Title

The Interplay between Physics and Mathematics within History and Philosophy of Science & Science Education

Abstract Course

Historical epistemology of science is one of the possible approaches to understanding the history and philosophical foundations of science combining historical/epistemological aspects (i.e., primary sources, historical hypothesis, shared knowledge, epistemological interpretations) and using logical and mathematical inquiring. By following this historical–epistemological standpoint, one might ask: what are physics and mathematical objects in a theory? For example in 19^th century, one can see scientific theories (particularly, mathematical and physical quantities along the experiments, modeling, properties and structures) which work in a unique discipline: physics mathematics (or mathematics physics). It is not a mathematical physics as mathematical application of physics or vice–versa, but rather it is a new way to work with science. New methodological approach to solve physical (in origin) problems where the quantities may be physical and mathematical at the same time (first novelty), and measurements are not a priority or a prerogative (second novelty) to make a coherent physical science. In addition, it is a structured discipline among mathematical quantities and physical structures (including logic and language) in order to “[...] reducing [experimental electric and magnetic] phenomena into scientific form [...]” (Maxwell 1865, p. 459). By focusing on mathematics, physics and its relationship, an interdisciplinary approach among history, philosophy, epistemology, logic and foundations of physical and mathematical sciences might be adopted. In this talk, some historical-philosophical case-studies on relationship physics-mathematics are presented and educationally discussed, i.e.: lack of relationship physics-logics, space and time in mechanics, mechanics and thermodynamics, ad absurdum proofs, non-Euclidean geometries and the space in physics, planetary model and quantum mechanics, infinite-infinitesimal and measures in laboratory, heat-temperature-friction, and reversibility phenomena, concept of set and field, continuum-discrete models in mechanics and theory of elasticity of the XIX cent., hypothesis ad hoc in the theory, local-global interpretation and differential equations-integral, point-range and physical phenomena, mechanics, kinetic model of gases and thermodynamics.

References

1. Bussotti P, Pisano R (2014) Newton’s Philosophiae Naturalis Principia Mathematica “Jesuit” Edition: The Tenor of a Huge Work. Accademia Nazionale Lincei-Rendiconti Matematica e Applicazioni 25: 413–444
2. Gillispie CC, Pisano R (2014) Lazare and Sadi Carnot. A Scientific and Filial Relationship. 2nd edition. Dordrecht. Springer NL
3. Maxwell JC (1865) A dynamical theory of the Electromagnetic field. Philosophical Transactions of The Royal Society of London CLV :459–512
4. Mellone M, Pisano R (2012)  Learning Mathematics In Physics Phenomenology And Historical Conceptual Streams , Problems Of Education In The 21st Century 46:93–100
5. Pisano R (2009) Towards High Qualification For Science Education. The Loss Of Certainty”, International Journal of Baltic Science Education, 8/2:64–68
6. Pisano R (2010)  On Principles In Sadi Carnot’s Theory (1824). Epistemological reflections. Almagest 2/1:128–179
7. Pisano R (2011) Physics–Mathematics Relationship. Historical and  Epistemological notes. In: Barbin E., Kronfellner M. and Tzanakis C., (eds.), Proceedings of the ESU 6 European Summer University History And Epistemology In Mathematics, Verlag Holzhausen GmbH–Holzhausen Publishing Ltd., Vienna, pp. 457–472
8. Pisano R (2011) Textbooks, Foundations, History Of Science and Science education  In : Problems of education in the 21st century 35:5–10
9. Pisano R (2012) Historical Reflections on Physics Mathematics Relationship In Electromagnetic Theory  In: Barbin E., Pisano R., (eds). The Dialectic Relation between Physics And Mathematics In The XIXth Century. Springer, Dordrecht, pp 31–57.
10. Pisano R (2013) On Lagrangian in Maxwell's electromagnetic theory. Scientiatum VI. História das Ciências e das Técnicas e Epistemologia. The University of Federate University of Rio de Janeiro Press, Brazil, 44-59
11. Pisano R (ed.) (2015) A Bridge between Conceptual Frameworks, Science, Society and Technology Studies. Dordrecht. Springer NL [forthcoming]
12. Pisano R, Bussotti P (2012)  Galileo And Kepler. On Theoremata Circa Centrum Gravitates Solidorum And Mysterium Cosmographicum. History Research 2/2:110–145
13. Pisano R, Bussotti P (2013) Open problems in mathematical modelling and physical experiments: exploring exponential function. Problems of education in the 21st century 50:56–69
14. Pisano R, Bussotti P (2014a) Notes on mechanics and mathematics in Torricelli as physics mathematics relationships in the history of science. Problems of Education In The 21st Century 61/61:88–97
15. Pisano R, Bussotti P (2014b) Historical and Philosophical Reflections on the Culture of Machines around the Renaissance. How Science and Technique Work? Acta Baltica Historiae et Philosophiae Scientiarum 2/2:20-42
16. Pisano R, Capecchi D (2013) Conceptual and Mathematical Structures of Mechanical Science in the Western Civilization around 18th Century. Almagest 4/2:86-121
17. Pisano R, Capecchi D (2015) Tartaglia’s science weights and Mechanics in XVI century. Selections from Quesiti et invention diverse: Books VII–VIII. Dordrecht. Springer, NL [forthcoming]
18. Pisano R, Casolaro F (2011) An Historical Inquiry On Geometry In Relativity. Reflections on late Relationship Geometry–Physics (Part Two). History Research 1/1: 47-60; (Part Two)” History Research 2/1:56–64
19. Pisano R, Gaudiello I (2009) Continuity and discontinuity. An epistemological inquiry based on the use of categories in history of science. Organon 41:245–265

Contact

pisanoraffaele@iol.it