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Trajectory Discontinuity and Morphogenesis: The Implications of Catastrophe Theory for Archaeology

Published online by Cambridge University Press:  20 January 2017

Colin Renfrew
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Abstract

The problem of discontinuity in the behavior of culture systems-the last stronghold of the anti-processualists-is discussed. Abrupt change in behavior can now be described in terms of smooth changes in the underlying causative factors by means of Rene Thom"s Theory of Elementary Catastrophes. The theory suggests insights not only into discontinuities with respect to time ("sudden" changes) but into the differentiation of forms as the result of bifurcations (morphogenesis). Although existing applications of the Theory in the social sciences lack quantitative precision, they offer a deeper understanding of crucial mechanisms of social evolution and, it is suggested, go far toward solving the discontinuity problem in archaeology.

Type
Articles
Information
American Antiquity , Volume 43 , Issue 2 , April 1978 , pp. 203 - 222
Copyright
Copyright © The Society for American Archaeology 1978

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References

Adams, R. E. W. 1973 The collapse of Maya civilization: a review of previous theories. In The Classic Maya collapse, edited by Culbert, T.P., pp. 21–34. University of New Mexico Press, Albuquerque.Google Scholar
Amson, J. C. 1974 Equilibrium and catastrophic models of urban growth. In Space time concepts in urban and regionalmodels (London Papers in Regional Science 4), edited by Cripps, E. L., pp. 108–28, Pion, London.Google Scholar
Binford, L.R. 1965 Archaeological systematics and the study of culture process. American Antiquity 31:203–10.Google Scholar
Brookfield, H. C. and Hart, D. 1971 Melanesia, a geographical interpretation of an island world. Methuen and Co., London.Google Scholar
Chillingworth, D.R.J. 1976a Differential topology with a view to applications (Research Notes in Mathematics 9). Methuen and Co., London.Google Scholar
Chillingworth, D.R.J. 1976b Structural stability and mathematical models: the role of the catastrophe method. In MathematicalModelling, edited by McClone, R. and Andrew, J., pp. 231–58. Butterworth, London.Google Scholar
Chisholm, M. 1968 Rural settlement and land use. Methuen and Co., London.Google Scholar
Clark, J. G. D. 1966 The invasion hypothesis in British archaeology. Antiquity 40:172–89.CrossRefGoogle Scholar
Clarke, D. L. 1968 Analytical archaeology. Methuen and Co., London.Google Scholar
Dodson, M. M. 1976 Darwin's law of natural selection and Thorn's theory of catastrophes. Mathematical Biosciences . 28:243–74.Google Scholar
Ferguson, J. A. 1976 Investment decisions and sudden changes in transport. Surveyor 9th July 1976:10–11.Google Scholar
Flannery, K. V. 1968 Archeological systems theory and early Mesoamerica. In Anthropological archeology in the Americas, edited by Meggers, B. J., pp. 67–87. Anthropological Society of Washington, Washington D.C. Google Scholar
Flannery, K. V. 1972 The cultural evolution of civilizations. A nnual Review of Ecology and Systematics 3:399–426.Google Scholar
Fowler, D. H. 1972 The Riemann-Hugoniot catastrophe and van der Waals’ equation. In Towards a theoretical biology 4:essays, edited by Waddington, C. H., pp. 1–7. Edinburgh University Press, Edinburgh.Google Scholar
Isnard, C. A. and Zeeman, E. C. 1976 Some models from catastrophe theory in the social sciences. In The use of models in social sciences, edited by Collins, L.. Tavistock Press, London.Google Scholar
Maruyama, M. 1963 The second cybernetics: deviation amplifying mutual causal processes. A merican Scientist 51:164–79.Google Scholar
