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Ad hoc "communities" working on proofs are turning science into a clash of cults

Genuine scientific knowledge changes according to results, not according to communities

Elsewhere: Tetragraviton wrote a wonderful essay, The Black Box Theory of Everything, about a time machine that throws you to the 1960s for you to present an unreadable code, including QCD simulators, the Black Box, as your theory of hadrons. It works. Does it make sense to suggest quarks and partons when the Black Box works and quarks and partons yield "no new predictions"? The Black Box is a counterpart of the Standard Model and Tetragraviton explains why it's unreasonable to say – as some critics of science do say (Tetragraviton calls their view "the high school picture" of science which I don't fully understand) – that a new, more unified or readable, theory giving the same predictions "is not science". What is and isn't science shouldn't depend on historical accidents. I subscribe to every word.
A day ago, David Roberts wrote a comment with a link to some topics in hardcore category theory, mostly related to the initiality principle, and implicitly suggested that everyone judging the value and validity of Mochizuki's work has to follow this particular hardcore category theory stuff.

I don't believe this claim at all. I think there exists no evidence whatsoever that this stuff is useful let alone crucial for understanding Mochizuki's work – or most other results in mathematics. In fact, I have serious doubts about any kind of usefulness or depth of the page mentioned by Roberts. It seems like an overly formalized talk about something whose beef amounts to almost nothing, a Bourbaki on steroids. And this kind of intimidation, "you have to study and worship some particular formal texts, otherwise you're not allowed to speak" is exactly the wrong atmosphere in Western mathematics that I have criticized.

Mochizuki's theory remains controversial but it passes basic tests, has smart enough advocates, and has actual papers with hundreds of pages of actual results. It's just a higher level of scholarship than a random webpage on a blog in Austin. Indeed, I am worried that the Western researchers – including mathematicians – are increasingly turning from proper scholars producing rigorous papers to fans of some web pages filled with superficial, ideologically or emotionally driven, claims.



"An Observer", a commenter, later mentioned that the true motivation behind Roberts' comment could have been his pride about
A Communal Proof of an Initiality Theorem
kickstarted by mathematician Mike Shulman (UC San Diego) in September 2018. And I want to say a few more words about this "new format of science".



Mike Shulman has mentioned some disagreements between people doing "homotopy type theory" (HoTT) and launched a volunteer project that should have settled some questions about types, functors, and categories – questions that virtually none of us understands. While we don't understand any details, we still understand the basic philosophy of the management of such projects.

Just to know the result in advance, half a year later, namely two days ago, the same Mike Shulman wrote that the initiality principle is not addressed – your opinions should be what they were before. It means that he admits that the volunteer project hasn't produced any results. It's not known whether it will.



But let's return to September 2018. A bunch of people discussed some incomprehensible technicalities about category theory and differences between various kinds of this community collaboration. The result was – as announced in the last comment – that about 40 people have signed up as volunteers. It's "awesome" but will need some "effort" to organize. To have an intuitive idea how many people is 40, see the Ringo Czech's picture of Ali Baba and the 40 Thieves above. ;-) (The author of the painting is a former lawmaker and famous singer, not a baby, just to be sure.)

Volunteers are fashionable and masses of people who sacrifice themselves – e.g. by skipping classes every Friday – are fashionable. Let's ask: What has just happened? How should you understand the 40 people? Can they do mathematics? Do they do mathematics? Is the societal system they have just created an effective way to do research? Is it a way to preserve the quality and impartiality of the research?

I think that most of these questions must be answered by a "No". It's a bad idea to organize research in this way. It's bad from the viewpoint of effectiveness and motivation to do hard work – and it's also bad from the viewpoint of quality and integrity of science. Why is it so?

First, you must compare this community with the normal way of doing mathematical or similar research. The normal research is done by individuals or their teams who have a potential to discover something and, if it works, they actually discover something. It's like gold. And they must share it. Their possessing a part of this gold is an important part of their motivation that they needed from the beginning. Sometimes, people are uncertain whether someone deserves to be a co-author of a paper. Sometimes people try to be nice and inclusive. Sometimes they end up arguing about the list of authors.

