Rob Freeman wrote: (01)
> On Feb 5, 2008 3:54 AM, Ed Barkmeyer <edbark@xxxxxxxx> wrote:
>> Chaotic response is a behavior of a model under certain conditions. It
>> is proper to say that the model is probably not "valid" or "good enough"
>> under those conditions to predict anything about the system being
>> modeled.
>
> Are you saying, not only "meaning" or the weather, but all chaotic
> behaviour is really only a manifestation of models which are not "good
> enough"? (02)
No. I should have been more careful about what I wrote. (03)
We have observed in many cases that mathematical models or discrete
simulation models of certain systems demonstrate chaotic responses to
certain stimuli, when the systems in question simply respond by moving
to a different, although less predictable, understood dynamic state. In
those cases, the problem is clearly that the model isn't faithful to the
behaviors of the system. (04)
There are systems that actually have chaotic response to very minor
perturbations in certain regions, or in the self-symmetric case, in some
parts of every region. (05)
My point was that one cannot conclude from chaotic behavior in a model
that that behavior is reflected in the behavior of the modeled system.
It may just be that the model breaks down in that region. We must come
to recognize true chaotic behavior by experimental observation. (06)
And trying to validate that kind of stimulus-response performance
experimentally is quite tricky. You have to ensure that the values of
the two experimental stimuli are different but close enough to
demonstrate the chaotic response, and that usually requires very fine
control and measurement of the stimulus. Further, you have to be
convinced that there is no other uncontrolled variable operating to
produce the difference in effect. And most of the simulation model
failures occur precisely because they don't take account of some
unexpected influential variable. (The mathematical models tend to fail
because the model uses an understood function to approximate an unknown
one, and the behaviors of those functions diverge in some region. Once
you make reliable experimental observations in the region, it is easy to
see the functional divergence. That was the point of Mary Payne's
observation -- the tangent of the closest machine value to pi/2 is still
representable as a machine value, and the tangent of the next value
beyond that has a different sign.) (07)
-Ed (08)
--
Edward J. Barkmeyer Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263 Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263 FAX: +1 301-975-4694 (09)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (010)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (011)
|