Wednesday, July 15, 2015

Abstraction and Formalism

Abstraction and Formalism:  These are not really the same, though they are related.

To our essay about Abstraction Fetishism among Harvard math majors, an appendix for  physicists:

The most practical person must realise that abstract arguments (by which we really mean  arguments with a tremendously wide range of applicability)  are a necessity … now that science has grown so vast.  If the engineer is willing to overcome his nostalgia for the practical, and embark on the study of Lagrange’s equations in a spirit of abstraction, he will be rewarded by having at his disposal a powerful tool for the study of electrical networks, which are not ‘dynamical systems’ in the ordinary mechanical sense, but nonetheless behave as if they were.
-- John Synge & Byron Griffith,  Principles of Mechanics (1942, 1959), p. 411

Graduate students in theoretical physics … are very often impressed with “formalism” -- the formal apparatus of their subject. … I suffered … from an infatuation with beautiful formalism.  Working with Viki Weisskopf was a most effective remedy against the excesses of such an infatuation.  He never ceased to harp on the importance of … understanding, by means of simple arguments, the physical meaning of a theory …
-- Murray Gell-Mann, “The Garden of Live Flowers”, in Selected Papers (2010), p. 27

Re quantum theory:

This formalism has provided us with a revolution in our picture of the real physical world  that is far greater  even than that of  … general relativity.
Or has it?  It is a common view among many of today’s physicists  that quantum mechanics provides us with no picture of ‘reality’ at all!  The formalism of quantum mechanics, on this view, is to be taken as just that:  a mathematical formalism.
-- Roger Penrose,  The Road to Reality (2004), p. 782

That last clause provides a deflationary use of the term “formalism”, utterly at odds with the connotation in the first.

The full essay can be viewed here:

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