In my last post I relied on an observer to determine whether a system is or is not complex. I have run across a potential work-around. It comes from “A Universe of Consciousness” by Edelman and Tononi. The authors, focused on a neurological explanation for consciousness, posit the necessity of viewing the human brain as a complex adaptive system. Using an interesting twist on information theory they propose measuring complexity using the system itself as the observer.

In effect they take a complex system, isolate it then split it in two . First they measure the entropy of each of the two parts,  then they measure how one part of the system affects the rest of the system and vice versa.  As they say, “If the system is isolated then from the point of view of that element, the only information available is given by the difference in the state of the rest of the system that makes a difference to the state of the element.” Their approach uses a statistical methodology to measure to what extent the entropy of the overall system is accounted for by the entropy of the subpart and vice versa. They argue high values of complexity correspond to an optimal synthesis of  functional specialization and functional integration within a system. For example, a crystal (as they point out) is functionally integrated but not complex due to a lack of functional specialization. Meaning all the molecules are tightly connected but there is zero molecular specialization, in effect, nothing happens the system is in a state of equilibrium. While a gas would be low in complexity due to a lack of integration, lots of stuff going on but what one molecule does will have very little affect on any other random molecule. In this case the system is chaotic. Now, I have to admit, I’m bothered by their use of the word “optimal” but, by effectively making the system it’s own observer they seem to have minimized the need for an external observer and potentially offered a quantitative measurement of complexity.

However, even if one accepts the above approach as a measurement of complexity I don’t think it addresses the need for an external observer to measure Emergence. My understanding is Emergence is different than complexity or rather Emergence is born of complexity. A new layer or pattern comes into being due to the complexity (is this the only criteria?) of the underlying layer. But, the ant hill (to take a typical example of emergence) is only seen as an emergent pattern if identified by the external observer. In fact, the ant hill itself, does not seem to meet the definition of complex as given above. Perhaps it could be called a “ceiling pattern” since the ant hill does not seem to give birth to any further complexity and therefore there’s no further evidence of Emergence. As I write this I find myself wondering if one might argue that there are two kinds of emergence, a “ceiling pattern” or perhaps non-complex emergence and Emergent Complexity. Perhaps the difference is, not only that Emergent Complexity gives birth to more layers of complexity but also it has the potential to be its own observer.