Similarity Among Physical Phenomena Recognized on the Basis of the Classification of Existing Knowledge

Year 2020, , 47 - 54, 31.08.2020

Antonios Kanavouras Frank Coutelieris

https://doi.org/10.33187/jmsm.691846

Abstract

This work presents the synthetical mathematical analysis of available knowledge regarding physical phenomena of research interest. The work is not focusing on providing the phenomena according to the physical laws but rather because of them, hence, it is grounded on the philosophically defined concept of "similarity", and progresses to the mathematical treatments of those factors and parameters that are involved into the similarity validation among physical phenomena.A critical validation regarding the effectiveness of such an approach was also performed, in order to conceptualize the relevance of the factors and parameters interactions as a potential control tool against engineering-based hypothesis. Such factors and parameters are generated through the description and delimitation of the system of interest. A "matrix" is used for the classification of the existing knowledge regarding this system. It is consisted of the categorical descriptors of the system in question and the levels of these descriptors.A mathematical analysis of this "matrix" supports that all the existent perceptions of a physical phenomenon constitute a four-dimensional vector space. Within this space, the concept of similarity allows for the definition on which of a specific non-linear mapping that might be applied to strictly classify the existing knowledge about the phenomenon in question.Similarity is used here to define the conditions and the constrains that this mapping must satisfy. In conclusion, the applicability of the suggested approach on an engineering approach regarding a physical problem, was also demonstrated in this study.

Keywords

Similarity, classification matrix, physical phenomena, linear algebra, engineering assets

References

• [1] R. Giere, Scientific Perspectivism, University of Chicago Press, Chicago, USA, 2006.
• [2] H. Douglas, The irreducible complexity of objectivity, Synthese, 138 (2004), 453–473.
• [3] T. S. Kuhn, The Structure of Scientific Revolutions, University of Chicago Press, Chicago, USA, 1962.
• [4] P. Feyerabend, Explanation, Reduction and Empiricism, Scientific Explanation, Space, and Time, (Minnesota Studies in the Philosophy of Science, Volume III), H. Feigl, G. Maxwell (editors), University of Minneapolis Press, USA, 1962.
• [5] P. Kroes, Structural analogies between physical systems, Brit. J. Philos. Sci., 40 (1989), 145-154.
• [6] I. Hacking, Representing and Intervening. Introductory Topics in the Philosophy of Natural Science, Cambridge University Press, UK, 1983.
• [7] S.G. Sterrett, Models of machines and models of phenomena, Stud. Philos. Sci., 20 (2006), 69-80.
• [8] C. Glymour, On some patterns of reduction, Philos. Sci., 37 (1970), 340-353.
• [9] S.G. Sterrett, Physical models and fundamental laws: Using one piece of the world to tell about another, Mind Soc., 3 (2002), 51-66.
• [10] I. Kant, The Critique of Pure Reason (Translated by J. M. D. Meiklejoh), University of Adelaide Press, Adelaide, AUS, 2014.
• [11] A.S. Troelstra, H. Schwichtenberg, Basic Proof Theory, Cambridge University Press, Cambridge, UK, 2000.
• [12] K.R. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge, Harper, New York, USA, 1963.
• [13] A. Kanavouras, F.A. Coutelieris, Systematic transition from description to a prediction engineering model for the oxidation in packed edible oils, J. Food Chem., 229 (2017), 820-827.
• [14] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, Wiley, New York, USA, 1960.