Statistical Thinking and Statistical Physics

STATISTICAL THINKING AND STATISTICAL PHYSICS Gheorghe S ĂVOIU * Abstract. This paper presents a framework for the design and analysis of Statistics as a scientific way of thinking. Contemporary Statistics for economists and for physicists are not complete or harmonized disciplines. Models for statistical ways of thinking and problem solving have been developed, and continue to be developed, not only by teachers but also by scientific researchers / practitioners. Today it becomes possible for method and concepts of statistical physics to have real influence in statistical thinking or economic thinking, but it is also possible that economical and classical statistical methods and concepts can influence physics thinking too. In a comparison to classical statistical thinking, a new science like Econo- physics – primarily focused on analysis of financial markets and its important achievements defining new statistical mechanics of money distribution – have revealed that heterogeneous in reality must be explained with homo- geneous in theory. Econophysics will continue to contribute due to its statistical physics method to statistical and economic thinking in a variety of distinctive directions, ranging from macroeconomics to market micro- structure. A modern book of Statistics must contain statistical physics and statistical quantum approaches too. Finally, this is another role of this paper to underline the importance of the method of statistical physics to unify and simplify statistical thinking for economist, physicists and econophysicists. Keywords: statistics, physics, econophysics, statistical way of thinking, statistical physics, method of statistical physics. 1. Introduction Specific economic theories are constructed from rationality which is the same thing as maximizing expected utility by applying the basic postulates to various economic situations. The new science called Econophysics by Rosario Mantegna and H. Eugene Stanley at the second Statphys-Kolkata conference (Chakrabarti BK, 2005), in 1995, follows the path of care mergers as astrophysics, biophysics, geophysics etc. and it is based on the observation of similarities between economical systems and concepts and those from physics, using the methods from statistical physics. There is * University of Pite şti, e-mail: gsavoiu@ yahoo.com 85 nothing new in the close relationship between physics and economics. A lot of the great economists did their original training and took their models in and from physics, and the influence of physics is clearly evident in many of economic theory’s models. But it is well known too that physics had the more dominating effect on the development of formal economic theory. Its molecular statistical theory of thermal phenomena, furthered the cause of mechanical atomism and population-based thinking. The empirical and theoretical impact of the relativistic and quantum frameworks of physics cemented new, deeper boundaries. Relativity captured space, time and gravi- tational interacttion; quantum mechanics, matter and the rest of forces (Stanford Encyclopedia of Philosophy ). The adequate use for concepts and methods of population-thinking in economics and the role of the envi- ronment have been developed to study a new kind of complex dynamical system like the economical or the financial one. The relation that has tran- spired between economics and physics, in the over past two decades seems very likely to be a model for the future, and the purpose of this paper is to identify the potential of Econophysics through its new domains and results. 2. What is the adequate meaning for statistical thinking? Some of the main techniques used by Statistics were initially developed by mathematicians, and some of the first ideas and models of thinking associated with economists were developed by statisticians. Many economists try to use statistical models too, for the study of a broader variety of economic phenomena’s trends and dynamics. Models for statistical ways of thinking and problem solving have been developed, and continue to be developed, by teachers and researchers or practitioners. All the introductory courses in Statistics, are designed not only to provide the student with the basic concepts and methods of statistical analysis for product and processes, but even for developing a scientific way of thinking and these contain: the need for data and information; the importance of data production and indices or indicators; the omnipresence of variables and variability in the processes; the utilization of a scale for measuring and modeling of variability, the importance of testing hypothesis; the inference from a selected part (sample) to the all investigated population; the final explanation of variation etc. Special mental habit always characterized professional statisticians, and never the amateurs in scientific researches. These distinctive habit is a broad and a very precisely view, or overall framework, in which to put a particular problem (of phenomena’s variation). 86 Some econophysicists seek to integrate their findings with classical Statistics’ theory and statistical thinking, but many others, seeing it as useless and limited, seek to replace its conventional way, with the new and broader view of Statistical Physics thinking. 3. What is the adequate meaning for contemporary econophysics and for econophysics’ thinking? The field of research known as Econophysics, has alternative names like Financial physics and Statistical finance and this only for being initially a new development of two different disciplines like Finance and Physics. But in the last few years, more and more work has been done outside the field of Finance. Rosario Mantegna and Eugene H. Stanley have proposed the first definition of Econophysics as a multidisciplinary field or “the activities of physicists who are working on economics problems to test a variety of new conceptual approaches deriving from the physical sciences” (Mantegna RN, Stanley HE, 2000). From the classical Physics side, Econophysics is mainly considered to be restricted to the principles of statistical mechanics, which is the application of probability theory to large numbers of physical objects which are related to each other in a certain way, while from the Economics site, macroscopic properties are viewed as the result of interactions at the micro- scopic level of the constituents, and Econophysics becomes for economists which have always encouraged the application of quantitative and formal methods “the investigation of economic problems by physicists” (Roehner B, 2005). But somehow the Econophysics is more interesting viewed by its practitioners, as a revolutionary reaction to standard economic theory that threatens to enforce a paradigm shift in thinking about economic systems and phenomena. Yakovenko relevant definition considers that Econophysics is an “interdisciplinary research field applying methods of statistical physics to problems in economics and finance” (Yakovenko VM, 2007). Econophysicists, making use of the statistical physics analogy, rather than a thermo dynamical one, adopt a constructive-theory-type approach. And thus their without prior models are microscopically realistic, and where the parameters hold some physical meaning that are derived from the data and are physically well-founded by providing basic mechanisms for the phenomena. Modern Econophysics, a very rapidly developing area, proposes the application of methods from statistical physics, the physics of complex systems and science of networks to macro/micro- economic modeling, financial market analysis and social problems (from 87 demographical to cultural, from real economical convergence to social cohesion problems, etc.). Contemporary Econophysics’ thinking using new perspective, applies to economic phenomena various models and concepts associated with the physics of complex systems (e.g. statistical mechanics, condensed matter theory, self-organized criticality, microsimulation etc.) Econophysics’ new way of thinking becomes more and more a translation of the Statistical Physics into real individuals and economic reality. Where the curious statistical properties of the data are fairly well-known amongst economists, but still remain a puzzle for economic theory, that will be the right place where physicists must come on stage lights with their method and techniques, and so they are defining a new model of thinking. For econophysicists, the universality of the statistical properties is their starting point, and for this new and stable vision of the truth, the most recently awarded Nobel Prizes, in the last decade, recognize outstanding original contributions that use statistical physics’ methods to develop a better understanding of socio- economic problems. The interest of physicists in financial and economic systems has roots that date back to 1936, when Majorana wrote a pioneering paper, published in 1942 and entitled Il valore delle leggi statistiche nella fisica e nelle scienze sociali , on the essential analogy between statistical laws in physics and social sciences. Many years later a statistical physicist Elliott Montroll coauthored with Badger W.W, in 1974, the book Introduction to Quanti- tative Aspects of Social Phenomena. The application of concepts as power-law distributions, correlations, scaling, unpredictable time series and random processes to financial markets was possible during the past two or three decades years, because physicists have achieved important results in statistical

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