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Dijkgraaf, parameters, and omnipresent Šmoitian trolls

MathPix is a rather amazing app for your phone. Write e.g.\[

\int_{-\infty}^{\infty} e^{-x^2} dx

\] with your hand, take a photo of this expression while it's in the rectangle, and the app will convert it to perfect \(\rm\LaTeX\) and calculate that it's \(\sqrt{\pi}\), with graphs and analyses by WolframAlpha. It's like PhotoMath for adult mathematicians. Hat tip: mmanuF@Twitter
Robbert Dijkgraaf is the director of the Institute for Advanced Studies in Princeton, New Jersey – he is the boss of Edward Witten and he would be a boss of Albert Einstein if Einstein avoided death in the 1950s. He's also a late co-father of matrix string theory (and once a co-author of mine).

In the Netherlands, he's a rather well-known scientific talking head. So if you search for "Robbert Dijkgraaf" on YouTube, you will get videos from Dutch TV where Dijkgraaf talks about Einstein for an hour and stuff like that.

Well, Dijkgraaf just posted the newest text at the Quanta Magazine:
There Are No Laws of Physics. There’s Only the Landscape.
He says that there are dualities in string theory which physically identify two or several seemingly different descriptions, but there's still a huge landscape of possible effective laws that are left. The article doesn't say much more – except that it's possible for a Chinese to cook a Chinese food and notice it's identical to an Italian food. ;-)

Well, dualities in the world of cousins seem rather unlikely.

Now, this could have been a helpful popular article some 20 years ago. But today? What kind of reactions would you expect from the readers?

Since 2006, the science sections of the mainstream media have been almost totally conquered by crackpots that are parroting the holy words by Mr W*it, Mr Sm*lin, and similar self-anointed populist opinion makers. The religious anti-physics wave has created thousands of aggressive trolls and tens of thousands of their sockpuppets who spend hours by trying to find places on the Internet where they could write something like: "String theory has many solutions so there must be something wrong with it!" They use a much worse language, however.

Well, sorry, comrades, equations of physics have the number of solutions they prefer. Unless you may rule out some number of solutions, then you must treat all the possible numbers – and the theories predicting those numbers – equally.

So it was guaranteed that the article wouldn't be received well. After a day, Dijkgraaf's short essay has attracted two comments, by users named Weylguy and Steve Blazo, and both of them parroting the W*itian garbage. In that way, they reveal that they're hopeless morons but W*it has trained these stupid puppies to feel smart while parroting these idiocies, so these morons do feel smart.

They frame their W*itian dictum as a response to Dijkgraaf's assertion that string theory has no parameters. Well, more precisely,
string theory has no adjustable non-dynamical continuous dimensionless parameters.
This statement says that if there is an apparent number whose value may be a priori adjusted and must be chosen to make predictions using string theory, it must be either
  1. dimensionful such as \(c,\hbar\): no theory may predict their values because these values depend on the choice of units, i.e. social conventions, and social conventions can't really be calculated from a fundamental physical theory based on crisp mathematics. Adult theoretical physicists normally use units with \(1=c=\hbar=\dots\), so these parameters are no longer adjustable.
  2. Or discrete – one has to decide that we live around a particular vacuum that is chosen from a finite set or a countable set. That covers the choice of the vacuum from the often repeated \(10^{500}\) possibilities.
  3. Or dynamical: the parameter is actually the vacuum expectation value of a scalar field with a vanishing potential (so all values are allowed and stable), a modulus. When such moduli (non-stabilized scalar fields) exist, they cause additional "fifth forces" violating the equivalence principle. Because we haven't observed those, it should mean that we live in a vacuum where no non-stabilized moduli exist.
OK, these three points summarize the three main subtleties that beginners may misunderstand when they discuss parameters in quantum field theory or string theory. Some people want \(c\) in SI units to be calculated from the first principles. Or they ask whether \(c\) is changing with time, and so on. Well, in the SI units, \(c\) is by definition constant – and the trend is to redefine the units so that all the other universal constants such as \(\epsilon_0,\hbar,k_B\) are universal constants too.

Obviously, we can't calculate that some people decided to define one meter as 1/40,000,000 of the circumference of the Earth, and how this unit of length got refined.

Some other people misinterpret the discrete parameters. When you only have to pick a discrete label, you're picking "much less information" than if you determine the value of a real, continuous, adjustable parameter. After all, a real number needs infinitely many digits to be specified. A number between 1 and 99 only needs two decimal digits to be specified, and even an element of a set with \(10^{500}\) elements may be fully determined by specifying 500 digits. That number (500) is actually comparable to the number of digits in the parameters of the Standard Model that are in principle measurable with the accuracy that may be obtained in this Universe.

Steve Blazo wrote:
The comment that string theory has less free parameters then the standard model is kind of ridiculous, each member of the "landscape" is it's own free parameter. So string theory instead of less free parameters has like \(10^{500}\) more.
You know, idiots such as this one have been made self-confident because W*it told them that they know what is the most important thing they have to know and repeat. It's the delusion written above. So they scream it with the same passion and for the same reason as the Islamic terrorists are screaming "Allahu Akbar". But sorry, comrades, Allah isn't great and each member of the landscape doesn't bring a new parameter.

