re: previous messages on "Semantics" and "SD is not differntial equations"
IMO, SD is a methodology. It consists of a. the stock-and-flow
modelling grammar, and b. the simulation based on discrete-time
of fixed-interval with deterministic difference-equation approach (approach M).
It may be better to classify the target problems into two types:
P. industrial/ social/ economic, and
Q. science/ engineering/ biology.
The original development, when described as Industrial Dynamics (ID),
was attempting to study type P problems by transforming them into a model
that can be feasiblly simulated by digital computer. Otherwise the
continuous-time deterministic diffrential-equation approach (approach
N), typical for type Q problems, was not readily applicable to type P problems.
Conventionally, type P problems are basically associated with
approach M, and type Q with N.
(Note: The word "continuous" system in the original ID context is not
actually representing mathematical continuity. Virtualy the meaning
should be "smooth" system/ process. "Smoothing" has already importantly
mentioned in ID as part of the transformation.)
Theoretically, type P problems should be basically associated with
approach M, and type Q with N. But practically ID stock-and-flow grammar
is sometimes suitable for use with approach N for type Q problems.
The reality is that nowadays SD can be applied to both P and Q types.
When solving type P problems (as classical application),
SD is used to approximate the P problem to a transformed M-oriented model
that can be suitably simulated by approach M.
When solving type Q problems,
SD is used to approximate the Q problem to a transformed M-oriented model
that can be suitably simulated by approach M, but M in this way is only an
approximation of N. N is theoretically used to analyse Q but N is not
actually used in a SD simulation.
Enough for now!
Shaun TANG
stang@fcit.monash.edu.au
Semantics - What is SD?
-
gallaher@teleport.com (Ed Gallah
- Member
- Posts: 39
- Joined: Fri Mar 29, 2002 3:39 am
Semantics - What is SD?
>In SD0131 Shaun TANG discussed diffeq and SD
Please look at Shauns original message to obtain the terminology. I wont
repeat it here.
Shaun, I found your sorting into type P and Q to be interesting and
though-provoking. I agreed with most of what you said, except:
>Theoretically, type P problems should be basically associated with
>approach M, and type Q with N. But practically ID stock-and-flow grammar
>is sometimes suitable for use with approach N for type Q problems.
>The reality is that nowadays SD can be applied to both P and Q types.
I cannot speak for engineering, but for biology I see no a priori reason to
believe that "theoretically, biology problems -should- be associated with
diff eq."
I want to again state that I have nothing against diff eqs, except that
they are more difficult, and require much more extended and rigorous
training than does S&D diagrams.
If one has the time and the inclination to do this intellectual power
lifting, go for it! (Keeping in mind that a working knowledge will also
require an understanding of matrix algebra and numerical analysis.....)
But I have yet to see a strong case provided here for the -advantages- of
diff eq over SD.
(...other than a large installed user base in many disciplines, a somewhat
perverted advantage at best; after all, witness PCs ms Macs; but thats
another story....)
There may very well be some advantages to diff eqs, but I am not aware of
them. Perhaps others can enlighten me.
Since there is NOT a large installed user base of diff eq-ers in biomedical
research, why force people to go this route? Right now the very strong
impetus is to just not do quantitative system analysis, or to even think
about it. We are seeing very dramatic and exciting advances in molecular
biology, but this is creating a larger and larger supply of exciting,
disconnected factoids.
Putting these pieces together requires a systems approach, and no amount of
specracular reductionist work is going to change this.
Obtaining more and more detail about the structure and chemical composition
of an airplane wing, engine components, etc. etc. is very useful. However,
wouldnt it be nice to put all the pieces together (i.e. a complete system)
and test it in a wind tunnel before flying passengers?
It sure would be nice if we took this approach before new meds were
released! Despite isolated examples to the contrary, this is not the way
biomedical research is done.
Simple example: Hypertension.
BP system includes brain (controller), sensors (carotid artery pressure
sensor), blood volume, and pipes.
BP is too high for any number of unknown reasons. Current drugs include
vasodilators (increase the volume of the pipes -> decrease pressure), and
diuretics (salt and water loss -> decreased volume -> decreased pressure).
Response of the body: Sensor detects decrease BP, sends info to brain.
Brain says, "Uh-oh, the BP is too low", sends out signals to in increase
heart rate and strength, and *constrict the blood vessels* (!!) Ooops!
Adopting a systems approach changes our perspective:
Perhaps the BP is too high because the sensor is sending an incorrect
signal telling the brain that the BP is too low?!
In any event, suppose we could find a drug which affects the -sensor-, and
*increases* the signal sent to the brain.
