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Saying No makes physicists what they are

Physics simply cannot try to incorporate every idea that is out there

I borrowed the phrase in the title from the award-winning ads for the Czech Budweisser beer (sold as Czechvar in the U.S.) and modified it. What's going on? Florin Moldoveanu wrote another hodgepodge of mathematical definitions pretending to be relevant for physics,

What is Noncommutative Geometry?
As far as I can say, he does a much worse job in conveying the basic meaning or definition of noncommutative geometry than the first paragraphs of even the mediocre introductions to the subject.

In the first paragraph, his article said (before the problem was pointed out and fixed):
... I think it was Young (the Young from Young-Mills) who said something like: there are two kinds of mathematical books: ...
Kashyap was the first one to correct Florin. You know, it's not an isolated typo. It's a sign of clear ignorance of fundamental concepts. The co-author of non-Abelian gauge theories was Chen-Ning Yang, not Young. Note that Yang is a Chinese name while Young is an English name. One just can't misspell such things repeatedly unless he is completely ignorant of particle physics.

Item 8 of Baez's crackpot index instructs you to add 5 points for each mention of "Einstien", "Hawkins" or "Feynmann". You know, when someone writes the names in this way, it's not a rigorous proof that he is a crackpot but the correlation is huge. A large percentage of crackpots love to spell the names in these ways – and virtually no real physicist would do such a thing. (The case of Yang-Mills vs Young-Mills is analogous.) A real physicist encounters the names of Yang and Mills so often (he either reads them or writes them) that it's just impossible to misspell the first name as a name from a totally different language.

Let me get to the more important point. At the end of the hodgepodge of mathematical ideas related to noncommutative geometry, Moldoveanu spends the last two sentences by his opinions about the relevance of mathematical ideas to physics research:
On the other hand, writing off noncommutative geometry as a mathematical fantasy without physics merits is arrogant. If you want to make new contributions in physics, does it make any sense to use the state-of-the-art mathematics from 100 years ago and ignore recent advances in math?
There are lots of problems with this attitude. Where can I start?

The word "arrogant" is cute. The goal of natural science isn't arrogance or the elimination of it. The goal of natural science is to find and establish the true statements about Nature. The sentence saying that "something is arrogant" simply cannot be a legitimate argument in or against anything in science. Even if you defined the word "arrogant" in some way, it would still fail to answer the key question whether the proposition is true or false.

Physicists are sometimes said to be arrogant just for knowing and pointing out the basic fact that they have found the fundamental laws governing at least all the known phenomena in the everyday life. If this knowledge is called "arrogance", well, physics is then obviously impossible without "arrogance".

Similarly, an overwhelming majority of theoretical particle physicists don't try to construct Connes-like models of gauge theories coupled to fermions formulated as "theories on noncommutative geometries" because they have been shown something from these ideas and they didn't see any evidence or nontrivial tantalizing hints in these ideas. Or they simply didn't make sense. And predictions didn't work.

(Moldoveanu's claim that particle physicists – and/or particular people like your humble correspondent – denounce all of noncommutative geometry is highly misleading. They are – or at least I am – disagreeing with a particular prescription how to "derive" the Standard-Model-like gauge theories with fermions from some noncommutative geometry framework.)

They wrote off this research program not because they are "arrogant" but because according to their evaluation of the content of this program building upon their expertise, they either concluded that it was downright wrong or they just didn't see enough value to join that research. Physicists and scientists in general must be allowed to make this conclusion. The right to say No is a defining part of the culture of the scientific epoch. It was a key development that allowed the scientists to stop saying Yes to all the church officials and the group think of the public and investigate ideas impartially and carefully, with Yes and No being given approximately equal chances to become the final answer of any research.

If someone wants to prevent scientists from saying No to a proposition or an idea again and the only excuse for this prevention is that "No" is "arrogant", he has nothing to do with the scientific way of thinking and he is really trying to bully everyone who wants to think scientifically. "Arrogant" may be a useful adjective with a negative flavor outside science (but even there, the usefulness of this whining is heavily overrated) but in science, the adjective has no "damning power". If someone claims that it's "arrogant" to realize that the people promoting things like loop quantum gravity in 2016 have skulls full of feces, well, then indeed, physicists who are any good simply have to be arrogant. It's an essential prerequisite for physics research to be able to deduce these elementary conclusions.

