Discrete and continuous
Posted: Fri Apr 26, 1996 3:07 pm
Ive been holding back on this discussion, but finally feel that I have to
point out that there is a lot of literature on this topic. The topic
emerged naturally in my study of the history of feedback thought -- the
index of Feedback Thought contains the entries - continuity and
discreteness - continuous point of view - difference equations -
differential equations - discreteness - events - message loops each of
which has references to at least ten places in the text, and some to a lot
more. Some of the stuff covered here shows how smart people got confused
about dynamic feedback systems by using difference equations instead of
differential equations, and some shows how different the contributions are
when one is thinking in terms of discrete events and decisions and when
one is thinking in terms of policy structure and dynamics. Some of it
shows how many in one line of feedback thought in the social sciences came
to center on discrete events and messages, thus drifting away from ideas
like loop polarity, which peopl in the other thread seem to emphasize so
much. I think we need more data for this discussion.
Weve been tending to discuss this topic on the list as an issue of
"representation" -- the choice of differential or difference equations,
or event-oriented simulation packages or whatever. But fundamentally the
topic is about how we are trying to think about the system. The choice
of how we are trying to think about the system has a lot to do with our
purpose -- we might think that electricity is fundamentally (really) a
discrete thing (electrons or smaller bits) but we might know that we can
do wonders designing electronic circuits if we think of electricity as a
flow. Same goes for population or inventory, at some sufficient level of
aggregation and conceptual distance. Our simulations are tools for our
thinking, so we should push the discrete/continuous questions in the
direction of thinking and away from representation.
To bring the matter close to home: The article by R.G. Coyle ("A System
Dynamics Model of Aircraft Carrier Survivability", SDR 8,3(fall 1992):
193-212) is, in my view a discrete model, formulated that way because the
author was intentionlly thinking in discrete event terms when he built
it. He used COSMIC/COSMOS, a DYNAMO-like language intended for system
dynamics modeling. One can imagine a continuous representation of that
dynamic system, where aircraft carriers and planes ebb and flow on
continuous paths rather than steps from 6 to 7 or 583 to 584. To help
focus our discussion on discrete and continuous, we might well ask what
does one learn in each repsentation? Are there differences in what one
learns? Rod MacDonald is addressing just that question. We might help
our list discussion along if more of us tackled such a question.
...Geo
-----------------------------------------------------------------------------
George P. Richardson G.P.Richardson@Albany.edu
Rockefeller College of Public Affairs and Policy Phone: 518-442-3859
University at Albany - SUNY, Albany, NY 12222 Fax: 518-442-3398
-----------------------------------------------------------------------------
point out that there is a lot of literature on this topic. The topic
emerged naturally in my study of the history of feedback thought -- the
index of Feedback Thought contains the entries - continuity and
discreteness - continuous point of view - difference equations -
differential equations - discreteness - events - message loops each of
which has references to at least ten places in the text, and some to a lot
more. Some of the stuff covered here shows how smart people got confused
about dynamic feedback systems by using difference equations instead of
differential equations, and some shows how different the contributions are
when one is thinking in terms of discrete events and decisions and when
one is thinking in terms of policy structure and dynamics. Some of it
shows how many in one line of feedback thought in the social sciences came
to center on discrete events and messages, thus drifting away from ideas
like loop polarity, which peopl in the other thread seem to emphasize so
much. I think we need more data for this discussion.
Weve been tending to discuss this topic on the list as an issue of
"representation" -- the choice of differential or difference equations,
or event-oriented simulation packages or whatever. But fundamentally the
topic is about how we are trying to think about the system. The choice
of how we are trying to think about the system has a lot to do with our
purpose -- we might think that electricity is fundamentally (really) a
discrete thing (electrons or smaller bits) but we might know that we can
do wonders designing electronic circuits if we think of electricity as a
flow. Same goes for population or inventory, at some sufficient level of
aggregation and conceptual distance. Our simulations are tools for our
thinking, so we should push the discrete/continuous questions in the
direction of thinking and away from representation.
To bring the matter close to home: The article by R.G. Coyle ("A System
Dynamics Model of Aircraft Carrier Survivability", SDR 8,3(fall 1992):
193-212) is, in my view a discrete model, formulated that way because the
author was intentionlly thinking in discrete event terms when he built
it. He used COSMIC/COSMOS, a DYNAMO-like language intended for system
dynamics modeling. One can imagine a continuous representation of that
dynamic system, where aircraft carriers and planes ebb and flow on
continuous paths rather than steps from 6 to 7 or 583 to 584. To help
focus our discussion on discrete and continuous, we might well ask what
does one learn in each repsentation? Are there differences in what one
learns? Rod MacDonald is addressing just that question. We might help
our list discussion along if more of us tackled such a question.
...Geo
-----------------------------------------------------------------------------
George P. Richardson G.P.Richardson@Albany.edu
Rockefeller College of Public Affairs and Policy Phone: 518-442-3859
University at Albany - SUNY, Albany, NY 12222 Fax: 518-442-3398
-----------------------------------------------------------------------------