–Or Why are the Two illustrations Technically Equivalent?
Free Fall Experiment in 20th century parlance.
In the physical sciences, at least, the language has always been Mathematics. However, in the early 20th century, Mathematics and Physical Science started upon a path of divergence; and Quantum Mechanics and Einstein’s Relativity became the common language in which mathematical language was more complex than experimentation. The mathematics became more than a tool but “a means justifying an end.” Mathematicians explored nuances of physical theory in ways that were not always amenable to practicing physicists—as evidenced by mathematical movement such as the secret Nicolas Bourbaki Society: http://www.britannica.com/EBchecked/topic/75700/Nicolas-Bourbaki. The secret Bourbaki society revised the methods in which mathematics were practiced and taught—and the late 20thcentury served to launch a “counter-movement” of sorts against the reforms. Experimentation is the bedrock of science and the truly successful theoreticians understand how to intertwine physical insights with mathematical formulas. (If you happen to peruse calculus books from 40 years past do a comparison of today’s standard—you may notice a difference!) Currently, the paradigm is more amenableto physical application, while the Bourbaki reforms were algebraic (and less intuitive, physically).
In “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” which appeared in print in February 1960 *; the author—(mathematician) Eugene Wigner effectively argues: mathematics truly serves as a tool for the scientist. In a style indicative of his genius, Wigner states that scientists such as Kepler, and Galileo realized that observation must trump mathematical formalism. Kepler, who was renown for his mathematical skills, did not understand the orbit of Mars within his mathematical paradigm. Kepler turned to Tycho Brahe’s data—but he struggled because of his preconceived paradigm. Eventually, Kepler established his three laws, but only when he understood his “data” by the true light of Nature. Galileo, the father of experimentation, realized that science depends heavily upon regularity (and not upon a drastic contrast of actions). It was Galileo who first looked for regularity in the falling masses from the Tower of Pisa; he further discerned this pattern in the inclined plane experiments. To the 21st century physicist, it is as if this observation is second nature , but in the 17th century—it was revolutionary.
* “The unreasonable effectiveness of Mathematics in the Natural Sciences” appeared in Communications of Pure and Applied Mathematics vol. 13 No.1 (February 1960)
Eugene Wigner’s 1963 Nobel Address may be found here: http://www.nobelprize.org/nobel_prizes/physics/laureates/1963/wigner-lecture.html