ArXiv, comments, and “quality control”

Those of you who browsed the arXiv recently may have seen a link to a user survey on top of the page (as of now, apparently no longer online) (update: still available here, until April 26). I ignored it a few times, until a friend brought this particular bit to my attention.


Sure enough, I took the survey. As it turned out, the arXiv was also asking for feedback on what it calls “quality control”: actions such as rejecting “papers that don’t have much scientific value,” flagging papers that have “too much text re-use from an author’s earlier papers” (self-plagiarism) or from papers by other authors (plagiarism), or moderating pingbacks (such as links from blogs or articles) before they appear on the arXiv.

Internet comment sections are in decline everywhere you look. They are mocked, ridiculed, despised. Many websites have closed them already; others have seen their comments become a racist, sexist bog of eternal stench from which any reasonable person is best advised to stay away. I’ve talked about it here at length, with examples and links, and it’s very easy to google up more if you wish.

I’m often told that if a comment section is restricted to “registered” mathematicians posting under their real names, the conversations will be polite and civil, with the rare instances of abuse identified as such and condemned by the community. If that’s what you think, consider that much of what passes for “normal” interactions between mathematicians is viewed as passive-aggressive, if not downright abusive, just about everywhere else. We all know what referee reports can look like, or grant proposal reviews, or MathSciNet blurbs. If you believe that non-anonymity will solve the problem, I could give you many examples of questions from the audience in seminars and conference talks that were at least as problematic as any referee reports I’ve seen.

Women, in particular, get far too many comments questioning our competence, implying that we might not know the basic literature, that we might not really understand our own results, that said results might turn out to be false or trivial if only someone qualified had a look, or some such. We’re also subject to gendered standards of “professionalism” that do not allow us to respond in kind and give as good as we get. But if you tell me that men, too, can get inane, confused, or malicious comments–why, yes, I agree. More reason to refrain from making the arXiv more like YouTube. There’s enough abusive behaviour in mathematics already, on all sides. We should not mandate a form of discourse that has been shown empirically to promote and escalate it. Nor should we mandate having it attached in perpetuity to our formal publication records.

As for “quality control”: there have been well publicized cases where the arXiv moderators might have overstepped in rejecting papers and blacklisting authors. I’m not a fan of flagging papers for “substantial overlap,” either. We often write several consecutive papers in the same area, introducing the same notation each time, stating the same conjectures or prior results for reference, and so on. We might even reuse parts of the same TeX file for such purposes. None of this amounts to plagiarism or self-plagiarism, nor should it trigger red flags.

Now, here’s what all this might mean for the future of the arXiv. Allow me a little bit of speculation here.

The arXiv has become the universally accepted default repository for mathematicians, not only because it provides a service we need, but also because, in not attempting to do more than that, it gives us no reason to not use it. We don’t have to worry that the paper might not “qualify,” that it’s too long or too short, or too expository, or not sufficiently tailored for the “right” audience. We simply post what we think is right. We expect and welcome feedback (I often post papers on the arXiv prior to journal submission, specifically for that purpose), but the site does not allow public abuse or internet flame wars, so no need to worry about that. The bare-bones structure is not a bug, it’s a feature that has been essential for the arXiv’s success.

Currently, the arXiv has little competition. It works well enough for most of us and we have no reasons to look elsewhere. That might change. Discontent breeds business opportunities. The competing site viXra, started by physicists who were dissatisfied with the arXiv’s moderation practices, failed to gain much ground; but if the arXiv were to amp up its “quality control” in ways that test our tolerance, and especially if it were to implement comments and ratings, there just might be a critical mass of scientists willing to try such alternatives. I know I would be looking for them, and I’ve heard from others (including well known mathematicians, and not only women) who feel the same way.

It would be more than ironic if, say, Elsevier or Springer were to set up a competing open access repository where, for a small fee around $100, authors could post their papers on a site guaranteed to be free of comments and ratings. That would obviously discriminate against those unable to pay $100, but there’s nothing stopping anyone from setting up such a site if there is demand, as I assume there would be. Grant holders in many countries are now subject to open access policies that practically mandate the posting of papers on repositories; should we no longer wish to post on the arXiv, we’ll need an alternative. I can’t promise that I wouldn’t switch to a Springer or Elsevier site, in such circumstances. It would be even better if non-profit organizations, such as the AWM for example, were to set up their own preprint archives where the terms of service would reflect the preferences of the membership.