Finally, the last sentence of his text says
If you want to make new contributions in physics, does it make any sense to use the state-of-the-art mathematics from 100 years ago and ignore recent advances in math?
Of course it makes perfect sense. It is an utterly misguided strategy to try to do cutting-edge physics research by copying contemporary mathematical papers. Mathematics – including new one – is obviously useful in physics. But not all of it is useful.

Whether some particular mathematical results or methods are useful in a physics discipline or subdiscipline must be (and is) decided by physics arguments. The answer may be Yes and No. It's usually No. The idea that by simply copying pieces of fresh mathematical papers and selling them as physics, one may sensibly hope that it will make a great contribution to physics is utterly idiotic and Moldoveanu is a complete idiot if he believes such things.

Even in cases when the mathematics was fully developed and "waited" to be used by physicists, physicists were more likely to rediscover it. In particular, the deepest revolution of the 20th century physics, the birth of quantum mechanics, occurred when Werner Heisenberg began to play with observables as if they were tables with numbers. That's how he called them – at the critical moments of his research, he wasn't actively aware of the fact that mathematicians had used such tables and called them "matrices" for quite some time.

Clearly, this rudimentary ignorance of the part of mathematics that was most relevant for his own contribution to physics didn't hurt him much. He was forced to arrange observables into the form of matrices by physical arguments so he just did it and rediscovered everything that was important to make this new framework of physics work.

Similarly, when Einstein was developing the general theory of relativity, he had many possibilities and the old Riemannian geometry – which had been a part of the mathematical literature for decades – turned out to be relevant. But it would have made no sense if Einstein were just trying to pick random – or all – papers from the mathematical libraries and make them relevant in physics. That's simply not how physics may work because physics chooses the right ideas according to physical arguments. A big mathematical task may sometimes have to be solved but in physics, there's always a level of decisions and principles "above mathematics" that chooses which mathematical concepts and methods are relevant and which are not. This level "above mathematics" always makes the empirical facts – or basic conditions for them to exist – to be the ultimate arbiters even when some mathematical argumentation has to do most of the heavy lifting.

To pick mathematical papers and declare them relevant in physics randomly or according to purely mathematical criteria cannot lead anywhere, at least not systematically. At the end, physicists are usually ahead of mathematicians when it comes to the discovery of basic concepts or patterns that are ultimately parts of both fields (mirror symmetry is a beloved modern example). Mathematicians are usually followers in the grandest scheme of things. Sometimes, mathematicians are ahead.

But the fields play an asymmetric role: While a mathematician can turn basically any interesting idea or concept pursued by physicists into the object of purely mathematical research (because every topic that may be formulated rigorously is OK in mathematics), a physicist (or natural scientist) simply cannot "import" every idea from mathematics because he's constrained by Mother Nature and Her preferences in mathematics.

Bonus: the ads

Several followups were filmed in more recent years but the two initial ads remained classics:

A well-known actor-dissident Jan Tříska who emigrated says: "To stay in a country where a tyrant forces its people to play in a farce? I will rather give up the roof above my head and face hostile elements. ... I say No. I say farewell. Let the devil take over the tyrant who serves Him. I will no longer bring logs to him." – Saying No makes us what we are. Budweiser Budvar.

Olympic winner Lukáš Pollert who controversially sold his gold and other Olympic medals for CZK 150,000 ($6,000) and gave the money to the Drop In charity helping drug addicts: "I have nothing against sports as such. But to do it at the top level even after the age of 30 looked a bit infantile to me. I didn't want to turn to a mere collector of medals. That's not why I had studied [medicine]. I sold them because they had no value for me. I have completely different goals in my life." – Saying No makes us what we are. Budweiser Budvar.

Czech Budweiser Budvar was using the slogan to sell its conservative attitudes – the brewery has kept the late 19th century traditions, avoided some fashionable changes of the brewing technology and privatization offers. This point is made in one of the more recent episodes of the "No is what..." ads.

A good saloon keeper must also be capable of saying No, e.g. to the temptation to tap less beer than expected.

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