Mathematics has an Occupy moment
The Occupy Wall Street movement means a lot of things to a lot of people, but one of the things it pretty much universally represents is the concept of agency.
Instead of sitting passively by and allowing a dysfunctional system to detract from a culture, the participants in Occupy want to object, to reform the system, and if that doesn’t work, to build a new system. And the crucial point is that they feel that they have the right (if not obligation) to do so. Moreover, they wish to construct a new paradigm built on democratic understanding of the shared goals of the system itself, rather than letting whomever is in power decide how things work and who benefits.
I feel like there’s an analogy to be drawn between this process and what’s happening now in the fight between mathematicians and Elsevier, and for that matter the publishing world (as has been pointed out, Springer has the same issues as Elsevier, even though people like Springer a lot more).
It may seem like the fight against Elsevier is only a small part of the mathematics system, in that it’s really only one publisher of many, and some people (like the journal of Topology) have already gone ahead and started new journals that don’t share the more toxic properties that the Elsevier journals have. I don’t think that narrow view is justified.
In fact, part of tearing down Elsevier has to include a broader understanding of how antiquated the entire academic publishing world is, which immediately begs the question of what we need to build to replace it. This is not unlike the Occupy movement’s goal to replace the current financial system with another which would primarily serve the needs of the citizens and only secondarily the desires of bankers. A tall order to be sure, but luckily for mathematicians their system is less complicated, and moreover the community is much more empowered.
Why am I waxing so poetic over this struggle? Because, at the heart of the question of “what is the new system” is the even more fundamental question, “what do we, as a community, wish to treasure and what do we wish to discard?”. After all, we already have arXiv, or in other words a repository of everything, and the question then becomes, how do we sort out the good stuff from the crap?
I want to stop right there and examine that question, because it’s already quite loaded. Let’s face it, people don’t always agree on what it means for something to be good versus crap, and if there was ever a time to examine that question it’s now.
Here’s a thought experiment I’d like you to do with me. Since leaving academic mathematics, I’ve realized the enormous value of being able to explain mathematical concepts to broader audiences, and I’ve been left with the distinct impression that such a skill is underappreciated inside academic mathematics. In the past 8 months, since writing this blog, I’ve become sort of a hybrid mathematician and journalist, and it’s kind of cool, if unfocused. But what if I decided to really focus on the journalism side of mathematics inside mathematics, would that be appreciated?
So the thought experiment is this. Imagine if, every 6 months, I moved to a new field of mathematics and acted as a mathematical journalist, interviewing the people in math about their work, their field, where it’s going, what the important questions are, etc., and at the end of the 6 month gig I wrote an expository article that explained that field to the rest of the mathematicians. I’d do that every 6 months for 20 years, and I’ve covered 40 fields. Assuming I’m as good at explaining things as I say I am, I’ve really opened up these fields to a larger audience (albeit still math folks), which may allow for better communication between fields, or may avoid redundant work between fields, or may simply enrich the understanding of what’s going on. From my perspective, the work I’d be doing would really be mathematics, and would further the overall creation of mathematics.
However, think about those expository articles I’d be writing. They wouldn’t be original, nor would they be particularly hard- if anything the goal would be for people to understand them. Would they ever get published in a top journal (as of now)? I don’t think so. And please don’t suggest that papers like this, written by famous people in their fields, have been well-received. This is true but I claim more a result of the reputation of the writers than because of the content.
Let’s go back to the question of how we sort papers on arXiv. For some people, this question is really confusing and even scary. They fear that any system besides the one now in place would devalue contributions that are more technical, harder, and less accessible over results that are easy, flashy, and amenable to pop culture sound bytes. I exaggerate for effect, but this is the gist of worries I’ve been hearing. For these people, which I will call “the traditionalists”, the most they want to do is to circumvent the publishers’ fees but otherwise keep intact the referee system, whereby there are gatekeepers who choose experts to anonymously review papers. The publishers are the organizers of this system, and by inviting people to be editors for their journals essentially anoint the gatekeepers.
I actually think those traditionalists should be afraid, but not exactly for the reasons that they think. Instead of worrying that their hard, technical papers won’t be appreciated, they should worry that other, totally different kinds of skills will be appreciated. Of course in the end it’s the same result, namely that the top universities may not forever be populated exclusively by people who prove wonderfully difficult, original and ground-breaking results. They could also include people who are the great story-tellers of mathematics and are appreciated for their gifts of understanding and disseminating mathematics, as well as their broad understanding of the field.
