The Accidental Mathematician

Random thoughts on publishing and the internet


I doubt that there is anyone reading this blog who does not also read Tim Gowers, but in case you missed it, here’s his blog post proposing a hypothetical alternative publishing model in mathematics: essentially, a massive website combining the functionality of arXiv, Math Overflow, and more. There is also a revised (mostly scaled down) version, where the website would mostly serve as a venue for exchanging constructive feedback.

I’m old enough to remember the days when most math departments had pre-printed postcards with requests for journal offprints. (“Dear Professor [fill in the blank], I would be most grateful if you could send me an offprint of your article [fill in the blank] that has appeared in [fill in the blank]”. That’s what the offprints were for, mostly. They also looked much better than a manuscript typed on a mechanical typewriter, with handwritten math symbols.) Scientific journals actually served to disseminate information back then – checking new issues in the reading room was an important part of keeping up with recent developments. Ah, the good old times.

Dissemination is in our own hands now. I usually check the arXiv every day, but it’s been years since I last bothered with the current journals in the library, other than to look up published versions of papers that I’d already seen as preprints. Of course we will want to take ownership of the rest of the publishing process: the record-keeping, the peer review with its twin goals of debugging papers and evaluating their merit. These are functions that are worth keeping. I do use the library on a regular basis for older articles; I’d rather cite a stable, debugged journal article (where possible) than a preprint that could get replaced or pulled down tomorrow; and, as inaccurate as it can be to judge papers by the journals they appear in, I’d rather have such (approximate) marks of the quality of my work in place than leave it to each year’s departmental committee on merit pay increases to try to figure out all over again what I’m doing and why it’s supposed to be important.

It’s clear enough that any alternative publishing model will likely be internet-based, with interactive components possibly similar to Math Overflow or blog comment sections. It has also been noted that women have significantly less visible presence on MO than they do in research mathematics overall. One might ask, therefore, whether switching to an internet forum-based model of publishing could have the side effect of alienating women mathematicians and driving them out of the field.

In this regard, most discussions of why women don’t participate in something or other tend to follow the same three-step outline:

1) Men come up with a list of reasons why they think women don’t participate.

2) Men decide that these are not valid reasons.

3) Therefore, women should just get over it and participate! Problem solved.

But when I started thinking of what I’d want from a future publishing and peer review model in general, and what would make such a model women-friendly, I came up with pretty much the same principles from both angles: fairness, professionalism, adherence to merit-based procedures, having error-correcting mechanisms built into the system. These are all good for women, but they’re also good for mathematics. The list below isn’t meant to be complete; feel free to add more in comments.

Decentralization. I would not be in favour of one huge, centrally designed website for all our math publishing and peer review needs, possibly with one numerical scale to rank us all. To be clear: I think that arXiv is great. I don’t hang out much on Math Overflow, but I’m glad that it’s there and I would have likely become a heavy user if it had been introduced a few years earlier. What I would not welcome is the mixing of different functionalities and rankings, the assigning of numerical scores to apples and oranges alike. If you don’t see why this could be a problem, I might suggest reading this first:

Amos and I once rigged a wheel of fortune. It was marked from 0 to 100, but we had it built so that it would stop only at 10 or 65 One of us would stand in front of a small group, spin the wheel, and ask them to write down the number on which the wheel stopped, which of course was either 10 or 65. We then asked them two questions:

Is the percentage of African nations among UN members larger or smaller than the number you just wrote?

What is your best guess of the percentage of African nations in the UN?

The spin of a wheel of fortune had nothing to do with the question and should have had no influence over the answer, but it did. “The average estimate of those who saw 10 and 65 were 25% and 45 respectively.”

So, if you’re ranking on a scale from 1 to 100 a paper written by someone ranked in the 98th percentile of frequent commenters on the site, in an area of mathematics whose “hotness” is 90%… OK, I’ll leave it there.

Mathematics is an ecology that would not benefit from having everyone compete directly against everyone else all the time. Emerging research areas often grow in small niches first before hitting it big time. A less fashionable area might carve out a bit of room for itself – and thus live to see the day when it becomes fashionable again. (Additive number theory comes to mind.) A centrally planned megasystem might recreate the complex environment that we have now, or it might not. And if mathematicians in some area felt that they were getting the short end of the stick… why, they might even come up with the idea of having a specialized journal for themselves! That’s why I wouldn’t really expect such a centralized system to last very long, even if people could be convinced to buy into it in the first place, which is not likely.

