With the advent of easy-to-use computers and software we can all build on the
mathematical descriptions of a system and carry them further. The world is not a
static or comparative static process, and so the models treating it in that way will
become obsolete, and are perhaps even misleading. We can now investigate in great
detail and with great precision the system’s behavior over time, its movement
toward, or away from, equilibrium positions, rather than restrict the analysis to an
equilibrium point itself.
An understanding of the dynamics and changing interrelationships of systems,
such as social, biological, and physical systems, are of particular importance in a
world in which we face increasing complexity. In a variety of disciplines scientists
ask questions that involve complex and changing interrelationships among systems.
How do mutation and natural selection affect the distribution of genetic information
in a population? How does a vaccination program affect the spread of a disease? All
good modeling processes begin (and end) with a good set of questions. These
questions keep the modeler focused and away from the miasma of random exploration. Starting with a clear question in mind also helps the modeler decide when
the model is done—namely when it yields a satisfactory answer. Conversely,
modelers who start with the intention to “model the behavior of a system,” without
ever having articulated what the question is that they wish to address, tend to keep
on going, in part because there always seems to be an aspect of the real world that
has not yet found its way into the model, and as a result, the model is perceived as
incomplete. And, of course, it will always be incomplete. But should the model ever
include all the parts of reality, then it will be as complex as reality, and the modelers
will have altogether missed the point of modeling.
Models help us understand the dynamics of real-world processes by mimicking
with the computer the actual but simplified forces that are assumed to result in a
system’s behavior. For example, it may be assumed that the number of people
migrating from one country to another is directly proportional to the population
living in each country, and migration decreases the further these countries are apart.
In a simple version of this migration model, we may abstract away from a variety of
factors that impede or stimulate migration, besides those directly related to the
different population sizes and distance. Such an abstraction may leave us with a
sufficiently good predictor of the known migration rates, or it may not. If our
answers do not compare sufficiently well with reality, we re-examine the abstractions, reduce the simplifying assumptions, and re-test the model for its new predictions. The results will not only be a better model of the system under
investigation but most importantly a better understanding of our conception of
that system, showing us whether we were indeed able to identify and properly
represent the essential features of that system.
We cannot overstress the fact that one should keep the model simple, even
simpler than one knows the cause and effect relationship to be, and only grudgingly
add additional features to the model when it does not reproduce the real effects.
After all, it is not the goal to develop models that capture all facets of real life
systems. Such models would be useless because they would be as complicated as
the systems we wanted to understand in the first place. The real quest of dynamic
1.2 Static, Comparative Static, and Dynamic Models
7
mathematical descriptions of a system and carry them further. The world is not a
static or comparative static process, and so the models treating it in that way will
become obsolete, and are perhaps even misleading. We can now investigate in great
detail and with great precision the system’s behavior over time, its movement
toward, or away from, equilibrium positions, rather than restrict the analysis to an
equilibrium point itself.
An understanding of the dynamics and changing interrelationships of systems,
such as social, biological, and physical systems, are of particular importance in a
world in which we face increasing complexity. In a variety of disciplines scientists
ask questions that involve complex and changing interrelationships among systems.
How do mutation and natural selection affect the distribution of genetic information
in a population? How does a vaccination program affect the spread of a disease? All
good modeling processes begin (and end) with a good set of questions. These
questions keep the modeler focused and away from the miasma of random exploration. Starting with a clear question in mind also helps the modeler decide when
the model is done—namely when it yields a satisfactory answer. Conversely,
modelers who start with the intention to “model the behavior of a system,” without
ever having articulated what the question is that they wish to address, tend to keep
on going, in part because there always seems to be an aspect of the real world that
has not yet found its way into the model, and as a result, the model is perceived as
incomplete. And, of course, it will always be incomplete. But should the model ever
include all the parts of reality, then it will be as complex as reality, and the modelers
will have altogether missed the point of modeling.
Models help us understand the dynamics of real-world processes by mimicking
with the computer the actual but simplified forces that are assumed to result in a
system’s behavior. For example, it may be assumed that the number of people
migrating from one country to another is directly proportional to the population
living in each country, and migration decreases the further these countries are apart.
In a simple version of this migration model, we may abstract away from a variety of
factors that impede or stimulate migration, besides those directly related to the
different population sizes and distance. Such an abstraction may leave us with a
sufficiently good predictor of the known migration rates, or it may not. If our
answers do not compare sufficiently well with reality, we re-examine the abstractions, reduce the simplifying assumptions, and re-test the model for its new predictions. The results will not only be a better model of the system under
investigation but most importantly a better understanding of our conception of
that system, showing us whether we were indeed able to identify and properly
represent the essential features of that system.
We cannot overstress the fact that one should keep the model simple, even
simpler than one knows the cause and effect relationship to be, and only grudgingly
add additional features to the model when it does not reproduce the real effects.
After all, it is not the goal to develop models that capture all facets of real life
systems. Such models would be useless because they would be as complicated as
the systems we wanted to understand in the first place. The real quest of dynamic
1.2 Static, Comparative Static, and Dynamic Models
7