illustrated in the use of "gravity" (2) models for urban
planning: by reference to Newtonian physics, urban
gravity models have been developed to an extent not
likely without the existence of this structural equiva-
lence.,
3. Simplified deduction - a model facilitates
deductive reasoning and so points to implications previ-
ously not suspected. Consequences of the propositions
and assumptions of the underlying theory can be formally
and rigorously traced.
4. Empirical framework - formulation of a theory
in symbolic terms establishes a framework for empirical
investigation, the results of which can be structured for
meaningful statistical analysis. The model establishes
data categories and suggests verification tests. This frame-
work for inquiry allows comparison of the results from
togical argument and empirical analysis. A professional
Field develops its theoretical base through just such inter-
play of deduction and induction, which can be consider-
ably enhanced by the use of models.
Our goal is to formulate models which are subtle and rich
enough to adequately reflect reality, yet not so complex
as to defy manipulation. Practical problems which arise
at this stage are admittedly difficult, but most turn out
to be of a computational nature and so eventually solva-
ble.
Many complex urban situations, however, are not tracta-
ble by ordinary analytic techniques: the mathematics may
become too difficult or the exact nature of the functional
relationships may not be fully understood. These diffi-
culties can be circumvented by using computer simulation
which can handle problems beyond the effective grasp of
mathematical analysis and which has considerable toler-
ance for unverified assumptions and unexplained relation-
ships. Models too complex even for simulation can be
broken into submodels and solved sequentially. Models
that overrun the capacity of the largest computers can be
handled by interrupted simulation, in which the model
user stops the computer at decision or judgment points,
chooses from among alternative courses and sets the
computer on that course (3). Imperfect models containing
relationships not sufficiently understood for reduction to
mathematical form can be similarly handled.
Models and Theory Development
Models are more than simply the end products of theo-
rizing. The relation of theory to model during the process
of discovery is extremely subtle and involves constant
alternation between inductive and deductive reasoning.
The process is a varied as snowflakes, but the following
will serve to illustrate its complex nature.
Random observations of a class of events give rise to
suspicion of a pattern of regularity which, stated as a
crude generalization, becomes a working hypothesis. This
hypothesis is used to formulate classes of relevant data
necessary for its testing and data are gathered systemat-
ically and analyzed with reference to the hypothesis. The
hypothesis is found to be partially wrong - as are most
hypotheses - so it is changed and extended to fit the
data. The new hypothesis, which we may now call a
theory, is converted to a model; its clarity is improved
in the process. In this form it is seen to be similar to an
established class of models about which considerable
theory already exists. By analogy with that theory, the
theory under development is broadened. The new model
is now ready for test as a prediction tool.
To test the predictive powers of the model, its parameters
are fitted using historical data; the model is then "solved"
with current data to "predict" the present. This process of
retrospective prediction by manipulating parameters con-
tinues until the model can accurately predict the present.
At this point the model represents a current theory and is
ready for use in prospective prediction: it must now be
tested over time and under varying conditions. Thetheory
cannot be "proved" but only supported or strengthened by
empirical evidence; its generality can be denied by a
single contrary example.
The theory can now be stated once more in plain language.
Its justification, its model, and the account of its devel-
opment, when they appear in print, almost always sound
very different from the actual development process. More
than one write-up leaves the erroneous impression that
the theory sprang full-blown from the analyst’s brow, and
that the model is but a symbolic recapitulation.
We stated earlier that one measure of the development of
a field of knowledge was the extent of its structured theo-
retical base. We promised to argue that this is partially
equivalent to saying the extent to which it employs ab-
stract models for analysis and prediction. We have now
shown the relationship of modeling to the development of
theory; we have not yet, however, explained the qualifi-
cation implied in the phrase, " partially equivalent".
The qualification stems from the concept of structure, for
a structured theoretical base requires more than just the
use of models in theory development: it also requires the
accumulation of many theories - narrow and broad, special
and general, ranging over the science, overlapping,
contributing and conflicting - until enough has accumu-
mulated for articulation into a structured base. Clearly,
the structuring process can be greatly facilitated if the
component theories are expressed in symbolic form. The
field of urban planning is only now beginning to develop
theory; it will be many years before it possesses a struc-
tured theoretical base comparable to that of, for instance,
economics.
Simulation
Unlike the laboratory scientist, the urban planner can
seldom manipulate the objects of his study to find their
best arrangement or to discover their natural properties or
laws. The scales of cost and time are usually too large to
allow for experimentation with the physical elements of
planning, and controlled experimentation with the social
elements is rarely a possibility.
By building a simulation model (4) to represent urban
functions, the planner can create an artifical environment
for experimentation. He can then test his hypothesis and
translate his results into statements about the urban
environment. Just as this process of simulation can serve
as a laboratory for the development of theory, so it can
be used to test the consequences of alternative public
policies and programs.
The power of simulation rests in its ability to accept weak
and inelegant theory, a class into which most urban theory
currently falls. Descriptive statements which can be re-
duced to the logic of a computer program can constitute
the model; precise equations are not necessary.
We can identify four distinct stages of abstraction in the
ARCH+ 2 (1969) H.8