I'll attempt to identify the core of the recent Mathematics and XYZ thread, going back to Nick's original kernel:
Nicholas Thompson wrote: > All, One of the running arguments I have with one of my favorite > colleagues here in Santa Fe is about whether Mathematics is (or > isn't) different from all other intellectual enterprises, such as > psychology or philosophy. in that, unlike them, mathematics "adds > up," in the long run. Contrary to psychologists and philosophers like > me, who are besotted with ephemeral traditions and ideologies, and > keep changing the rules of the game, mathematicians have built a > structure that is not subject to vicissitudes and whims of > intellectual history. (I hope I have represented this argument > fairly.) Although I have tried to give him as little comfort as > possible, I confess that I have been impressed more and more by this > argument as I continue to read accessible works on the history of > mathematics. The core of the question came up several times. In essence, it's about whether or not progress (or accumulation) is illusory or objectively real, and whether math exhibits progress more obviously than other domains. We fleshed out the question by claiming and counter-claiming about whether math is a purely social construct or whether it is (and how it might be) hooked directly to reality, even to the extent that reality may be mathematical. So, there we are. Was anything achieved in this meandering thread? Most certainly. Are the achievements quantifiable? Most definitely not. In any case, I feel the pressure to shut up for awhile. [grin] So, I will comply. -- 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
