Full text: ARCH+ : Studienhefte für architekturbezogene Umweltforschung und -planung (1969, Jg. 2, H. 5-8)

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
	        

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