Abstract
Authors writing about Time have struggled to choose between a scientific instantaneous Now, with zero duration, or an experiential Now with some undefined small positive duration. The difficulty is resolved by the infinitesimal of Abraham Robinson. This article offers the nonstandard or “hyperreal” line as a model for Time, thereby to resolve a persistent controversy of the meaning of “Now.” As a “monad” in the Leibnizian time axis, “Now” is a time interval shorter than any standard positive interval, yet longer than any infinitesimal.
Reprinted with permission from Springer Science. The original version of the paper appeared in:
S. Wuppuluri & G. Ghirardi (Eds), “Space, Time and the Limits of Human Understanding”, Springer – The Frontiers Collection, ISBN: 9783319444185.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bachelard, G., 1932, “The Instant,” in R. Durie, 64–95
Bergson, H., 1911, “The Cinematographic View of Becoming,” , Chapter 4 of Creative Evolution, 304–311, Holt, Rinehart and Winston
Capek, M., 1973, “Time,” in Dictionary of the History of Ideas, Ed. Philip P. Wiener, Volume IV, 389–398, Charles Scribner’s Sons
Dorato, M., 2015, “Presentism and the Experience of Time,” Topoi, 34, 265–275
Durie, R., 2000, Time & the Instant, Manchester, Clinamen Press
Grunbaum, A., 1969, “Modern Science and Zeno’s Paradoxes of Motion,” in W. Salmon, 200–250
James, W., 1890, The principles of psychology, Henry Holt & Co.
Miller, I., 1982, “Husserl’s Account of our Temporal Awareness,” in H.L.Dreyfus, Ed., Husserl, Intentionality and Cognitive Science, The MIT Press
Pockett, S., 2003, “How long is ‘now’? Phenomenology and the specious present,” Phenomenology and the Cognitive Sciences 2: 55–68.
Robinson, A., 1966, Nonstandard Analysis, North-Holland Publishing Company
Robinson, M., 2015, “Humanism. The Spirit of Our Time,” The Nation, 301: (19), November 9, 27-32
Sachs, J., Ed., 1998, Aristotle’s Physics, Rutgers University Press
Toulmin, S. & J. Goodfield, 1965, The Discovery of Time, Harper & Row
“Perception of time,” Encyclopedia of Philosophy
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Hersh, R. (2017). “Now” Has an Infinitesimal Positive Duration. In: Sriraman, B. (eds) Humanizing Mathematics and its Philosophy. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-61231-7_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-61231-7_4
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-61230-0
Online ISBN: 978-3-319-61231-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)