Representation, interpretation, and theories of information

Introduction: On the first page of Shannon’s (1948) paper there are a few lines that are often quoted as providing a starting point for interpreting Shannon’s theory of information: The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point. Frequently the messages have meaning. … These semantic aspects of communication are irrelevant to the engineering problem. It is entirely appropriate to take Shannon’s words of wisdom seriously, that the theory has nothing to do with the meaning of messages. That said, it is a mistake to dismiss all intentional concepts while interpreting the theory. In fact what I will demonstrate in this chapter is that focusing on the representational and interpretive aspects of theories is vitally important for understanding the definition of information provided in Timpson (2013), and how Shannon information theory and quantum information theory are related. These aspects have heretofore not been sufficiently appreciated with respect to the framework for understanding information theories developed by Timpson (2004, 2013) and Duwell (2008). I will be correcting that problem in this chapter, and arguing that information theory in general, and Shannon and quantum information theories in particular, involve far more conventional aspects than has been realized, and explain why they do so. In order to appreciate the pragmatic aspects of communication, it is essential to draw one’s attention to some basic features of representation and interpretation, which is the focus of Section 2. In Section 3, I will present the relevant aspects of Shannon’s theory to bring out the features that are so important to understanding what information is. This section also raises a problem for the definition of information and proposes a resolution to the problem. The problem will illustrate how important users of Shannon’s theory are in determining what constitutes successful Shannon information transfer. In Section 4, I will outline quantum information theory and raise another problem for the definition of information. Again, the resolution to the problem will depend on recognizing just how important users of quantum information theory are in determining what constitutes successful quantum information transfer. The resolution to the problem will also illustrate important differences between Shannon information theory and quantum information theory.