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
Wally's World 
This is really interesting stuff, Wally! It’s funny–when I read your header, I immediately thought of the “Six Degrees from Kevin Bacon” game we used to play as kids. Then I explored your links and realized that this “Erdos-Bacon” number is a real thing! I wonder why Kevin Bacon (lol)? I, too, have never been a huge fan of math. However, I am a musician, and music relies on several underlying mathematical principles (rhythm and measures, for example). I totally agree with your point that we must “embrace our own illiteracies” in order to learn new ones, even when it’s uncomfortable to do so. Great observation!
Wow, I worried so much about this post – did I articulate well enough what I was trying to say – you got it! Thanks for your comments. I’ve since thought more about the math thing and for me it was always the “preciseness” of it that I didn’t seem to embrace. In other words, something is either right or wrong in math. Oddly enough, I’m beginning to think that preciseness is a good thing. I’m a huge fan of all kinds of music and it is probably the preciseness of rhythm and measures that makes it so enjoyable. This class sure has taken me places I never expected to go!
The first idea that came to mind was the activity on the Google class regarding connectedness. Did that activity prompt you to write this entry? I learned years ago about the degrees of separation when I taught in Roanoke. I discovered through conversations at a party how people that I just met actually knew people from other aspects of my life. This made a huge impact on me and caused me to consider what I discussed and revealed in conversation. Years later, I consider carefully what I place in print.
I’m not a huge fan of mathematics, yet found myself enthralled with elementary mathematics because of the connected way in which it was taught. The precision with higher levels left little room for my creativity.
I spent much of last spring trying to explain that Adult Literacy was not just teaching adults how to read traditionally, but to explore all of the different literacies that we encounter on a daily basis. (I’ve added quite a few new words to my vocabulary since I became an adult learner!)
Yes, I “stumbled” across the concept of six degrees in the Google search course. I wasn’t familiar with it and it fascinated me so I did a little research on it. Initially, I was turned off by the whole idea that a formula could be behind connecting people socially. However, the more I’ve contemplated the idea, the more I like it. The more you understand about how to apply the “formula”, the more precise will be your connections! Perhaps, I could learn to like math after all!
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Hmm interesting concept, six steps seems so close! You make a good point for learners, “embracing one’s illiteracies in order to gain new literacies”…similar to unlearning the old to learn the new. I see this as a mantra for life-long learners especially in regards to evolving technology. Did you discover this algorithm within Diigo or elsewhere?
Actually, the “Six Degrees of Separation” came out of the Google Power Search Course. Who knew! One of the things I love about these courses – never know where a “nugget” might be hiding! Seek and ye shall find!
You know that in Richmond, there are only 3 degrees of separation. Everybody knows everybody!
I really like your definition of the core of adult (or maybe lifelong?) education as “the intentional act of embracing one’s illiteracies in order to gain new literacies.”
Only 3 degrees of separation in Richmond, huh – that’s funny! And probably accurate!
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