Lots of research is done by individual researchers – and it's particularly true in mathematics. Teams may also work. As a wise instructor in Prague liked to say,
The best type of work is teamwork. But two is already too many.
Very true. You know, papers may be written by 1 or 2 or 3 or... 7... or 3,000 authors. But the large numbers are surely not a desired outcome by themselves. When all other "absolute" quantities are equal, you don't want a large number of co-authors because they decrease the visibility, they decrease the size of your slice of a fixed pie that the paper will discover. With some fluctuations, the size of the slice should also translate to your funding and material well-being. The correlation is normal which is why sane people know why they don't want the list of authors to insanely grow. And it's worse than that. Because the responsibility may be left to someone else, the individual members of a large team simply find it natural to work less than they would work in smaller teams.

A real scientist only wants to build a large team if there's some actual work to be done that requires the large number. But in these "community" efforts, they apparently think it's a kind of a "victory" when they get a large number of collaborators, such as 40. But there's nothing to celebrate. It's just 40 people who wrote their names to a web form. Writing 40 names they have known since the age of 3 isn't too impressive a piece of work. And everything else is uncertain! So that was my first point, the complete misunderstanding of the fact that small teams are simply better for the motivation and credit of the authors and this motivation statistically leads to better outcomes.

Now, the second question is the quality and competence of the members. There is a difference between this "Ali Baba and the 40 Thieves" format of science and normal groups of collaborators on a paper. In a normal team that writes a paper, the team just doesn't accept everyone who applies! ;-) This has very good reasons. Most people wouldn't help – because they are either unfamiliar with the topic or expected to be lazy or something else. Such bad members' contribution could be worse than zero, it could be – and often is – negative. They introduce mistakes and distract etc. So as an author who has a meaningful project – a realistic potential to find some gold – you just don't want random freeloaders to arrive and "volunteer" to take a part of your gold! Everyone who still has some common sense understands this point. Those who don't apparently believe some ideology that is stronger than their common sense.

With "communities" like Shulman's where everyone may apply, you are guaranteed to get some really useless or downright counterproductive members. Think about it: If you have no filters in between the river and your kitchen, you will sometimes drink some mud, dead fish, used condoms, and plastic packaging from yogurts. So the quality of the "team" will almost certainly be low. Equally importantly, when there's no one who can keep the applicants away, there's usually no one who can "grade" the applicants and assign them to different "castes", either. In practice, you will have no protection against the harmful contributions from the bad members. Instead, the "community" philosophy will push the other members to deny that someone is harmful at all! But be sure that in a team where everyone may be accepted, many members will be harmful.

So you basically end up with 40 random people who want to affect "homotopy type theory", to mention this particular example. It's just absolutely terrible. I am sometimes presenting these left-wing collectivist methods to "deal with problems" as some very new disease of the recent decade. But of course I realize it's not really so. The question about the "wisdom of volunteers" is exactly the same one that Feynman encountered in the 1960s (half a century ago) when he was a member of a committee choosing the textbooks on science (Judging Books By Their Covers):
[...] The man who replaced me on the commission said, "That book was approved by sixty-five engineers at the Such-and-such Aircraft Company!"

I didn't doubt that the company had some pretty good engineers, but to take sixty-five engineers is to take a wide range of ability--and to necessarily include some pretty poor guys! It was once again the problem of averaging the length of the emperor's nose, or the ratings on a book with nothing between the covers. It would have been far better to have the company decide who their better engineers were, and to have them look at the book. I couldn't claim that I was smarter than sixty-five other guys--but the average of sixtyfive other guys, certainly!

I couldn't get through to him, and the book was approved by the board. [...]
Note how universal these observations are. They perfectly apply to the "homotopy type theory community". In Feynman's case, he was the only one who actually carefully read the books while perfectly knowing the physics that the kids were supposed to partially learn. I know this feeling very well – at least 5 authors of books, including a president of a country, have told me that no one has read their text at any moment of their lives more carefully than I did. When I get some work to optimize someone's text, I just do it. Seriously. And sometimes, when I would have gotten zero credit for doing some hard work whose importance didn't look "objectively high" from my perspective, I just refused to do hard work. It's common sense.

