What Is Research?

May 29, 2010

Miscellanea

Some things I’ve been reading about:

  • Concept inventories: These are tests designed to determine the extent to which people have an understanding of basic concepts in a particular area. The Wikipedia article on concept inventory provides a decent introduction. Concept inventories were introduced in physics, with the Force Concept Inventory (FCI) being used to determine people’s understanding of mechanics. Here’s the Google Scholar results for Force Concept Inventory, including this paper by Hestene, Wells, and Swackhamer that describes the detailed construction of the inventory. The force concept inventory led Eric Mazur, an experimental physicist at Harvard University, to change his style of teaching introductory physics. Here is a YouTube talk by Mazur where he describes how the concept inventory led him to change his style of teaching introductory physics courses.

  • Open notebook science: Here is the Wikipedia entry on open notebook science, replete with links to various discussions of the subject. The UsefulChem blog has plenty of discussions and links related to open notebook science. Here is Michael Nielsen’s article/blog post on the future of science, with discussions of open notebook science and related ideas.

  • Moore method: Much of inquiry-based learning (IBL) in college mathematics courses is based on the Moore method and its derivatives. The Moore method was pioneered by topologist Robert L. Moore at the University of Texas, and is often also called the Texas Method. The idea is that the instructor, instead of teaching students, gives them problems to solve on their own and listens to them as they attempt to present their solutions to their peers and the instructor. Here’s the Wikipedia article on the Moore method. Here is the Legacy of R. L. Moore project and here is the University of Texas Discovery Learning Project. There’s a three-part video series (1, 2 and 3) about the Moore method. You can also view this book about the Moore method (limited preview via Google Books). See also this Math Overflow discussion on the Moore method.

  • Cognitive load theory: Here is Sweller and Chandler’s original paper (1991) on the subject and here are the Google Scholar results on the query. Cognitive load theory attempts to look at learning in terms of the cognitive load imposed on the learner. It identifies three kinds of load: intrinsic load, which is the load that naturally arises from trying to learn, extrinsic load, which is the load that arises due to distractions and does not help with learning, and germane load, which is load that the learner takes on to get a deeper understanding and form better connections within the material. The goal of good instruction should be to assess how much intrinsic load a given learning task entails, try to minimize the extrinsic load, and use whatever extra space there is to add in germane load.

May 28, 2010

Planetmath and Mathworld losing out to Wikipedia

Filed under: Web structure,Wikipedia,Wikis — vipulnaik @ 10:59 pm
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As I’ve mentioned earlier (such as here), it has seemed to me for some time that both Planetmath and Mathworld are losing out as Internet-based mathematical references to Wikipedia. I don’t expect that there has been absolute decline in the traffic to these websites — the growth of the Internet by leaps and bounds would mean that a website has to make a fairly active effort to lose users. But I do expect that more and more of the new users who are coming in are treating Wikipedia more as a first source of information.

From the preliminary results of a recent SurveyMonkey survey: out of 29 respondents (most of them people pursuing or qualified in mathematics), 24 claimed to have used Wikipedia often, and the remaining 5 to have used it occasionally for mathematical reference information. For Planetmath, 22 people claimed to have used it occasionally, and 7 to have heard of it but not used it. For Mathworld, 5 people claimed to have used it often, 16 to have used it occasionally, 7 to have heard of it but not used it, and 1 to have never heard of it.

In response to a question on how Planetmath and Mathworld compare with Wikipedia, the nine free responses were:

  • Planetmath now loads too slowly, so I seldom use it. Even when I did use it often, I found that the articles tended either to be too incomplete, or too tailored to people who are already experts. Many Mathworld pages are still much better than many Wikipedia pages, but Wikipedia is more comprehensive.

  • planet math is slow!!! mathworld has more graphics and less maths.

  • Material is generally better presented on Mathworld, but the topics are more limited.

  • Not as much information as Wikipedia and not as well arranged

  • I usually find Wikipedia to be my first source and only go to Mathworld or Planetmath if wikipedia fails me. I guess that means Wikipedia is better.

