The increase of our knowledge of nature and the multiplicity of phenomena to be studied and investigated has led to specialization in pure and applied science and in practical work. In many instances the individual branches of science became isolated from each other to a considerable degree.

The establishment of the closest ties between the individual lines of knowledge, theoretical as well as practical, is one of the important aims of scientific thought. The analysis of the nature of the factors, used for the quantitative expression of physical processes, shows that many of them have a striking similarity as far as energy is concerned. Such similarity, and even identity, leads one to the conclusion that the concept of energy can serve as the basis for the unified interpretation of physical and, possibly, other phenomena of nature. This paper, which deals with physical processes, is an attempt toward such unification.

The conformity of mathematics and physics has so far been taken for granted. Philosophical explanations of that fundamental fact have never been satisfactory, mathematical explanations never had been attempted. In the following a fundamental theorem for the conformity of mathematics and physics will be demonstrated.

Mathematics can be defined as the science of Number, physics as the science of Matter. The elementary constituents of mathematics are the prime numbers, those of matter the particles, particularly protons and electrons. The only essential property of these elements as such is their existence, given within a given complex or space. Their fundamental relation is their distribution within their respective spaces. The theorem of the distribution of primes in the arithmetical series of numbers is the fundamental theorem of mathematics. The fundamental theorem of physics would be a theorem of the distribution of particles in geometrical space. If it were shown that both theorems were equal, the essential conformity of mathematics and physics would be mathematically demonstrated.

Up to the present time the science of physics has given us no purely physical theory by which the characteristic formal properties of sensation can be derived. No explanation of the sense world purely in terms of the postulated physical world has been forthcoming, so that the psychologist has had either to ignore sensations or consider them as at least partially unaccountable additions to the entities of physics.

That there is, nevertheless, a purely physical explanation of the sense world we hope the following pages will make clear. We will present a theory in which the characteristic properties of sensation are derived from postulated physical entities.

In a paper read before the last Congress for the Unity of Science, Dr. Milton Singer distinguishes three main phases in the recent history of logic. The achievement he considers most characteristic of the first period is the development of the class calculus or so-called Boolean algebra. It begins with the work of Boole and DeMorgan and culminates in Schroeder's Algebra of Logic. In a minimum formulation, the results of this first stage can be summed up as, first, simplification and generalization of the traditional syllogistic machinery by means of a rather efficient new symbolism, and, second, adoption of the axiomatic method. To restate the last point: Boolean algebra was, since Leibniz, the first explicit attempt to construct what we call a formal system or calculus. Not realized at that time, however, or at least not adequately expressed, was the importance of the more recent distinction between scientific calculi on the one hand and purely linguistic or logical calculi on the other. As a consequence of this lack of explicit insight, the class calculus appeared to be on a par with scientific calculi, say, for instance, axiomatized geometry, Euclidean or otherwise. Its analytical character, even if it was seen, could not be formulated.