA is unique. It doesn't quite prove the existence of God who created humans to His own image. We cannot see God's DNA in the sequences that would distinguish us from monkeys and other life forms that were not created to His image. ;-) Believe me, billions of people in the world - including very nice women and men - are profoundly disappointed by molecular biology because of these and related reasons. I won't even try to tell them that they share 96% of their DNA with chimps because they could get insulted!

See also Evolution and string theory for more comments about this analogy.

What can they do about their disappointment? Well, they may pray and they may dream about a different, better Universe where God's traces can be identified in our DNA and where this preferred DNA sequence of God may be calculated. The calculation could perhaps use some hints from the Bible, they think. But that's about it: they can't do much more than that (in the past, they could at least burn the heretics at stake to get some relief) and so far they haven't presented the Biblical calculation. ;-)

The number of "candidate animals" i.e. the number of DNA sequences that are as long as the human DNA is roughly 10^{billion}, much bigger than the number of semi-realistic vacua often estimated as 10^{500}. The human DNA doesn't show any uniqueness of the human race. It cannot be calculated from the first principles. It is disappointing and ugly. It is true and paramount for biology, too. Sorry: but maybe humans are not that special, after all. It might perhaps be the right time to start to consider this possibility, 150 years after it was demonstrated to be true. ;-)

The different DNA sequences don't give us "different versions of Darwin's theory". There is only one theory and the wide variety of DNA sequences is an essential feature (or a prediction) of this theory!

The situation of the number of vacua in string theory is philosophically isomorphic. Many people, including your humble correspondent, would sentimentally prefer a theory where all the other vacua were absent. It would simplify our life a lot. But science is not about a wishful thinking. The large number of vacua that are a priori usable instead of ours has been established to be very large. It is extremely unlikely that this insight will ever be undone.

The only big related question that remains to be answered is whether physicists have any chance to identify the correct vacuum.

The anthropic people have essentially given up, believing that the "landscape" is just too vast and too chaotic: they use circular reasoning to assure themselves that our Universe has to "live" in a large, chaotic segment of the landscape where nothing can be determined with any certainty. And they think that vague statistical analyses of the landscape and qualitative predictions are the only possible advances that can be done beyond the present point, in the future. And they might be right or "effectively right", for one reason or another.

The other people, including myself, know that at least in principle, there can exist all kinds of methods to determine which vacuum is actually right - either by analyzing their detailed theoretical properties and comparing them with the experimentally measured properties of our world; or by finding a hypothetical selection principle that makes our vacuum (and perhaps a few other vacua) dramatically more likely than others.

Whether our vacuum is "random" and "anonymous" or whether it can be identified - and whether it makes sense to spend time with this big task (which is a different question!) - remains to be seen. So far the right vacuum hasn't been identified, so the anthropic opinion is confirmed by the "status quo" (in the same way as the opinion that "science has ended" was confirmed by the "status quo" at any other point in the history of science, too, until the following morning when science continued).

But the observation that at some level, there exists a large number of candidates for "the vacuum" has been pretty much established (at least in the case of supersymmetric AdS vacua where the number of possible subtleties that could "kill" the vacua seems extremely low). In fact, our world doesn't look "quite so unique and symmetric" and it indicates that the number of "equally fundamental or symmetric" vacua must be much larger than one, to say the least.

And yes, I consider the people who disagree with this statement to be complete deniers of the scientific evidence. The large number of vacua in quantum gravity is an established fact of science. It will never be undone, much like we will never return to the idea of a Flat Earth. This insight is not the last insight of science but it is an insight of science.
Misunderstanding: Second of all, string theory is only formulated perturbatively. A full non-perturbative definition of the theory doesn't exist.
Reality: This statement is also wrong and even if one formulated a more careful but similar statement that would be technically correct, it would be morally wrong because the same thing could be said about quantum field theory, not just string theory, so one can't ever justify the application of this observation as an argument against the step (or leap) from quantum field theory to string theory. More generally, it is also sociologically illogical to present quantum field theory and string theory as "foes" because they are not only equivalent in some contexts but a large portion of the best QFT experts in the world are actually string theorists.

Let me add some details about the perturbative expansions.

A full, exact, non-perturbative definition of many superselection sectors of string/M-theory is known. That's completely equivalent to the situation in quantum field theory.

Maldacena's AdS/CFT correspondence shows that some superselection sectors of quantum gravity - i.e. string theory - are completely equivalent to certain quantum field theories. These theories, such as the N=4 supersymmetric gauge theory, can be e.g. put on a lattice. There are some subtle remaining problems with supersymmetry on the lattice, despite the progress in deconstruction etc. But whatever these problems are, they are equally serious or equally solvable for string theory and for quantum field theory because in this subset of backgrounds, they're really the same theories.

