A theory of pragmatic information and its application to the quasi-species model of biological evolution

Abstract

‘Standard’ information theory says nothing about the semantic content of information. Nevertheless, applications such as evolutionary theory demand consideration of precisely this aspect of information, a need that has motivated a largely unsuccessful search for a suitable measure of an ‘amount of meaning’. This paper represents an attempt to move beyond this impasse, based on the observation that the meaning of a message can only be understood relative to its receiver. Positing that the semantic value of information is its usefulness in making an informed decision, we define pragmatic information as the information gain in the probability distributions of the receiver's actions, both before and after receipt of a message in some pre-defined ensemble. We then prove rigorously that our definition is the only one that satisfies obvious desiderata, such as the additivity of information from logically independent messages. This definition, when applied to the information ‘learned’ by the time evolution of a process, defies the intuitions of the few previous researchers thinking along these lines by being monotonic in the uncertainty that remains after receipt of the message, but non-monotonic in the Shannon entropy of the input ensemble. It also follows that the pragmatic information of the genetic ‘messages’ in an evolving population is a global Lyapunov function for Eigen's quasi-species model of biological evolution. A concluding section argues that a theory such as ours must explicitly acknowledge purposeful action, or ‘agency’, in such diverse fields as evolutionary theory and finance.