In other words, a democratic system actually looks different from a oligarchy, and that’s not necessarily bad, although the oligarchs may think it is.
I’m going to make a prediction, namely that there will be two different systems in place in 15 years. Neither will involve traditional publishers, but one of them will keep that refereeing system intact whereas the other will be more of a crowd-sourced referee system. Maybe it will be something like this idea of Yann LeCun, for example. Maybe it will be better for women. That would be cool.
By the way, I want to be clear that I’m not suggesting all papers are written equally. There really are people who make huge contributions to their fields through proving hard, creative theorems. I just think there are also people who contribute to mathematics in other ways, that also require hard work and excellent skills. And there aren’t just two skills, of course; I just simplified matters for this discussion.
The discussion of the future of academic publishing is raging, as I posted about here. And that discussion is really important in itself, and the fact that so many people are participating in it, and figuring out the shared values of the mathematics community, is democracy in action. I fully believe we are witnessing a historic moment, and it’s weirdly, and happily, happening without police intervention, pepper spray, or drum circles.
mathbabe 
Let’s not get carried away with the with-us-or-against-us thinking. I’m on record expressing skepticism about crowd-sourcing the evaluation system, in particular I worry that it could be worse for women. Does this make me a “traditionalist” who can’t see the value of an expository paper? I’ve done a lot of expository work myself and would love for it to be better appreciated.
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Sorry if I seem to imply with-us vs. against-us. Actually I mean to say this: that it may start out with two camps, but I think with further iterations people on either side will relax and see the value in becoming more flexible. In fact I think the two sides will eventually converge to something in between.
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I don’t see why it would ever have to come down to two camps. Why not have two or more systems coexisting? Maybe one system would be better for “research” papers and one for “expository” ones, although the line wouldn’t necessarily be sharp. I could see myself functioning within several different models, choosing between them every time I have a paper to submit, the same way that I now choose between journals.
Also, on the subject of a crowd-sourcing system having no gatekeepers: what about Terry Tao’s blog? Or Scott Aaronson’s, for example? They would certainly play the role of gatekeepers by promoting the papers they like, and we might as well call them that.
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Agreed! There’s no reason two systems can’t coexist. It might make it harder for people to decide once and for all whether a paper is “important” because the two metrics may disagree- but that seems to me like an argument for two systems, not against them.
And I do agree that there are gatekeepers to some extent, because they have their blogs. On the other hand, anyone is free to start a blog.
At the same time, maybe people do trust their opinions on mathematics, at least in their fields, more than they trust other people’s opinions, and maybe that’s totally appropriate. In other words, I think it’s important to distinguish between a gatekeeper in a discussion about how to set up a referee system and an authority on whether a given paper is deemed “important.” For my part, I wouldn’t think that Terry Tao’s opinion on how the system should be set up is any more valid than anyone else’s.
Cathy
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“how do we sort out the good stuff from the crap”
How I wish I could be brief as possible! I’m trying. Whether in academia, funding, publishing, whatever, there is an established, hierarchic/bureaucratic culture now beginning to be challenged. A problem is that broad input decreases “resolution.” My proposal is perhaps off key. I believe there are enough self-sacrificing academic and non-academic scientists around to build a new open source movement. The idea is to propose “cheap” research projects to as large and interested audience as possible. The downside is that opportunists will behave unethically (I know many reviewers who are merely on the hunt for fresh ideas). So what? Love of knowledge and self-satisfaction should be its own reward.
I’m impressed by models with concrete examples. Here’s such an example —
Harry Potter Novels
Official translations of all the novels are available in French, German, Italian, and Spanish. With a budget of ~$1000 or so and available software, the following statistics could be procured (perhaps by an enterprising HS student) —
In each language, the number of words and (orthographic) characters.
That would provide a data set invaluable for the study of “orthographic depth,” a topic that has been hanging around with armchair types for ages. For an excellent, related, but “expensive,” study, see “Foundation literacy acquisition in European orthographies” (Seymour et al, 2003).
Finally, you know everyone (secretly) likes to read something they wrote. With forbearance, here is a Fable, the first one I wrote —
(A long time ago (late 4th Mill BC), writing was invented in Mesopotamia and Egypt. Although both streams arose independently, they shared a common inspiration– Picture->Idea –which resulted in (less iconic) Cuneiform and (more iconic) Hieroglyphics. Some of it had to do with writing materials. The Mesopotamian script was inscribed on damp clay with a stylus, driving the script toward a more abstract, less iconic, representation. In my fable, I poke fun at iconicity in general.)
