Off on a non-math tangent today....
John Brockman's Edge group puts out a question each year to be answered succinctly by a multitude of cutting-edge scientists/thinkers. The resultant responses (and books) always make for interesting reading. The 2010 question was "Is the internet changing the way you think?" All (~170) sometimes redundant, but also diverse, responses are here (or you can buy the book):
http://www.edge.org/q2010/q10_index.html#responses
Among the most interesting responses to me are these (in no particular order):
Alun Anderson
Clay Shirky
David Eagleman
Jaron Lanier
Robert Sapolsky
Emanuel Derman
Stanislas Dehaene
The main Edge website is here: http://www.edge.org
And the 2011 question is already posted here: http://www.edge.org/q2011/q11_index.html
Finally, all their prior year questions can be found here: http://www.edge.org/questioncenter.html
The question of what the internet is doing to the human brain and thought is a fascinating one with a wide spectrum of varying opinions. Mathematics is one of the areas where the collaborative nature of the Web (call it "hive mind," "wisdom of large groups," "crowd-sourcing," or any number of other terms) is already proving its efficacy... of course there can also be such a thing as the "madness of crowds!"
My own view is that the intrinsic social and cognitive power that the internet wields will ultimately bulldoze over any of the potential negative effects that may come along with it. Politically, we may already be seeing the benefits in the deposition of long-entrenched autocracies, by populations (digitally) conjoined and organized for the first time in human history. Time will tell... but it is certainly an interesting era (and possibly even inflection point) to be alive, observing human civilization evolve!
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