Most work in urban modelling to date has proceeded under the tacit assumption that there are mechanisms of urban process, either deterministic or nondeterministic, which can be approximately described in models. An alternative hypothesis is suggested proposing that urban process as such cannot be objectively specified, although urban system behaviour may appear deterministic or nondeterministic according to the frame of representation chosen by the modeller. Besides explaining the paradox of the relative predictive success of certain simple deterministic models in the face of more sophisticated theories stressing the impossibility of deterministic evolution, this hypothesis also throws light on the reason why physical analogies may work in the field of urban studies. This latter point is elaborated by means of an illustration involving the ‘Brussels paradigm’ of bifurcation. It is suggested that predictive ability and success of analogical transfer both depend on the presence in a model of a ‘logical prior’, a formal element which, being nonempirical, maintains its validity, not only in repeated applications across time and space, but also in transfers from one substantive field to another.
Get full access to this article
View all access options for this article.
References
1.
AllenP M, 1982, “Evolution, modelling, and design in a complex world”Environment and Planning B995–111
2.
AshbyR W, 1956An Introduction to Cybernetics (Methuen, Andover, Hants)
3.
AtkinR H, 1977, “Q-analysis: Theory and practice” research report X, Department of Mathematics, University of Essex, Colchester, England
4.
BattyMMarchL, 1976, “The method of residues in urban modelling”Environment and Planning A8189–214
5.
BeaumontJ R, 1980, “Towards a conceptualization of evolution in environmental systems” WP-282, School of Geography, University of Leeds, Leeds, England
6.
BrotchieJ FRoyJ RSharpeL, 1981, “Urban impacts of technological change” paper presented to the international conference on structural economic analysis and planning in time and space, University of Umea, Sweden, June; copy available from the authors, CSIRO Division of Building Research, Highett, Victoria, Australia
7.
BungeM, 1972Method, Model and Matter (D Reidel, Dordrecht)
8.
BurkeF E, 1972, “Technical and resource constraints in forecasting models for long range science strategies” in Operational Research in Industrial Systems Ed. BrennanJ (Hodder and Stoughton, Sevenoaks, Kent) pp 77–94
9.
CastiJ, 1981, “Systemism, system theory and social system modeling”Regional Science and Urban Economics11405–424
10.
ChaitinG J, 1975, “Randomness and mathematical proof”Scientific American28issue 5, 47–55
11.
CloughD J, 1964, “Application of the principle of maximizing entropy in the formulation of hypotheses”Canadian Operational Research Society Journal253–70
12.
ColemanJ S, 1964Introduction to Mathematical Sociology (Free Press, New York)
13.
CouclelisH, 1977Urban Development Models: Towards a General Theory PhD thesis, University of Cambridge, England
14.
CouclelisH, 1982, “Philosophy in the construction of geographic reality” in A Search for Common Grounds Eds GouldPOlssonG (Pion, London) pp 105–138
15.
CouclelisH, 1983, “Prior structure and spatial interaction” paper presented to the International Symposium on New Directions in Urban Modelling, University of Waterloo, Ontario, July; copy available in mimeograph form from H Couclelis
16.
EddingtonA, 1958The Philosophy of Physical Science (University of Michigan Press, Ann Arbor, MI)
GaleS, 1972, Review of The Entropy Law and the Economic Process by Georgescu-RoegenNJournal of Regional Science12479–482
19.
GardnerM, 1970, “The fantastic combinations of John Conway's new solitaire game LIFE”Scientific American23issue 4, pp 120–123
20.
Georgescu-RoegenN, 1971The Entropy Law and the Economic Process (Harvard University Press, Cambridge, MA)
21.
GlanvilleR, 1978, “The nature of fundamentals, applied to the fundamentals of nature” in Applied General Systems Research Ed. KlirG J (Plenum, New York) pp 401–409
22.
HoY-S, 1979, Book review of Fundamentals of Measurement and Representation of Natural Systems by RosenREnvironment and Planning B6472–474
23.
HobsonA, 1971Concepts in Statistical Mechanics (Gordon and Breach, New York)
24.