If comments or ratings are allowed retroactively, on papers already posted to the arXiv, then it’s far from clear to me that the arXiv would be able to hold on to such papers. My contract with the arXiv is, essentially, that the arXiv has my permission to distribute my articles on its website and its mirror sites. It does not have my permission to cross-post them on Reddit and Hacker News. By the same token, it does not have my permission to post them on a future site that might continue to use the URL, but would function in substantially different ways. That would have to be renegotiated. Individual mathematicians may have little power in that regard, but if major publishers become involved as per the above, and if they decide to encourage researchers to move their past publications to their servers, then I could think of some interesting ways in which this could develop.

My crystal ball here may well be less than perfect, but I think that some version of this would have to happen. If the arXiv wishes to remain the universal default repository for scientists in the covered areas, the plain vanilla model is the only one that will do that. Quality control is better left to journals, and for those authors who wish to have public discussions about their papers, a wide range of blogs and social media is available. Any changes that alienate a substantial group of users will inevitably lead to the rise of competition, and so within a few years we might well see a variety of arXiv-type sites with different functionalities and user bases.

And that would essentially end the arXiv as we know it.

Update, July 8, 2016: for those coming late to it, I’m also quoted in this Wired article by Sarah Scoles.

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The mathematics of wheel reinvention

The first talk I attended at this year’s JMM in Seattle was Tim Gowers’s lecture on how the internet and mass communication might change mathematics. Tim started out by listing some of the more dysfunctional features of how we do mathematics today, then suggesting how they might be improved. I very much agree with that part, and I would like to mention a few points from it here.

Our basic and most important unit of discourse is a research article. This is a fairly large unit: effectively, we are required to have a new, interesting and significant research result before we are allowed to contribute anything at all. Any smaller contributions must be bundled and packaged into units of acceptable size, or else they go unacknowledged. A comparison that came to my mind was having to conduct all transactions in twenty-dollar bills. Whatever your product is, you would have to sell it for $20 or else give it away for free, with nothing in between. It should not be difficult to see why this would not be am ideal environment for doing business. We should have smaller bills in circulation. It should be possible to make smaller contributions–on a scale of, say, a substantive blog comment–and still have them count towards our professional standing.

Our culture is extremely competitive. We value beating others more than we value helping them. All that matters is getting “there” first and scooping everyone else on our way. Intermediate results are worth far less. Additionally, this prioritizes one specific type of contributions over all others, even in those cases where a different order of priorities might be more reasonable. A good expository paper might have more impact on its area of mathematics than a middling research article; and yet, expository work is rarely, if ever, taken seriously by funding agencies and tenure committees.

We spend a great amount of time and energy on reinventing the wheel. A mathematician working on a problem might start with relatively small reductions, observations and lemmas that, by themselves, do not qualify as journal-publishable units; if that effort is not successful, these smaller contributions are lost and the next person working on the same problem has to reprove them all over again. Moreover, information such as “this method didn’t work, and here’s why” might be very useful to that next person. If nothing else, a great deal of time might be saved that would otherwise be spent on trying out unsuccessful approaches. Yet, there is currently no system in place to circulate such information and reward those who provide it.

Consider also how we work and collaborate. We are all gifted in different ways: some are better at imagining new ideas, some at asking questions, some at turning informal sketches into rigorous proofs, some are walking encyclopedias of the relevant literature. Yet, we have decided that each of us has to be self-sufficient and do all of these things equally, instead of allowing people to focus on what they do best and forming collaborations based on complementary skills. (I’d add that such collaborations obviously exist, including in my own experience. We just pretend, at least in official paperwork, that this does not happen.)

I agree with all of this, and I’d love to see us abandon the old ways and adapt new ones. We are far too invested in forcing everyone to fit the same mould. In a profession we like to call creative, I’d love to see more diverse and varied career paths and modes of expression. I’d love to see the flow of information a little bit less hampered by our ambition and competitive instincts. Think of all the theorems we could prove if we allowed more people into the field and, instead of hampering their intellectual power, harnessed it to the full.

