[Fis] order/disorder/causality

Let me respond/comment Michel's, Karl's and Bob's postings (religion of
probability and definition of order). I would agree with Karl on Natural
numbers. Regarding Bob's combinatorial examples there is a single assumption
that numbers of possibilities should be hardly dependent on - discrete or
continuous space (incl. functional space too). So there can be an enormous
amount of calculated possibilities of various event's combinations, but in
reality different combinations are not equally possible. So number of
possible outcomes (or degrees of freedom) is usually reduced to some minimum
when those events/objects become a part of a larger system. Thus a complete
set of these most probable states each one dependent on it's own attractor
starts behaving like a discrete system with large although limited number of
different states with discontinuous transitions among them. Those states are
usually characterized by probability distributions or some "limits of
tolerance". So in reality there are more similar (although I would not dare
saying identical) events than unique. That's why Case Based Reasoning (AI
approach to problem solving) works so well even for weather predictions or
various diagnosing tasks for machines and humans in technology and medicine.
Even ratios of species in a natural community follow certain patterns of
occurrence - they are never changing continuously, but always in a jumpy
manner. The same can be said about periodic system of chemical elements -
one can not use whatever sort of regression based on continuity to predict
characteristics of an element. But Mendelejev's periodical law based on
discrete assumptions can handle the problem quite easily. And eventually the
same is true for any natural phenomenon - spatial and functional transitions
among cells, atoms, molecules, and everything that we call objects or events
in our 4 dimensions - always occur as jumps. If one takes a real (not
modelled) gradient of salinity or temperature changing with depth in a lake
or sea, then the one again would notice many small jumps instead of an
ideal" continuous change. Now if the one assumes that "the word should be
continuous (somebody prove it please !) and all the rest of it is just a
noise" he will necessarily arrive to the conclusion as Bob wrote : "the
fabric of causality manifests holes everywhere, at all levels"... But is
this true ?..
Wouldn't the following sentence be more correct then: "the fabric of our
XXI-st century knowledge still manifests holes everywhere, at all levels".
Isn't it so that violation of the causality law would also mean violation of
the I-st law of thermodynamics ? So if causality "shows a hole" somewhere in
physical world this should also mean the disproportion of
energy/matter/work/entropy and also a violation of E=mc2 during this "holy"
event. Shouldn't the law of causality play the same role in science as the
I-st law in Thermodynamics (the I-st law of Cyberdynamics ;-) should sound
great ! ) ? But what if "causality holes" are true. Then let's remember
Lorenz who has got totaly different results with his famous system of
equations just because the computer rounded down the numbers stored in
memory. Is then our Universe a computer like the one Lorenz worked with
which tries to round-down numbers that seem too big for calculations and
thence "causality holes", unpredictable behavior, chaos ? Which assumption
is true then ?
 
Definition of order...
Here I would agree with Karl again. It seems like the "order" relates with
synchronicity i.e. interacting elements making a system are more orderly
then independent elements that do not make a system. Then a level of order
(in between these two marginal states) could be calculated as ratio of sync
among elements. Thus order of a perfect system would be equal to 1, order of
chaotic mixture of some independent non interacting parts eq 0. Let's found
what's in between on a real-world example - the Internet by taking a subset
of the internet - 1000 web sites located somewhere. Next step pinging (IT
term) those sites and looking whether they respond or not (how many packages
lost). if 900 sites responded ("were in their places" as Karl wrote), and
100 failed to respond, then system of those 1000 web sites would have a
degree of order eq to 0.9. Probably it should be considered as relatively
high... But the hard part in this is that in nature elements interact in
several ways/levels depending on the purpose of the system(s) they are parts
of. So in this case degree of order should be based on correct responses at
different communication levels (who knows their number ?). And then posibly
adding up those ratios and dividing from number of levels - thus calculating
an average degree of order in the system :-). Just a speculation...
 
Best regards
Viktoras
 
 

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Received on Wed May 5 15:58:26 2004