Database Reference
In-Depth Information
when we encounter novel situations
8
. While it is easy to show that mental models
can be quite inaccurate, most of us do trust them in a wide range of (inappropriate)
settings. This is why we must develop formal models. We must complement our
thought processes and to reflect upon the workings and outcomes of formal mod-
els to sharpen our thinking. Formal models are based on an expressed logic, and
they can form an analogic base—a repertoire of relationships on which to draw for
problem solving.
Unfortunately, at least in their early years of education and employment, most
people lack the analogic base of experience to draw on for their problem solving.
This presents a kind of dilemma: if analogy is useful in problem solving and prob-
lem solving is fostered by drawing on analogies, how does one get the experience
to build the analogic repertoire? The dilemma suggests an education plan where
the analogic process itself is taught along with carefully structured problem solv-
ing. One may be exposed to classes of problems, each capable of being solved by
generally the same analogic form. Later, the flaws of following the analogy too far
can be pointed out and perhaps multiple analogies—each leading to a good solution
form—can be demonstrated.
In any event, our topic is structured to offer you a large set of modeling expe-
riences, hoping that this set forms a sufficient experience base to launch you well
into the world of modeling. With this set of modeling experiences, new problems
can at first be broken into pieces that suggest analogies to items in this experience
base. For example, our earlier models have analogies with water held temporarily
in lakes, with the stock of capital in an industry, with a general population growth
model, with a mechanical production line—the list seems endless. Once analogies
are formed, the new problem begins to look solvable. As the model matures, the ex-
act connection to the original analogies may be forgotten and a new modeling form
may have been created.
1.7 STELLA's Numeric Solution Techniques
In this section we provide a brief description of, and basic mathematical background
information on, the numeric techniques available in STELLA to solve the equations
that define a model. Knowing about these techniques will be important in under-
standing how the computer arrives at model results, the accuracy of your results,
and methods to improve accuracy.
From the models above we have seen that STELLA calculates the value of a
stock in a given time period t based on the value of that stock a time step earlier plus
the net of the inflows and outflows that occur over that time step. Generally, if X(t)
is the stock in time period t, F(t, X(t),
.
)
are net flows that depend on time, the size
of the stock X(t) itself and possibly other parameters in the model (denoted by
.
),
and small time steps DT then
8
Tversky, A. and D. Kahneman, The Framing of Decisions and the Psychology of Choice,
Science,
Vol. 211, 1981, pp. 453-458.
