BAK-SNEPPEN MODELS FOR THE EVOLUTION OF STRUCTURED KNOWLEDGE
DOI:
https://doi.org/10.17770/sie2016vol4.1543Keywords:
Structured knowledge, Ontogeny versus Phylogeny, Mathematical teaching, Bak-Sneppen Model, Partitioned Frames and EvolutionAbstract
Scientific knowledge is subject to a twin evolution, since its development towards novelty creates disconnections and inconsistencies, while the need of structure requires order and method so that transmission and comprehension can be ensured. Models of biological evolution can help to understand many social and economical phenomena where the search for optimality is hindered by voluntary or random competition. Bak-Sneppen is one of the most significant models because it balances at best explication power and simplicity. Unlike cellular automata models, Bak-Sneppen models join locality and globality. The authors try to re-read these models in the framework of mathematics, where, despite its high developped structure, knowledge waves can hinder comprehension both of pupils and of scholars. Some paradoxes are shown, where a greater knowledge diminishes efficiency and capability.
Downloads
References
Alighieri, D. (2001). The Divine Comedy: The Inferno, The Purgatorio, and The Paradiso. Translated by Ciardi, J.. New York: Signet Classics.
Ausloos, M., Clippe, P., Pekalski, A. (2004). Evolution of economic entities under heterogeneous political/environmental conditions within a Bak-Sneppen-like dynamics. Physica A: Statistical Mechanics and its Applications, 332, 394-402.
Bak, P. (1996). How Nature Works: The Science of Self-Organized Criticality. New York: Springer-Verlag.
Bak, P., Sneppen, K. (1993). Punctuated equilibrium and criticality in a simple model of evolution. Physical Review Letters. 71(24), 4083-4086.
Barbay, J., Kenyon, C. (2001). On the discrete Bak-Sneppen model of self-organized criticality. Proceeding of the Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 928-934). Washington, DC.
Brischi, S., Marzano, G. (2015). Management e Rottamazione. Milano-Udine: Mimesis, 19-20.
Brunk, G. G. (2000). Understanding Self-Organized Criticality as a Statistical Process. John Wiley & Sons, Inc., 5 (3), 26-33.
Cavalli, A. (1998). Sociologia, Enciclopedia delle Scienze Sociali, VIII. Roma: Treccani.
Chang, T. F. M., Iseppi, L., Droli, M. (2015). Extra-core production and capabilities: where is the Food Industry going?. International Food and Agribusiness Management Review, 18, 105-126.
Droli, M., Chang, T. F. M., Iseppi, L., Piccinini, L. C. (2014). Managing trade contacts in HotRest intermediate markets: a resource-based view analysis in EU countries. Tourism Economics, 20, 757-778.
Duesenberry, J. S. (1949). Income, Savings and Theory of Consumer Behaviour. Cambridge Massachusetts: Harvard University Press, 89-125.
Eco, U. (2003). Dire quasi la stessa cosa. Esperienze di traduzione. Milano: Bompiani, 95-138.
Freudenthal, H. (1975). Wandelingen met Bastiaan. Pedomorfose, 25, 51-64.
Freudenthal, H. (1983). Wie entwickelt sich reflexives Denken? Neue Sammlung, 23, 485-497.
Freudenthal, H. (1991). Revisiting Mathematical Education. China Lectures. Dordrecht: Kluwer Academic Publishers. Sect. 2.3.3.
Kubler, G. (1972). The Shape of Time. New Haven: Yale University Press.
MacCormick, J. (2012). Nine Algorithms that Changed the Future. Princeton: Princeton University Press, Chapters 2 and 3.
Meester, R., Znamenski, D. (2002). Non-triviality of a discrete Bak-Sneppen evolution model. Journal of Statistical Physics, 109, 987-1004.
Petit-Cocorda, J. (1985). Morphogenèse du Sens. Paris: Presses Universitaires de France, Part. Chapter 5.
Pfeffer, J., Sutton, R. (2006). Hard Facts, Dangerous Half-Truths, and Total Nonsense. USA: Harvard Business School Press, p. 8.
Piccinini, L. C., Lepellere, M. A., Chang, T. F. M. (2013). Utopias of Perfection and their dystopias. SOCIETY, INTEGRATION, EDUCATION. Proceedings of the International Scientific Conference, v. 3, p. 189-200, june. 2013. ISSN 1691-5887.
Piccinini, L. C., Lepellere, M. A., Chang, T. F. M., Iseppi, L. (2014). Partitioned Frames in Bak Sneppen Models. Italian Journal of Pure and Applied Mathematics, 33, 461-488.
Piccinini, L. C., Taverna, M., Chang, T. F. M., Tubaro, G. (2015). Perception, Connotation, Translation of Numbers. SOCIETY, INTEGRATION, EDUCATION. Proceedings of the International Scientific Conference, v. 3, p. 183-192, may. 2015. ISSN 1691-5887.
Piccinini L. C., Lepellere, M. A., Chang, T. F. M., Iseppi, L. (2015). Endogenous Control in a Ternary Lotka-Volterra Model and its Applications. Italian Journal of Pure and Applied Mathematics, 35, 677-704.
Schlemm, E. (2012). Asymptotic Fitness Distribution in the Bak-Sneppen Model of Biological Evolution with four Species. Journal of Statistical Physics, 148, 191-203.
Taverna, M., Piccinini, L. C., Chang, T. F. M., Iseppi, L. (2013). Structures and Paths for the Exploration of Landscape-Cultural Mosaic. SOCIETY, INTEGRATION, EDUCATION. Proceedings of the International Scientific Conference, v. 1, p. 517-527, may. 2013. ISSN 1691-5887.
Turcotte, D. L. (1999). Self-organized criticality. Reports on Progress in Physics, 62, 1377-1429.
Vicario, G. B. (1984). Private communication to L.C. Piccinini. Udine: Department of Mathematics.
