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Interpersonal exchange and collaboration to develop and pursue common goals goes further than “learning” or “working” in their mainstream definitions.  This article will look at examples drawn from Linux, Wikipedia, and my own work on PlanetMath, with a few surprises along the way, leading us to new ways of thinking about how to do co-design when building systems for peer learning and peer production.

Co-working as the flip side of convening

Linus Torvalds: The first mistake is thinking that you can throw things out there and ask people to help. That’s not how it works. You make it public, and then you assume that you’ll have to do all the work, and ask people to come up with suggestions of what you should do, not what they should do. Maybe they’ll start helping eventually, but you should start off with the assumption that you’re going to be the one maintaining it and ready to do all the work. The other thing–and it’s kind of related–that people seem to get wrong is to think that the code they write is what matters. No, even if you wrote 100% of the code, and even if you are the best programmer in the world and will never need any help with the project at all, the thing that really matters is the users of the code. The code itself is unimportant; the project is only as useful as people actually find it.

In fact, we can think of contributors as a special class of “user” with a real time investment in the way the project works. We typically cannot “Tom Sawyer” ourselves into leisure or ease just because we manage to work collaboratively, or just because we have found people with some common interests.  And yet, in the right setting, many people do want to contribute! For example, on “Wikipedia, the encyclopedia anyone can edit” (as of 2011) as many as 80,000 visitors make 5 or more edits per month. This is interesting to compare with the empirical fact that (as of 2006) “over 50% of all the edits are done by just .7% of the users… 24 people… and in fact the most active 2%, which is 1400 people, have done 73.4% of all the edits.”  Similar numbers apply to other peer production communities.

A little theory

In many natural systems, things are not distributed equally, and it is not atypical for e.g. 20% of the population to control 80% of the wealth (or, as we saw, for 2% of the users to do nearly 80% of the edits). Many, many systems work like this, so maybe there’s a good reason for it. Let’s think about it in terms of “coordination” as understood by the late Elinor Ostrom. She talked about “local solutions for local problems”. By definition, such geographically-based coordination requires close proximity. What does “close” mean? If we think about homogeneous space, it just means that we draw a circle (or sphere) around where we are, and the radius of this circle (resp. sphere) is small.

An interesting mathematical fact is that as the dimension grows, the volume of the sphere gets “thinner”, so the radius must increase to capture the same d-dimensional volume when d grows!  In other words, the more different factors impact on a given issue, the less likely there are to be small scale, self-contained, “local problems” or “local solutions” in the first place.

As a network or service provider grows  (like a MOOC as opposed to a Collaborative Exploration, for example), they typically build many weak ties, with a few strong ties that hold it all together.  Google is happy to serve everyone’s web requests – but they can’t have just anyone walking in off the street and connecting devices their network in Mountain View.

By the way, the 2006 article about Wikipedia quoted above was written by Aaron Swartz (“over 50% of all the edits are done by… 24 people”, etc.), who achieved considerable notoriety for downloading lots and lots of academic papers with a device plugged into MIT’s network. His suicide while under federal prosecution for this activity caused considerable shock, grief, and dismay among online activists. One thing we could potentially take away from the experience is that there is a tremendous difference between a solo effort and the distributed peer-to-peer infrastructures like the ones that underly the PirateBay, which, despite raids, fines, jail sentences, nation-wide bans, and server downtime, has proved decidedly hard to extinguish. According to a recent press release: “If they cut off one head, two more shall take its place.”

Co-working: what is an institution?

As idealists, we would love to be able to create systems that are both powerful and humane.  Some may reflect with a type of sentimental fondness on completely mythical economic systems in which a “dedicated individual could rise to the top through dint of effort.”  But well-articulated systems like this do exist: natural languages, for example, are so expressive and adaptive that most sentences have never been said before.  A well-articulated system lends itself to “local solutions to local problems” – but in the linguistics case, this is only because all words are not created equal.

Dr Seuss: My brothers read a little bit. Little words like ‘If’ and ‘It.’ My father can read big words, too, Like CONSTANTINOPLE and TIMBUKTU.

We could go on here to talk about Coase’s theory of the firm, and Benkler’s theory of “Coase’s Penguin”. We might continue quoting from Aaron Swartz. But we will not get so deeply into that here: you can explore it on your own!  For now, it is enough to say that an institution is a bit like a language.  This will help us a lot in the next section.

Designing a platform for peer learning

PlanetMath is a virtual community which aims to help make mathematical knowledge more accessible.

In my PhD thesis [1], I talk about my work to turn this long-running website, which since 2001 had focused on building a mathematics encyclopedia, into a peer produced peer learning environment. We wanted to retain all of the old activities related to authoring, reviewing, and discussing encyclopedia articles, but we would also add a bunch of new features having to do with mathmatical problem solving, an activity that is suitable for mathematical beginners.

My first translation of this idea into a basic interaction design was as follows.  People can continue to add articles to PlanetMath’s encyclopedia: they can connect one article to another (A$\rightarrow$A) either by making one article the “parent” of another, or, more typically, via an inline link. Like in the old system, users can discuss any object (X$\rightarrow$T), but now there is more structure: problems can be connected to articles (A$\rightarrow$P) and solutions can be connected to problems (P$\rightarrow$S).  Instead of explicitly modeling “goals,” I decided that problems and articles could be organized into “collections,” the same way that videos are organized into playlists on YouTube, and that the user would get encouraging directed feedback as they work their way through the problems in a given collection.  I described a few other types of objects and interactions, like questions and answers, groups, and the ability to change the “type” of certain contributed objects. 

The next step was to do a complete overhaul of PlanetMath’s software system, to build something that could actually do all of that.  After deploying the realized system and doing some studies with PlanetMath users, I realized the design summarized above was not complete.  Note that this is very much along the lines of what Linus Torvalds said above: I did the design, and me and a small group of collaborators with their own vested interests built the system, then we put it out there to get more ideas from users.

The main thing that was missing from the earlier design was the idea of a project.  From interviewing users, it became clear to me that it would be helpful to think of every object as being part of at least one project: everything should have someone looking after it!   Importantly, getting back to the very beginning of this article, each project can define its own purpose for existing.  Here’s how I put it in my thesis:

Actions and artifacts are embedded within projects, which can be modeled in terms of informal user experience and formal system features. Project updates can be modeled with a language of fundamental actions. Projects themselves model their outcomes, and are made “viable” by features that connect to the motivations and ambitions of potential participants.

The key point is that the evolving design describes a sort “grammar” for the kinds of things that can be done on PlanetMath.  In the updated design, projects are something like paragraphs that combine simple sentences.  The language can be extended further, and I hope that will happen in further study.  In particular, we need to understand more about how the “sub-language” of project updates works (compare the Roadmap pattern described in this handbook).

The discussion continues: Reliving the history of mathematics as a peeragogical game?

These notes have shown one approach to the design of spaces for learning and knowledge building. Although the article has focused on mathematics learning, similar reflections would apply to designing other sorts of spaces for learning or working, for instance, to the continued development of the Peeragogy project itself! Perhaps it can contribute to the development of a new kind of institution.

Doug Breitbart: It occurred to me that you could add a learning dimension to the site that sets up the history of math as a series of problems, proofs and theorems that, although already solved, could be re-cast as if not yet solved, and framed as current challenges which visitors could take on (clearly with links to the actual solutions, and deconstruction of how they were arrived at, when the visitor decides to throw in the towel).


  1. Corneli, J. (2014).  Peer Produced Peer Learning: A Mathematics Case Study.  Ph. D. thesis.   The Open University.