But that's not how 40 or 65 random people approach the question. In Feynman's case, lots of the members gave "great grades" to textbooks that had 200 blank pages in between the covers. It was still a wonderful textbook. They couldn't even notice that the book was empty! And this is just an extreme example. There are also lots of people who do open the books but their looking is so incredibly superficial that it's virtually useless, too. And some people may have read the textbooks carefully but they didn't really understand the physics – and how it's connected to other disciplines and real-world problems – well enough.

Now, the "committees" and "communities" are pretty much designed to be democratic institutions where every member has the same power to influence opinions. What can be the outcome? The outcome is rather unavoidable: the opinions and conclusions produced by such committees have a bad quality. Some collective decision making can work in some respects but if the committee members must actually do lots of hard work to end up with a high-quality conclusion, you may be pretty certain that most of the members just won't do this work, so the average will be mostly the average of the people who didn't do it well enough.

Feynman's committee was dominated by engineers in an aircraft company. Shulman's "homotopy type theory" may be restricted to mathematics PhDs. Or mathematics PhDs with some extra minor conditions. But whatever institutional filters you impose, you are still likely to end up with the dominance of guys who aren't very good at doing this job. Yet the "community" arrangement promises them to get a predetermined piece of the gold (well, predetermined at the moment when the total list of members is known).

Don't you understand why it's bad? It's really bad for the same reasons why the communist economy doesn't work. Some people may be eager to divide the wealth and consume it but for this process to sustainably work, there also has to be someone who produces the wealth. And they don't care about this portion much. They believe it happens automatically. Marxists believe that those who really did produce the wealth or who led the production – the capitalists – didn't do much useful work. When you eliminate them and the mechanisms that power capitalism, you get socialism which collapses once it runs out of other people's money.

Someone may write contrived sentences and formulae about "homotopy type theory" but if he doesn't understand these basic matters, he is simply not an intelligent person.

Fine. So I suppose you understand why the average quality and "vigor needed to work" is low for these "communities" that are de facto composed of volunteers where everyone (or everyone passing some superficial filters) can join. But there's something even worse than the "low quality". It's their wrong motivation and the wrong type of pressures that start to spread in the scientific field.

The volunteers' motivation is mostly wrong because they pretty much want to add their name as a "vote" to some prejudice and philosophy, in the absence of actual results. And maybe they sign up because that improves their image – that's how the image dynamics seems to work these days. And even when the "community" of volunteers is created, this community affects the researchers' thinking about the questions in a mostly illegitimate, unscientific way. As I wrote in the subtitle,
in proper science, the scientific opinions and knowledge changes when new solid evidence or argumentation is actually presented and may be verified by the readers.
However, in a field dominated by a "community" or "communities",
the very existence of a "community" shapes what some people want to say (or believe) or dare to say because they are afraid of offending the "community". The community is effectively a mob that bullies everyone.
And it's just terribly bad for science. In science, it's the results or the evidence that matters – or should matter. When some brute force or intimidating number of members of a "community" start to affect people's thinking, it's no longer science. It's a culture dominated by mobs and bullies – and as I previously discussed, most of the bullies unavoidably suck as experts. The real problem is that these "communities" usually and unavoidably push the people's opinions in some direction without or before they actually find any convincing evidence. They unavoidably treat their plans, faith, and wishful thinking as if they were results, at least partial ones.

In real science, this kind of activity simply doesn't change anything. You may spend 50 years by screaming that there's something wrong about quantum mechanics, naturalness, or string theory, you may collect 40 or 4,000 signatures, and you may sell one million copies of six books with these claims to some laymen but unless you present some evidence that makes sense and that actually respects the current standards known to the best scientists who study these questions, your influence on science remains strictly zero. To misunderstand this simple point means to misunderstand the scientific thinking – to confuse science with some shouting matches between mobs of hecklers. Science isn't what an average person – a heckler or not – believes. Science is not what wins in a shouting match.

It's ironic that in most cases, such "communities" or "lists of petitioners" and similar lists still represent a small minority of the field, at least when they're established. But the very fact that they're organized – or just written down in a list – makes them "stronger". They turn into a formidable mob. And this "added value" of the "community" is the wrong thing. Clearly, just by some signature, no actual new scientific evidence was found or presented. When people generally start to care about signatures or the counting of activists and volunteers, they cease to think freely and scientifically. The delicate and impersonal scientific forces that affect the scientific knowledge are replaced by the brute force of mediocre people.

