FOM: On introducing new abbreviations
mthayer at ix.netcom.com
Mon Nov 10 09:40:29 EST 1997
On Oct 23, Harvey asked:
>Question with psychological, and sociological overtones: when do formulas get too complicated, >so that mathematicians simplify them by introducing new abbreviations? We all know that this is >a crucially interesting matter, since otherwise mathematicians could not actually be done. >Maybe there is a complexity theorem here somewhere - and maybe this is related to the fact >that, also, humans generally can only efficietnly process relatively short sentences and phrases.
If you are not already aware of it, there is a lot in the experimental literature on what George Miller called "The magic number 7 +/- 2". This evidence supports the conclusion that "clumping-up" or consolidating things into higher order chunks is a necessary part of human perception and thought processes. Of course there is also the somewhat newer work which point out how good we are at pattern matching, which may work in a different way.
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