  • Planetmath is dying, Mathworld is static.

  • I find wikipedia much more useful than Mathworld. Mathworld’s pages are very technical, which is not what I am looking for on the internet usually. Usually I am looking for someone’s nice conceptual understanding of a topic or definition (through nice examples), and Wikipedia usually has lots of these.

  • Planetmath is quite useful to find proofs. Mathworld is very specialised, but it has a few nice bits of information sometimes. They seem to both be quite stagnant compared to Wikipedia.

  • They can’t keep up. There was probably a time when PlanetMath was a better reference than Wikipedia, but it’s fading fast. I think their ownership model isn’t conducive to long term quality.

(See the responses to these and other questions here and take the survey here).

The general consensus does seem to confirm my suspicions. Why is Wikipedia gaining? Here are the broad classes of explanations:

  1. It’s just a self-reinforcing process. The more people hear about and link to Wikipedia, the more people are likely to read it, the more people are likely to edit it and improve it. But if that’s the case, why did Wikipedia ever get ahead of Mathworld and Planetmath? Two reasons: (i) its more radically open editing rules (ii) Wikipedia covers many areas other than mathematics, so people come to the site more in general. Also, since it covers many areas other than mathematics, it can better cover content straddling mathematics and other areas, such as biographies of mathematicians, and historical information that is relevant to mathematics. This creates a larger, strongly internally linked, repository of information.

  2. Planetmath’s owner-centric model (as mentioned in one of the responses) where each entry is owned by one person, does not create a conducive environment for the gradual growth and improvement of entries.

  3. The appearance of content is better on Wikipedia. Prettier symbols, faster loading, better internal links, better search. This is definitely an advantage over Planetmath, which has slow load times in the experience of many users (as indicated by the comments above) though perhaps not so much over Mathworld.

  4. Google weights Wikipedia higher (because of the larger size of the website and the fact that a lot of people link to Wikipedia). This is related to (1).

  5. The people in charge of Mathworld and Planetmath simply lost interest. Mathworld is largely run by Eric Weisstein, an employee at Wolfram, who seems to have recently been trying to integrate metadata about mathematical theorems and conjectures into Wolfram Alpha. Developing Mathworld continually to a point of excellence does not seem to have been a top priorty for Weisstein or his employer Wolfram Research (that hosts Mathworld) over the last few years. The people running Planetmath also may have become less interested in continually innovating.

Given all this, is Wikipedia the best in terms of: (i) the current product or (ii) the process of arriving at the product? While I’m far from a Wikipedia evangelist, I think that the answer to (ii) is roughly yes if you’re thinking of broad appeal. Anything which beats Wikipedia will probably do so by being more narrowly focused, but it may then not be of much interest to people outside that domain. A host of many such different niche references may together beat out Wikipedia for people who care enough to learn about a multiplicity of references. For those who just want one reference website, Wikipedia will continue to be the place of choice in the near future (i.e., the next 3-4 years at least, in my opinion).

Currently, Wikipedia is an uneasy mix of precise technical information and motivational paragraphs. It makes little use of metadata to organize its information; on the other hand, it is easy to edit and join in. The mathematics entries cannot be radically changed in a way that would make them radically different in appearance from the articles on the rest of the site. This opens up many niche possibilities, some of which are being explored:

  1. Lab notebooks, where people store a bunch of thoughts about a topic, without attempts to organize them into something very coherent. Here, good metadata and tagging conventions could allow these random lab notebook-type jottings to cohere into an easily accessible reference. This would be the mathematical version of open notebook science, a practice that is slowly spreading in some of the experimental sciences. nLab (the n-category lab) is one example of a “lab notebook” in the mathematical context. This is great for motivation, and also for understanding the minds of mathematicians and the process of mathematical reasoning.

