Last issue I waxed poetic about some informal communities I was involved in. I've been reading a few books about what makes a good community.1
One was Simone Weil's "The Need for Roots," which provides an interesting philosophical take. This book was written in the late 1940's at the request of France's government-in-exile, the "Free French Forces." They wanted advice on how to revive France after the devastation of defeat and occupation. France's collapse, which took only about six weeks, took French leaders by surprise. Weil writes,
The sudden collapse of France in June 1940, which surprised every one all over the world, simply showed to what extent the country was uprooted. A tree whose roots are almost entirely eaten away falls at the first blow. If France offered a spectacle more painful than that of any other European country, it is because modern civilization with all its toxins was in a more advanced stage there than elsewhere, with the exception of Germany. But in Germany, uprootedness had taken on an aggressive form, whereas in France it was characterized by inertia and stupor.
It's not a typical introduction to a book that is (in part) about building community. She further frames the discussion around what she calls the "needs" and "obligations" of humankind. Some needs are primal and some are spiritual.2 "Needs" contrast the classical notion of rights. For Weil, rights are amorphous and detached from humans, while needs and obligations form a duality intimately connected to human interaction. Humans have a need to eat, and one who has plenty of food is obligated to share. Weil focuses more, however, on the less clear-cut "needs of the soul." An example is the need for a baseline level of respect, which she calls the need for "equality." The obligation is to respect others.
When two contrary obligations come into conflict, Weil argues that one must give. And, that the measure of a well-ordered community is how infrequently such situations occur. Obligations to humans extend to obligations to a community, insofar as that community provides for the needs of its members.
We owe a cornfield respect, not because of itself, but because it is food for mankind. In the same way, we owe our respect to a collectivity, of whatever kind—country, family or any other—not for itself, but because it is food for a certain number of human souls.
A lot of modern writing about community building focuses on either building a "buzz" (often around a product or company), or vague poetry on inclusion and fulfillment. Very little describes what fulfillment looks like, and how the dysfunction of a poorly managed community subverts fulfillment. Weil describes 14 concrete needs that form her framework of what "fulfillment" looks like (the link summarizes them, but I'll reiterate the summary when referring to them below):
Finally, back to mathematics, I'd like to go over the existing mathematical communities and ask to what extent they fulfill their obligations to meet these "needs of the soul." Since there are 14 needs, I'll just discuss the ones that interest me.
Weil defines "responsibility" as the need to feel useful to others, and to be able to take initiative in carrying out that usefulness. Professors have no shortage of administrative and teaching responsibilities, But the attitude among many academics is that these activities distract from research.
A more preferable sort of responsibility arises when one can help a fellow researcher with a research problem. Naturally, you want to help your community members.
To help someone else solve their problem, you need to be in the right place at the right time. The person must have a problem you can quickly grasp, and it needs to be feasible to solve with the tools you know. Math is specialized. Research departments tend to hire world experts on narrow topics. This makes opportunities scarce, and is why field-specific conferences are a common mixing pot for collaboration.
The reliance on rotatin conferences as a meeting ground for intellectual community also subverts the grounding of the community around a physical space (like the math building of a university). In my experience, conferences which rotate their location make each instance (of the same conference series) feel a bit foreign.
Moreover, the "usefulness" of any given bit of research is usually too far removed from the application. The satisfaction feedback loop is diluted. Competition for popular research topics can result in marginal progress on a popular topic, or decent progress on an unpopular topic. Both might make one look back on their work and wonder, what was it all for? A mathematician who fears this may crave responsibility.
The stackexchange websites are notorious for making question askers feel bad by closing their questions. Here is a recent example, but it's happened to me often enough. This is a clear lack of equality, which Weil defines as applying a baseline respect to all. It also shows a lack of security, as a question asker is constantly second-guessing whether their question is good enough for the community. These qualities seem to boil down to a small group of moderators embodying a toxic culture. I read through the comment threads on this meta post and it was clear that the community highly values removing "low quality material," which corresponds to Weil's need for hierarchism. This is doubly reinforced by the emphasis on votes, badges, and reputation scores.
That emphasis has eroded the ability of math enthusiasts to ask questions that don't have immediate answers. In other words, freedom of opinion is stamped out, because the community was designed to only deal with questions for which opinion has no bearing.