While the lattice descriptions might arguably be the only approach to formulate four-dimensional quantum field theories non-perturbatively, we have actually many more methods to do the same thing in string/M-theory: so the situation in string/M-theory is better in this respect than the situation in quantum field theory. The BFSS matrix model (also known as M(atrix) theory) is an exact, non-perturbative definition of a sector of string/M-theory - namely M-theory on an infinite, 11-dimensional flat space. An ordinary quantum mechanical model - with degrees of freedom X,P,theta extended into matrices - can be demonstrated to coincide with M-theory in 11-dimensions if the size of the matrices is sent to infinity. We can calculate physical quantities for finite N and send N to infinity, to obtain the M-theoretical result. It's as well-defined as undergraduate quantum mechanics.

If you are irritated by the absence of strings in the 11-dimensional vacuum and by the absence of an adjustable coupling constant "g" in the BFSS matrix model, you may also write down the non-perturbative definition of screwing string theory due to your humble correspondent that was later renamed to matrix string theory by Dijkgraaf, Verlinde, and Verlinde (DVV). ;-) It has type IIA (or heterotic E8 x E8) strings in it, as the four authors proved. Nevertheless, the exact, non-perturbative definition exists for any "g". You don't have to expand anything. In fact, the key new contribution by DVV was to show that you could expand matrix string theory in "g" - and get the right stringy perturbative interactions, as I expected - which required some extra work.

Similar definitions don't exist for all superselection sectors of string/M-theory at this point.

But it's also the case that we don't possess non-perturbative definitions of all quantum field theories, either. Even if we had these definitions, it wouldn't mean that we can immediately calculate all non-perturbative phenomena out of them. When you try to calculate physics of a strongly coupled system, you always need some kind of cleverness - e.g. a good choice of the "effective degrees of freedom". This general wisdom holds for string theory and for quantum field theory, too (besides condensed-matter physics: ask the fractional quantum Hall effect people where their stunning pride comes from!).

In string theory, we know many more non-perturbative phenomena - and many more of their relationships - than we know in quantum field theory.

So once again, the situation in string theory is better than the situation in quantum field theory. The higher number of string-theoretical non-perturbative effects, dualities, and insights to learn may be attributed to the "larger size" of string theory. But again, this "large size" shouldn't be surprising because string theory is understood to be a broader theory that should include all correct wisdom of quantum field theory, general relativity, and much more. So it must obviously tell us much more about the fundamental objects, phenomena, and their relationships. And it is doing so beautifully, indeed. Theories should be as simple as possible but not simpler.

As Edward Witten correctly observed, string theory has proven to be remarkably rich, more so than even the enthusiasts (like your humble correspondent) tend to realize. There are still many things to be learned about non-perturbative (and perturbative?) physics of string theory which is why people are still working on it intensely.
Misunderstanding: Third, string theory describes perturbative expansions about fixed spacetime backgrounds.
Reality: First of all, this half-incorrect statement irrationally mixes two issues that have nothing to do with one another. In the previous section, we have explained that it is simply not true that string theory is only known or defined perturbatively. After all, most of the insights found since 1995 are actually concerned with non-perturbative physics. Many non-perturbative effects, quantities, and their relationships are known. Explicit non-perturbative definitions of some vacua are known, too.

So the adjective "perturbative" makes the sentence incorrect. Now, remove this word and think about the statement that string theory expands physics around fixed spacetime backgrounds. It is true and it is inevitable, too. Every consistent theory of quantum gravity must be doing so, at least when it gets to the "real work".

If you consider infinite spacetimes - such as AdS spaces or flat spaces - they have a particular behavior in the asymptotic region at infinity. All doable processes can only deal with a finite amount of energy and a finite amount of energy is never enough to "rebuild" the space at infinity. That's roughly why states in any theory of quantum gravity - and, in fact, any quantum field theory - decompose into the so-called "superselection sectors" that don't speak to each other.

As long as a theory is consistent with the very simple observation that a doable (finite-energy) experiment cannot rebuild the space at infinity, it associates a superselection sector with every (classical) configuration or every (quantum) state in its Hilbert space. There is no way to avoid it. So any particular calculation of the Hilbert space has to be made for particular choices of the superselection sectors - for particular behavior of spacetime at infinity.