  2. Something that focuses on a particular aspect of mathematical activity. For instance, Tricki, called the Tricks Wiki, focuses on tricks. Other references may focus on formulas, others may focus on counterexamples, yet others (such as the AIMath wiki on localization techniques and equivariant cohomology) may focus simply on providing extensive bibliographies. Somewhat more developed examples include the Dispersive Wiki and complexity zoo (actually, a computer science topic, but similar in nature to a lot of mathematics). Some may focus on exotic tricks of relevance to a particular mathematical discipline. There is some cross-over with lab notebooks, as the tricks become more and more exotic and the writing becomes more and more spontaneous and less subject to organization into an article.

  3. Highly structured content rich in metadata that is intended to provide definitions, proofs and clarify analogies/relations. Examples include the Group Properties Wiki [DISCLOSURE: I started it and am the primary contributor] which concentrates on group theory. The flip side is that the high degree of organization uses subject-specific structures and hence must be concentrated on a particular narrow subject.

There are probably many other niches waiting to be filled. And there may also be close susbstitutes for reference sites that weren’t created as references. For instance, Math Overflow, though not a reference site, may play the role of a reference site once it accumulates a huge number of questions and answers and adopts better search and specific tagging capabilities. Similarly, thirty years from now, the contents of Terry Tao’s weblog may contain a bit on virtually every mathematical topic, in the same way as Marginal Revolution have a bit on almost all basic economic topics (I say “thirty years” because economics is in many ways a smaller subject than mathematics).

May 9, 2010

Survey on math resources on the Internet

Filed under: Culture and society of research,Web structure,Wikis — vipulnaik @ 6:08 pm

I have put up a medium-length survey on the use of math resources on the Internet. The survey is a preliminary one — the results of this will be used in designing more sophisticated surveys. Take the survey here:

http://www.surveymonkey.com/s/T2CBTZJ.

You can view the survey results here (but don’t do this before taking the survey!):

http://www.surveymonkey.com/sr.aspx?sm=aaYWJUl4DF9hjvM4AqrQxhgmev4PNRiYa8MJbwhLs9w_3d.

January 14, 2010

Math overflow: further notes

Filed under: Culture and society of research,Thinking and research — vipulnaik @ 12:17 am
Tags:

I mentioned Math Overflow a while back (also see the general backgrounder on math overflow on this blog). At the time, I hadn’t joined Math Overflow or participated in it. I joined a week ago (January 6) and my user profile is here. Below are some of my observations.

Surprising similarity of questions with questions I’ve asked in the past

Looking over the group theory questions, I found that a number of questions I had asked — and taken a long time to get answers to — had been asked on Math Overflow, and had been answered within a few days. The answers given weren’t comprehensive; I added some more information based on my past investigations into the topics, but it was still remarkable that these questions, most of which aren’t well known to most people in the subject, were answered so quickly.

  • The question Are the inner automorphisms the only ones that extend to every overgroup? is a question that I first asked more than five years ago, when still an undergraduate. I struggled with the question and asked a number of group theorists, none of whom were aware of any pasy work on these problems. I later managed to solve the problem for finite groups, and then my adviser discovered, from Avinoam Mann, that the problem was tackled in papers by Paul Schupp (1987) and Martin Pettet (1990), along with the many generalizations that I had come up with (some variants of the problem seem to remain unsolved, and I am working on them). You can see my notes on the problem here and you can also see my blog post about the discovery here.

  • The question When is Aut G abelian? was a question that I had been idly curious about at one point in time. I couldn’t find the answer at the time I raised the question, but stumbled across the papers a few months later by chance (all well before Math Overflow). It’s interesting that the question was so quickly disposed of on Math Overflow. See also my notes on such groups here.

  • The question How can we formalize the naturality of certain characteristic subgroups is a more philosophical question with no real concrete answers, which I’ve considered for a long time too.

  • The question Balancing problem in combinatorics that I had, based on a generalization of an Olympiad question I had seen, turns out to be part of something called rainbow Ramsey theory, as the answer suggests.

Two things stand out: (i) all these questions are questions whose answers are not well-known (the people I asked didn’t know the answers offhand) but are questions that many people do ask (ii) On Math Overflow, they were dealt with quickly.

