Sorin Solomon

Title: Markov Webs and Distributed Causality

Classical linear logic postulates a time ordered linear chain of cause-effects links that lead to the desired outcome. Most of the revolutionary developments in the last decade have a very different structure: their outcome is the collective effect of a multitude of causes. Such processes can be designed and controlled only in terms of a logistics and causality that involves simultaneously the entire set of involved agents: if somebody is killed in a stampede the police will not be looking for the suspect that trampled first (or last) over his body. Rather, they will look for the people responsible for the emergence of the collective panic! Moreover, they will take measures to block in future events the feedback loops that such a collective causality enables. On the positive side, the collective causality allows systems to undergo spontaneously quick positive changes based on such feedback loops as it was the case with WWW, Google, portable telephones, mp3 etc.

The classical description of dynamics is formulated in terms of systems of differential equations (e.g. Newton laws). For the  description of systems with a large number of interacting bodies one usually adopts a statistical approach (e.g. Statistical Mechanics, Markov Chains, Monte Carlo Simulations) which sacrifices the details and the exact timing of the events. The excuse is that each event is determined only by events immediately preceding it rather then events in the arbitrary past. Moreover, time is often divided in slices and the various cause and effect events are assumed to take place in accordance to this arbitrary slicing. There is consequently a confusion between the needed relaxation of the linear causality and the un-waranted relaxation of the precision in the timing of various events. This is dangerous: it is often a matter of life and death to preserve the correct ordering of events and their interconnection rigorously down to the lowest time scale.?To this effect we introduced the concept of Markov Webs or Markov Nets (MN) which allows one to represent exactly the collective causal structure of events in natural systems composed of many interacting agents. The Markov Net concept preserve the causal dependence of the effects on the events collectively causing them but makes no assumption or approximation on their  timing (e.g. an event taking place currently may be influenced by events that took place at arbitrary times in the past. The Markov Net formalism preserves exactly the collective causality and timing of the events. Moreover, in a Markov Net the possibility exists that an event is affected (or even prevented)  if other events happen in the meantime between its initial causation and its expected occurrence.

At the epistemological level, we aim to contribute to the break with the Aristotelian syllogistic linear causality that attempts to pin to every effect a well-defined cause.  In our methodology, we reserve a crucial role for the interactions and the positive feedback loops that such a collective vision of causality enables. As an example, in the present study we consider three types of interactions:
top-down in which the macro-state of the system influences the individuals (e.g., the group identity, the market sentiment);
bottom-up in which the individual micro-events (e.g., individual statements, change of allegiance, bankruptcy) contribute to the macro-state and its perception;
peer-to-peer in which the particular individuals are influencing one another 'by direct contact' (e.g., word-of-mouth, contagion, payments default).

We present analytical, numerical and simulations of such models and confront them to empirical data from distributed social , economic and biological systems.