yes, but the continuity of the formula is not built like nor function like the continuity of the roof. The formula is a simulation for the mind, an 'explanation', and quite unlike the real thing assembled with multiple scale of organization way beyond explanation... The huge simplification is to use our simplistic 'explanations' and a guide to exploring and engaging in the real thing that is beyond explanation, fully appreciating the value of both!
Phil Henshaw ¸¸¸¸.·´ ¯ `·.¸¸¸¸ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 680 Ft. Washington Ave NY NY 10040 tel: 212-795-4844 e-mail: [EMAIL PROTECTED] explorations: www.synapse9.com > -----Original Message----- > From: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] On Behalf Of Owen Densmore > Sent: Thursday, July 26, 2007 11:08 AM > To: [EMAIL PROTECTED]; The Friday Morning Applied > Complexity Coffee Group > Subject: Re: [FRIAM] Diff & Contin. to Nick! > > > On Jul 25, 2007, at 10:53 PM, Peter Lissaman wrote: > > >> 2. DIFFERENTIABILITY AND CONTINUITY (Nicholas Thompson) > > Nick: Let me be your math consultant! Taught that stuff at Caltech > > many years!! The mathematicians are horn swogglin' you with mis- > > understood function theory! A'course the f'n roof is > continuous. If > > it weren't the rain would come through! It is trivial to write a > > continuous function, f(x) defined for 0<x <=c and g(x) defined for > > c<x<1 with f(c) = g(c), with the peak at x=c and a > different slope > > for x=c, than for x>c. But the function is continuous. > Just like a > > roof ridge. A geometric function has, at each point, some degree > > of continuity, denoted by C N, where N is the order of the first > > discontinuous derivative. The triangular roof frame rafter is C1, > > meaning continuous in ordinate, discontinuous in slope. Smoother > > shapes have continuity of higher derivatives. Analytic functions > > have infinite continuity (thanks to M. Cauchy!). Airfoils have to > > be very smooth, but they can't be infinity smooth, since we > need to > > tailor the pressure distribution to control separation, and the > > trailing edge must usually be sharp. Some of my airfoils of the > > olden days, when we did this by hand, were C16 > .... > ============================================================ 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