Mees, A. I. 1975 The revival of cities in mediaeval Europe. Regional Science and Urban Economics 5:403–25.CrossRefGoogle Scholar
Pitt, D. A. and Poston, T. n.d. Determinacy and unfolding in the presence of a boundary. (Unpublished paper)Google Scholar
Poston, T. and Stewart, I. N. 1976 Taylor expansions and catastrophes (Research Notes in Mathematics 7). Pitman, London.Google Scholar
Renfrew, C. 1972 The emergence of civilisation: the Cyclades and the Aegean in the third millennium B.C. Methuen and Co., London.Google Scholar
Renfrew, C. n.d… Systems collapse. In Transformations: mathematical approaches to, culture change, edited by Renfrew, C. and Cooke, K.. Academic Press, New York. (In preparation)Google Scholar
Renfrew, C. and. Poston, T- n.d, Settlement shift and catastrophe theory. In Transformations: mathematical approaches to culture change, edited by Renfrew, C. and Cooke, K.. Academic Press, New York. (In preparation)CrossRefGoogle Scholar
Russell, J. C. 1958 Late ancient and mediaeval population. Transactions of the American Philosophical Society, New Series, 48 part 3:1–152.Google Scholar
Sabloff, J. A 1973 Major themes in the past hypotheses of the Maya collapse. In The Classic Maya collapse, edited by Culbert, T. P., pp. 35–42. University of New Mexico Press, Albuquerque.Google Scholar
Sewell, M. 1975 Kitchen catastrophe. Mathematical Gazette 59:246–249.Google Scholar
Stewart, I. 1973 The magnificent seven. Manifold 14:6–13.Google Scholar
Sussmann, H. J. and Zahler, R. S. In press Catastrophe theory as applied to, the biological and social sciences: critique. Synthese, forthcoming.Google Scholar
Thom, R. 1969 Topological models in biology, Topology 8:313–35. Google Scholar
Thom, R. 1975 Structural Stability and Morphogenesis. W. A. Benjamin, Reading, Mass.Google Scholar
Thompson, M.In press The geometry of confidence: an analysis of the Enga te and Hagen moka; a complex system ofceremonial pig giving in the New Guinea Highlands. In Rubbish Theory, by Thompson, M-, Paladin, London.Google Scholar
T.H.E.S, 1975 How catastrophe theory may teach us all the wrong lessons. Times Higher Education Supplement 5:Deeember 1975:12.Google Scholar
Wagstaff, J. M. 1976 Some thoughts about geography and Catastrophe Theory, Area 8:316–20.Google Scholar
Wilson, A. G. 1976 Catastrophe theory and urban modelling: an application to model choice. Environment and Planning A,8:351-56,19,73 Embryology, differentiation and catastrophe theory, Manifold 15:17–3,3,Google Scholar
Zeeman, E-C. 1971 The geometry of catastrophe. Times Literary Supplement 10, December 1971:1556-7.Google Scholar
Zeeman, E-C. 1972a A catastrophe machine. In Towards a theoretical biology 4: essays, edited by Waddington, C. H., pp. 276–82. Edinburgh University Press, Edinburgh.Google Scholar
Zeeman, E-C. 1972b, Differential equations for the heartbeat and nerve impulse. In Towards a theoretical biohgy 4: essays, edited by Waddington, C. H., pp 8–67. Edinburgh Univeisity Press, Edinburgh.Google Scholar
Zeeman, E-C. 1974a On the unstable behaviour of stock exchanges. Journal of Mathematical Economics 1:39–49.Google Scholar
Zeeman, E-C. 1974b Primary and secondary waves in developmental biology. A.M.S. Lectures on Mathematics in the LifeSciences 7:69–161.Google Scholar
Zeeman, E-C. 1976a Catastrophe theory. Scientific American 234:65-83. Google Scholar
Zeeman, E-C. 1976 b Euler buckling. In Catastrophe theory, — Seattle 1975, Lecture Notes in Mathematics 525. Springer-Verlag, Berlin–Heidelberg.In press Applications of catastrophe theory. Proceedings of the Tokyo international conference on manifolds, Google Scholar
Zeeman, E-C. 1973.Google Scholar