I think the situation is similar in many other established areas of mathematics — the answers are out there, but they are not well-known, probably because these problems are not “important” in the sense of being parts of bigger results. But they are questions that may naturally occur as minor curiosities to people studying the subject. These curiosities may either go unanswered or may get answered — but the answers do not spread to the level of becoming folk knowledge or standard textbook knowledge, because they aren’t foundational for any (as yet discovered) bigger results.

Math Overflow now provides a place to store such questions and their answers — thus, next time you have one of these questions, a bit of searching on Math Overflow would yield the question and the answers provided and stored for posterity. Apart from the questions I had thought of, consider this one that somebody thought up and turned out to have been considered in multiple papers: When is A isomorphic to A^3?.

The situation is probably different for areas where new, cutting-edge questions are being asked — i.e., areas where the questions are charting “new” territory and are helping build the understanding of participants. Some people told me that this is likely to be the situation with areas such as topological quantum field theory or higher category theory.

Skills needed and developed

So what skills are needed to participate in Math Overflow, and what skills get developed? In order to answer questions quickly, a combination of good background knowledge of mathematics and the ability to search ArXiV, Mathscinet, JSTOR, Google Scholar, and other resources seems necessary. In order to ask questions, it seems that a combination of a lot of background knowledge and a natural curiosity — of the bent needed for research, is what is needed.

Pros and cons of posting on Math Overflow

The obvious pro seems to be that a lot of people read your question. The sheer number of readers compensates for the fact that most people, even experts in the area, may not immediately know the answer. Because of the larger number of people, it is likely that at least a few will either have come across something similar or will be able to locate something similar or will be able to solve the question because he/she gets curious about it. It was pretty exhilerating when a minor question that I didn’t feel equipped or curious enough to struggle with was answered by somebody who came up with a construction in a few hours (see collection of subsets closed under union and intersection), or when a question I had about elementary equivalence of symmetric groups was answered within a few days (see elementary equivalence of infinitary symmetric groups).

The potential con could be that people may be tempted to ask a question on Math Overflow without thinking too much about it. This probably does happen but I don’t think it is a major problem. First, the general quality of participants is quite high, so even if people ask questions without thinking a lot about them, chances are there is something interesting and nontrivial about the question — because if there weren’t, people of the profile contributing would have been able to solve it even without a lot of thought. Further, even if a question is a good exercise for a person specializing in that subject — so he/she should struggle with it rather than ask others, it may be good for a specialist in another subject to simply ask.

The voting (up/down) system and the system of closing questions that are either duplicates or not suitable for Math Overflow for other reasons (such as undergraduate homework problem), combined with a reputation system for users linked to the votes they receive, seems to be a good way of maintaining the quality of the questions.

A revision of some of my earlier thoughts

In a blog post almost a year ago titled On new modes of mathematical collaboration, I had expressed some concern regarding the potential conflict between the community and activity that is needed to have frequently updated, regularly visited content, and the idea of a steady, time-independent knowledge base that could be used as a reference. mathematics blogs, with regular postings and comments, and polymath projects, which involve collaborative mathematical problem-solving, are examples of the former. Mathematics references such as Mathworld, Planetmath, the mathematics parts of Wikipedia, The Springer Encyclopedia of mathematics, ncatlab, Tricki, and the Subject Wikis (my idea) are some examples of the latter, to varying degrees and in different ways. The former generate more activity, the latter seem to have greater potential for timeless content.

Math Overflow has the features of both, which is what makes it interesting. It has a lot of activity — new questions posted daily, new answers posted to questions, and so on. The activity, combined with the points system for reputation, can be addictive. But at the same time, a good system of classification and search, along with a wide participatory net, makes it a useful reference. I’m inclined to think of its reference value as greater than what I thought of at first, largely because of the significant overlap in questions that different people have, as I anecdotally describe above.

Math Overflow stores both mathematical data — questions and their answers, as well as metadata — what kind of questions do people like to ask, what kind of answers are considered good enough for open-ended questions, how quickly people arrive at answers, what kind of questions are popular, how do mathematicians think about problems, etc. This metadata has its own value, and the reason Math Overflow is able to successfully collate such metadata is because it has managed to attract high-quality participants as well as get a number of participants who are very regular contributors. Both the data and the metadata could be useful to future researchers, teachers, and people designing resources whether of the community participation type or the reference type.