Math Overflow fares better. Their line, "only research level questions," coupled with an alternative for non-research-level (stackexchange), gives them the ability to close questions without as much toxic fallout. This demonstrates a fulfillment of Weil's need for "order," which she defines as structuring society in such a way that minimizes situations in which obligations conflict. Since math stackexchange is less ordered, especially since, despite their list of what constitutes an acceptable question (it includes questions about software that mathematicians use), the example conflict linked above was a closed question that could have been slightly edited to become in scope, since it is about software that mathematicians use (LaTeX). Hierarchism subverted order.
Math twitter provides an interesting counterpoint to the other communities discussed so far. Equality, liberty, and freedom of opinion are maximized, and I personally have both given and received specific, concrete help on math topics, so responsibility feels satisfied. It does often devolve into memes and shitposts, though, and there's no boundary between math Twitter and "not math Twitter." This can be bad or good, with a good example being when mathematical experts rallied to reply to a TikTok teen on the topic of whether "math is real", and a bad example being the recent disingenuous "debate" over 2+2=4.3
These things add to the chaos. Order and hierarchism are lacking. Nothing is sorted or organized, context collapses, and well-meaning, similarly-valued people find themselves in conflict. For some, this leads to a feeling of terror (lack of security), for some it leads to a lack of respect.4 When nobody has the authority to resolve disputes, disputes tend to fester.
Twitter is also one of the few mathematical communities where community members can face punishment for bad behavior. Weil writes that punishment "must be regarded as a supplementary form of education," and that it must be accompanied by consent on the part of the punished to reform. She also writes,
The relative degree of immunity should increase...as you go down the social scale. Otherwise the hardships inflicted will be felt to be...abuses of power... Punishment only takes place where the hardship is accompanied...in retrospect by a feeling of justice.
Math twitter (and social media in general) does not handle this as well as it could. Punishment is not "solemn," as Weil writes it must be, but closer to a dog pile. However, on Twitter punishments are usually more severe as social status increases. One part that it misses from Weil's framework is that the punished do not seem to often consent, or feel justice was served.
In my view, the needs that are missing from math Twitter are the two property needs. Content posted on Twitter, even when I'm helping someone or being helped, does not feel like it's my own, nor does it feel like I'm building a collective thing of value. It's a passing dopamine hit. Tweets drift down the timeline into oblivion, and you are left feeling it was time wasted. When I feel there is something on Twitter worth diving into deeply, or worth perserving long term, I turn to long-form writing.
Blogs don't really feel like a community at all, or at least, I haven't managed to make my blogging feel like it's part of a larger community of bloggers. There is little concrete interaction. The collective property need is missing.
They also don't feel like they are particularly fulfilling on the responsibility front. Though many people have told me they enjoy my blog, the feedback loop is again too diluted, and I never understand how, exactly, my work helps them solve their problems, if it does at all—it may just be good entertainment.
That said, running a long, successful blog (and the book that grew from it) provides the best fulfillment of private property that I have known. It fills me with pride and confidence to know that I did all that, even if some of the older writing makes me cringe. I want that to extend to some sort of community. One of like-minded technical writers exchanging ideas, but also meeting in person to discuss, challenge, inspire, and build upon each other. A primary obstacle to that, of course, is the lack of compensation for the work put in.
What other aspects of mathematical community have you found helpful? Harmful? I'd be interested to hear your thoughts.
To labour is to place one's own being, body and soul, in the circuit of inert matter, turn it into an intermediary between one state and another of a fragment of matter, make of it an instrument. ... The world only gives itself to Man in the form of food and warmth if Man gives himself to the world in the form of labour. ... At times there is a superabundance of youthful energy eager to spend itself and not finding a suitable outlet; at other times there is exhaustion and the will has ceaselessly to supplement, at the expense of a very great strain on itself, the lack of physical energy.
Two are both called "The Art of Community." The first one I read, by Jono Bacon, was not very good, and I gave up half way through. The second, by Charles Vogl, is better, but I haven't finished it yet. ↩
Spiritual doesn't necessarily mean religion. One of Weil's major themes is on the spiritual nature of physical labor, though for her that does take a religiously spiritual flavor. ↩
I am embarrassed to admit I have casually disrespected people on Twitter, and I try to do better. It takes work to prevent the message you want to get across from being muddied by a crass, clumsy, or hasty delivery. ↩