Abstract
In this concluding chapter we will try to explain the fundamental role of empirical regularities of socio-economic spatial phenomena in the construction of theories in spatial analysis and regional science. These empirical regularities help to construct new theories by developing new mathematical schemes, which are not derived from exact sciences. The last centuries of scientific enquiry were characterized by growing differences between the development of exact sciences (mathematics, physics, and chemistry) and their “soft” counterpart (socio-economic, socio-ecological, biological and behavioral sciences, etc.). These differences were essentially based on the application of mathematical methods. Theories of exact sciences are mathematically formulated and use methods of modern mathematics and computer science. The “soft” sciences avoid the use of mathematical language, but the processes of mathematization and computerization increasingly spread in their theoretical development. The discrepancy between the theories of exact sciences and socioeconomic sciences is the direct inheritance of the separation and differentiation of sciences from previous millennia.
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References
Von Bertalanffy, L. (1962). General system theory – a critical review. General Systems, 7, 1–20.
Bourbaki, N. (1960). Elements d'histoire des Mathematiques. Paris: Herman.
Casti, J. (1981). Systematism, system theory and social system modeling. Regional Science and Urban economics, 11, 405–424.
Caratheodory, C. (1911). Uber den variabilitats bereich der fourier'schen constanten von positiven harmonischen functionen. Rend. Circ. Mat. 32, Palermo, 198–201.
Dendrinos, D., & Sonis, M. (1990). Chaos and Socio-Spatial Dynamics. New York: Springer.
Dorfman, R., Samuelson, P., & Solow, R. (1958). Linear Programming and Economic Analysis. New York: McGraw-Hill.
Dreze, J. H. (1974) Axiomatic theories of choice, cardinal utility and subjective probability. In J. H.Dreze (Ed.) Allocations under Uncertainty: Equilibrium and Optimality. (pp. 3–23) London: Macmillan.
Haken, H. (1983). Advanced Synergetics, Instability Hierarchies of self-organizing systems and devices. Berlin: Springer.
Hilbert, D. (1899). Grundlagen der Geometrie. Lepzig.
Luce, R. D. (1959). Individual Choice Behavior. New York: Wiley.
Planck, M. (1944). Urspung und Auswirkung wissenschaftlicher Ideen. In M. Planck Wege zur Physkalishen Erkenntnis, (pp. 242–257) Leipzig.
Perroux, F. (1964). Industrie et Creation Collective. Tome 1. Paris, Presses Universitaires de France.
Poncelet, J. (1965). Traite des Proprietes Projectives des Figures. Paris: Gauthier-Villars.
Prigogine, I. (1980). From Being to Becoming. San Francisco: W H Freeman.
Prigogine, I. (1984). Order out of Chaos. New York: Bantam Books.
Rapoport, A. Mathematical aspects of general systems analysis. General Systems, 11, 3–11.
Samuelson, P. (1952). Spatial equilibrium and linear programming. American Economic Review, 40, 283–303.
Sonis, M. (1980). Locational push-pull analysis of migration streams. Geographical Analysis, 12, 80–97.
Sonis, M. (1981). Diffusion of competitive innovations. Modeling and Simulation, 12, Part 3, 1037–1041.
Sonis, M. (1982). The decomposition principle versus optimization in regional analysis: The inverted problem of multiobjective programming. In G. Chiotis, D. Tsoukalas & H. Louri (Eds.), The Regions and the Enlargement of the European Economic Community, Athens, Eptalofos, (pp. 35–60).
Sonis, M. 1986 A contribution to the central place theory: Superimposed hierarchies, structural stability, structural changes and catastrophes in central place hierarchical dynamics. In R. Funk, A. Kuklinsky (Eds.) Space-Structure-Economy: A Tribute to August Loesch. Karlsruhe Papers in Economic Policy Research, 3 159–76.
Sonis, M. (1983a). Spatio-temporal spread of competitive innovations: An ecological approach. Papers of the Regional Science Association, 52, 159–174.
Sonis, M. (1983b). Competition and environment – a theory of temporal innovation diffusion. In D. Griffith & A.Lea (Eds.) Evolving Geographical Structures, The Hague, Martinus Nijhoff, (pp. 99–129).