On the other hand…

On the other hand, Math Overflow is not the answer to all problems, particularly the ones for which it was not built. Currently, answers to questions on Math Overflow are broadly of the following three types (or mixtures thereof): (i) an actual solution or outline of a solution, when it is either a short solution arrived at by the person posting or an otherwise well-known short answer (ii) a link to one or more pages in a short online reference (such as an entry on Wikipedia or any of the other reference resources mentioned above) (iii) a link or reference to papers that address that or similar questions.

For some questions, the links go to blog posts or other Math Overflow discussions, which can be thought of as somewhere in between (ii) and (iii).

With (i), the answer is clearly and directly presented, and the potential downside is that that short answer may not provide a general framework or context of related results and terminology. With (ii), a little hunting and reconstruction may need to be done to answer the question as originally posed, but the reference resource (if a nice one) gives a lot of related useful information. (iii) alone (i.e., without being supplemented by (i) or (ii)) is, in some sense, the “worst”, in that reading a paper (particularly if it is an original research paper in a journal) may take a lot of investment for a simple question.

In my ideal world, the answer would be either (i) + (ii), or (ii) (with one of the links in (ii) directly answering the question), plus (iii) for additional reference and in-depth reading. But there is a general paucity of the kind of in-depth material in online reference resources that would make the answer to typical Math Overflow questions by adequately dealt with by pointing to online references. So, I do think that an improvement in online reference resources can complement Math Overflow by providing more linkable and quickly readable material in answer to the kinds of questions asked.

October 31, 2009

Math websites falling into disuse?

Filed under: Uncategorized — vipulnaik @ 3:06 pm
Tags: ,

Since I recently blogged about Math Overflow website, I’ve been wondering what happened to various other math websites that once looked promising, and how they’re faring. Some of them seem to be going strong, but none of them seem to have been exploding in popularity.

Tricki

I blogged twice about Tricki, the Tricks Wiki, which went live in April 2009 (see the annoucement by Tim Gowers). Tricki held a lot of promise. Of late, the enthusiasm seems to have slowed down, though this might be a temporary phenomenon. The most recently created article and the most recent comments appear to be two weeks old as of today (October 27, 2009). According to Alexa data, the site has a rank of 1,200,000+ worldwide and about 550,000-600,000 in the United States. For comparison, subwiki.org, which I run, has Alexa data showing a site rank of 500,000-550,000 in the world and 150,000-200,000 in the United States, while Math Overflow has Alexa data showing a rank of 350,000 worldwide and about 60,000 in the United States (the numbers you see clicking on the links may be different if you don’t view this post within a few hours of my writing it).

Tricki also hasn’t been mentioned on Gowers’ blog since June 25, 2009 and on Terence Tao’s blog since August 2009.

Is the Tricki falling into disuse? Clearly, the initial spate of interst seems to have subsided, but it might well regain a slower and steadier momentum in some time.

Planetmath

I remember a time when Wikipedia had much less mathematical content than planetmath, which was one of the first places to check mathematics on the Internet. Planetmath appears to be going strong, though not as strong as before. While their message forum seems reasonably active, their latest addition was about a week ago, and they seem to be getting somewhere between 0 and 2 new articles in a day, and around the same number of revisions a day. Not exactly dead, but not bubbling with life. Their Alexa data indicates fairly steady performance with a traffic rank of around 130,000 over the last six months, but a decline over a longer timeframe — setting the drop-down parameter to “max” below the chart shows that their traffic rank and daily pageviews have been following over the longer run. Why? Decline in quality? Probably not — it’s more likely that people are increasingly using Wikipedia.

October 27, 2009

Are textbooks getting too expensive?

