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Re: [ontolog-forum] Axiomatic ontology

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Jakub Kotowski <jakubkotowski@xxxxxxx>
Date: Wed, 06 Feb 2008 09:41:06 +0100
Message-id: <47A972A2.7090001@xxxxxxx>
Rob Freeman napsal(a):
> So chaos need not be all bad. It would make sense if we stored our
> information this way. Otherwise we would just be wasting bits.
>   
Not to mention Ramsey's theorems from which it follows that complete 
chaos is impossible :)
(just roughly: if you take a sufficiently large graph you will always 
find a complete subgraph on n vertices or its complement - i.e. n 
vertices with no edges between any two of them).    (01)


> -Rob
>
> On Feb 6, 2008 2:18 AM, Ed Barkmeyer <edbark@xxxxxxxx> wrote:
>   
>> Rob Freeman wrote:
>>
>>     
>>> 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"?
>>>       
>> No.  I should have been more careful about what I wrote.
>>
>> 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.
>>
>> 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.
>>
>> 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.
>>
>> 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.)
>>
>>
>> -Ed
>>     
>  
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>       (02)


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