Sunday, February 03, 2008 9:15 AM, Francis McCabe wrote: (01)
''I think that what is going on may be a little deeper.... Now, there is
some evidence that the universe is not truly continuous:
it may be granular both with respect to space and with respect to time.'' (02)
The universe is the largest continuous entity, continuing both in time and
space. The chaos theory doesn't mystify the nature of the world more than it
is. But it evidences to its puzzling complexity, it attests that the
universe is a cosmic-scale nonlinear dynamic complex system governed by
reciprocal interactions of its numerous parts. (03)
All nonlinear effects in nature and society studied by nonlinear sciences
and represented by nonlinear equations can be accounted by the same causal
mechanisms: nonlinear causality (as causal loops) producing nonlinear
self-acting phenomena (expressed as soliton solutions), as in general
relativity, nonlinear QM, nonlinear optics, the planet's weather system,
global economy and finance and international politics. A timely appreciation
of nonlinear effects in the global stock exchange allowed Soros (and his
Quantum Fund) reputedly to make billions, knowing the nonlinear behavior of
economic fundamentals and risk-factors such as interest rates, commodities,
currencies, stock indices. (04)
The implication of chaos is the complexity of causality as the nonlinear
relationships between changes, processes or events, where a small input
change (infinitesimal disturbances in the initial conditions) in one part of
a complex system may end up in a large effect in toto. (05)
So, the real meaning of ''chaos'' is not ''disorder'' but rather a
higher-order dynamic organization; for a chaotic system is a deterministic
and principally predictable phenomenon, whose behavior is determined by
nonlinear causal laws. (06)
The moral of the whole story is to build a consistent ontology of entities
and relationships, including such a unique natural phenomenon as a nonlinear
causality http://en.wikipedia.org/wiki/Causality. (07)
Azamat Abdoullaev (08)
----- Original Message -----
From: "Francis McCabe" <frankmccabe@xxxxxxx>
To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
Sent: Sunday, February 03, 2008 9:15 AM
Subject: Re: [ontolog-forum] Axiomatic ontology (09)
>I think that what is going on may be a little deeper.
>
> Stipulating for a moment the continuous function argument. In any
> digital system, in any countable system actually, you can approximate
> a real number's value to any desired level of precision.
>
> Now, there is some evidence that the universe is not truly continuous:
> it may be granular both with respect to space and with respect to time.
>
> If your approximation of a continuous function is more accurate than
> that granularity, then it can make no difference in the observed
> results. I.e., digital simulations of fractal functions and chaotic
> predictions can be as accurate as the universe will allow anyway.
>
> However, the weather man does not need to go to this level of accuracy
> to get results that are best explained in terms of chaos theory. The
> results of a prediction are unstable at any level of accuracy: the
> higher the accuracy the longer the stable prediction; but the pattern
> is the same.
>
>
> On Feb 2, 2008, at 10:34 PM, Rob Freeman wrote:
>
>> On Feb 3, 2008 12:11 PM, Randall R Schulz <rschulz@xxxxxxxxx> wrote:
>>> On Saturday 02 February 2008 19:47, Rob Freeman wrote:
>>>>
>>>> Why can't we model chaotic behaviour on a digital computer Randall?
>>>
>>> Because digital computers cannot represent or process real numbers.
>>
>> That's a good point.
>>
>> Here's Wikipedia to put it in context:
>>
>> "An early pioneer of the theory was Edward Lorenz whose interest in
>> chaos came about accidentally through his work on weather prediction
>> in 1961. Lorenz was using a simple digital computer, a Royal McBee
>> LGP-30, to run his weather simulation. He wanted to see a sequence of
>> data again and to save time he started the simulation in the middle of
>> its course. He was able to do this by entering a printout of the data
>> corresponding to conditions in the middle of his simulation which he
>> had calculated last time.
>>
>> To his surprise the weather that the machine began to predict was
>> completely different from the weather calculated before. Lorenz
>> tracked this down to the computer printout. The computer worked with
>> 6-digit precision, but the printout rounded variables off to a 3-digit
>> number, so a value like 0.506127 was printed as 0.506. This difference
>> is tiny and the consensus at the time would have been that it should
>> have had practically no effect. However Lorenz had discovered that
>> small changes in initial conditions produced large changes in the
>> long-term outcome. Lorenz's discovery, which gave its name to Lorenz
>> attractors, proved that meteorology could not reasonably predict
>> weather beyond a weekly period (at most)."
>> http://en.wikipedia.org/wiki/Chaos_theory
>>
>> So this presents a problem.
>>
>> To draw the analogy, though, Lorenz didn't react to his discovery by
>> abandoning computer modeling of the weather, or by assuming the
>> weather was not really chaotic after all. He just accepted that tiny
>> inaccuracies meant that any digital copy of the weather would diverge
>> from the original over time.
>>
>> I'm guessing chaos is still assumed in all modern models of the
>> weather, and further I'm assuming all those models are still digital.
>>
>> Digital models of the weather may be imperfect, but presumably to
>> ignore chaos when you try to model the weather is not to model the
>> weather at all.
>>
>> Note: there's an interesting corollary to this idea of sensitivity to
>> arbitrarily small differences in initial conditions. It would mean
>> that, assuming a chaotic model, any "copy" we might one day be able to
>> make of an individual's thoughts would immediately start to diverge
>> from the original. So while one day it may be possible to copy
>> someone's thoughts, according to this model it would never be possible
>> to predict them (beyond a week or so :-)
>>
>> -Rob
>>
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