[Top] [All Lists]

Re: [ontolog-forum] Axiomatic ontology

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Rob Freeman" <lists@xxxxxxxxxxxxxxxxxxx>
Date: Sun, 3 Feb 2008 14:34:19 +0800
Message-id: <7616afbc0802022234p32ffa0c0qf811b322019ecaa4@xxxxxxxxxxxxxx>
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.    (01)

That's a good point.    (02)

Here's Wikipedia to put it in context:    (03)

"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.    (04)

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    (05)

So this presents a problem.    (06)

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.    (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)

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.    (09)

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 :-)    (010)

-Rob    (011)

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    (012)

<Prev in Thread] Current Thread [Next in Thread>