John Paul Fullerton wrote:
>I've
>just taken the introductory course on differential equations in college at
>age 37 and find that the emphasis is much toward learning a set of math
>techniques and learning when to apply those techniques. The question of
>what a differential equation is and why it appears in scientific
>investigations is accounted for early in the textbook and from then on
>it's techniques and applications.
and followed with good points, which I enjoyed. John, you remind me of two
episodes in my study, which may be worth to share in a thread about "Junk"
Science.
First week at university, first lectures on calculus, first lesson, the
math professor came in and stated (I say: informed us about his motivation
to spend time on ignorants like us - full expert mode): "About 50% of you
will pass the exams. Only less than 10% will understand what I am going to
teach you. But those surely not more that 2 of you have the potential to
guide our society in future. And this potential should not be wasted."
Since then I have always viewed mathematics as a mere tool, something that
can be used, something incapable of deciding about its applicability. As a
revenge to that professor I viewed math as a slave, a creature to serve in
the description of the world. I passed the exams, but I certainly was not
one of those two - one of the few things I was sure about, that I didn't
want to be! Since I met At de Lange here in the list, he is doing a good
job in curing that wound slowly. But it takes time.
Later, I wanted to know what students of economy learn, when they are
taught "operations reseach (OR) methods". So I visited a lecture on
"operations research methods in marketing". The professor gave us a nice
overview on the scope of applicability: "OR is about optimization of
parameters in a model. Depending on the model, various kinds of
optimization methods can be applied: linear, one or multidimensional,
stochastic... Creating the model of reality which is the input to OR is
not the task of OR." Yet he spent some time explaining how models are
derived. It burnt down to: "If you have chess in reality, the model will
be something like Tic-Tac-Toe. Not exactly Chess, but OR can be applied."
After the lesson I went to the professor and asked him: "If models that
can be handled by OR do not reflect the marketing systems they ought to
model, why then a lecture on OR in marketing?" He answered totally serious
and honest: "The students have to learn those methods as part of the
curriculum. Marketing provides only the background and language. Some
students relate easier to marketing, others prefer organisational
development or strategic decision making." (Since then I call this a
"marketing approach to didactics".) And now all those students are out and
try to apply what they have learnt. It cannot be wrong, they learnt it at
university! Did ever anybody say that it is easy to jump into the cold
water of reality when coming from university?
It is not a problem of the mathematics. Its a problem that the chosen
example from reality does not fit. They do not fit although the validity
of mathematics is completely independent from the example to which it is
applied.
Systems thinking is about modelling (hopefully) relevant parts of reality
in (calculable) models. On a scale of "scope of applicability" starting
with, lets say linear algebra for linear optimization: where are the other
methods of OR? And where are the nonlinear differential equations based
system dynamics? How much of an improvement are these? Then, what about
Demings "profound knowledge" or At de Langes "creative course of time"?
Liebe Gruesse,
Winfried
--"Winfried Dressler" <winfried.dressler@voith.de>
Learning-org -- Hosted by Rick Karash <rkarash@karash.com> Public Dialog on Learning Organizations -- <http://www.learning-org.com>