Glen says, > The idea was that math is just the transformation of one set of > sentences into another set of sentences by a particular grammar. This > is (weakly) analogous to the transformation of a piece of paper from one > shape to another. But then the idea driving you to do that is your own inspiration, the image of the swan, or the special one-to-one mapping, or whatever. How it fits into your own world of ideas and experience is what actually guides the direction in which you look for things to prove. It could be that in constructing math to be meaningful to mathematicians it's just a social convention that is being mapped, and not intrinsic forms of the universe, or that quite other intrinsic forms of the universe would be explored by others with different experience could they master the technique and get into the club.
Phil > -----Original Message----- > From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On > Behalf Of glen e. p. ropella > Sent: Wednesday, October 08, 2008 7:36 PM > To: The Friday Morning Applied Complexity Coffee Group > Subject: Re: [FRIAM] Origami metaphor (Level b) > > Thus spake Nicholas Thompson circa 10/08/2008 04:13 PM: > > Glen said (I think it was glen) > > > > "It's just like folding a piece of paper. Someone hands you a piece > of > > paper and you fold it into an origami swan. Did you _discover_ the > > swan? Or did you invent the swan?" > > > > And Nick replies ... > > > > You all know by now how I feel about metaphors. Nick thinks being > serious > > about metaphors is REALLY IMPORTANT <==rude shouting! > > So, when I say what I am about to say, I am not just nit-picking. I > hope. > > > > Isnt the metaphor backwards? Given the uniqueness of the solution, > isnt it > > more like you had been handed the swan and "discovered" that it was > just a > > square piece of paper? > > Well, it wasn't really a metaphor. It's a simile and/or an analogy. > [grin] > > But, no, it's not backwards any more than it's forwards. The analogy I > intended to make was between paper folding and math, not between an > origami swan and a solution to a sudoku puzzle. Sorry for not being > clear. > > The idea was that math is just the transformation of one set of > sentences into another set of sentences by a particular grammar. This > is (weakly) analogous to the transformation of a piece of paper from one > shape to another. > > To make an analogy between the solution to a puzzle and a particular > shape, one would have to add more constraints to the shape being > sought. > One might then be able to determine the uniqueness of a particular > shape given those constraints. But such an analogy would be even > weaker > and wouldn't help explain Wittgenstein's position, I don't think. > > -- > glen e. p. ropella, 971-219-3846, http://tempusdictum.com > > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