I do not believe, however, that such changes are inevitable, and I have very little faith that they will be forced by the internet and other means of mass communication. It takes more than technology to change the culture. The early evidence is not encouraging. The basic discourse unit is still the research paper, except that we now post these on the arXiv. Other types of research contributions are still not being counted towards career progress, even as the subject comes up in discussions over and over again. We are as competitive and territorial as ever. The Polymath projects came and went; one was successful, another one was somewhat productive, others fizzled out. They did attract more participants than conventional math collaborations, but they never became truly “massive” as originally envisioned. People still ask questions on Math Overflow, and sometimes they get useful answers, but it never became the universal communication and collaboration platform that some of its early enthusiasts seemed to imagine. Other, smaller discussion boards went mostly unnoticed. There’s not much actual research that gets done on public blogs or social networks.

At the end of the talk, someone raised the diversity point in a question. The participants in Polymaths, Math Overflow and other similar projects are even less diverse than the general population of research mathematicians. Is there a reason why women and minorities tend to stay away from such venues? What can mathematicians do to ensure that all of us feel welcome to participate? I do not feel that Tim really answered that. He said (and I hope that I’m summarizing it fairly) that all those changes are just going to happen, like it or not, because they bring a more efficient way of doing mathematics and nobody will want to give up on that. It is an unfortunate fact that some people feel less comfortable on the internet, but in the end we will all just have to get over it.

I would like to suggest a different answer.

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Various updates

Polynomial configurations in fractal sets: Kevin Henriot, Malabika Pramanik and I have posted a paper where we prove the following result: if a measure μ on a fractal set E in Rn has Fourier decay with some exponent β, and if it also obeys a ball condition with exponent α close enough to n (depending on β and on the constants in both conditions), then it must contain nontrivial configurations given by certain types of systems of matrices with a polynomial term. This is somewhat similar to my earlier paper with Vincent Chan and Malabika Pramanik, on configurations given by systems of linear forms, but there are significant differences. One is of course the polynomial term: we use stationary phase estimates to control the corresponding part of the “counting form” Λ. (Interestingly, while said stationary estimates apply to functions much more general than polynomials, the polynomial form of the nonlinear term is required for the “continuous” estimates which are based on a number-theoretic argument.) Another is that any rate of Fourier decay β>0 suffices, with the caveat that α must be close enough to n, where “close enough” now depends on both the constants and β. This improvement is due to more efficient use of restriction estimates, and extends to the result with Chan and Pramanik as well as my earlier paper with Pramanik on 3-term arithmetic progressions in fractals. A recent result of Pablo Shmerkin shows that the dependence on constants cannot be removed: he proves, for example, that there exists a 1-dimensional (but of Lebesgue measure 0) Salem set on the line that does not contain a nontrivial 3-term arithmetic progression.

Fractal Knapp examples: Kyle Hambrook and I have been asked on various occasions whether our “Knapp example” for fractal sets on the line could be extended to fractals in higher dimensions. In this paper, we combined our construction (with modifications due to Chen) and the classical Knapp example on the sphere to produce fractal Knapp examples of dimension between n-1 and n in Rn.

My profile for Women in Maths: this was published a while ago, in case anyone here is interested.

It’s been a while since I posted any photos here, so here’s one I took today. There will be more on my Google+ page.


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A response to Scott Aaronson

Scott Aaronson has been kind enough to respond on his blog to a couple of my tweets. I would like to thank him for his interest and engagement, and encourage everyone to take the time to read his entire post. There is also an excellent discussion in the comments.

Much of the discourse focuses on the use and misuse of jargon in social and physical sciences, and specifically on words such as “privilege,” “delegitimization,” or “disenfranchised.” I’ll address that in a moment, but let me first say that my main reason for objecting to the comment that started this discussion was the phrase “This isn’t quantum field theory” at the end. I understood this, in the context of that comment and the comment to which Aaronson was responding, and in light of the similarity to the well known phrase about rocket science, to imply that social sciences do not have the same complexity as quantum field theory and should not need a multilayered structure where concepts are defined, compared, then used to define further concepts, whereupon the procedure is repeated and iterated, so as to make advanced discourse possible and manageable. Aaronson has now explained that this would be an oversimplification of his position, and I’m glad to stand corrected.

