Nick, Leave us not conflate clarity, concision and expressiveness. One may make tradeoffs, for example one may choose one computer language for its large number of libraries and ability to say a great many things in many ways, at the expense of concision and clarity.
As to envy, I think there is a kind of envy of the different kinds of communities. Compare, for example, the N-Category cafe with, say, Slashdot. In the latter, a CS person may begin to feel after a short while that one is wasting one's time, in a way one does not in the former, even if one does not consistently feel entirely sure of what is being said in the former. In contrast to the statement "If you know where you are standing in mathematics, you know where you stand", I would say "If you know where you are standing in mathematics, you can appreciate better where you *might* stand". One can certainly have this appreciation in a CS world, though I have a sense that in Mathematics there is a closer sense of the history of one's particular community and therefore why people talk about particular mathematical subjects the way they do - the frames (as Lakoff would use the term) are both more transparently indigenous and explicit. This seems to me particularly the case wrt algebra and topology (oh yes and category theory); oddly, the more universal something seems (e.g. Euclidean geometry), the less historically grounded it feels. I'm not sure of the origins of the notion that mathematical formalisms convey "safety". Surely one's appreciations are open to challenge; somebody else drills a hole through one's cherished mappings, or opens up some new field that in retrospect seems obvious to all in the midst of what one thought were fundamental truths. Mathematics seems a more dangerous approach to reality; there are fewer "Turing Machine" like constructs upon which one may rely. It seems again that "safety" is more a matter of taking refuge in the nature of the mathematical community and its history. This community and its history is not as anecdotal as in many areas of science. There is a kind of "mathematics of the silos" that lets you explore one silo while also mapping it into the others. Both highly focused and highly open. So, envy; I suppose so. And if we can find ways to rationally bind our model of how CS is done closer to the way Mathematics is done, Make The Most Of It. Unlike sausage and law, one can only love formalisms if one loves watching them being made. Carl Nicholas Thompson wrote: > 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
