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Mathematical Language as a Bridge Between Conceptualization of Motion and Experimental Practice

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Part of the book series:History of Mechanism and Machine Science ((HMMS,volume 27))

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Abstract

In this paper we try to distinguish two different styles of experimental practice—roughly speaking the Galilean and the Newtonian. They differ in the way they intertwine mathematics and experimentation. We offer a theoretical reconstruction of the transition from the Galilean to the Newtonian experimental practice. It seems that this transition was brought about by gradual changes of the conceptual framework for the representation of motion. The aim of the paper is to argue that in many of these changes Cartesian physics played an important role.

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Notes

  1. 1.

    Even though air pressure (which we will discuss below) is not directly accessible to ordinary experience, there is nevertheless a directly observable phenomenon—the strange behavior of the water pumps that refuse to pump water from depths greater than a certain limit—that is accessible to ordinary experience.

  2. 2.

    Geometrical transition means that the basic representation of motion isgeometrical (as opposed to adynamic one): it describes motion as a change ofposition in space rather than as a change of state. Further,geometrical transition represents motion astransition, which means that the focus of attention is on the starting point and the terminal point of motion, while the process of motion itself does not enter the representation. (This does not mean that the change ofstate or theprocess of change is not thought about, but only that they are not included into the representation of motion. Thus even though Aristotle understands change as a becoming, in the definitions of (violent) motions these aspects do not enter.).

  3. 3.

    Geometrical flow means that the representation of motion is stillgeometrical, it concerns a change of position in space and not a change of state. Nevertheless, it is aflow. It represents motion as a continuous passing along a trajectory (as opposed to atransition from the starting position to the terminal one).

  4. 4.

    It seems that theextended body of Cartesian physics is closer to thecosa of theCossists than to the Aristotelianpragmata. An extended body enters into mechanical interactions with other bodies just like acosa enters into algebraic relations with other quantities. Furthermore, an extended body has only mechanical properties just like acosa has purely algebraic ones.

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Acknowledgements

I would like to thank Gábor Boros for his support and encouragement. The paper was written in the framework of theJan Evangelista Purkyně Fellowship at the Institute of Philosophy of the Academy of Sciences of Czech Republic in Prague.

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Authors and Affiliations

  1. Institute of Philosophy, Academy of Sciences of the Czech Republic, Prague, Czech Republic

    Ladislav Kvasz

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  1. Ladislav Kvasz

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Correspondence toLadislav Kvasz.

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Editors and Affiliations

  1. Department of Physics, Lille 1 University Science and Technology, Villeneuve d’Ascq, France

    Raffaele Pisano

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Kvasz, L. (2015). Mathematical Language as a Bridge Between Conceptualization of Motion and Experimental Practice. In: Pisano, R. (eds) A Bridge between Conceptual Frameworks. History of Mechanism and Machine Science, vol 27. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9645-3_13

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