Again, a theory that doesn't allow the space to extend to these asymptotic regions or that doesn't allow the geometry in these regions to be described by a well-defined geometry fails to agree with the very existence of space (that is demonstrably much larger than the short-distance fundamental scale, to say the least) and is instantly ruled out. These asymptotic regions may have many shapes - and flat and AdS-like backgrounds are the simplest ones to be described by accurate equations - but such fixed asymptotic regions of spacetime must be allowed and respected, otherwise the theory would be instantly dead.
Misunderstanding: Any respectable fundamental theory of quantum gravity must be background-independent.
Reality: The topic of background independence, which is pretty much equivalent to the previous section (but I have also divided the discussion into two parts, in order to follow the cartoon), has been explained many times - see background independence and background independence in AdS spaces for two examples.

The people who like to say the same stupid thing as the boy from the cartoon usually severely misunderstand what the adjective "background-independent" means: the meaning they actually associate with this quasi-religious adjective is incompatible with basic physical consistency criteria. They think that their "background independence" should prevent a theory from considering physics at specific backgrounds, in specific superselection sectors.

Carlo Rovelli even thinks that one should find a background-independent propagator. He may even believe that he has found one. ;-) So far, he hasn't noticed that his combination of words, a "background-independent propagator", is a special example of another oxymoron, namely "Taylor expansions without a point to expand around". Propagators are defined to be the inverse (continuous) matrices of quadratic fluctuations around a particular background: they're determined by the kinetic (quadratic) terms in the action expanded around the background. No background, no propagators.

As argued above, every consistent theory living in an infinite space must agree with the existence of superselection sectors; must allow for the existence of realistic superselection sectors that resemble the nearly flat space we inhabit; and must be able to predict what happens in these sectors because virtually all quantitative questions we can ever ask about in physics have this form (and it is highly questionable whether there exist any quantitative yet background-independent questions at all). The people who use the word "background independence" incorrectly and quasi-religiously don't seem to get any of these points.

And maybe, they're getting these points but they have already switched to a dishonest discourse in which it is better for them to repeat things they know to be untrue. That's widely believed to be the case of Mr Lee Smolin.

Second, there is a question whether the very character of a theory depends on the "background" or the "superselection sector". It can be demonstrated that string theory doesn't depend on the background: the local phenomena are always isomorphic. While the separation of the states into superselection sectors is inevitable in any physical theory, the character of local physics should be independent of the choice of the sector.

It can be demonstrated in perturbative string theory and other formulations of string theory that the identity of the theory is independent of the superselection sector. A modification of the background can be shown to be physically indistinguishable from a condensation of a particular configuration of strings (or their non-perturbative counterparts, if we consider non-perturbative physics) that existed in the original background: see, for example, Why there are gravitons in string theory. If these strings (or M&M's) have to change the asymptotic conditions, they must be associated with non-normalizable states in the Hilbert space but these states may still be linked to the ordinary, normalizable, finite-energy excitations.

So physics of string theory is surely independent of the background: every choice of the background leads us to the same theory. A completely different question is whether this independence is "obvious": physicists ask whether it is "manifest". The latter is pretty much an aesthetic, not physical, question, and our sense of beauty may often mislead us.

As in most questions, the background independence is manifest in some approaches but not others. For example, there exists a way to define string theory that is very analogous to quantum field theory (with infinitely many fields, if expanded into point-like component fields). It's called string field theory (not to be confused with all of string theory: "string field theory" is just a small sub-discipline within string theory). It works well for open strings only, especially if they're bosonic, but it gives us a new perspective on many questions related to perturbative physics and D-brane states.

String field theory for the 26-dimensional open bosonic string can be formulated in a manifestly background-independent way. The action is "S = Integral Phi*Phi*Phi" as long as you define the integral and the star-product properly. (Yes, I've been designing T-shirts with this equation.) Their (integral, star) definitions are formally independent of the background and individual backgrounds are associated with (the BRST operators connected with) particular "vacuum solutions" of the equations of motion, "Phi*Phi = 0". The condensation of "infinitesimally perturbed strings" generates the whole background, smooth geometry, and its nilpotent BRST operator.

But you should have already understood that real, quantitative physics only begins when one picks a background, a superselection sector. Before one does so, many of the objects are too formal and cannot be associated with particular numbers. A physicist should always be careful about such formal manipulations: he should always ask whether his formula can generate very particular numbers that can be in principle both calculated and measured in the appropriate Universe.

Martin Schnabl was extremely conservative about this important principle which is why his new remarkable "vacuum solution" to string field theory, once it was found, was and is so much more meaningful - and so much more correct and important - than dozens of "formal" results that generated "infinity minus infinity" expressions whenever you wanted to analyze them in detail. His solution is linked with some rather deep mathematics (on the boundary between complex calculus and number theory), too.