Now the brain says, "Uh-oh, the BP is too high!" And it sends out signals
which slow the heart, decrease the strength of contraction, and DILATE the
blood vessels.
Voila! The BP goes down!
Do we diff eqs to understand these concepts? Or to conduct thoughtful
experiments? Or to understand why the system sometimes responds in
unexpected ways?
I dont think so.
Id rather have ten active cardiovascular labs around the country doing
this work, collaborating, adding to each others work, builiding and
testing models, etc., rather than one or two highly skilled mathematicians
trying to put the pieces together in isolation.
And whether you believe this or not, I can categorically tell you that
these mathematicians will be largely ignored BY THE PEOPLE IN THE LABS
COLLECTING THE DATA! Thats just the way biology works. I dont agree
with it, I dont like it, but thats the way it is!
SD for the masses! Diff eq for the elite!
ed
(Ed Gallaher)
gallaher@teleport.com
Please look at Shauns original message to obtain the terminology. I wont
repeat it here.
Shaun, I found your sorting into type P and Q to be interesting and
though-provoking. I agreed with most of what you said, except:
>Theoretically, type P problems should be basically associated with
>approach M, and type Q with N. But practically ID stock-and-flow grammar
>is sometimes suitable for use with approach N for type Q problems.
>The reality is that nowadays SD can be applied to both P and Q types.
I cannot speak for engineering, but for biology I see no a priori reason to
believe that "theoretically, biology problems -should- be associated with
diff eq."
I want to again state that I have nothing against diff eqs, except that
they are more difficult, and require much more extended and rigorous
training than does S&D diagrams.
If one has the time and the inclination to do this intellectual power
lifting, go for it! (Keeping in mind that a working knowledge will also
require an understanding of matrix algebra and numerical analysis.....)
But I have yet to see a strong case provided here for the -advantages- of
diff eq over SD.
(...other than a large installed user base in many disciplines, a somewhat
perverted advantage at best; after all, witness PCs ms Macs; but thats
another story....)
There may very well be some advantages to diff eqs, but I am not aware of
them. Perhaps others can enlighten me.
Since there is NOT a large installed user base of diff eq-ers in biomedical
research, why force people to go this route? Right now the very strong
impetus is to just not do quantitative system analysis, or to even think
about it. We are seeing very dramatic and exciting advances in molecular
biology, but this is creating a larger and larger supply of exciting,
disconnected factoids.
Putting these pieces together requires a systems approach, and no amount of
specracular reductionist work is going to change this.
Obtaining more and more detail about the structure and chemical composition
of an airplane wing, engine components, etc. etc. is very useful. However,
wouldnt it be nice to put all the pieces together (i.e. a complete system)
and test it in a wind tunnel before flying passengers?
It sure would be nice if we took this approach before new meds were
released! Despite isolated examples to the contrary, this is not the way
biomedical research is done.
Simple example: Hypertension.
BP system includes brain (controller), sensors (carotid artery pressure
sensor), blood volume, and pipes.
BP is too high for any number of unknown reasons. Current drugs include
vasodilators (increase the volume of the pipes -> decrease pressure), and
diuretics (salt and water loss -> decreased volume -> decreased pressure).
Response of the body: Sensor detects decrease BP, sends info to brain.
Brain says, "Uh-oh, the BP is too low", sends out signals to in increase
heart rate and strength, and *constrict the blood vessels* (!!) Ooops!
Adopting a systems approach changes our perspective:
Perhaps the BP is too high because the sensor is sending an incorrect
signal telling the brain that the BP is too low?!
In any event, suppose we could find a drug which affects the -sensor-, and
*increases* the signal sent to the brain.
Now the brain says, "Uh-oh, the BP is too high!" And it sends out signals
which slow the heart, decrease the strength of contraction, and DILATE the
blood vessels.
Voila! The BP goes down!
Do we diff eqs to understand these concepts? Or to conduct thoughtful
experiments? Or to understand why the system sometimes responds in
unexpected ways?
I dont think so.
Id rather have ten active cardiovascular labs around the country doing
this work, collaborating, adding to each others work, builiding and
testing models, etc., rather than one or two highly skilled mathematicians
trying to put the pieces together in isolation.
And whether you believe this or not, I can categorically tell you that
these mathematicians will be largely ignored BY THE PEOPLE IN THE LABS
COLLECTING THE DATA! Thats just the way biology works. I dont agree
with it, I dont like it, but thats the way it is!
SD for the masses! Diff eq for the elite!
ed
(Ed Gallaher)
gallaher@teleport.com