Links

BBC News - http://news.bbc.co.uk/2/hi/programmes/more_or_less/5176698.stm

Judith Kleinfeld’s website - http://www.judithkleinfeld.com/

After hearing about the small-world phenomenon and six degrees of separation, it seemed appropriate to search for recent attempts to duplicate Stanley Milgram’s famous experiment from 1967. Some experiments mentioned in lecture today, such as the e-mail experiment by Dodds, Muhammed, and Watts, came up multiple times in a Google search. An experiment in 2008 from Microsoft Corporation seems to be the most recent attempt to study six degrees of separation on a large scale. With the many links supporting six degrees of separation, I expected a relatively equal number of links to pages attempting to negate or disprove the idea, but one name continued to show up, Judith Kleinfeld.

Judith Kleinfeld, a professor of Psychology at the University of Alaska Fairbanks, published articles and papers on her personal website discussing the possibility of six degrees of separation turning out to be an academic myth. She discusses problems with statistically significant evidence in Milgram’s papers, and further develops how these experiments need to be looked at from a psychological perspective, not just mathematical modeling. Although these articles were published in 2002, Kleinfeld describes people need to view the small-world phenomenon critically. From the psychological perspective, she hopes to study how race and social groups create real barriers to six degrees of separation along with the noticeable wealth barrier.

After reading Kleinfeld’s articles, I agree a psychological perspective may help broaden the research done by mathematics focused scientists, but Milgram’s research cannot go unnoticed, even with its relatively low statistical relevance. His research popularized the study of human networks and connectivity, and as the world becomes more connected every day, the research done by those after him holds more significance. Even if six-degrees of separation proves to be a myth now, the growth of communications technology inherently makes connectivity a function of time. As long as basic communication devices continue to drop in price, and global connectivity expands, the viability of six-degrees of separation (or possibly less) can rise.

By design, Milgram’s experiment allows for human error by all the participants involved. Given n total starters, and assuming i starters have some degree of separation from the specific person, then i starters (as well as those along the path chosen) have an optimum node choice leading to fewest degrees of separation, and n-i starters have no paths of connectivity to the person. In Milgram’s experiment, any individual (starters or others along a path) could have chosen a sub-optimum node, leading to excess degrees of separation for the original optimal path and a higher median for the entire experiment. The letters which didn’t get to the specific individual include the n-i starters with no connectivity plus the t letters thrown away on sub/optimal paths. If i letters reach the specific individual on optimum (read fewest degrees of separation) paths, then the only way for the median degree of separation to be greater than 6 (for i starters based off of Milgram’s experiment) is if the t letters originally thrown away now produce a median degree of separation greater than 6 along their optimum paths.

Given improved computer technology and research capabilities, the concept of Milgram’s experiment can be reapplied to any group of individuals without having them interact at all. By storing personal data given by each individual about who they have relationships with, a computer can select optimum paths connecting any individual to any other or show no connectivity between any two people. A downside to this concept comes from obtaining all of the information needed to create a real social network and possibly storing the information given the size of the network being analyzed. As technology improves, the possibility of running this experiment seems more viable.