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diff --git a/posts/2017-08-07-mathematical_bazaar.org b/posts/2017-08-07-mathematical_bazaar.org new file mode 100644 index 0000000..64bf335 --- /dev/null +++ b/posts/2017-08-07-mathematical_bazaar.org @@ -0,0 +1,213 @@ +#+title: The Mathematical Bazaar + +#+date: <2017-08-07> + +In this essay I describe some problems in academia of mathematics and +propose an open source model, which I call open research in mathematics. + +This essay is a work in progress - comments and criticisms are +welcome! [fn:1] + +Before I start I should point out that + +1. Open research is /not/ open access. In fact the latter is a + prerequisite to the former. +2. I am not proposing to replace the current academic model with the + open model - I know academia works well for many people and I am + happy for them, but I think an open research community is long + overdue since the wide adoption of the World Wide Web more than two + decades ago. In fact, I fail to see why an open model can not run in + tandem with the academia, just like open source and closed source + software development coexist today. + +** problems of academia + :PROPERTIES: + :CUSTOM_ID: problems-of-academia + :END: +Open source projects are characterised by publicly available source +codes as well as open invitations for public collaborations, whereas +closed source projects do not make source codes accessible to the +public. How about mathematical academia then, is it open source or +closed source? The answer is neither. + +Compared to some other scientific disciplines, mathematics does not +require expensive equipments or resources to replicate results; compared +to programming in conventional software industry, mathematical findings +are not meant to be commercial, as credits and reputation rather than +money are the direct incentives (even though the former are commonly +used to trade for the latter). It is also a custom and common belief +that mathematical derivations and theorems shouldn't be patented. +Because of this, mathematical research is an open source activity in the +sense that proofs to new results are all available in papers, and thanks +to open access e.g. the arXiv preprint repository most of the new +mathematical knowledge is accessible for free. + +Then why, you may ask, do I claim that maths research is not open +sourced? Well, this is because 1. mathematical arguments are not easily +replicable and 2. mathematical research projects are mostly not open for +public participation. + +Compared to computer programs, mathematical arguments are not written in +an unambiguous language, and they are terse and not written in maximum +verbosity (this is especially true in research papers as journals +encourage limiting the length of submissions), so the understanding of a +proof depends on whether the reader is equipped with the right +background knowledge, and the completeness of a proof is highly +subjective. More generally speaking, computer programs are mostly +portable because all machines with the correct configurations can +understand and execute a piece of program, whereas humans are subject to +their environment, upbringings, resources etc. to have a brain ready to +comprehend a proof that interests them. (these barriers are softer than +the expensive equipments and resources in other scientific fields +mentioned before because it is all about having access to the right +information) + +On the other hand, as far as the pursuit of reputation and prestige +(which can be used to trade for the scarce resource of research +positions and grant money) goes, there is often little practical +motivation for career mathematicians to explain their results to the +public carefully. And so the weird reality of the mathematical academia +is that it is not an uncommon practice to keep trade secrets in order to +protect one's territory and maintain a monopoly. This is doable because +as long as a paper passes the opaque and sometimes political peer review +process and is accepted by a journal, it is considered work done, +accepted by the whole academic community and adds to the reputation of +the author(s). Just like in the software industry, trade secrets and +monopoly hinder the development of research as a whole, as well as +demoralise outsiders who are interested in participating in related +research. + +Apart from trade secrets and territoriality, another reason to the +nonexistence of open research community is an elitist tradition in the +mathematical academia, which goes as follows: + +- Whoever is not good at mathematics or does not possess a degree in + maths is not eligible to do research, or else they run high risks of + being labelled a crackpot. +- Mistakes made by established mathematicians are more tolerable than + those less established. +- Good mathematical writings should be deep, and expositions of + non-original results are viewed as inferior work and do not add to + (and in some cases may even damage) one's reputation. + +All these customs potentially discourage public participations in +mathematical research, and I do not see them easily go away unless an +open source community gains momentum. + +To solve the above problems, I propose a open source model of +mathematical research, which has high levels of openness and +transparency and also has some added benefits listed in the last section +of this essay. This model tries to achieve two major goals: + +- Open and public discussions and collaborations of mathematical + research projects online +- Open review to validate results, where author name, reviewer name, + comments and responses are all publicly available online. + +To this end, a Github model is