Differential equations
Posted: Thu Apr 03, 1997 9:33 am
You raise some very interesting points.
> Differential equations are difficult, confusing, weak, and
> unrealistic. They often mislead students as to the nature of systems.
Thanks for saying this. While Ive studied ODEs and PDEs in school and
used them some at work, I can remember feeling more comfort when working
with analog computers in school to simulate real world processes (now you
can guess my vintage), and I enjoy working (at the relatively low skill
level that I do) with SD simulations to model processes I see today.
> The mathematics alone does not give an adequate feeling for the real world.
I remember as far back as freshman physics learning that good math skills,
without a seat of the pants understanding of the world, wouldnt solve many
problems.
> On teaching dynamics in K-12, we are trying that through the "Road Maps"
> designed for "fun" as Jaideep Mukherjee fears. If they are done as
> intended, with all the book readings and computer exercises, I estimate
> that they will take 150 hours.
This brings me to the point of my question . Some on this list seem to
have argued in favor of SD being practiced only after serious study in a
university program (at the graduate level?) with the opportunity for the
prospective SD person to receive feedback on their modeling efforts. I can
see the benefits of such study. Some in the SD community (vendors,
perhaps?) seem to suggest the "democratic notion" that SD can be done
relatively easily by using todays tools and the admittedly good manuals
they provide. The democratic part of this seems very appealing, but I
recognize the danger of models (any models, not just SD models) not
matching reality.
Your posting seems to suggest a middle ground, that of the Road Maps. Im
part way through them, and I do find they help my thinking and working. I
also recognize that Im not an accomplished modeler (but I may be above the
median of those within half a mile of my desk).
How concerned are you about the work someone does who is working through
the Road Maps and using SD in a practical sense? What risks do you see in
the conclusions they may be drawing which they should take special pains to
avoid? Must those risks be ameliorated through undergraduate or graduate
courses, or is there another way? In particular, some of us have
difficulty in returning to a college campus (financial or personal
responsibility, geographic distance, etc.). Also, I think most (all?) of
us have heard multiple times that (college) educations are about learning
how to learn, so we should be able to do some of this ourselves, right?
I suspect the answer involves a combination of SD theory (e.g., skills in
how to represent reality effectively in a model and how to check the
results of that model for validity) and consulting practice (e.g.,
effective techniques for capturing and representing knowledge which the
"client" has and for working with that client to explore the ramifications
of the model openly and honestly to ensure that the resulting model is
believable).
Thanks for any (more) advice which may help generate more useful models and
more professional modelers.
Bill
PS: Having said all this, I recognize I wouldnt presume to teach myself a
skill such as playing a musical instrument, for example, without a private
teacher unless it were purely for fun. Theres too much about both
technique and about results in music that is really hard to get from
reading and really inefficient and arguably ineffective to get from
observation. These may be primarily characteristics of physical
activities, though.
--
Bill Harris Hewlett-Packard Co.
R&D Engineering Processes Lake Stevens Division
domain: billh@lsid.hp.com M/S 330
phone: (425) 335-2200 8600 Soper Hill Road
fax: (425) 335-2828 Everett, WA 98205-1298
> Differential equations are difficult, confusing, weak, and
> unrealistic. They often mislead students as to the nature of systems.
Thanks for saying this. While Ive studied ODEs and PDEs in school and
used them some at work, I can remember feeling more comfort when working
with analog computers in school to simulate real world processes (now you
can guess my vintage), and I enjoy working (at the relatively low skill
level that I do) with SD simulations to model processes I see today.
> The mathematics alone does not give an adequate feeling for the real world.
I remember as far back as freshman physics learning that good math skills,
without a seat of the pants understanding of the world, wouldnt solve many
problems.
> On teaching dynamics in K-12, we are trying that through the "Road Maps"
> designed for "fun" as Jaideep Mukherjee fears. If they are done as
> intended, with all the book readings and computer exercises, I estimate
> that they will take 150 hours.
This brings me to the point of my question . Some on this list seem to
have argued in favor of SD being practiced only after serious study in a
university program (at the graduate level?) with the opportunity for the
prospective SD person to receive feedback on their modeling efforts. I can
see the benefits of such study. Some in the SD community (vendors,
perhaps?) seem to suggest the "democratic notion" that SD can be done
relatively easily by using todays tools and the admittedly good manuals
they provide. The democratic part of this seems very appealing, but I
recognize the danger of models (any models, not just SD models) not
matching reality.
Your posting seems to suggest a middle ground, that of the Road Maps. Im
part way through them, and I do find they help my thinking and working. I
also recognize that Im not an accomplished modeler (but I may be above the
median of those within half a mile of my desk).
How concerned are you about the work someone does who is working through
the Road Maps and using SD in a practical sense? What risks do you see in
the conclusions they may be drawing which they should take special pains to
avoid? Must those risks be ameliorated through undergraduate or graduate
courses, or is there another way? In particular, some of us have
difficulty in returning to a college campus (financial or personal
responsibility, geographic distance, etc.). Also, I think most (all?) of
us have heard multiple times that (college) educations are about learning
how to learn, so we should be able to do some of this ourselves, right?
I suspect the answer involves a combination of SD theory (e.g., skills in
how to represent reality effectively in a model and how to check the
results of that model for validity) and consulting practice (e.g.,
effective techniques for capturing and representing knowledge which the
"client" has and for working with that client to explore the ramifications
of the model openly and honestly to ensure that the resulting model is
believable).
Thanks for any (more) advice which may help generate more useful models and
more professional modelers.
Bill
PS: Having said all this, I recognize I wouldnt presume to teach myself a
skill such as playing a musical instrument, for example, without a private
teacher unless it were purely for fun. Theres too much about both
technique and about results in music that is really hard to get from
reading and really inefficient and arguably ineffective to get from
observation. These may be primarily characteristics of physical
activities, though.
--
Bill Harris Hewlett-Packard Co.
R&D Engineering Processes Lake Stevens Division
domain: billh@lsid.hp.com M/S 330
phone: (425) 335-2200 8600 Soper Hill Road
fax: (425) 335-2828 Everett, WA 98205-1298