Second opinions. This is related to what I’ve said already about decentralization, but important enough to be mentioned separately. Right now, if my paper is rejected by A Prestigious Journal (good but not good enough, etc.), I can send it right off to Another Prestigious Journal. Chances are that the second journal will use a different referee and their opinion will be independent of the first one – and different from it. (And my paper will find a happy home.) This doesn’t mean that either journal acted in bad faith. There can be genuine differences of opinion as to how interesting or significant a given result might be.

But let’s say that my paper gets posted instead to a peer review website and the first review is negative. Every follow-up reviewer now has to address that. It’s tempting to think that we’ll just all be fair to each other, that any misguided or unfair opinions will be banished through the magic of downvoting. I wouldn’t count on it.

First, if a strongly dissenting opinion gets posted subsequently, there’s a good chance that the discussion will devolve into a shouting match, possibly on an unrelated subject. The comment page for my paper will become an unpleasant place to visit and most colleagues will just stay away, regardless of the actual merit of my work.

More likely to happen, though, is what happens in real life. We’re all human. I’ve seen sloppy and biased professional assessments, and I’ve seen some that can only be explained by unbridled partisanship if not downright malice, and I’m sorry to report that there isn’t always a long line of colleagues waiting for their chance to correct the record. People are busy enough already. They’re not always willing to risk their relationship with someone they know by speaking out on a subject where they don’t see themselves as unquestioned experts. And, well, they don’t want to be the impolite person who derails the discussion and makes the whole place unpleasant, so they maintain the decorum and tone down their disagreement.

This aspect of decentralization is especially important for women. Social change happens in small increments, one department at a time, one hire at a time. We’ve all heard the story of how David Hilbert convinced the Gottingen mathematics department to hire Emmy Noether. Well, if he’d had to run a Europe-wide referendum on that, chances are that Noether would have never had a paid university position in Germany.

Controlled anonymity. Much has been made of the anonymity of the journal referees. The editors, however, are not anonymous. They select the referees, make judgement calls, sign their names on acceptance and rejection letters. It’s their responsibility to try to send my paper to someone conscientious and knowledgeable enough in my area of research. It’s also their responsibility to arbitrate fairly any disputes between authors and referees and to step in when either side takes too many liberties.

The anonymity of the referees must be preserved. There’s no other way that people will submit frank and candid feedback. But anonymity can also lead to abuse and flame wars, usually “won” by those with the most time on their hands, as happens again and again in online comment sections. There must be an editor or moderator in between who chooses or at least approves the referees, knows their identities and does not allow Gawker-style comments from the peanut gallery.

Which brings us to the last point for now.

Moderation and civility. Mathematics blogs and websites, including Math Overflow, tend to be quite light on moderation. This works well enough when the discussion is about the finer points of the theory of C* algebras. When the topics get more contentious, though, the thread often gets hijacked by a few commenters with strong opinions; even if everyone else disagrees with them and says so, that still does not undo the damage, which is that it becomes impossible to have an interesting, informative or enjoyable discussion in the same space. (I could link to any number of threads on women in math here.)

All political or general interest bloggers with good comment sections know this and moderate their comments heavily and aggressively. This doesn’t just mean deleting the most blatantly offensive and threatening comments and allowing everything else. Most major newspapers have policies like that, and their comment sections are awfully depressing to read. Compare this to Juan Cole’s comment rules, for example. Guess what? He actually gets good comments. On Middle Eastern politics, not exactly an uncontroversial subject. Many other blogs have similar policies, although they don’t always state them as explicitly.

Women get targeted particularly often for trolling, harassment and violent threats, including on academic blogs. Any math publishing site with a comment section will have to deal with this. It will also have to deal with lesser offences such as mansplaining. This isn’t usually considered serious enough to warrant banning a commenter, but nonetheless women will avoid (if they can) any websites where such behaviour is common.

I moderate comments on this blog and I’m not going to get into topical discussions on any sites where comments are not moderated. Of course, when I say that X is mansplaining, X might think that he’s just stating obvious truths that I’ve failed to understand. That is why I don’t see how websites with comment sections might breach contentious issues and discuss them productively without an aggressive moderator who, moreover, has to take sides from time to time. And that is why I don’t think that we can have genuinely contentious but still productive exchanges on general purpose websites where no one in particular takes responsibility for the content. A good discussion section on a blog is probably the best we can hope for.