Fri, 19 May 2006 08:00:37 -0700 On 5/18/06, Stephen J. Turnbull <stephen@xemacs.org> wrote: > >>>>> "Ben" == Ben Tilly <btilly@gmail.com> writes: > > Ben> Given the known power laws governing the distribution of > Ben> articles of interest for researchers, it is extremely > Ben> unlikely that Metcalfe's Law applies in Tom's setting. > > Get out of your ivory tower, man! The fact that it's not interesting > to you doesn't mean that it's not interesting to somebody. Of course most of us are interesting to someone. My point was that very, very few of us are interesting to everyone . Therefore most people do not derive much value from the potential connections to most other people. > The point that Tom is making is that from the point of view of the > distribution network, documents become a homogeneous commodity since > finding "something interesting to the customer" is O(1), not O(N) > (where N is the number of documents). > > That is the assumption you need to discuss. But on the basis of that > assumption, your "known power laws" do not apply to the distribution > network. Sorry, but you've completely misunderstood my argument, probably because I did not provide it. Bradford's Law (sorry, I mixed the name up with Benford's Law) says how many interesting articles a researcher will find after searching a given number of journals. From Bradford's Law, for a large number of journals n, the number of articles of interest that can be found will be proportional to log(n). The number that a researcher will find using a traditional library search will be fixed because researchers do not actually search more than a few journals. So the actual value (measured here in number of articles found) will be between a fixed number and proportional to the log of the number of articles that are available. The actual number will depend greatly on how effective the search techniques are that the researcher can use (Google is very effective). Note that this is very, very far from being linear per person. Now one can argue many details of this example in trying to project out to the value of all articles across all researchers. For instance not all researchers are created equal, but from Lotka's law of scientific productivity, given n researchers of a minimum level of productivity, the excess from some being better than the others is about n * log(n) * that level of productivity. Conversely not all interesting articles are created equal. However Zipf's law allows us to project that if you find k articles above a threshold of interest, then the most intersting should be k times as interesting as the threshold. From which one can add another potential factor of log(n). However people have a limited amount of attention that they can give, so one can *also* use Zipf's Law to project that your total interest in the fixed number of best articles that you can read is directly proportional to how many articles there were of a threshold where you would previously have called them interesting. So across all of these factors the best estimate could be artued to n log(n) > >> Tom isn't talking about a mature network, he's talking about > >> one in its infancy. > > Ben> True, but I suspect that doesn't matter much. My point about > Ben> mature vs immature is one of size, not age. > > Ben> That is, there is a significant difference between being part > Ben> of a network of 1000 people and one of 100,000 people. But > Ben> the difference between 100,000 and 10,000,000 is not just a > Ben> big gap. So until you hit significant size, the larger > Ben> competitor has a significant advantage. After you both hit > Ben> significant size, this advantage becomes fairly small. > > No. The *absolute advantage* continues to increase as size increases. > The fact that rate of increase is *positive* is what matters at the > margin. In the contexts where your argument makes sense the absolute > advantage *decreases* at the margin. > > >> Also, you should remember that in terms of dynamics, a mature > >> industry will be increasing with the rest of the economy, ie, > >> exponentially. In an industry where costs can be expected to > >> fall while prices are rising linearly with time ... I'm sure > >> you can draw the picture, too. > > Ben> In a competitive industry, sometimes falling costs result in > Ben> falling prices and profits that might go up and might go > Ben> down... > > This industry is not going to be competitive unless its organization > changes radically. That's Tom's thesis. > > Ben> However size is not the only factor. While collaborative > Ben> content is big and will get bigger, there are limits to what > Ben> you can do with it. For instance wikipedia has a > Ben> demonstrated history of accidentally *discouraging* experts > Ben> from getting involved > > It's not an accident, it's essential (cf. Fred Brooks). I won't touch > Wikipedia in my areas of expertise. I didn't need to experience it in > that context to know what I would be getting into. And it's quite > clear that Wikipedia is mostly written by wannabes, incompletely > researched and content-biased. Often enough there's a clear political > bias, too. > > It is nonetheless extremely useful, because for any given human the > set of knowledge for which he has even wannabe status is of measure > zero. And it may be successful enough to evoke a Gresham's Law of > Encyclopedias unless somebody figures out a way to take advantage of > the medium for high quality encyclopedias. That's where Tom is going. > > However, it is that "Gresham's Law" that convinces me that copyright > will continue to have a role indefinitely. It is just wishful > thinking to believe that people in general will contribute their > expertise to *others'* areas of interest unless they are directly > compensated for not blathering about what interests them most. > > -- > Graduate School of Systems and Information Engineering University of Tsukuba > http://turnbull.sk.tsukuba.ac.jp/ Tennodai 1-1-1 Tsukuba 305-8573 JAPAN > Economics of Information Communication and Computation Systems > Experimental Economics, Microeconomic Theory, Game Theory >