Collaborators Description

Contingency is a key component of the theory of social systems elaborated by the German sociologist Niklas Luhmann. The theory describes a vision of society as a self-reproducing (autopoietic) system of communicative interaction. It is based on the work of Talcott Parsons (sociology), Edmund Husserl (philosophy), Heinz von Foerster (cybernetics), Humberto R. Maturana/Francisco Varela (evolutionary biology), and George Spencer Brown (mathematics).

This collaboration is a common interdisciplinary work involving a sociologist and theoretical physicists. Our ultimate goal is to design a multi-agent model using the theoretical background of Luhmann’s theory and based on a mathematical formalization of a social process in which expectation-driven communication results in learning. We especially want to explore knowledge diffusion and interactive knowledge generation (innovation) in various social structures, represented essentially as dynamically evolving graphs. Primarily, we adopt a general point of view of modeling from theoretical physics and only secondarily intend to have an ``as realistic as possible’’ model. Rather than putting ``everything’’ in, the focus is to distinguish a few features in Luhmann’s theory that are relevant for our purposes, and propose a model of expectation-driven interaction that is a possibly rough first step, but is tractable either on an analytical or computational level. In particular, it is promising to use an approach based on dynamical systems theory and statistical mechanics to analyze models of social interactions, and there is some research activity in this field. On the one hand, dynamical systems theory provides mathematical tools to study the dynamical evolution of interacting agents at the ``microscopic’’ level (specifically, the detailed evolution of each agent is considered). On the other hand, st atistical physics allows in principle a description at the mesoscopic level (groups of agents) and macroscopic level (the population as a whole).

We have introduced a mathematical model portraying interaction as an alternating exchange of messages by a pair of agents where memories of the past exchanges are used to build evolving reciprocal expectations. Agent memories are formulated using a number of probability distributions : ego and alter memories, accounting for past exchanges between two agents and response disposition showing individual preferences for the agents. A selection probability for messages is calculated from the memories, along with a randomizing term allowing for invention.Agent memories are formulated using probability distributions. A selection probability for messages is calculated from the memories, along with a randomizing term allowing for invention. The resulting ``interaction sequence’’ is quite rich and complex. To analyze the properties of the model, we focused on pairs of agents. Using analytic methods and computa tional simulations, we explored the asymptotic properties of the agent memories and selection probability as the number of messages exchanged becomes very large, identifying some conditions for the existence and uniqueness of stable asymptotic solutions. Additionally, we investigated numerically the rates of change in shorter interaction sequences. In fact, the pairwise interactions between agents depend on various independent parameters, and tuning them can lead to drastic changes in the model properties. These results are a necessary foundation for handling the intended multi-agent case.

We are currently working onto larger groups of agents. In particular, we have proposed extensions for investigating how inventions can be either adopted or rejected by the community of agents. Since an agent uses its response disposition with any of the other agents, the response disposition serves as a sort of general behavioral preference, in the form of messages and transitions between messages. By tracking changes to the response disposition, we can distinguish between successful and unsuccessful. In networks of agents, this approach would allow us to investigate how various network structures might facilitate or hinder the spread of inventions.


Papers appearing in refereed journals


Conference talks withoug proceedings

  • Cessac B., ``A Luhmann based model of communication, learning and innovation’’, EXYSTENCE conference, (Vienne, 24Septembre 2004), Invited.
  • Cessac B., *``A Luhmann based model of communication, learning and innovation’’, Madeira Math Encounters - MME XXV, (Funchal, 20-27 Mars 2004), Invited.