Theories and the flow of information. (English) Zbl 0848.00009

Mosterin, Jesus

Echeverria, Javier (ed.) et al., The space of mathematics. Philosophical, epistemological, and historical explorations. Revised papers from a symposium on structures in mathematical theories, Donostia/San Sebastian, Basque Country, Spain, September 1990. Berlin: Walter de Gruyter. Grundlagen der Kommunikation und Kognition. 367-378 (1992).

The paper discusses the rôle of mathematics in extending man’s natural capacities for detecting and processing information. The author presents the encoding of digital video data with the help of binary sequences as an example of encoded information of changing complexity. He discusses algorithmic information theory and universal Turing machines as devices for determining the degree of complexity of binary sequences. Mathematical description gives the rigid framework for creating the conditions for coding information. In particular the axiomatic method is discussed as a method for compressing information. Theoretical abstraction applied to concrete theories concerning, e.g., a common structure or form will lead to more efficient codification. By dropping concrete references of a theory it becomes open for multiple interpretation (“multiapplicability”). “An abstract theory is an efficient codifier of the information contained in many different concrete theories” (p. 376). The author gives examples especially from theoretical physics: applications of Newton’s theory to various systems, among them Coulomb’s theory of electrostatic and magnetostatic forces, applications of Maxwell’s equations of Faraday’s electromagnetic field and to Hertz’s ratio waves, and, in some length, various applications of string theory (pp. 376-377).
For the entire collection see [Zbl 0839.00019].

Reviewer: V.Peckhaus (Erlangen)

MSC:

00A30	Philosophy of mathematics
68P20	Information storage and retrieval of data
94A15	Information theory (general)

Keywords:

axiomatization; abstraction; information; algorithmic information theory; universal Turing machines; complexity