Even if you counted the choice of the element of the landscape as a parameter of the theory, and you shouldn't because this choice is actually dynamical, it's a single parameter. You may label the elements of the landscape by an integer \(N\) that goes from \(1\) to \(10^{500}\) and this single integer would be the one and only parameter of the theory. Saying that the number of values that a parameter can take is the same as the number of parameters is isomorphic to the claim that 2+2=22; or that a computer contains 256 animals times the number of bytes in the RAM. Only a total idiot can make such mistakes. The number of dimensions (axes) in a parameter space is something else than the number of points in that space.

The choice of \(N\) produces a much bigger diversity in the qualitative character of the effective laws of physics than e.g. the electric charge \(e\) does in QED. But that's no disadvantage. It's an obvious advantage, and a sort of required one for a candidate for a theory of everything. String theory derives rather messy effective theories such as the Standard Model out of nothing so it's obvious that the effective laws that string theory must be capable of producing must be rather diverse so that a generic one may be as messy as the Standard Model.

Incidentally, the omnipresence of the ludicrous number \(10^{500}\) is a proof that all these critics of string theory only parrot this garbage from each other just like the Islamic terrorists parrot "Allahu Akbar". None of them is capable of independent thought.

How many people who constantly repeat the number \(10^{500}\) could say where it originally came from? I think that none of them. Well, I can tell you: it was written in Section IV of a Douglas-Kachru 2006 paper. Douglas and Kachru – who didn't even write this vaguely estimated (later to be insanely popular) number to the abstract – admit that Lerche and pals had a similar estimate already in the 1980s – but Lerche ended up with \(10^{1,500}\). There was nothing truly new about the claim that the number of vacua may be this large – and the exponent is meant to be just "in hundreds" but no one really knows how many hundreds. Three years ago, Taylor and Wang claimed that the exponent is actually 272,000 if we allow a truly prolific class of F-theory flux vacua.

The other commenter, Weylguy, exhibits a similar fallacious reasoning:
Really? String theory has no free parameters? And there's only one string theory? Show me where the theory predicts that the electron has a mass of \(9.11 \times 10^{-31}\) kilograms and then I'll start believing that spacetime is composed of 10 or 11 dimensions, 6 or 7 of which are conveniently curled up so small they could never be observed.
A big point of Dijkgraaf's article above was that the electron mass shouldn't be expected to have a unique value because string theory has a landscape of possibilities. So if such a real number may be calculated, it must be in more natural units than kilograms, of course; and one must first determine the value of the discrete parameter that labels the elements of the landscape. So why is this Weylguy "demanding" something as a proof of string theory that Dijkgraaf explicitly wrote not to be the case according to string theory?

It's also demagogic to say that the extra dimensions are "conveniently" compactified. In reality, they are both conveniently and (what is more important) demonstrably compactified. Our not easily seeing the extra dimensions is an empirical fact, not just a matter of convenience, and scientists who are worth the name simply have to take empirical facts into account. Also, it's demagogic to implicitly suggest that the small size of the extra dimensions is unnatural. Instead, it is totally natural. The expected radius of the extra dimensions may be calculated from the dimensional analysis. And if there are no special considerations, the only length scale that may come out of this dimensional analysis is the Planck scale. Some special models – e.g. braneworlds and/or those with large or warped extra dimensions – may produce longer radii than the Planck scale. But they still give some finite estimates from some dimensional analysis enhanced by some parameteric dependence.

The finite value of the radius of the dimensions is absolutely natural. In fact, the large radius of the visible, macroscopic dimensions is more unnatural – and that unnaturalness is known as the cosmological constant problem.

There's no reason to think that the total number of spacetime dimensions is 4, there is nothing wrong mathematically about the numbers 10 and 11, they're in fact preferred by more detailed calculations, and there's nothing unnatural about the compactification to microscopic radii.

But the main point I wanted to convey is that Dijkgraaf seems to deny the reality in these media altogether. He wrote the text as if no "string wars" have ever taken place. But the string wars did take place more than a decade ago. Dijkgraaf was among those who preferred his convenience and didn't do anything at all to help me and others to defeat the enemy – so the enemy has won the battle for the space in the mainstream media. Until you realize your mistake, you can't ever write an article about string theory or state-of-the-art high-energy theoretical physics into similar media that will be well received. It's really painful if a director of the IAS hasn't been capable of noticing this fact because directors of important scientific institutions are exactly those who should know something about the atmosphere in various parts of the society.

If you ever want articles written for the popular magazines – including the Quanta Magazine – about modern theoretical physics to be meaningful again, you will first have to restart the string wars and win them. I am afraid that the society has sufficiently deteriorated over those 10+ years of your inaction that a physical elimination of the enemy may be needed.

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