So the genuine lesson is that any respectable framework in quantum field theory or any theory that generalizes it must eventually admit background-dependent calculations, in a sharp contrast with the stupid boy's proposition in the cartoon. Background-independent formulations - if they exist - must always be understood as a first, philosophical step to formulate the detailed, background-dependent theories. Only the latter can produce meaningful, measurable numbers that can be compared with observations.

It would be very pleasing to have a complete description of string theory that would cover all corners of its "landscape" and allowed us to calculate the properties of all vacua as solutions of some universal equations. Deep physicists have spent years with attempts to find such universal equations and they will surely continue to do so in the future, to one extent or another. (I didn't want to mention that the list includes your humble correspondent because I found the word "deep" more important and I wanted to avoid any self-glorification.)

On the other hand, such beautiful and universal equations that treat all possible corners of the landscape "democratically" are not guaranteed to exist. In some sense, we should expect that they don't exist - at least not to the extent to "directly tell us" which objects are weakly coupled at any point - because such equations would present all possible objects in all regions of the landscape as "equally fundamental" and "equally manifest" even though many of them are complicated bound states of each other.

Moreover, whether these equations exist or not has no impact on the question whether string theory is the correct fundamental description of the world around us as long as we determine our conclusions by the evidence rather than by the prejudices.
Misunderstanding: Fourth, in string theory, the Dirac operator and the gauge fields are...
Reality: I am not certain what the boy wanted to say because he was, thankfully to the girl, interrupted. :-)

But in string theory, the Dirac operator and the gauge fields are derivable, omnipresent, and essential aspects of low-energy physics that can be deduced to exist in any realistic enough vacuum. They play the same important role for the low-energy physics as they always did; the low-energy equations usually hold exactly in string theory, too. On the other hand, these old concepts are no longer the deepest or the "only deep" principles that underlie physics. In most approaches to string theory, they're secondary and can be shown to be consequences of more powerful unifying principles that generate other physical phenomena, too. They are also supplemented with infinite "towers" of heavier (and for real applications, less important) states that are important for the overall consistency of the theory.

For example, the gauge fields with Yang-Mills symmetries and the fermionic matter fields that follow the Dirac equation are just two consequences of the conformal symmetry in perturbative string theory (or superconformal symmetry: the superconformal zero mode on the worldsheet must annihilate the physical modes which directly gives us the Dirac equation in spacetime - nice). The same perturbative string theory also gives us a whole "Hagedorn tower" of states.

And the same perturbative string theory and conformal symmetry applied to closed strings (with antiperiodic fermions) also implies the existence of the metric tensor with the diffeomorphism symmetry (also known as gravity in general relativity), the critical dimension, and many other things. String theory also allows us to derive new, fundamental, and unexpected facts about gauge fields and the Dirac operator (look e.g. at the D-brane viewpoint on the ADHM construction).

At any rate, I know too much about the world to realize that evil must be confronted with fists. That's why I fully endorse the clever girl's reaction to the piles of rubbish that the talkative boy was emitting. And to make it really clear how much I endorse her ;-), let me reproduce her classical answer to her obnoxious foe in its entirety.
Summary: PAK! You keep talking like a bitch, I'm gonna slap you like a bitch. :-)
You can see that Clifford Johnson is using gloves to communicate with the excessively zealous anti-scientific commenters who are spamming his blog with bullshit. That can't protect him from trash-talking at aggressive smear blogs such as Not Even Wrong. There's no peaceful way to deal with this situation, Clifford.

So I kindly ask all the female readers to give a proper thrashing to every man who will emit the same crap as the unfriendly boy from the cartoon. I hope it is sufficiently politically correct for clever girls to beat disgraceful, dishonest, and sub-par kibitzers like the well-known one from Columbia University. Thanks a lot.


This posting originally included a link to the video of Pete the skateboarding dog. This four-legged surfer dude may have just found a theory of everything based on the E8 exceptional Lie group. ;-)

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reader PlatoHagel said...

I apologize Lubos if I may have caused some discord in your life. I hope the "point of view I had been demonstrating" was not to discourage the work that goes on in string theory.


reader Robert Dole said...

So angry...

reader Anonymous said...

You said at the start:

"I am worried about the coming world of an anti-scientific propaganda that makes theories and science unnecessary for most people who seem to prefer sociological arguments and conspiracy theories."

Are you aware that Google Ads fills your blog with Scientology publicity? Please, do something about it!

Regards, Jose Brox

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