fitting. Let me first describe how open +source collaboration works on Github. + +** open source collaborations on Github + :PROPERTIES: + :CUSTOM_ID: open-source-collaborations-on-github + :END: +On [[https://github.com][Github]], every project is publicly available +in a repository (we do not consider private repos). The owner can update +the project by "committing" changes, which include a message of what has +been changed, the author of the changes and a timestamp. Each project +has an issue tracker, which is basically a discussion forum about the +project, where anyone can open an issue (start a discussion), and the +owner of the project as well as the original poster of the issue can +close it if it is resolved, e.g. bug fixed, feature added, or out of the +scope of the project. Closing the issue is like ending the discussion, +except that the thread is still open to more posts for anyone +interested. People can react to each issue post, e.g. upvote, downvote, +celebration, and importantly, all the reactions are public too, so you +can find out who upvoted or downvoted your post. + +When one is interested in contributing code to a project, they fork it, +i.e. make a copy of the project, and make the changes they like in the +fork. Once they are happy with the changes, they submit a pull request +to the original project. The owner of the original project may accept or +reject the request, and they can comment on the code in the pull +request, asking for clarification, pointing out problematic part of the +code etc and the author of the pull request can respond to the comments. +Anyone, not just the owner can participate in this review process, +turning it into a public discussion. In fact, a pull request is a +special issue thread. Once the owner is happy with the pull request, +they accept it and the changes are merged into the original project. The +author of the changes will show up in the commit history of the original +project, so they get the credits. + +As an alternative to forking, if one is interested in a project but has +a different vision, or that the maintainer has stopped working on it, +they can clone it and make their own version. This is a more independent +kind of fork because there is no longer intention to contribute back to +the original project. + +Moreover, on Github there is no way to send private messages, which +forces people to interact publicly. If say you want someone to see and +reply to your comment in an issue post or pull request, you simply +mention them by =@someone=. + +** open research in mathematics + :PROPERTIES: + :CUSTOM_ID: open-research-in-mathematics + :END: +All this points to a promising direction of open research. A maths +project may have a wiki / collection of notes, the paper being written, +computer programs implementing the results etc. The issue tracker can +serve as a discussion forum about the project as well as a platform for +open review (bugs are analogous to mistakes, enhancements are possible +ways of improving the main results etc.), and anyone can make their own +version of the project, and (optionally) contribute back by making pull +requests, which will also be openly reviewed. One may want to add an +extra "review this project" functionality, so that people can comment on +the original project like they do in a pull request. This may or may not +be necessary, as anyone can make comments or point out mistakes in the +issue tracker. + +One may doubt this model due to concerns of credits because work in +progress is available to anyone. Well, since all the contributions are +trackable in project commit history and public discussions in issues and +pull request reviews, there is in fact /less/ room for cheating than the +current model in academia, where scooping can happen without any +witnesses. What we need is a platform with a good amount of trust like +arXiv, so that the open research community honours (and can not ignore) +the commit history, and the chance of mis-attribution can be reduced to +minimum. + +Compared to the academic model, open research also has the following +advantages: + +- Anyone in the world with Internet access will have a chance to + participate in research, whether they are affiliated to a university, + have the financial means to attend conferences, or are colleagues of + one of the handful experts in a specific field. +- The problem of replicating / understanding maths results will be + solved, as people help each other out. This will also remove the + burden of answering queries about one's research. For example, say one + has a project "Understanding the fancy results in [paper name]", they + write up some initial notes but get stuck understanding certain + arguments. In this case they can simply post the questions on the + issue tracker, and anyone who knows the answer, or just has a + speculation can participate in the discussion. In the end the problem + may be resolved without the authors of the paper being bothered, who + may be too busy to answer. +- Similarly, the burden of peer review can also be shifted from a few + appointed reviewers to the crowd. + +** related readings + :PROPERTIES: + :CUSTOM_ID: related-readings + :END: + +- [[http://www.catb.org/esr/writings/cathedral-bazaar/][The Cathedral + and the Bazaar by Eric Raymond]] +- [[http://michaelnielsen.org/blog/doing-science-online/][Doing sience + online by Michael Nielson]] +- [[https://gowers.wordpress.com/2009/01/27/is-massively-collaborative-mathematics-possible/][Is + massively collaborative mathematics possible? by Timothy Gowers]] + +[fn:1] Please send your comments to my email address - I am still + looking for ways to add a comment functionality to this website. |