HuaCPorellF, 1979, “A critical review of the development of the gravity model”International Regional Science Review497–126
25.
JaynesE T, 1957a, “Information theory and statistical mechanics: Part I”Physical Review106620–630
26.
JaynesE T, 1957b, “Information theory and statistical mechanics: Part II”Physical Review108171–190
27.
JaynesE T, 1967, “Foundations of probability theory and statistical mechanics” chapter 6 in Delaware Seminar in the Foundations of Physics Ed. BungeM (Springer, New York)
28.
JaynesE T, 1968, “Prior probabilities”IEEE Transactions on Systems Science and CyberneticsSSC-4, no 3, September, pp 227–241
29.
KurthR, 1960Axiomatics of Classical Statistical Mechanics (Pergamon Press, Elmsford, NY)
30.
MarchLBattyM, 1975, “Generalized measures of information, Bayes' likelihood ratio and Jaynes' formalism”Environment and Planning B299–105
31.
MargenauH, 1950The Nature of Physical Reality (McGraw-Hill, New York)
32.
PeirceC S, 1878, “The order of nature” reprinted in The Philosophy of Peirce: Selected Writings Ed. BuchlerJ (Routledge and Kegan Paul, Henley-on-Thames, Oxon) pp 224–227
33.
PostonTStewartI N, 1978Catastrophe Theory and Its Applications (Pitman, London)
34.
PrigogineI, 1971, “Unity of physical laws and levels of description” in Interpretations of Life and Mind Ed. GreneM (Humanities Press, Atlantic Highlands, NJ) page 1
35.
PrigogineI, 1981From Being to Becoming (W H Freeman, New York)
36.
PrigogineIAllenPHermanR, 1977, “Long term trends and the evolution of complexity” in Goals in a Global Community—A Report to the Club of Rome Eds LaszloEBiermanJ (Pergamon Press, Elmsford, NY) pp 1–63
37.
PrigogineIStengersI, 1979La Nouvelle Alliance (Gallimard, Paris)
38.
RifkinJ, 1981Entropy: A New World View (Bantam Books, New York)
39.
RosenR, 1978Fundamentals of Measurement and Representation (North-Holland, New York)
40.
RyleG, 1949The Concept of Mind (Hutchinson, London)
41.
ter HaarD, 1966Elements of Thermostatistics (Holt, Rinehart and Winston, New York)
42.
TimmermansH J PVeldhuisenK J, 1981, “Behavioural models and spatial planning: Some methodological considerations and empirical tests”Environment and Planning A131485–1498
43.
TontiE, 1976, “The reason for analogies between physical theories”Applied Mathematical Modelling137–50
44.
TribusM, 1959Thermostatics and Thermodynamics (Van Nostrand, Princeton, NJ)
45.
WebberM M, 1979Information Theory and Urban Spatial Structure (Croom Helm, Beckenham, Kent)
46.
WignerE P, 1964, “Events, laws of nature, and invariance principles” Nobel Prize Lecture, reprinted in 1967 in Symmetries and Reflections Ed. WignerE P (Indiana University Press, Bloomington, IN) pp 38–50
47.
WilsonA G, 1969, “The use of analogies in geography”Geographical Analysis1225–233
48.
WilsonA G, 1970Entropy in Urban and Regional Modelling (Pion, London)
49.
WilsonA G, 1979, “Some new methods for dynamic geographical modelling: Catastrophe theory and bifurcation” WP-954, School of Geography, University of Leeds, Leeds, England
50.
WilsonA G, 1981aCatastrophe Theory and Bifurcation (Croom Helm, Beckenham, Kent)
51.
WilsonA G, 1981bGeography and the Environment, Systems Analytical Methods (John Wiley, Chichester, Sussex)
52.
ZeiglerB P, 1976Theory of Modelling and Simulation (John Wiley, New York)
53.
ZinglerE K, 1972, Review of The Entropy Law and the Economic Process by Georgescu-RoegenNKyklosXXV fascicular 2, 392–393
