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Vol: 48(62) No: 1 / March 2003 Towards a Cognitive Model Based on Statistical Information M. Crisan Department of Computer and Software Engineering, University “Politehnica” of Timisoara, 1900 Timisoara, Romania, phone: (+40) 256-403256, e-mail: crisan@cs.utt.ro, web: http://www.cs.utt.ro/~crisan/ Keywords: cognitive modeling, scaling laws, Benford’s law, Zipf’s law, statistical linguistics, random texts. Abstract The paper explores the possibility of using scaling laws in developing a model of cognition, focusing upon the Benford’s law and Zipf’s law. Even if these laws found a statistical explanation, it is shown that deep causal laws can also be identified at the level of cognition. Benford’s law is related with the numbering process in observations and manifests as a result of a uniform mental awareness of numbers. Zipf’s law is related with language redundancy necessary for the language understanding process. The causal laws identified in these scaling phenomena are consistent with a hierarchical cognitive model developed previously by the author. References [1] S. Newcomb. “Note on the frequency of use of the different digits in natural numbers,” Amer. J. Math., 4 , pp. 39-40, 1881. [2] F. Benford. “The law of anomalous numbers,” Proc. Amer. Math. Soc., 78 (551-572), 1938. [3] T.P. Hill. “The first-digit phenomenon,” American Scientist 86, p. 358-63,.July-August 1998. [4] T.P. Hill. “Base-invariance implies Benford’s law,” Proc. Amer. Math. Soc., 123:3, 887-895, March, 1995. [5] T.P. Hill. “A statistical derivation of the significant-digit law,” Statistical Science, 10:4, 354-363, 1996. [6] M. Nigrini. “The detection of income evasion through an analysis of digital distributions,” PhD thesis, Dept. of Accounting , Univ. Cincinnati , Cincinnati OH, 1992. [7] M. Nigrini. “A taxpayer compliance application of Benford’s law,” J. Amer. Taxation Assoc., 18, 72-91, 1996. [8] Zipf, George K.; Human Behaviour and the Principle of Least-Effort, Addison-Wesley, Cambridge MA, 1949. [9] G. A. Miller: Introduction. Psycho-biology of languages by G. Zipf. MIT Press, Cambridge, MA, 1965. [10] F. Attneave. “Informational aspects of visual perception,” Psychological Review 61, 183-193, 1954. [11] B. Mandelbrot. Linguistique Statistique Macroscopique. In L. Apostel, B. Mandelbrot and A. Morf, Logique, Language et Theorie de l’Information, Paris: Presses Universitaires de France, 1957. [12] B. Mandelbrot. Adaptation d’un message a la linge de transmission. I & II. Comptes rendus (Paris). 232: pp. 1638–1640 and 2003–2005, 1951; Contribution a la theorie mathematique des jeux de communication. Institute of statistics, University of Paris, p. 124, 1953, An informational theory of the statistical structure of languages. Communication theory, W. Jackson Ed. Betterworth, 1953, Simple games of strategy occurring in communication through natural languages. Symposium on statistical methods in communication engineering. Berkeley, 1953. Appearing in Transactions of IRE (professional groups on information theory), 3: pp. 124-137. [13] G. Miller, Some effects of intermittent silence. American journal of psychology. 70: pp. 311-314, 1957. [14] M. Crisan. “Extending LOTH for Developing a Model of Cognition,” Sci. & Tech. Bulletin of University \"Politehnica\" of Timisoara, 46(60), Transactions on Automatic Control and Computer Science, 2001. [15] A. A. Tsonis, C. Schultz, and P.A. Tsonis. Zipf’s law and the structure and evolution of languages. Complexity. 2(5): pp. 12-13, 1997. [16] W. Li. Letters to the Editor, Complexity, 3(5): 9-10, 1998. [17] W. Li, \"Random texts exhibit Zipf\'s-law-like word frequency distribution\", IEEE Transactions on Information Theory, 38(6), pp.1842-1845, 1992 [18] R. Perline. “Zipf’s law, the central limit theorem, and the random division of the unit interval,” Physical Review E, 54(1), pp. 220-223, 1996. [19] G.A. Miller, E.A. Friedman. “The reconstruction of mutilated English texts,” Information & Control I, 38-55, 1958. |