“…Most recently, Damerow et al argue that Galileo had applied a rule of ‘proportionality between distance and velocity in the sense of the Aristotelian concept' (Damerow et al , 1992, p. 235), referring to a concept of velocity they take Galileo to have evidenced in a famous 1604 letter to Sarpi 8. .…”
Section: Confusions Over Galileo's Refutationmentioning
confidence: 99%
“…The refutation of space proportionality in the Discorsi is thus no refutation of these proofs but of the proportionality between the degree of velocity and distance under the presupposition of a proportionality between overall velocity and degree of velocity. But Galileo's argument is also incompatible with classical mechanics… (Damerow et al , 1992, p. 236)…”
Section: Confusions Over Galileo's Refutationmentioning
confidence: 99%
“… They write: ‘Galileo’s argument is also incompatible with classical mechanics, since, in classical mechanics, it does not follow that a motion whose velocity increases in proportion to the distance traversed must be instantaneous but rather that such a motion cannot begin at all from the state of rest' (Damerow et al , 1992, p. 236). …”
Note to typesetter: Please use attached high-res EPS images in place of the low-res imagesembedded in the text.
Abstract.Galileo's refutation of the speed-distance law of fall in his Two New Sciences is routinely dismissed as a moment of confused argumentation. We urge that Galileo's argument correctly identified why the speed-distance law is untenable, failing only in its very last step. Using an ingenious combination of scaling and self-similarity arguments, Galileo found correctly that bodies, falling from rest according to this law, fall all distances in equal times. What he failed to recognize in the last step is that this time is infinite, the result of an exponential dependence of distance on time. Instead, Galileo conflated it with the other motion that satisfies this 'equal time' property, instantaneous motion.
“…Most recently, Damerow et al argue that Galileo had applied a rule of ‘proportionality between distance and velocity in the sense of the Aristotelian concept' (Damerow et al , 1992, p. 235), referring to a concept of velocity they take Galileo to have evidenced in a famous 1604 letter to Sarpi 8. .…”
Section: Confusions Over Galileo's Refutationmentioning
confidence: 99%
“…The refutation of space proportionality in the Discorsi is thus no refutation of these proofs but of the proportionality between the degree of velocity and distance under the presupposition of a proportionality between overall velocity and degree of velocity. But Galileo's argument is also incompatible with classical mechanics… (Damerow et al , 1992, p. 236)…”
Section: Confusions Over Galileo's Refutationmentioning
confidence: 99%
“… They write: ‘Galileo’s argument is also incompatible with classical mechanics, since, in classical mechanics, it does not follow that a motion whose velocity increases in proportion to the distance traversed must be instantaneous but rather that such a motion cannot begin at all from the state of rest' (Damerow et al , 1992, p. 236). …”
Note to typesetter: Please use attached high-res EPS images in place of the low-res imagesembedded in the text.
Abstract.Galileo's refutation of the speed-distance law of fall in his Two New Sciences is routinely dismissed as a moment of confused argumentation. We urge that Galileo's argument correctly identified why the speed-distance law is untenable, failing only in its very last step. Using an ingenious combination of scaling and self-similarity arguments, Galileo found correctly that bodies, falling from rest according to this law, fall all distances in equal times. What he failed to recognize in the last step is that this time is infinite, the result of an exponential dependence of distance on time. Instead, Galileo conflated it with the other motion that satisfies this 'equal time' property, instantaneous motion.
“…Our treatment of these electron models follows the analysis of the experiments of Trouton and Noble in (Janssen, 1995(Janssen, , 2002b(Janssen, , 2003, which was inspired in part by the discussion in (Norton, 1992) of the importance of Laue's relativistic mechanics for the development of Gunnar Nordström's special-relativistic theory of gravity. The focus on the conceptual changes in mechanics that accompanied the transition from classical to relativistic kinematics was inspired in part by the work of Jürgen Renn and his collaborators on pre-classical mechanics (Damerow et al, 2004). Ultimately, our story is part of a larger tale about shifts in such concepts as mass, energy, momentum, and stresses and the relations between them in the transition from Newtonian mechanics and the electrodynamics of Maxwell and Lorentz to special relativity.…”
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