Quantal aspects of scientific information

Abstract

This paper is an attempt to clarify some aspects of the approach to experimentation suggested by the author in a recent publication in the Philosophical Magazine, (hereafter referred to as P.M.). The concept of "amount of information" is shown to have three distinct senses in current literature. Two of these are definable as numerical features of the logical pattern of propositional relations which we make to represent a result. The third measures the relative unexpectedness of the pattern, which may or may not be connected with its numerical features. Since logical patterns can be built up from discrete quantal elements, the information enabling them to be built is quantised by our use of 'yes-or-no' logical forms as scientific statements. The number of discrete 'elementary propositions' in a given description cannot be altered by any complete reformulation. This is seen to be the basis of our ability to 'barter' certain quantities for one another - e.g. accuracy for speed of response in a galvanometer or a communication-channel. The term "selective information" is suggested to distinguish the third sense of 'information' (called amount of detail in P.M.) from the first two, whioh measure respectively the number of independent features (structural information) and the weight of evidence or precision (metrical information) in a result. 'Selective information' is the measure of information currently used by communication engineers, and a distinguishing title appears to be essential. From the standpoint here adopted the various uncertainty-relations of physics illustrate a general axiom expressing the quantal nature of the logical descriptions which we make. Some other practical and theoretical implications of the theory are examined.