In general, individuals can be seen as optimizing a specific (very complicated) constraint function. That is, people in general desire security, health, wealth, fame, etc. and will actively work towards these goals. Now, this is interesting because not everyone is optimizing on the same constraint; however, there are a set of common traits that will on average always factor into the optimization. At the level of an individual, aspects of the constraint that do not fall within this average area are noise, and will have little or no significant impact on the overall optimization.

So we have a bunch of people essentially performing regression on some unknown but deterministic constraint. What happens when we connect them (a “social network” formed by interaction with others)?

We get a neural network, of course! Thus society is, in a very strong sense (because humans are so much better at intelligent behavior than computers are at the moment), intelligent.

Treating society as a neural net, we can extend some properties of neural nets formally to society:

1. The “Social Limit Theorem” – as more people interact and participate in a society, the society becomes capable of modeling more and more complex problems; its appearance becomes more “intelligent”. It’s merely an extension of a well-known property of a neural network, but can be rigorously proven with bias-variance decomposition. The consequence of this is overfitting and “brittle” behavior, as in a traditional neural net; the society becomes unable to adapt to new situations / patterns easily. This leads to the rather pervasive and positively deplorable social inertia that we are unfortunately exposed to on a daily basis. It is the reason an entrenched sociological philosophy, of any sort (political, economic, ethical, environmental, etc.) cannot easily change. It also explains why the ideals of one society (in effect, the pattern it has learned) do not necessarily work as well in other societies; the model does not generalize well to new problems due to the complexity of the fit.

2. Formalization of the “linking postulate” (and others among my sociological postulates) – There is a clear dependency between the overall behavior of society and the behavior of the individual nodes with high weights (influential people) because the individual variance of the optimization will be more clearly expressed as the node’s weight factors more into the overall decision of the network. This has the same type of effect on overall weight propagation as changing an influential node in an abstract neural network from linear to sigmoid would, for example.

3. If the constraint can be discovered, the overall behavior of the society could conceivably be represented as an abstract neural network (with a degree of error proportional to the overall variance from the mean, probably modeled by a normal distribution), though this may be computationally intractable due to the sheer size, number of interactions, and overall complexity of the optimization. Still, it may be possible to obtain a practical approximation.

4. This answers my previous question of how a society composed of primarily individualistic members could exhibit a fairly optimal behavior on the scale of the entire society while simultaneously fulfilling the individuals’ goals fairly well. The weights are modified as necessary for the optimization of the entire network; this optimization is performed by the individuals attempting to optimize their own goals. For example, people going to work do so to achieve financial stability and monetary gain. However, the amount of pay they receive depends on their benefit to their employer, which itself depends on the profitability of the organization, which depends on the organization’s benefit to the society. Thus, so long as society’s constraint ties local optimization to global optimization, the society will continue to progress.

There are some other consequences of this as well, but I have to get back to my dissertation.