Well, yea, you're onto a parallel design there. I'm usually referring to the individual instances of physical processes that correspond to the general models of 'basins of attraction'. As far as I can tell 'basins of attraction' are hypothetical constructs designed to improve the accuracy of statistical models and are a very useful construct but don't physically exist. What I find, anyway, when looking to see how patterns of organization develop in individual instances of emerging systems is a lot different, and so my language parallels the standard physics models but addresses different phenomena.
What I start from might be with identifying the boundary between the inside and the outside of the feedback loop network, finding the wiggly line separating the complex interior network of relationships that is acting as a whole and its environment. A 'growth curve' helps identify what things are involved in the same emerging process. It's good to mention that reading subtle changes in the evolution of the system from subtle changes in the continuity of the curve of the data does usually involve a projection of idealized continuity from the actual dots of measurements. I favor things that are much less heavy handed than splines for that. The useful assumption seems to be that there is a form there and it'll be easier to see if the 'clothing' you drape it with is loose fitting... Where the parallels separate is that when studying individual instances of anything there is no 'definition' of the system, and no feature of the physical thing which 'describes the state of the system' as an 'order parameter' might. As close to a 'state variable' as one might get is the hard to explain origin of a growth system, its starting design. Because growth structures are 'sticky' and accumulate around and branch off from the original loops, the character of the original loops remains to the end. It's not realistic to think of defining them, except if one were to experiment with them in structures *of* definition, because all physical things are undefinable, of course. What I've come to as a workable technical definition of a 'growth curve' is a period of time in a measured behavior when all the higher derivatives have the same sign. If for ising model a measure of it's behavior displays such curves then I'd say so. What may be difficult with the kind of lab setup used for helping to refine prediction models is that you'll have a hard time telling the difference between one run of the system and another, I'm not sure. If you can, and see eventfulness (presence of growth curves) in the trace of the differences, then you're in a position to ask pointed question about what made those system developments. You may not find the answer, of course, but you often find new stuff of some kind when you ask new questions. does that make any sense? Phil On 4/9/07, Stephen Guerin <[EMAIL PROTECTED]> wrote:
Phil, > 1) for change situations referred to as, [ before | gap?| > after ] Causal mechanisms that take time can generally be > found in the 'gap' but predictive models are often missing > because they can jump over gaps. I'm wondering where there may be some shared vocabulary between complexity-speak and your notion of growth curves. Is it possible that everything you mean by growth curves is captured by curves of phase-transitions? When you mention "gap" above, might that be the critical point in a phase transition where a system breaks symmetry and chooses between different basins of attraction. The occurence of the transition is predictable but which attractor will emerge, is not. Most models in complexity are concerned with such phenomena. Take an ising model as a classic example <http://www.ibiblio.org/e-notes/Perc/ising.htm>. As a regular array of mutually influencing agents, each decides to spin up or down depending on the states of its neighbors. Magnetization in this model is measured as the proportion of spin up or spin down in the populuation and is called an "order parameter" which is a low-dimensional variable that can describe the collective state of the system. Experimenters tend to not have direct control over order parameters. The parameters they can manipulate are called "control" parameters and in the ising model example, are things like initial configuration and temperature (degree that a spin ignores its neighbors influence and just randomly flips). Does this vocabulary map to yours? If you observe the graph of the magnetization order parameter in the ising model is it a "growth curve"? -Steve > -----Original Message----- > From: Phil Henshaw [mailto:[EMAIL PROTECTED] > Sent: Sunday, April 08, 2007 5:18 AM > To: 'The Friday Morning Applied Complexity Coffee Group' > Subject: Re: [FRIAM] predictive models v. causal mechanisms > > well, so can anyone add to the list of things that make them > different? > > 1) for change situations referred to as, [ before | gap?| > after ] Causal mechanisms that take time can generally be > found in the 'gap' but predictive models are often missing > because they can jump over gaps. > > > > Phil > > Re: > Sent: Friday, April 06, 2007 7:35 AM > To: 'FRIAM' > Subject: [FRIAM] predictive models v. causal mechanisms > > > > Big subject, but, first, are there useful ways tell the > difference? I think the main difference is between images > and things, a big clear difference, and very useful to be > able to distinguish. > > > Phil Henshaw ¸¸¸¸.·´ ¯ `·.¸¸¸¸ > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ > 680 Ft. Washington Ave > NY NY 10040 > tel: 212-795-4844 > e-mail: [EMAIL PROTECTED] > explorations: www.synapse9.com <http://www.synapse9.com/> > > >
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