On the theme of appropriate notation and how it empowers good thinking, an example from quantum mechanical circles: P. A. M. Dirac's "bra-ket" symbolism. A Dirac "bra" looks like < a | and a "ket" is written | b > — put them together to get a bracket, < a | b > which compactly symbolizes the overlap between quantum systems "a" and "b". An experiment "E" is a transformation operator. Put it in a bracket, < a | E | b > and you've got the chance that E turns state "b" into "a".
The bra-ket notation keeps track of the nasty algebra and resolves ambiguity ... making it easy to derive and solve the right equations. (There's a mountain of powerful mathematical machinery behind the bra-ket stage: complex numbers, vectors and matrices, integrals, Hilbert spaces, etc.) Like Feynman diagrams, or the upstairs-downstairs tensor subscript convention, or Leibnitz's method of writing derivatives and integrals in calculus, or the Arabic invention of the zero for place-value representation of numbers — nice notation, an efficient language for simplifying the complex.
(See ^zhurnal GoodNotation)
Wednesday, January 24, 2001 at 12:58:21 (EST) = 2001-01-24
(correlates: OneDeep, ExposureAndEncapsulation, Multiword link, ...)