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Mathematical Digest

Short Summaries of Articles about Mathematics
in the Popular Press

"Ignorance, Knowledge, and Outcomes in a Small World," by Mark Granovetter. Science, 8 August 2003, pages 773-774.
"More than six degrees separate us," by Phillip Ball. Nature Science Update, 8 August 2003.
"With E-Mail, It's Not Easy to Navigate 6 Degrees of Separation," by KennethChang. The New York Times, 12 August2003, page 3 Section F.
"Small World After All," by Erica Klarreich. Science News, 16 August 2003,page 103.

Each article deals with an e-mail experiment conducted by Peter Dodds, RubyMuhamad, and Duncan Watts asking 60,000 people to forward messages to anacquaintance who would then forward the message to his or her acquaintance andso on, so as eventually to reach one of 18 target people. This experiment wasan electronic update of an experiment done via U.S. mail over 30 years ago. Inthe original experiment, Stanley Milgram of Harvard found that lettersoriginating in Nebraska and sent to a friend---then sent on to a friend of afriend, etc.---that did reach a Boston stockbroker, did so in an average of sixsteps: Thus the phrase "six degrees of separation." In the current study, only24,000 people started a chain of messages and of those messages only 384reached their targets. The average length of the completed chains was four.Writes Klarreich: "Although six degrees seems like a small number of steps, insocial terms it represents an enormous gulf, Strogatz says. 'With the peoplewho are two steps away from you, the friends of your friends, the connection isalready getting a little hazy...Once the number is three, you have very littlepsychological connection to these people---they're three whole universes away.Six or seven steps is unfathomable.'" Messages that were sent to acquaintanceswere more likely to reach their targets than those sent to close friends. Theresearch article for this experiment is on pages 827 through 829 of the 8August issue of Science, titled "An Experimental Study of Search inGlobal Social Networks." The researchers are launching a new experiment thatallows senders to send email messages to more than one acquaintance. Volunteersfor the experiment can sign up here.

--- Mike Breen

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