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Re: [ontolog-forum] Axiomatic ontology

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Ed Barkmeyer <edbark@xxxxxxxx>
Date: Mon, 04 Feb 2008 14:54:01 -0500
Message-id: <47A76D59.3010905@xxxxxxxx>
Rob Freeman wrote:    (01)

> 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    (02)

I think this last statement may be false, in that it clearly depends on 
the nature and magnitude of the  model's response to the perturbation, 
not necessarily on the relationship of actual weather to the accuracy of 
any measured atmospheric property.  That is, its truth depends on the 
validity of the Lorenz model.    (03)

It is my recollection that the National Weather Service spent most of 
the 1960s and 1970s buying faster and faster computers to do higher and 
higher precision arithmetic on the Lorenz model and finally came to the 
conclusion that the model just wasn't that good.  NOAA and its 
counterparts worldwide have better physical models of global weather 
now, as a consequence of having made better measurements of atmospheric 
behaviors.  And they are still trying to improve their understanding of 
atmospheric physics.  The issue is not "real arithmetic" -- it is the 
characterizations of situations and the range of accuracies (of 
measurements, more so than calculations) in which the weather model in 
use is valid.    (04)

> 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.    (05)

Being very careful, this is a different issue.  Whenever computational 
values are converted, there is danger of their accumulating noise or 
loss.  In most cases, if you represent an arbitrary value in a different 
base or a different precision, you have a *different* value.  (Whether 
the difference is significant or not is another matter.)  Lorenz's 
problem was a transcription problem.    (06)

In addition, there is "bit rot" -- everytime you copy the same digital 
value across media, there is a small probability of a read error.  Yes, 
it is order 10^-10, but if you move the same megabyte 100 times, you are 
rolling the dice 10^9 times.    (07)

> 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.    (08)

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.  A lot of mathematical models used in engineering for 
estimating effects of load and pressure and temperature and so on are 
known to be "chaotic" -- small perturbations produce differences of 
enormous magnitude in the results -- in certain regions.  Experienced 
engineers simply don't use those models in those regions.  (Think of 
algorithms for evaluating the tangent of a number near pi/2.  As Mary 
Payne once described it, "computationally, the tangent function has a 
discontinuity, but no singularity.")    (09)

Some systems defy effective modeling because we know that they are 
self-symmetric.  I don't think we know enough to say that about the weather.    (010)

> 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.    (011)

I would never be so bold as to say this.  Perhaps some of the NOAA folk 
would.    (012)

In a similar way, I recall Azriel Rosenfeld (an image processing pioneer 
of the 1960s) saying that he was coming to the belief that sequential 
computational algorithms for analyzing images would never be able to 
replicate the capabilities of human and animal minds in analyzing 
images, and some different form of computation would be needed.  40 
years later, I don't know what the experts in that field believe.    (013)

-Ed    (014)

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    (015)

"The opinions expressed above do not reflect consensus of NIST,
  and have not been reviewed by any Government authority."    (016)

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