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APRIL 28-30 2015

Tuesday April 28th 2-6 pm
Wednesday April 29th 2-6 pm
Thursday April 30th 2-6 pm


EVERYONE WELCOME TO ATTEND ! write an email to buehlmann (at)

Natural Communication

Information theoretic processes of communication take place via a bidirectional modelling scheme of encoding and decoding information from one domain to another. Contrary to common belief, these communicative procedures of information transfer are not direct but always follow a particular type of a dynamically adjusted design suited to both, the characteristics of the involved domains, and the nature of the information to be exchanged or transferred. The basic attributes of this natural design may be summarized as follows: I. Information flow follows a circulatory pattern between the involved domains consisting of cycles of encoding/decoding or encrypting/decrypting information. II. The involved domains stand in a reciprocal relation to each other with respect to the circulation pattern of information flow. III. The information flow can be metaphorically thought of in terms of elastic cords binding the involved domains by means of a network of bidirectional connections. IV. Reciprocal encoding and decoding processes making up the information flow are of a categorial nature and always effected through universals of a non-spatiotemporal nature. V. The naturality of the design, meaning the non-dependence on ad hoc choices and conventions, is characterized by concrete invariance properties of the information flow itself in relation to the involved domains. VI. The pattern of information flow is not rigid. On the contrary, it is dynamically adjustable within the limits imposed by the invariance properties and can be metaphorically thought of in terms of processes of crystallization of the information flow. The above briefly described attributes characterizing the natural design of information exchange or transformation processes of communication can be formulated in a precise manner mathematically in the language of category theory, and in particular, in terms of the notion of categorial adjunctions. Category theory was born out of the discipline of homological algebra, which in turn traces its genesis in the merging of universal algebra with topology. The decisive moment in the history of mathematics, when for the first time the design pattern of information flow between different domains has been abstracted in structural and not merely arithmetical terms, has been the conception of Galois theory. The realization that the natural design of a communicative information flow follows universal rules required the recently conceived higher abstractions of category theory for a precise formulation. Notwithstanding this fact, this universal bidirectional modeling schema of information encoding/decoding is barely known outside of the arena of pure technical mathematics, and this is something that has to be remedied urgently in the very near future. The purpose of this course is precisely the familiarization and conceptual understanding of the basic notions involved in this schema. Bildschirmfoto 2015-01-28 um 18.55.03