… or Thank You to Paul Erdos, Stanley Milgrim, and Mark Granovetter
First published in February 2021, this is Gina’s rallying cry to reach out and build a community of case practice. Check out how IJIC can help you to do this here!
Gina Vega, Ph.D.
Editor-in-Chief, IJIC
How many of you know me personally? Nearly every single author of cases in IJIC has met me in person or in a virtual workshop or conference. This is quite a record, I believe, but one that has to change.
We’re all familiar with the concept of six degrees of separation, if only from the 1993 movie, but are you aware of the theoretical foundations of this idea? We can go way back in history to the origins of connectedness, but let’s begin with mid-20th century thought.
Paul Erdos, renowned prolific Hungarian mathematician, published more than 1,500 papers. (This factoid has no relevance to his contribution to this brief article, but I thought it was really interesting.) In honor of his fertile mind and copious productivity, friends created the “Erdos number,” representing the distance of his collaborators from himself. Erdos was number 0, and those who collaborated directly with him carried the number 1. Their collaborators were number 2, and so on. Approximately 200,000 mathematicians have an Erdos number, and 90% of them are lower than 8. This remarkable calculation indicated, in 2015, that 268,000 mathematicians had a median Erdos number of 5.
Stanley Milgrim applied the concept of degrees of separation ten years later in his Small World Experiment. (Do you hear that awful tune from Disneyworld when you read “Small World?”) He was interested in the idea that the US, with its lack of formal social structure, had created a system in which connectedness via social networks was accomplished through very few direct relationships. Earlier studies had shown that three degrees of separation existed across the US population, and Milgrim was determined to investigate this possibility. His Small World experiment involved sending packets from one person in, for example, Topeka KS to another individual unknown to the first in a distant city via friends of friends until the final individual was reached. The results of his experiment showed just under six contacts were necessary to make the final connection.
This led indirectly to the research done by one of my very favorite researchers, Mark Granovetter. Prof. Granovetter published the landmark study, “The Strength of Weak Ties,” in 1973 in The American Journal of American Sociology (78 (6): 1360-1380). The findings of this study have been applied to many social network situations, most familiarly to the job search conundrum. His concept of the value of strong ties and weak ties led to the further study of embeddedness in economics and complex social networks. Weak social ties, he argues, are the foundation of most of our information-carrying connections. Why? Because those with strong social ties already tend to share the same information base as we, while those with weak social ties have new information to share.
In social network theory, individual are referred to as “nodes” and connections between them are the “ties.” If we want to expand our networks, we are best off going through our primary nodes (strong ties) and connecting with their primary nodes (our weak ties), thus bringing the influence of more individuals into our own networks. The weak ties are the crucial bridge for information to be transmitted beyond one’s one-to-one network.
Which brings us to the point of this essay. In order to expand our reach and our contribution to the educational community, each of needs to reach out to our personal strong ties and through them to our weak ties or we risk becoming entirely insular and limiting our impact dramatically.
Here are two ways you can expand IJIC’s network to improve our reach and influence:
• I am asking each published author to author an additional case with a new co-author. This will automatically double our network. If you need help finding an appropriate co-author, please be in touch and I will help you find the right person to work with you.
• You can set up a community of practice in your own institution devoted to the “care and feeding” of case writers. You are likely the one with the most case writing experience in your school, so you could lead a small workshop for your colleagues and build a case writing community right there (or on your course management software until we can get back together in person). I will happily provide you with a set of guidelines, some slides, and operational suggestions to get you started – you have only to ask for the IJIC Case Writing Community packet, and we will get it out to you at no charge to our authors and at minimal cost to others. Find more information on the IJIC website!
I know we are all passionate about case writing, teaching, and research. Let’s share that passion with our weak ties and encourage them to submit their cases to IJIC so we can continue to grow and provide excellent quality materials to our teaching colleagues.
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