Tomorrow I will give a presentation for the Mathematical Sociology group of UNAM. The title and abstract are as follows:
Mathematical approaches to exploring the social mind
The sciences of man are sharply divided over the role played by sociality. On the one hand, cognitive science tries to reduce all explanations of behavior, including human social behavior, to a single person (and often even to nothing but a single organ: their brain). On the other hand, anthropology and sociology have long insisted that most (if not all) human behavior is an irreducible product of our shared socio-cultural environment. My research aims to build a bridge between these two viewpoints. In particular, I use mathematical models as formal proofs of concept for the possibility that the individual and the social co-determine each other. In order to illustrate this possibility I will present two case studies that are represent two different scales of sociality. First, I will briefly discuss a computer model of embodied agents in which a dyadic interaction process reconfigures the internal activity of each agent such that it exhibits mathematical properties that are in principle impossible for the agents in isolation. Second, I will present some results of a mathematical model that is loosely based on the social organization of the ancient Mexican city of Teotihuacan. The model demonstrates that local social interactions between agents who selfishly optimize their own utility can consistently give rise to globally optimal social configurations even without any a priori knowledge of the problem space.