Re:Douglas Hofstadter has a new book
by chubot on Wednesday April 03, 2013 @12:58PM
(#5487278)
I appreciate what you're saying, but see my response below about semantics.
If you are calling it a metaphor, then aren't you calling ALL equations metaphors? That is doing violence to the meaning of the word "metaphor".
There is for sure a "relation" (or association) between the symbols e^i*pi = -1 and the picture of a unit vector on a complex plane. But that relation is not a metaphor.
Re:Douglas Hofstadter has a new book
by Evbn on Wednesday April 03, 2013 @03:53PM
(#5488595)
You can prove that equality using pure analysis, or pure geometry, using appropriate definitions. The metaphor is the intuition that the two proofs are equivalent in an abstract sense.
If you are calling it a metaphor, then aren't you calling ALL equations metaphors? That is doing violence to the meaning of the word "metaphor".
There is for sure a "relation" (or association) between the symbols e^i*pi = -1 and the picture of a unit vector on a complex plane. But that relation is not a metaphor.