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:
“Have you ever been up in your plane at night, alone, somewhere, 20,000 feet above the ocean?... Did you ever hear music up there?... It’s the music a man’s spirit sings to his heart, when the earth’s far away and there isn’t any more fear. It’s the high, fine, beautiful sound of an earth-bound creature who grew wings and flew up high and looked straight into the face of the future. And caught, just for an instant, the unbelievable vision of a free man in a free world.”
—Dalton Trumbo (1905–1976)
“A pragmatic race, the Japanese appear to have decided long ago that the only reason for drinking alcohol is to become intoxicated and therefore drink only when they wish to be drunk.
So I went out into the night and the neon and let the crowd pull me along, walking blind, willing myself to be just a segment of that mass organism, just one more drifting chip of consciousness under the geodesics.”
—William Gibson (b. 1948)
“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)