How Iconicity Fell out of Favor Way back when, an Inventor appeared before the Ruler and said –“My invention seems a little complicated, but once you get it in mass production it could take off. It goes like this. First you get some wet clay and knead it just like dough for a loaf of bread and then flatten it out like it’s gonna be a little cake. Next, when your Minister of Information announces the latest Royal Decree, I’ll make some scratches on the little cake. Then I’ll put it out in the sun to dry…” The Ruler interrupts–“You’re wasting my fucking time. Get to the point or it’ll get to you.” “Yes, your Majesty. After the cake dries, I’ll look at the scratches and that’ll help me remember the Decree.” As the Inventor is dragged off to be beheaded, he yells–“Sir, my scratches will be Bigger every time your Name is mentioned!” The Ruler was not moved. That’s how iconicity fell out of favor. Moral: Bigger is not always Better.
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Mathematicians Organize Boycott of a Publisher
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I commented briefly on the Economist’s website regarding the boycott of Elsevier, saying
“Where exactly did the author of this piece get: “ArXiv’s papers, though subject to merciless post-publication commentary, are not formally peer-reviewed before they are posted. Their quality is thus rather uneven.” As a physicist who gets to read pretty much a up-to-the-minute cross-section of high-quality work on the ArXiv, I can most emphatically state that this is not the case. The reason is primarily reputational – by identifying myself as an author and accessing the large (my impression is, far greater than those who would pick up and read a respectable journal like Phys. Rev B or similar) audience that the ArXiv gets – I put my reputation on the line with each posting of a paper …”
Looking back over the last several months of postings on the archive in condensed matter physics, I would be hard put to find any one which did not below there. Or, to put it more accurately, any which I would not be surprised to see as a journal publication.
So I seriously wonder about the argument regarding the absence of peer review on the archive. It seems to me that it is about an efficient a system, unbiased by entry barriers, that one can get.
Regarding the larger point you made about popularizing mathematics, I wanted to point out that biologists have an efficient mechanism for this. They write review articles, at a level that is more ‘generalist’ than the technical papers they write, at a rate of about 1 review to 3 published papers in specialist journals. I don’t know why the other sciences and mathematics have not done this, but think this is mainly because progress is biology/biomedical sciences occurs on a far faster time-scale than progress in the other sciences or even mathematics.
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Seems that you’ve missed the Occupy point entirely.
You’ve listed theory and exposition as the two main types of writing. You’ve skipped the only one that counts: Application.
Every theory should be checked against reality. Does it describe something real? Does it help us to improve human life or improve some kind of product? If not, put it aside.
A theory that cannot be tested at all is not math or science. It is religion, and should be discarded instantly.
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I don’t remember listing types of writing actually. But if you are asking whether mathematics improves human life then I’d say yes it does, although I agree that it’s up for debate.
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This already happens in medical/health writing. Academic and pharma industry researchers do the studies and write the papers published in medical journals, and health journalists interpret these for non-specialist health practitioners, patients, and the lay audience. There’s a whole secondary industry of web publications like Medscape and MedPage Today, to “community-based” or patient advocate resources like HIVandHepatitis.com (of which I’m editor) and POZ and HCV Advocate. Those of us in the latter category are always struggling to afford access to the primary source material.
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Cathy, I think you raise an awesome point, which I wish I had the knowledge and energy to understand and write about carefully. Instead I’ll throw some thoughts.
The question of rating different characters of intellectual works, in particular depth/difficulty/riskiness versus important-but-predictable, is crucial to our society. It is basic to understanding its history, and predicting and influencing its future. It is also basic in personality psychology, in particular narcissists may be defined as people who value deferred rewards too highly (at least certain kinds of rewards).
http://en.wikipedia.org/wiki/Deferred_gratification
It is also basic in understanding science, and of the fundamental/applied divide. Researchers feel they do not need instant gratification, but can imagine that their mental processes will give them gratification, which is already in itself all the actual thing, it is the actual emotion, all that matters to her/him. (Then we should look at brain structures, chemistry, and dynamics involved. Think midbrain, basal ganglia, dopamine,…).
(Disclaimer: I am a narcissist, I still don’t know what to do about it, I try to find out.)
This is basic in the question of happiness, and understanding the value of money. Systematically, in macroeconomic discussions at least, money is equated with happiness: countries must develop as fast as possible, recession (low/negative production growth) is evil, Japan “lost” a decade, and crucially “third-world countries” or “developing countries” exist in the sense of “unaccomplished”, not-yet-there. And I think this is a very urgent issue to address in economy: what is happiness? And really the more I learn the literature the more I find that I have to think those things out for myself, and wish I have the strength to figure out interesting things, and publish them.
