Have you ever been in a group, and wondered why that group never grows beyond a certain limit?  It begs the question, ‘How many persons can be in a group before a conversation in which everyone participates becomes nearly impossible?’

Suppose you and I have a conversation.  Our communication is bidirectional: you have an idea, and I have a response; I have an idea, and you have a response, and so on.  I believe this is referred to as a channel of communication.

Now suppose Phil joins our conversation: you have an idea, Phil has a response, and I have a response; Phil has an idea, I have a response, and you have a response; I have an idea, you have a response, and Phil has a response, etc.

You have a channel of communication with me, a channel with Phil, and Phil has a channel with me; three channels of communication.

Suppose Gordon joins the three of us.  With four of us, you have a channel of communication with Phil, a channel with Gordon, and a channel with me (3).  Phil has a channel with Gordon and a channel with me (2).  And finally Gordon has a channel with me (1).  That is, with two people there is one channel of communication; with three there are three, and with four there are six.

What we are doing here is finding the number of combinations of N persons taken 2 at a time.  There is a formula for this:

N! / [ 2 * (N-2)] = N(N-1) / 2

This is a quadratic equation, which of course is nonlinear.  With eight people in a group, there are 28 channels of communication, or 4.5 times as many as there are with four.

In other words, we need to be very sensitive to the length of our conversational “bursts” as the size of our group grows.  With two persons in a one hour conversation, they could each talk for four fifteen minute bursts and still complete an entire conversational cycle (you have an idea, I have a response; I have an idea, you have a response).  With eight in a group, that maximal burst time is reduced to thirty seconds.  With twelve persons, that time becomes fourteen seconds.