(This blog post is a collection of links and random observations. No central point here.)

We’ve often been accused of being a generation with attention deficit, a generation spoiled by Google, Wikipedia, and the general ease of availability of information. Here are a few interesting articles to get started with this:

How the Internet is changing what we think we know: In this article, Larry Sanger, co-founder and initially the chief organizer of Wikipedia, says that “Information is easy, knowledge is diffcult”. His argument is that as information becomes easier and easier to find, knowledge, with the attendant hardwork and thought it entails, seems less and less lucrative. In an age where search engines answer our queries almost instantly, we may be all the less motivated to do the hardwork needed to figure things out.

It’s important to note that Sanger isn’t an anti-Internet reactionary in any sense; Sanger has been working on Internet-based projects with varying degrees of success (including Wikipedia, and a new encyclopedia project called Citizendium). Nor does he paint a rosy picture of a past where neither information nor knowledge was easy to find fast. Sanger, however, urges people to take seriously the responsibility that comes with gathering knowledge, to develop critical facilities and thinking, and to apply these critical facilities to the consumption of online information.

Nicholas Carr’s essay “Is Google making us stupid?” is in a somewhat different vein. Here, Carr laments the fact that as people do more and more of their reading online, they lose the attention and concentration needed to read longer, more involved books and arguments. Carr frames his argument more as a possibility to be warned against, than as a certainty that has come to pass. Carr is not quite an anti-Internet reactionary either, though he might be considered somewhat closer in description to one. Needless to say, there have been many thoughtful and thoughtless critiques of this, including this one by net evangelist Kevin Kelly. (Have you already left the site in an effort to keep up with the links?)

What do mathematicians and other academics have to say about the easy information that Google and other tools offer? A common refrain among academics and librarians is that Google and Wikipedia are fine starting points, but one should always go ahead and read primary sources. In fact, Wikipedia itself has a number of pages on how to do “research” with Wikipedia, for instance, this one. For the most part, mathematicians seem to be ignoring the effects of Google and Wikipedia on the structure and nature of mathematical knowledge. In my graduate year at the University of Chicago, I’ve so far caught three mentions of Wikipedia by professors. One professor, in an assignment, warned us that a certain page on Wikipedia had a subtle error in a definition. Another professor, while writing a good reference for material he taught, winked at us saying we could anyway find it all on Wikipedia. In a third instance, a professor pointed out, during a talk, that a Wikipedia entry on a topic had a subtle but grave error.

Google, too, has received a number of side mentions. In one notable instance, Professor Alperin said that, out of curiosity as well as professional need, he once asked Google how to classify all cyclic subgroups of an Abelian group, and Google churned out a paper written in the 1930s that answered the question. Another professor pointed out that Google was a very effective calculator. On other occasions, professors who do not remember URLs or websites simply tell us to Google them.

These mentions notwithstanding, there does not seem to, in general, be any cognizance of a fundamental shift in knowledge acquisition being brought about by sources like Google and Wikipedia. However, there are some mathematicians who’re moving into the new web era, and providing short chunky stuff that can be served in web-sized spoons (i.e., that can fit the attention span of surfers). Notable in this regard are the large number of blogs and wikis started by mathematicians. For instance, there is the Noncommutative geometry blog, where some noncommutative geometers post quick information about conferences, seminars, and ideas in the subject. There’s the Dispersive Wiki, which is an attempt to put together some stuff on PDEs related to dispersion. And then there are the large number of mathematicians who’ve got into blogging, including Fields Medalists like Terence Tao and Richard Borcherds. Their blog posts range from “today, in class we did this” to “hey, I have an idea” to the more well-thought-out articles discussing pros and cons of something or how to go about doing something.

Terence Tao, a great proponent of letting the public at large get an idea of what goes on inside mathematics, has experimented with a number of ventures, ranging from a blog book (a book in blog form) to making a contribution to Scholarpedia, a site that aims to aggregate scholarly articles on a wiki. However, enthusiasm such as Tao’s is still largely unshared by the mathematical community.

The mathematical community has also made efforts to recognize the new challenges and opportunities provided by tools like Google Scholar. For instance, This AMS report talks of the problem of searching a vast database of content using Google Scholar, which has no way of responding to questions like “find an expository article on this topic suitable for a first-year graduate student”. Certain solutions and approaches have been suggested.

On the whole, however, it seems to me that the mathematical community (and the academic community at large) has not fully registered the implications of the changing dynamic of knowledge. That’s because mathematicians, like all other human beings, are trapped in things as they stand now, rather than things as they could be. This is probably best exemplified by the passive way in which mathematicians have come to accept the growing role that Google and Wikipedia have come to play, without pausing to ask, “Okay, what’s going on!” Some have transformed this passive acceptance into jumping into the fray. In the biological sciences, where funding is replete, attempts to create impressive online databases and concept collections have received more attention; for instance, there’s Wiki Professional.