I think that stability is closely linked to happiness. Many people just do not strive for more than they have, I think that’s a good start to define happiness, because then we may separate different kinds of things to strive for, and striving dynamics, and therefore different kinds of happiness. And also because this directly leads to what drives society, and science. Researchers are relatively long-term and abstract strivers, while say investment-bankers are long-term materialistic strivers, and management people may be short-term abstract strivers in some senses, but here I see I would actually need finer characterization to support my point.
Then the industrial revolution may be seen as fueled by the understanding/belief that we should shut up and strive long-term, give money to the bankers, put up with capitalistic abuses, coupled with a favorable environment, we needed guys like Leibniz, Newton, Rousseau, Picasso,… who went high on endorphines and just seeked that out to the extreme, many (most? all?) of them falling into undesirable interpersonal dynamics in the process.
(As a side-note those pipe-dream psychological considerations seem useful starting point in understanding the history of science, in particular education, and influencing/deciding on education.)
So our Newtons/Gausses/Grothendiecks/Delignes/Conneses/Wittens (and Marcollis too in some important ways I believe) need to know they will be adulated, how much should we, versus valuing less (say) uncertain work? This is the hard question. We will need much computing power to answer it, and mathematicians and other theorists had better start modeling and calculating this -if they want to satisfy themselves, heh.
(As a positive note it seems that people like Einstein, Weierstrass, Hilbert fared relatively well in interpersonal relationships.)
A last note: I also think those ideas are relevant to understanding economic crises, especially the current one, where there is much uncertainty about what should be valued, how much to invest versus consume (a game between “consumers” versus “investors”/narcissists). And here comes the idea that we have probably run out of big scientific advances, we may reach a point of “absolute diminishing returns”, where society seen broadly (including natural resources, the whole planet actually) is as complex as possible, humans have very optimally coupled with their environment in the last centuries, and science is of precisely limited value. (In particular it is my opinion that we will see no “Singularity”, and I look forward to toy results limiting what we can do in biology/medicine, and computation -I think of Aaronson’s great 100k QC bet.)
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arXiv is by no means a “depository of everything”.
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Even if your hypothetical “math journalism” articles were amazingly written, I disagree with the notion that this would be a major contribution to mathematics as a whole. It sounds like you are talking about Notices-type articles. You seem to be suggesting that a great Notices article can be as valuable to the mathematical community as a great JAMS article, and I don’t really agree with this.
There is a very good reason why original research is valued over good exposition: Original research is harder. It’s a simple issue of scarcity. (I do agree that there is currently too little incentive to write things like survey articles, and I think that ought to be fixed.) I also do not believe that your hypothetical “great storytellers of mathematics” really exist, in the sense that I do not believe that a person can achieve that level of mastery over a field without being a successful researcher.
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How could they exist when our system selects for something so very different?
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Serge Lang has done a kind of “math journalism”, most notably through textbooks. He also inevitably added his own observations, and pedagogical innovations. You can count his textbooks too, and I believe that would compare nicely to your 40 fields figure -though most of his books deal with “basics”.
Pierre Cartier has done similar journalism at a more “difficult” level, through Séminaire Bourbaki articles.
(I think I had more good examples of such polymaths but I don’t remember.)
The modern take on this kind of journalism is math blogging. Terence Tao popularizes many areas of mathematics even if he does not make important contributions to them. For instance Perelman’s work, which I think he presented more from a problem-solving, tools-of-the-trade perspective, than others.
I think exposition is not “very” unfairly valued. There is a certain amount of disdain (there was toward Lang, not toward Cartier I think), but that is still healthy competition. I think we can aim to be more tolerant, to control ourselves more, but I don’t feel the system needs dramatic efforts on that front.
What I most feel lacking is quantitative modeling of the various interests involved, of the whole rating system, attempts to put numbers on utilities to various agents and link all those things together usefully, and at the very least determine where modeling will fail us because things are inherently uncontrollable, chaotic, and then we may just accept that. I really wish I had the energy to publish papers on that, and I hope the whole community will feel that need, to do more than throwing thoughts, feelings, or opinions -as I am doing.
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A couple of remarks on mathematical exposition:
The Notices of the AMS are great as is the Bulletin. Close to the latter but also somewhat complementary is the séminaire Bourbaki. There, experts really do make efforts to explain very technical result with a real view to usefulness (that is, not cutting down on details too much for plausible users, which are of course few). I think expository articles do have quite a bit of recognition (I believe there is a Steele prize for them, I remember Vogan’s E_8 article and Conrey’s Riemann hypothesis one).
