24 April 2009

Networks Add Connections & Value

A blog by Seth Godin pointed me to Kevin Kelly's blog and caused me to think deeply and post some of his writing here.

One thing leads to another. You may refer someone to this blog post or go to KK's blog to read more. It all adds up, or multiplies and creates networks that are far stronger and more pervasive than what you or I, writing and reading on our own little screens, can even imagine.

Don't let the math talk put you off. We don't do much math on Conversations@Intersections, but it is useful in discussing relationships and networks. Who watches Numb3rs on TV? It's one of my favourites, but I think it might be because of the Charlie's curly hair!

Ready? Here we go!

Self-Reinforcing Success

From Kevin Kelly's New Rules for the New Economy: Radical Strategies for a Connected World

Networks have their own logic. When you connect all to all, curious things happen.

Mathematics says the sum value of a network increases as the square of the number of members. In other words, as the number of nodes in a network increases arithmetically, the value of the network increases exponentially.* Adding a few more members can dramatically increase the value for all members.

[*I use the vernacular meaning of "exponential" to mean "explosive compounded growth." Technically, n2 growth should be called polynomial, or even more precisely, a quadratic; a fixed exponent (2 in this case) is applied to a growing number n. True exponential growth in mathematics entails a fixed number (say 2) that has a growing exponent, n, as in 2n. The curves of some polynomials and exponentials look similar, except the exponential is even steeper; in common discourse the two are lumped together.]

This amazing boom is not hard to visualize. Take 4 acquaintances; there are 12 distinct one-to-one friendships among them. If we add a fifth friend to the group, the friendship network increases to 20 different relations; 6 friends makes 30 connections; 7 makes 42. As the number of members goes beyond 10, the total number of relationships among the friends escalates rapidly. When the number of people (n) involved is large, the total number of connections can be approximated as simply n X n, or n2. Thus a thousand members can have a million friendships.

The magic of n2 is that when you annex one more new member,
you add many more connections; you get more value than you add.

How do you see this to be true in your life? In your social or professional interactions?
We know it is true of social networking online (Facebook) and in various shared interest groups via Google or Yahoo.

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