Na, I think even the most sophisticated math misses all the truly supple shape of natural form, and it it's of huge signifiance in our missunderstanding of natural phenomena.
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 Russell Standish > Sent: Friday, June 22, 2007 3:52 PM > To: The Friday Morning Applied Complexity Coffee Group > Subject: Re: [FRIAM] Seminal Papers in Complexity > > > On Fri, Jun 22, 2007 at 10:34:09AM -0700, Glen E. P. Ropella wrote: > > -----BEGIN PGP SIGNED MESSAGE----- > > Hash: SHA1 > > > > Michael Agar wrote: > > > As described in past posts, that's exactly what I'm > trying to figure > > > out--formal math definition doesn't help, metaphorical > use too vague. > > > Whatever the solution is, it's likely to be > propositional/schematic > > > rather than numeric and involve observer perspective/background > > > knowledge. I'll write more to the list when I think I'm > onto a solution. > > > > Formal math definitions do help. You just can't be myopic about it > > and restrict yourself to arithmetic. Open it up to higher math. > > > > It seems you want to generalize linearity to apply to _other_ > > composition functions. The typical definition of linearity applies > > only to addition, i.e. f(x+y) != f(x) + f(y). If you > abstract up just > > a bit, linearity means "on the same line", which is a way of saying > > "in the same space" where the space is 1 dimensional. It's > simply a > > closure under addition. > > Not just addition, but also scalar multiplication by a member > of a field. > > For any group G, one can consider the class of functions > f:G->G satisfying f(x+y)=f(x)+f(y). This induces a > linear-like property over N x G, ie for all a, b in N and for > all x and y in G, > > f(ax+by) = af(x)+bf(y) > > where ax = \sum_i=0^a x > > However such objects are not linear functions, and don't > appear to have a name. Perhaps they're not all that useful. > > > -- > > -------------------------------------------------------------- > -------------- > A/Prof Russell Standish Phone 0425 253119 (mobile) > Mathematics > UNSW SYDNEY 2052 [EMAIL PROTECTED] > Australia http://www.hpcoders.com.au > -------------------------------------------------------------- > -------------- > > ============================================================ > 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
