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Re: [ontolog-forum] Axiomatic ontology

To: Rob Freeman <lists@xxxxxxxxxxxxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Ed Barkmeyer <edbark@xxxxxxxx>
Date: Tue, 05 Feb 2008 13:18:39 -0500
Message-id: <47A8A87F.1030106@xxxxxxxx>
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)

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