Filed under: Uncategorized — vipulnaik @ 11:26 pm

I recently came across a post by John Baez on the n-category cafe titled Cheaper Online Textbooks?. Baez’s post has a number of interesting links: a piece on “Affordable Higher Education” by CALPIRG, a piece on the legislation based on this report by Capital Campus News, an article in the Christan Science Monitor on the rising cost of textbooks, and a blog post in the Chronicle of Higher Education on an e-textbook program. So, reading about all these posts, I began to wonder: are textbooks getting too expensive? And should anything be “done” about it?

Are textbook prices soaring?

So I decided to look at the range of calculus books. The general impression from the things I read seemed to be that it would be hard to get a decent textbook for under $100. So, I went and typed calculus on Amazon, and looked at the first page of search results. Among these search results was Calculus for Dummies ($12.99), Forgotten Calculus ($11.53), Calculus Made Easy ($26.95), Schaum’s Outline of Calculus ($12.89), and The Complete Idiot’s Guide to Calculus ($12.89). Most of these books would seem reasonable for a low-level introductory semester or two quarters in calculus — admittedly, they may not be suitable for all calculus courses, but if price really is a primary consideration, it isn’t as if there are no options. There is also a wikibook on Calculus and an old public domain book on calculus. If you want somewhat more advanced stuff for free, you can try MIT’s OpenCourseWare course on single variable course, which includes video lectures, their course on calculus with applications, and their course on multivariable calculus.

Okay, so perhaps calculus is a bad example? Well, I decided to pick point set topology. The standard book for this is the second edition of Munkres’ book, which I think is one of the best, and it costs $107.73 on Amazon. But searching for topology on Amazon gives a number of other considerably cheaper books, such as Mendelson ($7.88), Gamelin and Greene ($10.17), Springer Undergraduate Math Series book by Crossley ($23.40), Schaum’s Outline of General Topology ($12.89), among many others. None of them seem as good as Munkres, but they all cover the basic material — and reasonably well, it seems.

Of course, I have picked on calculus and topology, both topics that are more than fifty years old, and where most of the material that should be included in an elementary textbook is widely known. In other words, the field for writing books is wide open. No publisher or author has significant scarcity power. When we are looking at exotic topics such as the theory of locally finite groups, then yes, you probably wouldn’t find cheap textbooks. But most undergraduate-level textbooks would likely be of the level of calculus or topology texts, and not exotic texts on locally finite groups.

Why do instructors choose expensive textbooks when cheaper alternatives exist?

Why do instructors choose $100+ calculus textbooks or Munkres’ topology textbook when there are so many cheaper books available on the market? One explanation, pointed out in a comment to Baez’s post, is the “moral hazard” explanation. This states that instructors do not need to bear the costs of buying the textbooks, so they just prescribe the “best” textbook based on their personal criteria rather than taking the price into consideration.
(more…)

October 26, 2009

Polymath again

Filed under: Culture and society of research — vipulnaik @ 10:42 pm
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Timothy Gowers and Michael Nielsen have written an article for Nature magazine about the polymath project (I blogged about this here and here).

In the meantime, Terence Tao started a polymath blog here, where he initiated four discussion threads (1, 2, 3 and 4) on deterministic ways to find primes (I’m not quite sure how that’s proceeding — the last post was on August 28, 2009). (UPDATE: A new post (thread 5) was put up shortly after I published my blog post).

Around the same time, Gil Kalai started a polymath on the polynomial Hirsch conjecture (1, 2, 3, 4 and 5).

Also, some general discussion posts on polymath projects: by Tim Gowers and by Terence Tao.

It remains to be seen whether any of these projects are able to reach successful conclusions or make substantial inroads into the problem. If there is another success for a polymath project, then that would be a major booster to the idea of polymath projects. Otherwise, it might raise the question of whether the unexpected degree of success of the first polymath project led by Gowers (which aimed for, and got, an elementary proof of the density Hales-Jewett theorem) was an anomaly.