I also would like to speak to some of the other points that he makes about language, feminism, social science, and clarity of writing. I’ll try not to repeat the arguments that his commenters have already made, perhaps better than I could have done it. Still, I have no desire to hide (as some have suggested) behind Twitter’s 140-character limit and avoid making my case at more length. And so, here we are. I will just quote the last two paragraphs from Aaronson’s post, but please do go to his site to read the rest:

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Discrete Analysis

You may have seen Tim Gowers’s announcement last week, but if not, here’s the news: we are launching a new arXiv overlay journal called Discrete Analysis. The editorial board consists of Tim Gowers (who will be the managing editor) and Ernie Croot, Ben Green, Gil Kalai, Nets Katz, Bryna Kra, myself, Tom Sanders, Jozsef Solymosi, Terence Tao, Julia Wolf, and Tamar Ziegler. As should be clear from this list of names, the journal will focus on additive combinatorics and related areas such as harmonic analysis, number theory, geometric measure theory, combinatorics, ergodic theory. The temporary journal website is open now, in fact we have already received the first submissions.

“ArXiv overlay” means that we will not be “publishing” papers in the traditional sense. Most of us already typeset our own papers and use the arXiv for quick, reliable, stable worldwide dissemination of our results. It is not clear that mathematical journals can improve much on that; if anything, publication in established journals is currently more likely to impede the dissemination of science through paywalls or embargos than to facilitate it. What we can provide is a refereeing and certification service where we manage the peer review and, when the outcome of the review is positive, attest through publishing the link on the journal website that the paper has been judged to be of suitable quality for publication in Discrete Analysis. Tim’s post has much more information on both the scope of the journal and the technical details of how we expect it to work. If you are finishing an article in one of the covered areas of research, I hope that you will consider Discrete Analysis as a possible publication venue. I’m proud to be on its board.

A few more inside-baseball comments under the cut.
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A postscriptum on diversity and learning a language

“The man of the East cannot take Americans seriously because they have never undergone the experiences that teach men how relative their judgments and thinking habits are. Their resultant lack of imagination is appalling. Because they were born and raised in a given social order and in a given system of values, they believe that any other order must be “unnatural,” and that it cannot last because it is incompatible with human nature. But even they may one day know fire, hunger, and the sword.”

— Czesław Miłosz, The Captive Mind

I grew up in Europe, on the other side of the Iron Curtain. I’ve often had to try to explain my country of origin to those born and raised on this side of the Atlantic. Facts can be learned. It’s the lack of imagination that can be the greater problem. It’s disbelief that learning is in fact needed. It’s making assumptions instead of asking questions. It’s demanding a simple picture where the truth is complex. It’s presuming social or political homogeneity where the reality is ripe in conflict and discord. It’s failing, or perhaps not wanting, to understand just how far the circumstances of a different time and place might be from the here and now. and to accept that, were we placed there and then, we would likely behave the same way as those who were in fact so placed.

I’m neither a historian, nor a social scientist, nor willing to accept an unpaid second job. I can only do it in small steps, for my own pleasure. Even just for that, I needed a language that I could use. I needed examples and templates, in English, that I could try to work with. For a long time, I could not find what I wanted. English-language history books, for the most part, neither understood nor cared much about our life down on the ground. At the same time, I had too little in common with those Eastern European writers whose goal in writing was to distance themselves from their own background before witnesses who shared that background and, often, the distancing. That was not the argument I wanted to have. History has already passed judgement on communism and I’m satisfied enough with its verdict. I do, however, want to argue with those who view us with a mixture of pity and condescension, who consider the details of our history unimportant, who dismiss without looking the artistic and intellectual accomplishments of the Eastern Bloc as “couldn’t possibly have been any good,” who bounce the word “communism” here and there like a beach ball but have no idea how that system actually worked.

