The staccato roller coaster: a simple physical model of the staccato run
- Chunghyoung Lee
- … show all 1 hide
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
I present a simple model of Grünbaum’s staccato run in classical mechanics, the staccato roller coaster. It consists of a bead sliding on a frictionless wire shaped like a roller coaster track with infinitely many hills of diminishing size, each of which is a one-dimensional variant of the so-called Norton dome. The staccato roller coaster proves beyond doubt the dynamical (and hence logical) possibility of supertasks in classical mechanics if the Norton dome is a proper system of classical mechanics with metaphysical import. If not, challenges raised against the metaphysical significance of the Norton dome are shown to be challenges against various arguments for the dynamical possibility of supertasks, and the staccato roller coaster clearly shows the importance of meeting these challenges. And the staccato roller coaster can provide, as well as interesting lessons, illuminating analyses of Burke’s (Mod Schoolman 78:1–8, 2000) attempt to refute the dynamical possibility of the staccato run and Pérez Laraudogoitia’s (Synthese 148:433–441, 2006) rebuttal of it.
- Black, M. (1950–1951). Achilles and the tortoise. Analysis 11, 91–101. Reprinted in Salmon (1970).
- Burke M. (2000) The staccato run: A contemporary issue in the Zenonian tradition. The Modern Schoolman 78: 1–8 CrossRef
- Earman J. (1971) Laplacian determinism, or it this any way to run a universe. Journal of Philosophy 68: 729–744 CrossRef
- Grünbaum A. (1967) Modern science and Zeno’s paradoxes. Wesleyan University Press, Middletown, CT
- Grünbaum, A. (1970). Modern science and Zeno’s paradoxes of motion. In W. Salmon (Ed.), Zeno’s paradoxes (pp. 200–250). Indianapolis, IN: Bobbs-Merrill.
- Korolev A. (2007a) Indeterminism, asymptotic reasoning, and time irreversibility in classical physics. Philosophy of Science 74: 943–956 CrossRef
- Korolev, A. (2007b). The Norton-type Lipschitz-indeterministic systems and elastic phenomena: Indeterminism as an artefact of infinite idealizations. PSA 2008 Contributed Papers. http://philsci-archive.pitt.edu/id/eprint/4314. Accessed 30 April 2011.
- Malament D. (2008) Norton’s slippery slope. Philosophy of Science 75: 799–816 CrossRef
- Norton, J. (2003). Causation as folk science. Philosopher’ s Imprint 3. http://hdl.handle.net/2027/spo.3521354.0003.004. Accessed 30 April 2011.
- Norton J. (2008) The dome: An unexpectedly simple failure of determinism. Philosophy of Science 75: 786–798 CrossRef
- Pérez Laraudogoitia J. (1996) A beautiful supertask. Mind 105: 81–83 CrossRef
- Pérez Laraudogoitia J. (2006) A look at the staccato run. Synthese 148: 433–441 CrossRef
- Salmon W. (1970) Zeno’s paradoxes. Bobbs-Merrill, Indianapolis, IN
- Thomson, J. (1954). Tasks and super-tasks. Analysis 15, 1–13. Reprinted in Salmon (1970).
- Wilson M. (2009) Determinism and the mystery of the missing physics. British Journal for the Philosophy of Science 60: 173–193 CrossRef
- The staccato roller coaster: a simple physical model of the staccato run
Volume 190, Issue 3 , pp 549-562
- Cover Date
- Print ISSN
- Online ISSN
- Springer Netherlands
- Additional Links
- Staccato run
- Norton dome
- Industry Sectors
- Chunghyoung Lee (1) (2)
- Author Affiliations
- 1. Department of Philosophy, California State University, Fresno, 2380 E. Keats Ave., M/S MB 105, Fresno, CA, 93740, USA
- 2. Division of Humanities and Social Sciences, Pohang University of Science and Technology, San 31 Hyoja-Dong Nam-Gu, Pohang, Gyungbuk, 790-784, Republic of Korea