Math overflow

Filed under: Uncategorized — vipulnaik @ 10:26 pm
Tags:

In recent times, the Math Overflow website has been getting a lot of “press”, which is to say, it has been mentioned in some highly prominent math blogs. It was reviewed in Secret Blogging Seminar by Scott Morrison, who is also involved with Math Overflow, and it was mentioned by quomodocumque, Timothy Gowers, Terence Tao, the n-category cafe and others.

Math Overflow is a website where people can ask math-related questions (the questions should be of interest to people at the level of Ph.D. student or higher), answer the questions, and rate the answers. It uses the Stack Exchange software, which is used for many other websites, such as Stack Overflow. Funding for the website is being provided by Ravi Vakil of Stanford University, and it has a bunch of moderators — but anybody who earns enough points through participation can rise to the status of moderator. For more information, see the Math Overflow FAQ.

Participation on the website has been increasing rapidly since the first post (September 28). Here’s the Alexa data, which seem to indicate that usage has been growing (Alexa is not very reliable for low-volume sites, since it uses a small sample of users and most Math Overflow users may not be using Alexa’s toolbar).

The software and site layout seem well-designed to encourage participation. The long-term performance seems unclear, since a lot depends on how effectively the site is able to allow users to fruitfully explore past questions and answers and discover things similar to what interests them. But, as of now, it has a bunch of interesting questions, and seems to have reached the ears of a lot of people who’re interested in asking good questions and giving good answers.

August 9, 2009

Collaborative mathematics, etc.

Filed under: polymath — vipulnaik @ 12:51 am

UPDATE: See the polymath project backgrounder for the latest information.

It’s been some time since I last wrote about the polymath project (see this, this for past coverage), and an even longer time since I wrote an extremely lengthy blog post about Michael Nielsen’s ideas about collaborative science.

The first polymath project, polymath1, was about the density Hales-Jewett theorem. This was declared a success, since the original problem was solved within about a month, though the writing up of the paper is still proceeding. The problem for the project was proposed by Timothy Gowers.

Terry Tao (WordPress blog) has now started a polymath blog discussing possible open problems for the polymath project, strategies for how to organize the problem-selection and problem-solving process, and other issues related to writing up final solutions and sharing of credit.

In this blog post, Jon Udell reflects on how the introduction of LaTeX typesetting into wordpress was a positive factor in getting talented mathematicians like Terence Tao and Timothy Gowers into the blogosphere, and leading to innovative user projects such as the polymath project. Udell notes that introducing existing typesetting solutions into new contexts such as Internet blogging software can have profound positive effects. (more…)

July 29, 2009

Information costs and open access

Filed under: Uncategorized — vipulnaik @ 4:59 pm
Tags: , ,

In recent years, there has been a growing trend towards “open access” among librarians and academics. For instance, the University of Michigan recently held an Open Access Week, where they describe open access as:

free, permanent, full-text, online access to peer-reviewed scientific and scholarly material.

In an earlier blog post, I discussed some issues related to open access. Here, I attempt to look at the matter more comprehensively.

Rationales for open access

There are many rationales for open access. The simplest rationale is that open access means reduced cost of access to information, which allows more people to use the same research. Since the marginal cost of making research available via the Internet to more people is near zero, it makes sense from the point of view of efficiency to price access by yet another person to the research at zero.

Another rationale is a more romantic one: making scientific and scholarly publishing available openly allowsfor a free flow of ideas and a grander “conversation”. Support for this rationale also indicates that open access should be more than just free (in the sense of zero cost) access to materials, but also a license that permits liberal reuse of research materials in new contexts. Academia already has strong traditions of quoting from, linking to, and building upon, past work, but this form of open access seeks to provide a legal framework that explicitly specifies reuse rights that go beyond the traditional copyright framework of countries such as the United States. An example of such permissive licensing is the Creative Commons licenses.

As shorthand for these two rationales, I shall use cost rationale and conversation rationale.

Open access policies/mandates

One of the major problems the open access movement has faced so far is getting people to publish papers in open access journals. As long as the best papers continue to be published in closed-access journals, academics who want to read these journals will pressure their university libraries to subscribe to these journals, even when the journals overcharge. Thus, librarians are unable to push open-access terms on publishers. (more…)

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