1 The Birth of Science - MSRI

4.2 Instrumentation 91
of emptying of the main reservoir. The float valve, if indeed due to Archimedes,
may be one of the earliest feedback control devices.
Among the causes of error in water clocks considered in Antiquity was
the variation in the flow rate of water caused by temperature changes. 25
Much has been written about the transformation the concept of time page 128
underwent in the modern age because of clocks, 26 but in general it has not
been supposed that anything like the modern scientific concept of time
might have been known to the scientists to whom we owe the invention of
clocks. For example, Sambursky not only talks of the “inability [of ancient
scientists] to comprehend time as an independent variable” 27 but writes:
Galileo’s work was revolutionary . . . [also] in treating time as a mathematical
quantity which could be used in calculations . . . His proofs
are accompanied by graphs showing portions of time as sections on a
straight line. This geometrical representation of time by Galileo was
a step of first-class historical significance. 28
In fact, the use of time as an independent variable, geometrically represented,
enabled Hellenistic scientists to define many curves kinematically.
Archimedes, in his On spirals (neglected by Sambursky but studied with
attention by Galileo) explicitly considers the “axis of times” and uses it as
a fundamental geometrical entity. Time as an independent variable plays
an essential role in the Almagest, and to cite just one more example, Heron
makes interesting considerations on the subject in his Pneumatica and his
Mechanica, as we shall see.
Did the use of clocks change the concept of time in everyday life as well?
Besides the previously mentioned use of timers at trials, some indication
of a movement in this direction already in the fourth century B.C. is provided
by the case of the prostitute nicknamed Clepsydra, who “timed her
favours by the water-clock, stopping when it was emptied”. 29
25 This observation was made in a lost treatise by Theophrastus, On waters ( ), and is
mentioned by Plutarch (Quaestiones naturales, 914A) and by Athenaeus (Deipnosophistae, II, 42a–b).
Indeed the higher viscosity of cold water (to use the modern terminology) slows down the flow
noticeably. Athenaeus explains the slowdown with the words , “because of the pachos”,
a word that can mean both thickness and density, the two concepts seemingly being merged in his
mind. A similar explanation is given by Plutarch, who is perhaps Athenaeus’ direct source.
26 It suffices to recall the classic pages of Marc Bloch on the medieval concept of time ([Bloch: FS],
pp. 73–74) and the essay [Koyré: MPUP].
27 [Sambursky: PWG], p. 185.
28 [Sambursky: PWG], p. 239. Sambursky’s book cannot be ignored because it is the only one, as
far as I know, devoted to Greek “physics” (a subject generally regarded as nonexistent).
29 Athenaeus, Deipnosophistae, XIII, 567c–d (Gulick translation).
Revision: 1.14 Date: 2002/10/24 04:25:47