Sonis, M. (1984). Dynamic choice of alternatives, innovation diffusion and ecological dynamics of Volterra-Lotka models, London Papers in Regional Science, 14, 29–43.
Sonis, M. (1986). A unified theory of innovation diffusion, dynamic choice of alternatives, ecological dynamics and urban/regional growth and decline. Ricerche Economiche, 40, 696–723.
Sonis, M. (1991). A territorial socio-ecological approach in innovation diffusion theory: Socio-ecological and economic interventions of active environment into territorial diffusion of competitive innovation. Sistemi Urbani, 1–3, 29–59.
Sonis, M. (1992a). Innovation diffusion, schumpeterian competition and dynamic choice: A New Synthesis. Journal of Scientific & Industrial Research, Special Issue on Mathematical Modeling of Innovation Diffusion and Technological Change, 51, 172–186.
Sonis, M. (1992b). Innovation diffusion theory and the expansionmethod. In J. P. Jones III & E. Casetti (Eds.), Applications of the Expansion Method, (pp. 297–333) London: Routledge.
Sonis, M. (1997a). Socio-ecology, competition of elites and collective choice: Implications for culture of peace. In. G. E. Lasker (Ed.) Advances in Sociocybernetics and Human Development, Volume V: Culture of Peace, Human Habitat and Sustainable Living, IIAS-49-97. ISBN 0-921836-63-5, (pp. 77–83).
Sonis, M. (1997b). Linear bifurcation analysis with applications to relative Socio-spatial dynamics. Discrete Dynamics in Nature and Society, 1, 45–56.
Sonis, M. (2000). Non-linear socio-ecological dynamics and first principles of collective choice behavior of homo socialis. Progress of Theoretical Physics Supplement, 139, 257–269.
Sonis, M. (2001). Major actors in innovation diffusion process. In M. Fischer & J.Froelich (Eds.) Complexity, Knowledge and Innovation Systems, (pp. 317–341) Berlin: Springer.
Sonis. M. (2003). Discrete non-linear probabilistic chains. In M. Drachlin & E. Litsyn (Eds.) Functional-Differential Equations, Ariel, Israel, 10, 445–487.
Sonis, M., & Hewings, G. J. D. (1988). Superposition and decomposition principles in hierarchical social accounting and input-output analysis. London Papers in Regional Science, 19, 46–65.
Sonis, M., Hewings, G. J. D. & Guo, J.-M. (2000). A new image of classical key sector analysis: Minimum information decomposition of the leontief inverse. Economic Systems Analysis, 12, 401–423.
Sonis, M., Hewings, G. J. D. & Okuyama, Y. (2002). Trade typhoon over Japan: Turbulence metaphor and spatial production cycles feedback loops of the Japanese economy, 1980-85-90. Discrete Dynamics in Nature and Society, 7, 111–119.
Stevens, B. (1961). Linear programming and location rent. Journal of Regional Science 3, 15–26.
Von Neumann, J., & Morgenstern, O. (1953). Theory of Games and Economic Behavoir. (3rd ed.) Princeton: Princeton Academic Press.
Weber, A. (1909). Uber den Standort den Industries. Tubingen.
Weidlich, W., & Haag, G. (1983). Concepts and Models of Quantitative Sociology. Berlin: Springer.
Weidlich, W. (2000). Sociodynamics: A systematic approach to mathematical modeling in the Social Sciences. Singapore: Harwood Academic Publishers.
Weyl, H. (1935). Elementary theorie der konvexen polyeder. Commentarii Mathematici Helvetici, 7: 290–366. (English translation in H. W. Kuhn & A. W. Tucker (Eds.), 1950. “Contribution to theory of games”, Vol. I, Annals of Mathematical Studies, 24, Princeton).
Wiener, N. (1948). Cybernetics. New York: Wiley.
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Sonis, M. (2009). Conclusion. In: Sonis, M., Hewings, G. (eds) Tool Kits in Regional Science. Advances in Spatial Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00627-2_12
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