The Use of Analogies, Imagery, and Thought Experiments in Both Qualitative and Mathematical Model Construction

Abstract

Scientists often say that the reasoning methods they use in their research reports are more formal than the primary processes such as analogy and special case analysis by which they discover their findings. Polya coined the term “plausible reasoning” to describe the nonformal processes that mathematicians use on the way to a new discovery. This chapter presents a longer and more complete collection of plausible scientific reasoning operations on the spring problem than have been dealt with in previous chapters, and it culminates in a quantitative solution. In doing so, this chapter bridges from the domain of qualitative modeling into the realm of mathematical modeling. Arguments collected from the solutions of several subjects are combined together to give a more complete and coherent solution. The analysis of this composite solution will be the topic of the next three chapters.