Frictionless Plane As A Pragmatic Methodology
Galileo died 40 years before Isaac Newton's Philosophiae Naturalis Principia Mathematica which described normal force (Newton's third law of motion), inertia (Newton's first law of motion), and most importantly, Newton's law of universal gravitation; he died nearly three centuries before Albert Einstein published his theory of general relativity. Nevertheless, by thinking about the forces (as he understood them) acting upon an object on an inclined plane, Galileo came to understand the mechanics of the situation in a very fundamental way. From that understanding, he was able to extrapolate the general formula.
At bottom, the frictionless plane is a method of understanding otherwise opaque phenomena to make them receptive to experimentation and understanding. Galileo did not solve the inclined plane by performing experiments, considering the results, then attempting to reverse engineer a calculation that could accommodate those results. From what we now know, such an equation would have been incorrect, for any result is the combination of gravitational and frictional forces. Instead, he began thinking about how gravity works upon free-falling objects, and what about that force is the same, and what about it is different when an object moves down an inclined plane. It is this methodology that is so remarkable, and gives the frictionless plane its immense practical value.
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Famous quotes containing the words plane, pragmatic and/or methodology:
“Even though I had let them choose their own socks since babyhood, I was only beginning to learn to trust their adult judgment.. . . I had a sensation very much like the moment in an airplane when you realize that even if you stop holding the plane up by gripping the arms of your seat until your knuckles show white, the plane will stay up by itself. . . . To detach myself from my children . . . I had to achieve a condition which might be called loving objectivity.”
—Anonymous Parent of Adult Children. Ourselves and Our Children, by Boston Women’s Health Book Collective, ch. 5 (1978)
“Even if matter could do every outward thing that God does, the idea of it would not work as satisfactorily, because the chief call for a God on modern men’s part is for a being who will inwardly recognize them and judge them sympathetically. Matter disappoints this craving of our ego, so God remains for most men the truer hypothesis, and indeed remains so for definite pragmatic reasons.”
—William James (1842–1910)
“One might get the impression that I recommend a new methodology which replaces induction by counterinduction and uses a multiplicity of theories, metaphysical views, fairy tales, instead of the customary pair theory/observation. This impression would certainly be mistaken. My intention is not to replace one set of general rules by another such set: my intention is rather to convince the reader that all methodologies, even the most obvious ones, have their limits.”
—Paul Feyerabend (1924–1994)