🚀 go-pugleaf

In article <76441@ut-emx.uucp> johncobb@ut-emx.cc.utexas.edu (John W. Cobb) writes:
>In article <1992Jul20.153122.29180@murdoch.acc.Virginia.EDU>,
>crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass) writes:

>|>     This is good, if you take credit for 'chaos theory' for all of the
>|>     work going back to Poincare, then you are left with a dilemma.  Either
>|>     the subject is a rather evolutionary outgrowth of dynamical systems
>|>     theory with the addition of large computers to guide us, in which
>|>     case it seems difficult to justify assigning earthshattering importance
>|>     to it, or it is not, in which case it seems difficult to justify
>|>     taking credit for 90 year old results.
>                                                                        
>I think this point is fallacious. It is like saying that the discovery of the
>double helix structure of DNA is an "evolutionary outgrowth" of x-ray
>crystallography and has no "earthsattering importance". Even Newton admitted
>that if he had voiced some deep and fundamental ideas that he owed a
>debt of gratitude to the giants on whose shoulders he stood. The recent
>flurry of interest in chaos is indeed based upon a long history of previous
>results of great importance, but it is untrue to somehow imply that very
>little of the current work is fundamentally new -- it is.

     I did not say this.  I said that the importance was somewhat overstated
     and oversold.  I still say this.

     I also implied that certain proponents seem to have blinders that
     seem to shield the importance of most work done before about 
     1975.
  
     [stuff deleted]     

>Geometry. That this is an needed task is borne out by many of the comments
>on this newsgroup that reveal both a fundamental misperception about what
>chaos means and a refusal to acknowledge that it fundamentally changes
>notions about dynamics in physical systems where it exists (for example,
>sensitive dependance on initial conditions implies abscence of predictability).

     However, this, as well contains a misconception.  Sensitive dependence
     on initial conditions does not necessarily imply unpredictability of 
     all gauges of a system, just the one to which the system is sensitive.
     (for example the velocities of a fluid system may be completely 
     unstable while the total energy shows a nice smooth bounded behavior.
     If appropriate or possible, one might be better off reformulating the 
     system in terms of total energy and leaving the sensitive dependence 
     in the dustbin.)

                                  dale bass

>john w. cobb
>jwc@fusion.ph.utexas.edu


--
C. R. Bass                                           crb7q@virginia.edu
Department of Mechanical and Aerospace Engineering
University of Virginia
Charlottesville, Virginia                            (804) 924-7926