Rule of 162: Questions
April 26, 2007
Jeff Lyndsay writes:
Just curious, what makes you believe channel capacity is related to a geometric structure?
I think that channel capacity, the idea that we’re built to only handle a certain size societal group, is related to geometric structure because of a feeling that groups grow in layers. Let’s say you have a founder and he or she is represented by a sphere. If you pack spheres of people around this founder as closely as possible, you can fit twelve people-spheres. This packing represents direct and data-rich relationships. This would mean the founder would have to manage twelve such relationships. People in the outer layer would have to manage five, four with the surrounding people on the first layer and one with the founder.
Certain research indicates that humans chunk memory into blocks of seven plus or minus two, and when I think of my daily deep interactions with people, it is with a number significantly less than twelve, and around seven plus or minus two. So I don’t see the founder continuously holding twelve deep relationships, rather as the population of the outer layer reaches eleven, the founder migrates to the outer-layer to form a system of twelve. The most efficient structures in creating a two-dimensional system boundary are triangles, and when you remove the center founder-sphere, you can nudge the spheres in the outer shell into an icosahedron, a shape composed of triangles.
As you pack more people onto the icosahedron you get a second layer which will eventually be composed of 42 spheres. Then a third layer with a population of 92. And a third with a population of 162, the number I isolate as the number of the average person’s channel capacity.
But for me to choose 162 I have to claim that the inner layers migrate out to complete the outer layer being built. I think this migration occurs because if you keep the inner layers you will have a layer (the group of 42) trapped inside two layers (the group of 12 and 92). The people in that layer would have to deal with twelve deep relationships on a regular basis, which I find improbable to sustain.
This does not explain the biological connection between physical structures in the brain, but I bet there are correlates in the brain’s neocortex that mimic or at least can be mapped as tetrahedral closest-packing structures. Some of the research going into simulating aspects of the neocortex seem to indicate that the brain aggregates data through semi-triangular hierarchies. Still, I have no definitive answer.
PS: Feel free to use the image I have created as you wish.