On Mar 22, 2010, at 5:06 PM, glen e. p. ropella wrote: > Thus spake Nicholas Thompson circa 10-03-22 04:58 PM: >> Yes. I am sorry. That was my fault. There was a bit of a slipup between >> the "provost" and the professor. > > No worries! It looks like a great book and I expect I'll enjoy it when > I pop it off the queue. > >> Byers main point is that it is AMBIGUITY that makes maths great! But its a >> subtle argument because what he is really saying is ironic: as >> mathematicians strive to reduce amibiguity they inevitably generate more, >> and thus, against their feverish and futile resistance, does math progress. > > Very interesting. If there's one conviction I'm actually guilty of, > it's believing that irony (or, more accurately, paradox) is the ultimate > teacher. And ambiguity is closely coupled with paradox. (Warning: the > broken record begins again.) That's why I'm so fond of "Vicious > Circles" by Barwise and Moss. It's the closest body of math I've found > that tries to explain how cycles impact the definiteness of math. > > But it's wrapped in other stories, too. I remember once looking up > "impredicative definition" in the index of some overly large math > reference book in some library somewhere. (I lose track sometimes. ;-) > It told me to look at a particular page. That page made a vague > reference to the term "vicious circle". So, I looked up "vicious > circle". It took me to another particular page, which made a vague > reference to "impredicative definitions". If it hadn't been such a > large book, it would have been funny. Instead, I learned a valuable lesson.
Interesting mix of interests! Glen I wonder if you've ranged even further afield, and come across a book by Richard Rorty called Contingency, Solidarity, and Irony (1989) -- or maybe Rorty's first, fame-making book, Philosophy and the Mirror of Nature (1979)? Rorty was a modern American School pragmatist (a tradition which he broadly defined to include William James, Charles Peirce, John Dewey, as well as WVO Quine and Donald Davidson), and most of his life's work focused on debunking (or if that was not possible, discrediting) all sorts of perceived impediments to inter-subjective communication and coordination -- prerequisites for the social/political goals (e.g., understanding, cooperation) that he was more open about in his final years. One nice quote from Contingency about his own disciplinary labors, which could easily be applied to the current context: "Interesting [field of study] is rarely an examination of the pros and cons of a thesis. Usually it is, implicitly or explicitly, a contest between an entrenched vocabulary which has become a nuisance and a half-formed new vocabulary which vaguely promises great things... This sort of [discipline-specific research] does not work piece by piece, analyzing concept after concept, or testing thesis after thesis. Rather it works holistically and pragmatically." (p. 9) While this observation seems a bit exaggerated to me (i.e., narrow, stepwise analysis often accompanies the broader contest between rival paradigms), this actually sounds quite a bit like the work I'm participating in this week, at the Internet Engineering Task Force meeting in Los Angeles (esp. the Routing Research Group, which is trying to develop a consensus recommendation for a new Internet architecture to be developed over the next couple of years). Sadly, it also reminds me of an old grad school benefactor (whom you may actually remember Glen -- he sponsored my mid-1990s participation in the Swarm conferences where we met once or twice, and later spent a summer there as a visiting fellow -- the results of which were later memorialized in one of Simon Fraser's chatterbots). Sometimes those "vague promises of great things" on the other side of the next disciplinary fence can be so compelling that the lure of serial fence-hopping displaces the much more challenging but enduring work of fence removal and field integration. I learned may valuable (and ironic) lessons from that particular association... Regards all, TV ============================================================ 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
