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diff --git a/posts/2017-08-07-mathematical_bazaar.md b/posts/2017-08-07-mathematical_bazaar.md deleted file mode 100644 index 00a8724..0000000 --- a/posts/2017-08-07-mathematical_bazaar.md +++ /dev/null @@ -1,208 +0,0 @@ ---- -template: oldpost -title: The Mathematical Bazaar -date: 2017-08-07 -comments: true -archive: false ---- - -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! -[^feedback] - -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 --------------------- - -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 ------------------------------------- - -On [Github](https://github.com), 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 ----------------------------- - -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 ----------------- - -- [The Cathedral and the Bazaar by Eric Raymond](http://www.catb.org/esr/writings/cathedral-bazaar/) -- [Doing sience online by Michael Nielson](http://michaelnielsen.org/blog/doing-science-online/) -- [Is massively collaborative mathematics possible? by Timothy Gowers](https://gowers.wordpress.com/2009/01/27/is-massively-collaborative-mathematics-possible/) - -[^feedback]: Please send your comments to my email address - I am still looking for ways to add a comment functionality to this website. |