Or to paraphrase, if I may Nick, "Simple clear math has no environment. Math with an environment is no longer simple and clear".
Phil > -----Original Message----- > From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On > Behalf Of Nicholas Thompson > Sent: Wednesday, October 01, 2008 1:01 PM > To: friam@redfish.com > Subject: [FRIAM] Is programming a mathematical formalism > > Ever since I first came to Santa Fe, and joined the extensive > computation > culture here, I felt I have detected in the software people here > something > equivalent to the physics- envy that we psychologists are prone to: > let's > call it math-envy. Math-Envy seems to be that while programming is > subject > to the vicissitudes of any linguistic enterprise, mathematics displays > true > formalism.... "you always know where you stand" in mathematics. > > The more I have read ... most recently Rosen, Reuben Hersh, George > Laykof, > Monk's biolography of Wittgenstein --- the more it seems that the best > one > can say of mathematics is that "If you know where you are standing in > mathematics, you know where you stand" in mathematics. Take Zero for > instance, and minus numbers, and roots of minus numbers, etc., etc. > All of > these things are metaphoric extensions and, as Laykof points out, in > fact > zero is different depending on which of several metaphors one has in > mind > when one is using it. Thus, the sense of safety one gets in > mathematics > comes from the tendancy of mathematicians to hide out in deep silos, > rather > than from a greater power or universality of their inter-silo > discourse. > It is the same sense of safety that one gets in any monastery. Or, I > imagine, that one gets from deep involvement in any programming > language. > > Now, the proposition having been stated so baldly -- and no doubt > ineptly > -- by an outsider, I suspect that ALL mathematicians on the list will > now > agree that the case has been OVER stated and that, whatever the > differences > in degree of formalism within the various forms of mathematics, all > mathematics is clearer than other forms of argument, such as plain old > vanilla philosophy, or, say, experiment and proof in psychology. > Getting > you all to agree in this way will have been my highest achievement of > the > day. > > Nick > > Nicholas S. Thompson > Emeritus Professor of Psychology and Ethology, > Clark University ([EMAIL PROTECTED]) > > > > > > > > ============================================================ > 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
