ABSTRACT
The chapter provides historical context to help clarify the elegant operational mechanics of modern data analysis. It introduces data numeration, the concepts of discrete and analog data, and how all data analysis is based on the simple arithmetic of sums and differences to establish the signal's inverse differentiation and integration properties. These respective rise-to-run and area-under-the-curve properties are essential for combining environmental parameters into a quantitatively effective model of the signal. They are related by the two fundamental theorems of calculus, which hold that the signal is [1] the integral to within a constant of its derivative, and [2] the derivative of its integral. Analysis of a simulated discrete set of Galileo's free-falling body observations shows how the signal's differentiation and integration attributes may be established graphically and numerically. A review of the development of computational devices from the ancient, but still popular abacus through modern electronic computers shows a transformation from mechanical to faster, higher capacity, and more reliable electronic operations. The transformation was facilitated by Leibniz's late 17th century formulation of the binary number system and Babbage's early 19th century programmable mechanical computer. The latter development established the modern computer system involving the central processing unit [CPU] capable of performing input, output, arithmetic, and logical or Boolean operations.
