Re: [FRIAM] another idea for a generalized "nonlinearity" (was Re: Seminal Papers in Complexity)
Hating R: is like hating the air you breathe. On Jun 22, 2007, at 1:57 PM, Russell Standish wrote: On Sat, Jun 23, 2007 at 02:09:31AM -0400, Phil Henshaw wrote: One of the hurdles is the software... As powerful as they are I hate R, and Excel, and AutoCad, though I have nothing else to use... Why are you restricted to these packages? Are they just what you know, and you're not prepared to learn anything else, or does your company madate you use just these and nothing else, or is your computing platform just so weird nothing else will run on it. Can't be cost - there are just so many great open source packages for doing just about anything. Cheers -- -- -- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://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 Marko A. Rodriguez Los Alamos National Laboratory (P362-proto) Los Alamos, NM 87545 Phone +1 505 606 1691 http://www.soe.ucsc.edu/~okram 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
Re: [FRIAM] another idea for a generalized "nonlinearity" (was Re: Seminal Papers in Complexity)
On Sat, Jun 23, 2007 at 02:09:31AM -0400, Phil Henshaw wrote: > One of the hurdles is the software... As powerful as they > are I hate R, and Excel, and AutoCad, though I have nothing else to > use... > Why are you restricted to these packages? Are they just what you know, and you're not prepared to learn anything else, or does your company madate you use just these and nothing else, or is your computing platform just so weird nothing else will run on it. Can't be cost - there are just so many great open source packages for doing just about anything. Cheers -- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://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
Re: [FRIAM] another idea for a generalized "nonlinearity" (was Re: Seminal Papers in Complexity)
Just to rephrase, there's a great way to reapply all the basic theorems of calculus directly to real physical processes (skipping the interceding equations). Use data curves with an appropriate rule for determining a value and slope at any point by iteration. Works great and provides a crystal clear identification of the emergent non-linear phases of real processes. Like anything, you'd expect many questions, and slow beginning, then big strides. One of the hurdles is the software... As powerful as they are I hate R, and Excel, and AutoCad, though I have nothing else to use... 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 Glen E. P. Ropella > Sent: Friday, June 22, 2007 3:02 PM > To: The Friday Morning Applied Complexity Coffee Group > Subject: [FRIAM] another idea for a generalized > "nonlinearity" (was Re: Seminal Papers in Complexity) > > > -BEGIN PGP SIGNED MESSAGE- > Hash: SHA1 > > > I just realized there's another general sense of "linearity" > that some non-mathematical descriptions target, that of > "balance". The idea is that a system shows some sort of > balance where no one component contributes more than any > other component. Simple examples would be adding a nonlinear > term to a previously linear equation: > >1) z = a*x + b*y, changed to >2) z = a*x^2 + b*y > > Technically, (2) is linear because f(x,y) = f(x) + f(y) (note > that just because the sets described are not planes doesn't > mean the function is nonlinear). It is still describable as > linear because one can cleanly separate out the co-domain (by > definition) into X and Y. I.e. in the characterization of > the co-domain, X and Y contribute equally, any point in that > product space is fair game. > > But, if we were to bias it in some way, let's say we define > functions as going from the positive reals (R+) crossed with > the reals (f : R+ x R -> R). Then that may touch on > someone's intuition of what "nonlinear" means. > > That sort of concept is captured in linear algebra by the > concept of a "balanced set". E.g. R+ x R is not balanced > because R+ is not balanced. The set described by (2) above > is not balanced where (1) above _is_ balanced, even though > both are linear functions. Of course, in order for one to > have a sense of balance, one has to have a fulcrum about > which to balance. And sometimes its useful to describe > spaces that don't have such fulcrums (as in the affine plane > described previously). So the linear algebra "balanced set" > doesn't generalize very well, especially to vague > descriptions of spaces and mappings between them. > > Glen E. P. Ropella wrote: > > But, there's no reason you couldn't define the same _type_ of thing > > with other composition operators. All you need to do to have an > > unambiguous definition of what you mean by "linearity" is > to a) define > > the composition operator you're talking about and b) define the > > closure of that operator. Of course there are plenty of such > > constructs already, they just aren't referred to with the word > > "linearity". > > > 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 > > > > - -- > glen e. p. ropella, 971-219-3846, http://tempusdictum.com > I have an existential map. It has 'You are here' written all > over it. -- Steven Wright > > -BEGIN PGP SIGNATURE- > Version: GnuPG v1.4.6 (GNU/Linux) > Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org > > iD8DBQFGfBywZeB+vOTnLkoRAnM1AKDdMkLIf3LNW9pnhVA1M6wcoMQPMQCdERKI > UthB//12Jk4flYLe0c+PJhU= > =1Gja > -END PGP SIGNATURE- > > > 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
[FRIAM] another idea for a generalized "nonlinearity" (was Re: Seminal Papers in Complexity)
-BEGIN PGP SIGNED MESSAGE- Hash: SHA1 I just realized there's another general sense of "linearity" that some non-mathematical descriptions target, that of "balance". The idea is that a system shows some sort of balance where no one component contributes more than any other component. Simple examples would be adding a nonlinear term to a previously linear equation: 1) z = a*x + b*y, changed to 2) z = a*x^2 + b*y Technically, (2) is linear because f(x,y) = f(x) + f(y) (note that just because the sets described are not planes doesn't mean the function is nonlinear). It is still describable as linear because one can cleanly separate out the co-domain (by definition) into X and Y. I.e. in the characterization of the co-domain, X and Y contribute equally, any point in that product space is fair game. But, if we were to bias it in some way, let's say we define functions as going from the positive reals (R+) crossed with the reals (f : R+ x R -> R). Then that may touch on someone's intuition of what "nonlinear" means. That sort of concept is captured in linear algebra by the concept of a "balanced set". E.g. R+ x R is not balanced because R+ is not balanced. The set described by (2) above is not balanced where (1) above _is_ balanced, even though both are linear functions. Of course, in order for one to have a sense of balance, one has to have a fulcrum about which to balance. And sometimes its useful to describe spaces that don't have such fulcrums (as in the affine plane described previously). So the linear algebra "balanced set" doesn't generalize very well, especially to vague descriptions of spaces and mappings between them. Glen E. P. Ropella wrote: > But, there's no reason you couldn't define the same _type_ of thing with > other composition operators. All you need to do to have an unambiguous > definition of what you mean by "linearity" is to a) define the > composition operator you're talking about and b) define the closure of > that operator. Of course there are plenty of such constructs already, > they just aren't referred to with the word "linearity". 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 - -- glen e. p. ropella, 971-219-3846, http://tempusdictum.com I have an existential map. It has 'You are here' written all over it. -- Steven Wright -BEGIN PGP SIGNATURE- Version: GnuPG v1.4.6 (GNU/Linux) Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org iD8DBQFGfBywZeB+vOTnLkoRAnM1AKDdMkLIf3LNW9pnhVA1M6wcoMQPMQCdERKI UthB//12Jk4flYLe0c+PJhU= =1Gja -END PGP SIGNATURE- 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
