#simple pendulum

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Two Forms of Idealization.—A simple or ideal pendulum assumes a frictionless fulcrum, a weightless string, a point mass weight bob, absence of air drag, short amplitude (small-angle approximation where sinθ≈θ), inelasticity of pendulum length, rigidity of the pendulum support, and a uniform field of gravity during operation of the pendulum, inter alia. There may well be an infinitude of conditions that enter into the operation of an actual pendulum, and every condition eludes anything but approximation by a theoretical model. This is an ideal that no finite formalization can capture; actual pendulums can be made precise to an arbitrary degree, but they can never exhaustively converge on the properties of an ideal pendulum, as no ideal pendulum can exhaustively converge upon every wobble and tremor of an actual pendulum. Thus we must distinguish between that idealization used in science and without which science is impossible, on the one hand, and, on the other hand, that idealization that is impossible for science to capture in any finite formalization, but which can be approximated. A simple (i.e., ideal) pendulum is an example of the first; an exhaustive account of the factors that bear upon an actual pendulum is an example of the second. (Holism in confirmation, which is especially associated with Duhem-Quine thesis, is also an instance of this latter kind of idealization.) Both forms of idealization force compromises upon science through approximation; we accept a result that is “good enough,” even if not perfect, and each form of idealization implies the other. Thus one ideal, realizable in theory, is substituted for another ideal, unrealizable in theory.