Proper and full-blown science really is done purely by individuals and the collaboration between individuals is just a method for several individuals to outsource some work and get the information they need a bit more indirectly. But if they outsource the critical thinking about the whole, i.e. if all members start to believe that the most important questions will be correctly answered automatically by the "collective spirit" of the "community", it just ceases to be science. The big questions will be "determined" by some irrational dynamics of masses. Science existentially depends on critically thinking individuals. And when the scientific breakthroughs are deep, we may always say that science totally depends on scientific heroes.

There may be large collaborations, like lists of people who have helped to install magnets etc. A complex scientific achievement such as those at the LHC has many levels. But if we separated the complex achievement to levels, these levels still obey the condition from the previous paragraph. There are individuals who do particular things and they're responsible for various things. Sometimes they hire someone to do "a more straightforward task". But when it's so, it means that the task really is more straightforward and the true scientific advance is the less straightforward piece of work that is being done by the "employee" who hired the people for the more straightforward task. Sorry for these contrived sentences: my point is basically that in some large experiments that work, the boss should be and should deserve the title of the "principal investigator" because he or she is really the person who organizes the big-picture steps and others are fulfilling the more straightforward subtasks. (Well, there's a problem with political appointees who really hold chairs for the P.R. purposes and the actual top manager or managers of the experiment is someone else and much less visible. OK, the previous sentences were clearly about the latter person who is the most important one.)

The "community" type of research has already ruined some fields. Of course, the most politically sensitive ones were the first victims. So one may argue that climatology was hijacked and ruined by a similar "community research". These would-be researchers were actually political activists. They just needed to pass some superficial filters, like having a related PhD, and they could influence what "is believed" about the climate. Having a related PhD is an extremely unreliable filter. If you required a PhD from climatology, you could still have found thousands of scientifically illiterate – but politically fanatical – "researchers". And these have literally overwhelmed climatology. They spent their time not with careful scientific work and collecting and communicating results (through papers) that are as persuasive as possible; instead, they became "community organizers" whose task was to maximally increase the size of their mob (and the easiest way to do so is to maximally lower the scientific standards and collect as many scientifically poor but ideologically convenient people as possible). It's so bad that tens of millions of people don't even understand the elementary point that all the warnings about the globally dangerous climate science are merely pseudoscientific superstitions that some "communities" favored.

The mainstream opinion of real climatology still says that the climate change is mostly natural and has many natural aspects that are partially known and studied. But there are lots of "communities" of people who aren't good as scientists and who have contributed very little to the scientific research but who are organized activists – basically people of the type "everyone can join if your politics is good enough and you have a degree" – and their huge number has completely distorted the optics of lots of people who can no longer see what is the real science and what is the pseudoscience.

"Homotopy type theory" is surely less politically relevant. So it's harder for the "communities" doing this piece of abstract mathematics to convince large portions of the public that they're doing something that the portions of the public should root for. So it's unavoidable that "homotopy type theory" will remain an esoteric discipline relatively to the climate panic. But at a lower scale, when it comes to the counting of the reseachers, the qualitative problems with the "community approach" are the same. The "community approach" to any discipline, including "homotopy type theory", is equally dysfunctional.

Science must be done by critically thinking and (at least occasionally) intellectually hard-working individuals who also need some good luck – to be at the right place in the right time, and other things. When they have to overcome some obstacles, and it's what the most important ones have to do pretty much by definition of the importance, we may call them heroes. The discoveries are greatly valuable and analogous to gold. A society or the scientific culture that works cannot interpret this gold as some "stuff lying on the street that must simply be picked by volunteers".

Whoever wants to eliminate individuals, heroes, critical thinking, or proper attribution of credit from the scientific process is really promoting a destruction of science as we have known it for a very long time. He or she wants to replace science with a loosely connected network of NGOs, mobs of low-quality people who intimidate and silence others and who, in many cases, receive a totally undeserved income that should actually be classified as fraudulently acquired welfare fees. Too bad, the people with this kind of "volunteer-community-NGO" thinking are not ruining "just" the scientific disciplines, they are ruining most other structures that have evolved in the Western society and that are absolutely critical for the Western society.

And that's the memo.

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