It never occurred to me how math could factor into the concept of building a PLN. However, as I spent time this week exploring Diigo and building my personal “digital library” I stumbled across a concept that brought me face to face with just such an idea.
The concept of “Six Degrees of Separation”, first introduced by Frigyes Karinthy and popularized by John Guare basically proposes that every person is on average approximately six steps away from any other person in the world, so that a chain of “a friend of a friend” can be established on average to connect any two people in six steps or less. Researchers have actually established an optimal algorithm to calculate degrees of separation in social networks such as Twitter (Bakhshandeh, Samadi, Azimifar and Schaeffer, 2011).
The mathematical formula of “collaboration distance” goes like this:
“. . . two persons are linked if they are coauthors of an article. The collaboration distance with mathematician Paul Erdős is called the Erdős number. Erdős-Bacon numbers are a further extension of the same thinking. Watts and Strogatz showed that the average path length between two nodes in a random network is equal to log N / log K, where N = total nodes and K = acquaintances per node. Thus if N = 300,000,000 (90% of the US population) and K = 30 then Degrees of Separation = 19.5 / 3.4 = 5.7 and if N = 6,000,000,000 (90% of the World population) and K = 30 then Degrees of Separation = 22.5 / 3.4 = 6.6. (Assume 10% of population is too young to participate.)”
The internet has made the world smaller and there actually exists a formula behind the connectivity made possible through various digital applications. Fact is, however, the effective use of this algorithm has everything to do with one’s ability to navigate the web and appropriate the digital tools needed to make these vital connections. Thus, a type of digital literacy is needed in order to maximize the full potential of this algorithm. It is there that I find myself – fascinated by the concept of having so much opportunity available and yet challenged by a substantial lack of knowledge to fully maximize the benefit of this formula. I was never crazy about math.
This is where rubber meets the road for the adult learner – the willingness to be thwarted by the intentional act of embracing one’s illiteracies in order to gain new literacies. I must learn to cast aside frustration and be willing to press through. After all, I may only be a few clicks away from a vast network of invaluable connections.
R Bakhshandeh, M Samadi, Z Azimifar, J Schaeffer, “Degrees of Separation in Social Networks”, Fourth Annual Symposium on Combinatorial Search, 2011