Since Bourbaki’s heights clear exposition has been valued relatively forcefully I would say (partly as a countertrend to Bourbaki), and this has resulted in quite a nice supply of textbooks and monographs. I cannot tell too much how this gets actually valued by committees of all types but at least I am convinced intelligent people do their best to take those into account.
Finally wikipedia and mathoverflow are certainly not to be overlooked in terms of instructional impact. Wikipedia contribution have even contributed to at least one person getting tenure, and I can see that recognition growing. Mathoverflow is a hightech on-demand insight delivery system. And currently on math2.0 we are discussing a comment feature on arxiv articles which would afford at the same time review/rating of articles beyond a “score” and questions to the author resulting in nontrivial expository-value additions.
Thanks again for the forum, especially because I’d like to write articles on those things but all I manage is blog comments…
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The problem with commercial publishers is not that their journals are expensive, which they are, but that they are extremely poor value for the money.
“Surveys of [individual] journal [subscription] pricing … show that the average price per page charged by commercial publishers is several times higher than that which is charged by professional societies and university presses. These price differences do not reflect differences in quality. If we use citation counts as a measure of journal quality … we see that the prices charged per citation differ by an even greater margin.”
The problems are far broader than just mathematics and the high price of commercial journals. Last summer a workshop on The Future of Research Communication was held at Schloss Dagstuhl. It involved researchers, librarians and publishers, both commercial (e.g. Elsevier & Springer) and not-for-profit (e.g. PLoS). The follow-on is being organised here.
As part of the work to produce the workshop report, I wrote an overview of the problems with the current system, drawing on the excellent work of the UK House of Commons Science & Technology Committee (PDF) and the extensive peer-reviewed literature on research communication.
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I am not totally sure if this fits the discussion, but here is a startup that is working to rethink the academic publishing problem. MyDivvi I am not totally clear on the details, but it has a nice introductory video. I am curious to see what becomes of it.
Disclaimer: I am not involved with MyDivvi, I just ran across it the other day.
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I have discussed the “democratization” of science with others before, although usually they come from a more postmodernist/esoteric background. What does democracy really mean? Well, majority rule, essentially. So understood correctly, democracy in medicine would mean that group X holds a vote to decide whether homeopathy works. Democracy in math means that group X decides whether Cantor was right or not. Democracy in biology means that group X decides whether evolutionary theory should be accepted or not. I guess you can already see where I am going with this?
But it gets even better. The voters in a democracy are all the adult citizens of a state. Who are the voters in a democratically organized academic field? The professors? Everybody who has an indefinite position? Or are postdocs included? PhD students too? Students? Everybody who thinks they should be included because of a strong personal interest in the field? If no, would that not exclude very qualified laypeople? If yes, would that not open the door to all cranks who think they have overturned the theory of relativity with their never-thought-of-before “flashlight on a spaceship going at light speed” idea? Or should the voters be all the members of some academic society?
Yes, democracy is an ideal for politics that I share. Yes, crowdsourcing and all these other nice approaches made possible by the internet sound very attractive. But there is no way around it: in science (or academia in general), democracy would not work. First, there is one hard, unforgiving reality that we try to model and understand, and you cannot decide on reality with a majority rule vote. Second, there really are people who know better than the rest of us, and they are very, very few. Call them the oligarchy if you like, but gatekeepers are needed in a system where the qualification to judge the merits of any given piece of work is best depicted as a power graph. Third, every individual researcher needs some output with their name on it, both to be motivated through their own achievements and to present on their CV. “I have this paper in the Proceedings to my name” works in that sense, “I was one of two thousand people working on this Wiki” doesn’t, even if the Wiki is a truly marvelous resource.
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Further discussion on what to build as a better system for maths is going on at http://www.math.ntnu.no/~stacey/Mathforge/Math2.0/extension.php?PostBackAction=Blog Note that those who say we don’t want democratic consensus are forming a more biological model of how to improve things – get a few good alternative ideas up and running and then let all the systems compete. They will all evolve, including the existing journal system, to create an ecology of math publishing and research in which different systems serve different purposes.
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A contrary point of view:
http://galoisrepresentations.wordpress.com/2013/04/28/exposition-is-not-underrated/
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Comment here: https://plus.google.com/103061162497127117651/posts/BrxeUhYQNhA
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