“How can Mathematics Contribute to Social Sciences?”

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Time: 11 a.m - March 2th, 2006

Place: room “Seminario I” Dipartimento di Matematica

Program

11.30 - 12.30

Magnus Enquist, Stockholm University

“Cultural Evolution”

Human culture is cumulative, which means that beliefs, art, technology, society etc. are results of many generations of cultural change. In light of biological evolution, the rise of human culture is very rapid and the capacity for cumulative culture gives mankind a unique potential to change and improve life conditions, but also to impoverish and even ruin human existence. These observations offers several unsolved scientific puzzles. The scientific progress within this are of research may have been hampered by the lack of valid mathematical models. In my presentation I will discuss this.

12.30 - 13.30

Vittorio Capecchi, Università di Bologna

“Quality and Quantity”

15.00 - 16.00

Stefano Ghirlanda, Università di Bologna

“Models of cumulative cultural evolution”

I show some simple mathematical models of cultural evolution that analyze what is required for culture to accumulate over generations. Most theory of cultural evolution focuses on how culture is transmitted between individuals, but the models suggest that the role of individual creativity may be more important than usually acknowledged. Creativity is the only factor that can increase culture, because cultural transmission cannot, on its own, generate new culture. The models further suggest that accelerating accumulation of culture, often seen in prehistorical and historical records, can only occur if creativity is positively influenced by culture. Considering the origin of human culture, the models suggest that an increase in creativity may have been the first step toward human culture, because in a population of creative individuals there may be enough non-genetic information to favor the evolution of cultural transmission. Perhaps cumulative cultural evolution is rare in nature because other species have not reached a level of creativity as high as humans.

16.00 - 17.00

Letizia Bertotti, Università di Palermo

“Conservation Laws and Asymptotic Behavior of a Model of Social Dynamics”

A conservative social dynamics model is developed within a discrete kinetic framework for active particles. The model concerns a society in which individuals, distinguished by a scalar variable (the activity) which expresses their social state, undergo competitive and/or cooperative interactions. The evolution of the discrete probability distribution over the social state is described by a system of nonlinear differential equations. The asymptotic trend of their solutions is investigated. Existence, stability and attractivity of certain equilibria are proved.

17.00 - 18.00

Pierluigi Contucci, Università di Bologna

“Statistical Mechanics and Social Sciences: a Model for Immigration”

Using the methods of equilibrium statistical mechanics we introduce a model for cultural interaction between two different social groups. We study the average quantities before and after the interaction takes place and their behaviour in the parameter space.