Communication and understanding mathematical foundations and practical applications

Since Shannon’s and Weaver’s “Mathematical theory of Communication” it is well known that mathematical definitions of information or the degree of information respectively is possible. The great problem for a complete theory of communication is the exact definition of meaning in mathematical terms. I shall demonstrate how such a definition can be achieved in terms of complex systems theory. In particular it is possible to derive exact definitions of the degree of meaning, applied to semantical networks, and of the degree of information that is suited for the analysis of human communication. The degree of information as well as the degree of meaning is dependent on the geometry of the receiving systems, which are modeled as semantical networks. It can be shown that the knowledge about the geometrical structure allows predictions about the degrees of information and of meaning a message has for a certain receiving system, although of course only on the average. In a semantical application of these fundamental concepts it will be shown how a new self organized leaning neural network that we have developed is able to deal with linguistic ambiguities. Additional applications of the communication theory will be demonstrated, in particular an Internet meta search engine based on computing the degrees of information and meaning, and a computer based discourse analysis.