Discrete Chaos LO990

Doug Seeley (100433.133@compuserve.com)
30 Apr 95 05:48:45 EDT

Replying to LO845, Chas Barclay wrote...

...(paraphrasing) that my description of Discrete Chaos confusing because
i) Chaos was a strictly continuous phenomenon, and ii) the point about
Chaos is that it is essentially deterministic, and did not use any
stochastic (random) elements . I will try to clarify my use of this term
in the context of this question.

It is true that what is conventionally described as Chaos comes from the
bifurcation results in non-linear dynamic systems, an applied mathematics
discipline. Basically the complexity of possible behaviours in such
systems, including their sensitivity to minute changes in parameters,
reaches such a degree that the behaviour can only be called chaotic.

Now, I don't regard the use of the term Chaos by this branch of
mathematics to be their exclusive perogative. To do so, would be part of
the malaise of current Western thinking which grants an Authority to
Science and its assumptions about the exclusivity of an objective reality
which for many, including myself, denies a significant aspect of our
essential humanity. Consequently, I believe that metaphorical uses of
Chaos are perfectly valid as long as they are distinguished from that
particular mathematical use referred to above.

Hence, I feel it is legitimate to call another form of complex system
behaviour (other than non-linear continuous systems) chaotic, even when it
is treated mathematically and opportunistically, evoking some metaphorical
allusions with the phrase "discrete chaos".

There is a parallel to chaos in the complex behaviour of discrete systems.
Except for the Quantum perspective, which I leave outside of the scope of
our current discussion, statistical distributions can be looked at as not
describing any essential randomness, but rather as providing a succinct
and useful description which provides opportunities to "handle" the
complexity.

As an example, we can describe the arrivals of patrons at the cinema in
statistical terms; however, every one of the patrons could describe the
unique causality which brought them to the cinema at a specific time
(including recursive reference to other traffic situations). Randomness
and statistics then are good ways of handling the complexity of the world,
where questions regarding the ensemble behaviour, as opposed to individual
behaviour, are involved.

Hence, I take a more generic view of chaos that views it as "the
unpredictability of a particular system behaviour emerging from
potentially very, different and possibly divergent system behaviours,
especially in their impact upon their environment."

Consequently, in a simple queuing system, where say a Poisson arrival
pattern is matching a similar Poisson service pattern, theresulting
behaviour becomes "chaotic" in the above sense. Although, the long-run
statistical behaviour is known; i.e. the congestion grows infinitely; the
"experience" of a single realization of this system is very
unpredictable... it can swing wildly between an apparently stable
situation, to one that is congesting out of control, and back again until
the long-run behaviour eventually dominates. Queuing people usually focus
only on the long-run Average behaviour instead of particular realizations.
However, in an actual situation the "shit would hit the fan" as soon as a
run of congestion overwhelmed the local capacity. In live situations, it
is this individual experience which counts.

It was only when I watched many animations of this in validating our
simulation software, that this phenomenon really came home to me, and
correlated with the divergent ways of observing this that we were
witnessing in the field between managers and operations staff. Even
though I was very aware of the "theorectical" result, it required careful
observation of simulation animations to bring the point across about
individual behaviours.

Now about the issue of Discrete vrs. Coninuous.... Using my definition
above, there are many models in the field of Complex Systems which display
similarly chaotic behaviour or which have a sudden phase change in
behaviour which occurs unpredictably. The one I am most familiar with is
in the evolution of random digraphs, a very discrete model in which an
almost continuous parameter, the degree of strong connectivity can behave
very chaotically around one of these phase changes (see my posting on
Chaos and Complexity a week ago).

However, in response to Chas' comment that "continuous models are better
suited as corporate models where random variation is limited". I
personally responded,...

"We are having excellent results using discrete dynamic models as the
basis of decision support tools in all sectors of Australian business.
The prime methodological point in our consulting is that the lack of
acknowledgment of dynamics and random variation is producing very faulty
planning at the corporate level; it is especially evident in the way
bursty demands are handled. I would go as far as to say that the business
culture's assumptions that uniformity, continuity and lack of random
variation are doing much more harm than good, especially in creating an
enormous division between corporate financial views and the operational
views from the shop floor."

To which Chas replied... "In regards to what I work with, success and
failure of firms and the reasons why, I don't yet see how a discrete model
would supercede the ones I work with. I'll consider it though..."

We are finding that a combination of two things are contributing to the
failure of some companies, and hence, need to be acknowledged in strategic
considerations and planning. The first is that typical performance
measurements based upon cost acountancy or even activity based
accountancy, smear the very real impacts, which are crucial to
profitability, of random variation operationally and in bursty demand
scenarios. The point being that when the assumption that they can be
ignored is made, pure continuous modelling tends to be applied in
modelling in such a way that the assumption, no longer being made
explicitly, is rarely questioned again. We address this issue using a
technique we call event-based financial modelling, and not with typical
queuing methodologies.

The second major contribution to failures which we are observing, is the
lack of any valid linkages between individuals, individual work-centres
and functional divisions And the wholistic behaviour of the system. Once
alerted to this issue, it is not so hard to see how more wholistic
performance measurement an not only bring the organization into better
alignmnet, but can make relationships between different corporate elements
more harmonious.

Thanks for your stimulating questions, and by the way I agree with You
about Machiavelli.

Cheers, Doug Seeley

--
Doug Seeley:  compuserve 100433,133... Fax: +41  22  756  3957
	InterDynamics Pty. Ltd. (Australia) in Geneva, Switzerland
	"Integrity is not merely an ideal; it is the only reality."