Exploring mechanisms for closures

Exploring the mechanisms that allowed the physical formation of the abstract closures that define the operator theory

Gerard Jagers op Akkerhuis (ECCO seminar, 13 Mai 2011)

The talk will focus on the mechanisms behind closures. Yet, and even though this may sound strange, the closures in the operator theory do in principle not require a functional justification. The reason is that the operator theory focuses predominantly on the topological options that are available for any operator at a given level to construct any next higher level operator. A simple illustration of how topology limits the possibilities for constructing system types is the following. Starting with two separate circles (in a two dimensional world), there exist precisely two topological options. Either, two circles can connect via their outer border (this yields a topology of the form ∞) or, one circle can be placed inside the other (this yields a topology of the form ©). Whatever the kind of processes that allow the formation of a given topology, the outcome is predetermined, in its type, by topological possibilities. Evolution, when analysed at this abstract level, may thus be much more predetermined and predictable than we normally are used to think. Despite the relative independence of the operator theory from real life processes, it remains an exciting challenge to find solid argumentation for the selforganization processes that have allowed the formation of all the subsequent closure steps that define the operators in the operator hierarchy. In the talk the different levels of the operator hierarchy will be presented one by one, and everyone will be invited to discuss about the most likely mechanisms for the emergence of the different levels.


For preparation of the discussions, information about the operator theory (graphs, publications and power points) can be found at www.hypercycle.nl

Seminar talk slides are here