Everything is not connected Kevin Bacon 6 degreesEverything is not connected, thankfully. One thing I learned from studying network theory with some of the most remarkable people in the field was that: (1) not only is everything not connected but also (2) we wouldn't actually want everything to be connected.

A complete lattice where everything is connected is not something nature produces very often, if ever. For example, if all of our neurons were connected to all of our other neurons (1:1) we would all quickly go insane because the feedback would be overwhelming. We wouldn't want everything to be connected. Small world networks (the type of networks we see in the 6 degrees of Kevin Bacon game) are another example—in these networks, it is as important to understand how they are not connected as how they are. In fact, the very idea of "6 degrees" should indicate that everything is not connected to everything else, because it requires up to 6 "hops" to get from one node to another in the network. In this sense, there is a path from one node to another, but they are not literally connected. And, these small-world networks are special kinds of networks. There are networks where nodes are not connected by a path, for various reasons. In analyzing terrorism networks, we want to understand who is connected and who is not. In the hit show Survivor, to outplay, outwit, and outlast you must understand who is allied and who is not. These are just a few examples of many.

So, nature connects but it also does not connect. This is Distinctions (D) rule (is/is not) and Relationships (R) rule (action/reaction) combining to create what is and is not connected. D-rule asks what is and what is not? R-rule connects. D + R asks what is and is not connected.

Not only does nature not connect things, systems are more robust because of these non-connections. The robustness, resiliency, and complexity of a network is built as much on how it is not connected as how it is!  So next time you are trying to understand a system, ask yourself, "how are things connected?" And also be sure to ask yourself, "How are things not connected?"

You may also want to read why relationships alone are not enough.