Frank, (01)
If I understand you correctly, I agree. I know of at least two
theories which try to explain basic physics computationally. Karl
Zuse's is the oldest. (02)
E.g. http://www.idsia.ch/~juergen/digitalphysics.html (03)
So philosophically you may be able to go straight from your
computational model of the weather, to a computational model of the
basic physics, and cut out the idea of continuous values completely. (04)
Randall's rounding error point would stand for practical systems, of
course. It is an issue of how much information you are willing to
store. (05)
But, if understand you correctly, I agree the most interesting effects
will be above the level of rounding error. (06)
What I find most exciting is the way chaos acts as an enormous well of
new structure. Lack or order is not necessarily a bad thing. Rather it
can be thought of as freeing you to create new structure (if something
is ordered its structure is bounded.) (07)
For instance, W. J. Freeman's work makes much of the way an organism
seems to continuously fold experience into new configurations which
represent new perspectives on a stimulus. He makes a big point of
there being no "meaning" for an organism independent of intent. (08)
E.g. "Perceived time differs from world time in ways that are
determined by the neural mechanisms of intentionality." (09)
(Perception of Time and Causation Through the Kinesthesia of
Intentional Action, 2008.
http://www.springerlink.com/content/u25052w300187661/) (010)
So the great thing is you get all this new structure (liberated by
disorder.) From a meaning representation point of view this new
structure could be thought of as constantly letting you find new
relationships among data. From a linguistic point the new structure
might be thought of as constraining what what can be said (to explain
the detail of collocation, etc.) (011)
-Rob (012)
On Feb 3, 2008 3:15 PM, Francis McCabe <frankmccabe@xxxxxxx> wrote:
> 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. (013)
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