The Conversion of Phenomena to Theory: Lessons on Applicability from the Early Development of Electromagnetism

theories of modern physics, and the increasingly mathematical arguments used in their development, has led some to see the success of modern physics to seem mysterious or even magical. Looking at the development of equations in quantum theory, Steiner (1998) has argued that as a result of their being developed using various kinds of mathematical, rather than physical, analogy, their significant success in applications presents a challenge to a naturalistic explanation of the applicability of mathematics. The challenge to naturalism is supposed to come as a result of mathematics being anthropocentric. I will argue in a later section that this argument is problematic for several reasons, which are evident once we better appreciate how mathematical theories of nature are developed out of experience. The successful application of the theories of modern physics cannot be properly understood through a consideration of their development alone; one must also examine the process of development of the low level theories used in their construction. A proper understanding of the manner of the connection of physical theories, modern or otherwise, to phenomena requires at least a basic understanding of the connection of the theories to their origins in direct experience. An appreciation of the full depth of the connections of theory to experience, and hence the role played by experiential phenomena in their development, may serve as a basis for examining the connections of theory to phenomena beyond experience. This is because understanding the connections to experience will enable an elucidation of the reasoning used to develop theoretical characterizations of phenomena beyond experience, which should provide means for a clarification of the connection between the given theory and the natural phenomena to which it applies. The difficulty in studying theory development from the point of view of understanding the relationship of physical theory to experiential phenomena is that the low level physical theories used in the majority of cases of mathematical modeling in the physical sciences have a long and complex history. Generally speaking, tracing the full connection of the mathematics of a physical theory to experiential phenomena becomes increasingly complex the more recent the theory. For example, although certain experimental anomalies were key in the development of (non-relativistic) quantum mechanics, the theory has its roots in classical mechanics, classical electrodynamics and thermal and statistical physics, which have their own complicated connections to experiential phenomena as a result of their process of development. Further difficulty arises from the fact that these theories, in turn, were developed in part on the basis of prior theory. Thus, examining how knowledge of experiential phenomena is used to develop theoretical characterizations of phenomena beyond experience becomes quite a complex affair. This is not to suggest that understanding how theory relates to phenomena requires a full appreciation of the entire development of science. This is just to point out that modern physical theories have a deeply complex relation to the phenomena to which they apply as a result of the manner in which they, and importantly also the theories used in their construction, are developed. It is also to point out that developing a better understanding of the relationship of physical theories to natural phenomena requires a thorough look at how the low level theories in the physical sciences were developed. The physical theories of the 19th Century are of particular interest from the point of view of understanding the relationship of physical theories to natural phenomena. This is in part because it is the theories of this century that form the basis for much of modern physics