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, ...)*