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Another excellent example of the power of good notation to aid understanding and increase efficiency is Dirac, or Bra-Ket notation[1] used in Quantum Mechanics.

Another excellent example of the power of good notation to aid understanding and increase efficiency is Dirac, or Bra-Ket notation[1] used in Quantum Mechanics. This allows you to do all sort of calculations with wave functions without constantly grinding to a halt bogged down by integrals and conjugates all over the place. The ladder operators (aka raising & lowering), really put this notation to good use[2]. It would be tremendously tedious to manipulate such expressions repeatedly without the simplifying properties of Bra-Kets. Once you are done manipulating them you then use the rules of the bra-kets to transform it back into a plain old integral, evaluate, and you're done. I used to think they were very mysterious until I realised they were (essentially) notational convenience. [1]: https://en.wikipedia.org/wiki/Bra%E2%80%93ket_notation https://en.wikipedia.org/wiki/Bra%E2%80%93ket_notation [2]: http://www.tcm.phy.cam.ac.uk/~bds10/aqp/lec3_compressed.pdf http://www.tcm.phy.cam.ac.uk/~bds10/aqp/lec3_compressed.pdf

criddell 9y ago
Would you say the same is true for Feynman diagrams in QED?
- LolWolf 9y ago
  The same is true in the sense that they're actively helpful in 'hiding away' a large amount of complexity in relatively innocent-looking expressions, though Feynman diagrams are less of a tool of hiding information and more of a computational aide (e.g. it gives rise to a set of operations and a nice way of organizing them). You could see this as an actively distinct concept (Feynman diagrams are graphs which give rise to some algebraic structure, whereas Dirac's notation is an algebra in itself) or you can see them both as just a means of abstracting away many operations (e.g. in Dirac's notation, this would be multiplication by operators and inner products, both of which are integrals in some sense, as just a non-commutative type of multiplication) in really powerful notation.

criddell 9y ago

Would you say the same is true for Feynman diagrams in QED?

LolWolf 9y ago
The same is true in the sense that they're actively helpful in 'hiding away' a large amount of complexity in relatively innocent-looking expressions, though Feynman diagrams are less of a tool of hiding information and more of a computational aide (e.g. it gives rise to a set of operations and a nice way of organizing them). You could see this as an actively distinct concept (Feynman diagrams are graphs which give rise to some algebraic structure, whereas Dirac's notation is an algebra in itself) or you can see them both as just a means of abstracting away many operations (e.g. in Dirac's notation, this would be multiplication by operators and inner products, both of which are integrals in some sense, as just a non-commutative type of multiplication) in really powerful notation.