If you are reading this, you may have already seen my last post on the legacy of Communist and Soviet symbols in Poland:

I learned to give little thought to the walled-off parts of the city. The [Soviet] soldiers were easy to ignore in my daily life: they marched through our streets on their way to or from exercises, but otherwise they and their families stayed within their gated communities. I grew up mocking the unkempt buildings with newspapers in place of window curtains, but also reading children’s books from the Russian bookstore, which was open to the public; as a university student, I returned there for mathematical monographs unavailable in Polish. We resented that the Soviet food stores were well stocked even when ours were empty. Poles, especially children, would sometimes sneak in and shop there: a guard might look the other way, a Russian woman might allow a Polish kid to come in with her. I dreamed of travelling the world, becoming a scientist or an astronaut, but did not know and probably could not imagine what it might be like to live in a city without the Soviet army.

For comparison, here’s an article on how living with Confederate flags and statues in the south of the US was “like having a crazy family member.”

For those of us not born and bred below the Mason-Dixon, it can be really jarring to encounter symbols of the Old South sprinkled all over the place, as though by a casual hand. But given the ubiquity of these symbols, it makes sense that you’d kind of have to let them fade into the background, or you might never leave your house. […]

Everyone deserves to have local pride; it’s just that for a lot of black people in the South, getting to do that means having to swim in the racial messiness that comes with civic life there. The cultures of Southern black folks and Southern white folks have always been defined by a peculiar, complicated familiarity. That might explain why so many black folks have — by necessity — come to look on displays of the Confederate flag with something subtler than apoplexy, why Naima just rolled her eyes at the flags on her campus and moved on. Like a lot of black Southerners, she clearly had a lot more practice holding all of these ideas in her head at once than we Northerners do. The flag matters to her. Of course it matters. It’s just not the only thing that matters.

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The weight of dead symbols

The photos in this post are mine, from my visit to Poland in late May and early June. The full set, annotated and viewable as a slideshow, is available here. I have provided English-language links where I could, but much of the information I used is only available in Polish. I marked those links with an asterisk, to save you a click if you do not speak the language.


The Polish-Soviet Friendship (officially, Brothership-in-Arms) Monument in Legnica was built in 1951*. It stands in the Słowiański Square, right in the city center. Two soldiers, one Polish and one Soviet, shake hands while a little girl held by the Pole embraces both of them. Poland, invaded by Germany and the Soviet Union acting in agreement, then devastated in the conflict between them, occupied and plundered by both even as its soldiers fought on every front they could find, finally claimed by Stalin for his Soviet empire, had to be represented as a little girl with no memory, history or trust issues, happy in the care of her saviours. Of course the child had to be a girl. A boy might not project the same naivetė, helplessness or passivity.

The monument is still there. I photographed it just a few weeks ago. The inscription, “To the Soviet Army heroes, from the people of the Legnica region,” had been removed in the 1990s and was never restored. The statue was vandalized repeatedly; past renovations notwithstanding, the neglect is palpable.

From 1952 until the end of the Cold War, Legnica was home to the headquarters of the Soviet forces stationed in Poland*. From 1984 to 1990, it also hosted the central command of the Western Theatre of Strategic Operations of the Warsaw Pact: had the Pact attempted to invade Western Europe, the military directions would have been issued from there. Estimates point* to 80-100K Russian soldiers and civilians stationed in town and at various unmapped bases nearby at any given time. The precise numbers and locations were classified, as was the exact layout of the Soviet-occupied parts of the city, surrounded by walls and guarded by armed soldiers posted at each entrance. The largest one, the “Kwadrat” [Square], measured 39 hectares and was a miniature city within a city, self-sufficient with its own shops, hospitals, cinemas, pools and sport venues. In total, the Soviets occupied about a third of the city’s pre-war area.


I grew up not far from that monument. I often walked past it on my way back from school but rarely thought about it. We acquired the skill of inattention in response to the relentless barrage of words and images that ranged from the hostile to the nonsensical*. “Workers of the world, unite!” “PZPR [the communist party] – the working class’s party, the leadership of the nation!” “We build socialism for people and through people!” Above all, invocations of friendship and brotherly love between Poland and the Soviet Union. Unlike ordinary human friendships that enter quietly and tie little knots here and there, that friendship could not be anything less than eternal, was written into the Polish constitution and had to be pledged and re-pledged every day in the streets of every city. We learned to tune it all out except to mock it. That skill continues to come in handy. Corporate language, often no less Orwellian than Soviet propaganda, washes off me like water off an oiled plate. I can look at ads and zap them off my computer screen without ever engaging with their content. (Sorry, Google and Facebook.)

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