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| From the Recurring Patterns of Complex Systems Department. Posted on 01/28/2002. |
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At the retreat I went to the weekend before last, we were each asked to offer a word or small phrase that held special meaning for us. I'll save my word for a later post, but I was particularly intrigued by Clay Shirky's -- "small-world". Specifically, Clay expressed interest in the "small-world phenomenon," which probably has it's most popular expression in the notion of "six degrees of separation" and "Kevin Bacon is the center of the universe."I've learned to pay attention to what Clay calls out as important, and so I dug around the Web a bit for information on small-world.A good place to start is "Kevin Bacon, the Small-World, and Why It All Matters". It points out that though the small-world phenomenon began as a way to think of social networks, the essential structure of the network has been found in the ways that neurons interconnect, and in the power grid of the Western United States. Another good intro is "From Muhammad Ali to Grandma Rose".There's been research suggesting that the Web exhibits small-world traits.Those not afraid of math can enjoy, "The Small-world Phenomenon, An Algorithmic Perspective." The author's home page has links to a number of other tasty-looking (though quite wonky) papers.The sociology department at Columbia is conducting a Small World experiment, whose site includes the essay, "Could It Be A Big World After All?", that calls into question the assumptions of small-world social networks (which is stimulating Columbia's research).
8 comments so far. Add a comment.
Previous entry: "Heading Into the Heart of the Beast."
Next entry: "...Boxes...boxes....boxes everywhere!"
Comments:
COMMENT #1
Malcolm Gladwell's book The Tipping Point also discusses the small-world phenomenon and particularly the role of "connectors"--people who know lots of other people--in spreading memes.
Posted by Gene @ 01/29/2002 12:11 PM PST [link to this comment]
COMMENT #2
At the last BAYCHI mtg, this guy at HP Labs talked about large-scale Internet phenomena that one might expect to be chaotic/random, but turn out to be surprisingly predictable. http://www.hpl.hp.com/shl/projects/internetEcology/One example he (and a research associate) discovered was that every website in the world is on average 4.28 clicks from any other site on the Internet (doesn't mean you know how to get from any site X to any site Y, but that it's possible).
http://www.hpl.hp.com/shl/papers/smallworld/Here's the guy, Bernardo Huberman:
http://www.hpl.hp.com/shl/people/huberman/index_past.htmlHis book, The Laws of the Web: Patterns in the Ecology of Information:
http://mitpress.mit.edu/catalog/item/default.asp?sid=79F658D2-4F1C-4DF2-AEF2-E0BD15D7B256&ttype=2&tid=8498His section of HP Labs (Information Dynamics):
http://www.hpl.hp.com/shl/It's a small world after all.
Posted by ct @ 01/29/2002 01:21 PM PST [link to this comment]
COMMENT #3
The Bacon game and The Tipping Point are fascinating, as is the fact that I just found out that my sister-in-law's sister-in-law's cousin is the whining wife of Enron's Kenneth Lay.
Posted by bk @ 01/30/2002 02:22 PM PST [link to this comment]
COMMENT #4
Now for something completely different....History of the Small-world Problem
Could It Be a Big World After All?
What the Milgram Papers in the Yale Archives Reveal About the Original Small World Study
Judith Kleinfeld
Professor of Psychology
University of Alaska Fairbanks
October 2, 2000
http://smallworld.sociology.columbia.edu/history.html"On the basis of evidence in the Milgram papers on the small world study, located in the Yale archives, I raise questions about Milgram's famous finding that we live in a "small world" with six degrees of separation. A renaissance of scientific interest has occurred in the "small world problem" due to a mathematical demonstration of how random connectors in a network can create a small world. Psychological research is needed to examine the empirical realities and why people have strong emotional needs to believe we live in a small, small world. An explosion of interest in Stanley Milgram's "Small World Problem" is occurring outside the field of psychology. The stimulus is a 1998 paper in Nature which offers an intriguing mathematical explanation of how the "small world" phenomenon can be explained based on the presence of random connectors in a network (Watts & Strogatz, 1998). This fascinating mathematical demonstration, based on graph theory, is supported in the Nature article by only one empirical example from the social world: Calling two actors "connected" if they had ever been in a film together, Watts and Strogatz found that 225,000 film actors listed in the Internet Movie Database as of April, 1997 were separated from each other by only four steps. The example is intriguing and may well be a good analogy for certain other occupational networks, such as scientists or corporate businesspeople. Film actors, who shift social worlds with each film they make, however, are not a good analogy for the classic formulation of the small world problem: To what extent are people anywhere in the world connected? This problem includes illiterate farmers in rural India as well as corporate executives or teenage technophiles."
Posted by Smiling Jack @ 02/02/2002 10:27 AM PST [link to this comment]
COMMENT #5
Steve Strogatz, also at Cornell, has done some work on the small-world phenomenon in other contexts (beyond social networks). I went to grad school there and knew Jon Kleinberg (mentioned above) and met Strogatz. Interestingly, Kleinberg is now involved in a project I'm working on completely unrelated to what I did at Cornell. Perhaps there is something to this small-world conjecture, after all. Heh.
Posted by Medley @ 02/07/2002 05:32 AM PST [link to this comment]
COMMENT #6
I am interested how small world theory can be applied to family genealogy,particlarly around racially mixing of different cultures e.g. during slavery and colonisation in the British Empire. The question whether small world theory mean that ablack British person can related to a republican senator in Arizona or some from India can by six degrees knows George Bush.I welcome any suggestions related articles/websites
Posted by patrick vernon @ 04/13/2002 03:26 AM PST [link to this comment]
COMMENT #7
I am interested how small world theory can be applied to family genealogy,particlarly around racially mixing of different cultures e.g. during slavery and colonisation in the British Empire. The question whether small world theory mean that ablack British person can related to a republican senator in Arizona or some from India can by six degrees knows George Bush.I welcome any suggestions related articles/websites
Posted by patrick vernon @ 04/13/2002 03:26 AM PST [link to this comment]
COMMENT #8
I find this topic very interesting. I am doing a speech on it in class and am very happy to find all of these links to it. Thanks for your work!
Posted by Ashton Pierce @ 02/23/2003 04:49 PM PST [link to this comment]
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