Understanding mathematical abstraction in the formularization of Galileo's law
Abstract
Galileo's revolution in science introduced an analytical method to science that typifies the overall modern thinking of extracting, abstracting, and grasping only critical aspects of the target phenomena and focusing on “how”, which is a quantitative relationship between variables, instead of “why”. For example, to him, the question of 'why does an object fall' is of no significance; instead, only the quantitative relationship between distance from the falling object and time is important. Yet, the most fundamental aspect of his idea is that he introduced a quantified time t. When an object is projected horizontally, the distance travelled at some time in the horizontal direction is summed up as d ∝t, whereas the distance falling at some time in the vertical direction is summed up as d ∝ t². Here, the distance, which is a spatial attribute, is expressed as a function of time, t. That is, time is identified as a homogeneous amount that can be reduced to an algebraic number. It is now possible to calculate the laws of motion of things using functions of time. In this respect, mathematical time was a decisive variable in making mathematisation of physical nature practical. Because, according to atomic theory, vacuum exists between an atom and an object composed of atoms or between objects – ignoring factors that interfere with motion, such as friction – the space for absolute time, which is a mathematical time, can be geometrically defined. In order to justify this mathematical abstraction strategy, thought experiments were conducted rather than laboratory experiments, which at that time were difficult to perform.
Downloads
References
Brown, J. R. (1991a). The laboratory of the mind: Thought Experiments in the Natural Sciences. London: Routledge.
Brown, J. R. (1991b). Thought experiments: A platonic account. In T. Horowitz & G. Massey (Eds.), Thought experiments in science and philosophy (pp. 119–128). Lanham: Rowman & Littlefield.
Brown, J. R. (2011). The Laboratory of the mind: thought experiments in the natural sciences (2nd edition). London: Routledge.
Chalmers, A. F. (1999). What is this thing called science? (3rd edition). Cambridge: Hackett Publishing Company. Inc.
Cohen, I. B. (1985). The birth of a new physics. New York, London: W.W. Norton & Company.
Crease, R. P. (2003). The prism and the pendulum: the ten most beautiful experiments i science. New York: Random House.
Cushing J. T. (1998). Philosophical Concepts. Cambridge: The Press of the University of Cambridge.
Dolnick, E. (2011). The clockwork universe: Isaac Newton, Royal Society, and the birth of the Modern World. New York: HarperCollins.
Frank, A. (2011). About time: Cosmology and culture at the twilight of the big bang. New York: A Division of Simon & Schuster, Inc
Gillispie, C. C. (1990). The edge of objectivity. NJ: Priceton University Press.
Gottlieb, A. (2000). The dream of reason: A history of western philosophy from the Greeks to the Renaissance. WW Norton & Company.
Kuhn, T.S. (1970). The Structure of Scientific Revolutions (2nd edition). Chicago: University of Chicago Press.
McMulin, E. (1985). Galilean idealization. Studies in History and Philosophy of Science, 16(3), 247–273. https://doi.org/10.1016/0039-3681(85)90003-2
Miller, A. (1996). Insights of Genius. New York: Springer-Verlag. https://doi.org/10.1007/978-1-4612-2388-7
Moreland, J. P., & Craig, W. L. (2003). Philosophical Foundations for a Christian Wordview. Downer Grove, IL.: InterVarsity Press.
Nersessian, N. (1992). In the theoretician’s laboratory: Thought experimenting as mental modeling. In D. Hull, M. Forbes & K. Okruhlik (Eds.), PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 2, 291–301. East Lansing, MI: Philosophy of Science Association.
Norton, J. (1991). Thought experiments in Einstein's work. In T. Horowitz and G. Massey (Eds.), Thought Experiments in Science and Philosophy (pp. 129–148). Lanham: Rowman & Littlefield.
Norton, J. (1996). Are thought experiments just what you thought? Canadian Journal of Philosophy, 26(3), 333–366. https://doi.org/10.1080/00455091.1996.10717457
Oh, J.-Y. (2016). Understanding scientific inquiries of Galileo’s formulation for the law of free falling motion. Foundations of Science, 21(4), 567–578. https://doi.org/10.1007/s10699-015-9426-y
Oh, J.-Y. (2021). Understanding the scientific creativity based on various perspectives of science. Axiomathes; 1–23. https://doi.org/10.1007/s10516-021-09553-8
Park, J.-W., Chung, B.-H., Kwon, S.-G., & Song, J.-W. (1998). A study of high school students and science teachers understanding of ideal conditions involved in the theoretical explanation and experiment in physics: Part II – Focused on the implications to the physics learning. Journal of the Korean Association for Research in Science Education, 18(2), 245–266 [in Korean]
Runco, M. A. (2014). Creativity: Theories and themes: Research, development, and practice (Second Edition). New York: Elsevier Inc.
Trickett, S. B., & Trafton, J. G. (2007). “What if…”: The use of conceptual simulations in scientific reasoning, Cognitive Science, 31(5), 843–875. https://doi.org/10.1080/03640210701530771
Welling, H. (2007) Four mental operations in creative cognition: the importance of abstraction. Creativity research journal, 19(2–3), 163–177. https://doi.org/10.1080/10400410701397214
Abstract views: 461 PDF Downloads: 261
Copyright (c) 2022 History of science and technology
This work is licensed under a Creative Commons Attribution 4.0 International License.
License terms: authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License International CC-BY that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
The scanned copy of the "Agreement” on the authors" copyright transfer on the manuscript publication and the subsequent posting of the paper on the Internet (in * .pdf or * .jpg format) is to be attached to the manuscript of the paper.
By this agreement the author certifies that the submitted material:
- does not infringe the copyright of other persons or organizations;
- was not previously published in other publishing houses and has not been submitted for publication in other editions.
The author passes the editorial board of the journal "History of science and technology" rights to:
- publication of the article in Ukrainian (English and Russian) language and distribution of its printed copy;
- translation of the article into English language (for articles in Ukrainian and Russian language) and distribution of its translated printed copy;
- distribution of the article electronic copy, as well as electronic copy of the article English translation (for articles in Ukrainian and Russian), via any electronic means (placing on the official web-site of the journal, electronic databases, repositories, etc.) printed copy of the translation.
The author reserves the right without the consent of the editorial board and founders:
- Use the materials of the article in whole or in part for educational purposes.
- Use the materials of the article in whole or in part to write their own dissertations.
- Use the materials of the article for the preparation of abstracts, conference reports, as well as oral presentations.
- Place electronic copies of the article (including the final electronic copy downloaded from the official web-site of the journal) to:
- personal web-resources of all authors (web-sites, web-pages, blogs, etc.);
- web-resources of institutions where authors work (including electronic institutional repositories);
- non-commercial web-resources of open access (for example, arXiv.org).
In all cases, the availability of a bibliographic link to an article or hyperlink to its electronic copy on the official website of the journal is compulsory.