An informational theory of complexity
Hi there folks!
This time I am writing, because I just had an idea that I need to discuss. I was just reading the book Social Emergence: Societies as Complex Systems. I just read the first 4 pages, when I came across a paragraph that dicusses the nature of emergence and the philosopical debates around it. Yesterday, I was reading this article from Scientific American Mind: A "Complex" Theory of Consciousness.
This article in Scientific American Mind describes a theory by Giulio Tononi, called Integrated Information Theory (IIT).
IIT is based on two axiomatic pillars.
First, conscious states are highly differentiated; they are informationally very rich. You can be conscious of an uncountable number of things: you can watch your son’s piano recital, for instance; you can see the flowers in the garden outside or the Gauguin painting on the wall. Think of all the frames from all the movies you have ever seen or that have ever been filmed or that will be filmed! Each frame, each view, is a specific conscious percept.
Second, this information is highly integrated. No matter how hard you try, you cannot force yourself to see the world in black-and-white, nor can you see only the left half of your field of view and not the right. When you’re looking at your friend’s face, you can’t fail to also notice if she is crying. Whatever information you are conscious of is wholly and completely presented to your mind; it cannot be subdivided. Underlying this unity of consciousness is a multitude of causal interactions among the relevant parts of your brain.
Giulio Tononi
Tononi claims that since consciousness is information, we can use mathematical notions from information theory, such as entropy. Scientific American gives an equation that describes Φ.
Measured in bits, Φ denotes the size of the conscious repertoire associated with any network of causally interacting parts. Think of Φ as the synergy of the system. The more integrated the system is, the more synergy it has, the more conscious it is. If individual brain regions are too isolated from one another or are interconnected at random, Φ will be low. If the organism has many neurons and is richly endowed with specific connections, Φ will be high—capturing the quantity of consciousness but not the quality of any one conscious experience. (That value is generated by the informational geometry that is associated with Φ but won’t be discussed here.)
When I was reading the book Social Emergence: Societies as Complex Systems, a few thoughts came to me concerning the notion of emergence. Emergence is an elusive concept, but from what I’ve read so far, these are the first things that come to my mind that all can agree upon
1) It is produced by the effects of autonomous interacting agents, with no top-bottom guidance.
2) It must produce something that is more than the sum of its parts.
The first premise is pretty straightforward. The second however, isn’t very clear. The book for example says that the are three views. Some believe emergent phenomena have to be unpredictable, some irreducible, and some, novel. Joshua Epstein disagrees with the concept of irreducibility, since, if, for example, we executed an agent based model, we could, in theory, track the production of the phenomenon to the interactions of the agents. In this regard, he discards completely the notion of emergence. I agree that irreducibility is the wrong concept, but I can’t discard the notion of emergence, because it seems all too real to me.
I agree with the other two definitions, unpredictable (cannot be predicted given the properties of the constituents) and novel (none of the constituents holds the properties of the emergent. A society is composed of people, but a person is not a society).
More than the sum of its parts
Maybe we could formalize the phenomon of emergence through the use of information theory like in Tononi’s IIT. Maybe this theory can show the way for a quantification of the notion of emergence.
However, emergence, might really not exist, but not as Epstein put it. Emergence is a property of complex systems. Wolfram seems to support and idea that is a mixture of pancomputationalism (all the universe is a large computer and every process in it is a computation) and a belief in the purity of computational forms, pretty much like Plato’s belief it the purity of abstract forms.
Should this conjecture be right, then, the emergent phenomeon could in effect be belong to a class of scalable systems, that share the same properties in all constituents and in emergent phenomena as well.
System upon system
To explain this idea better, the behavior of individual people is dictated by their neural networks. The interaction of people, is the interaction of different neural networks among them. The same properties that are exhibited in a neural network, could be exhibited in the emergent phenomenon of society that is produced by the interaction of the neural networks among them. Of course, this is a simple example, since the interaction among people doesn’t involve neural networks in their purity, but physical objects as well (which constitute the "economy"), as well as other factors (geographical location, weather conditions, etc.).
Anyway, these are some things that just came to my mind and I had to share them with you! I hope you found this article inspiring!
