TIME ESSAY

Please note: These papers were prepared for the Greek Science course taught at Tufts University by Prof. Gregory Crane in the spring of 1995. The Perseus Project does not and has not edited these student papers. We assume no responsibility over the content of these papers: we present them as is as a part of the course, not as documents in the Perseus Digital Library. We do not have contact information for the authors. Please keep that in mind while reading these papers.

A Brief History of Time

(with apologies to Stephen Hawkings)

From Thales to Callippus

Chris Weinkopf
April 9, 1995

This paper is now featured on the Discovery Channel School Web site.

Table of Contents

  1. Introduction
  2. Initial Evidence of Time
  3. The Presocratics
  4. Changing Attitudes Towards Time
  5. The Platonic Application
  6. The Dawn of the Sundial
  7. Bibliography

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Introduction

Whether for agricultural, legal, or religious purposes, the ability to measure time was of the utmost importance in ancient Greece. Homer and Hesiod both suggest that men recognized some connection between the sun, stars, moon, earth, and time, but were unable to observe very effectively the cosmos for purposes of chronology. Only with the advancement of astronomy, beginning with Thales in the early sixth century BC, could the Greeks begin to utilize the heavens for designing accurate calendars and sundials. Eventually, Plato, in is Timaeus, would declare, “The sun, moon, and… planets were made for defining and preserving the numbers of time. “

With our without astronomy, casual observation over the course of one’s life makes the cyclical nature of seasons self-explanatory. One need have no appreciation of the earth’s orbit around the sun to discover that fall invariably follows summer, which is preceded by spring, the successor of winter. This order is unfailing, and easily discernible to the naked or even blind eye.

But as any resident of New England can attest, determining the beginning and the end of the seasons without the assistance of astronomical guides is not so easy. According to the earth’s location within its year-long orbit, the first day of spring 1995 was in late March, but the freezing temperatures which persisted for several weeks thereafter suggested otherwise. Climate, compared to astronomy, is a poor measure of season.

Knowledge of the advent or conclusion of seasons, however, is critical to the success of civilization. A farmer dependent exclusively on his own perceptions of season is at a grave disadvantage when he plants his crops. A premature warm front, for example, could cause him to plant too early. Conversely, belated warm temperatures might cause him to wait too long before planting, resulting in his crop’s destruction by winter frost before harvest time.

Likewise, the success of civic calendars hinges on their ability to correlate with the solar reality. Accuracy demands that calendars be based on the earth’s revolution around the sun. Imagine a society that chose to create a 200 day-long year, as opposed to our current 365.25-day long model. While the first month of the calendar might be in the winter one year, it would fall in the late spring the next. Not only would the civil calendar be useless for farmers, it would also render considerably more difficult the scheduling of outdoor festivals or any other event demanding a prior knowledge of the time of season.

Because the moon is easily visible and changes in appearance each day, it made a convenient basis of a calendar for many ancient societies. The lunar cycle, however, lasts only 29 or 30 days. Although the moon is sufficient for delineating months, it fares less well in determining years. A solar (tropical) year, as we know, lasts 365.25 days– a figure not conveniently divisible by 29.5. Twelve lunar months cover only 354 days. Thus the lunar calendar loses 45 days every four years. Keeping a lunar calendar consistent– that is, regulating it such that the same months fall in the same seasons from year to year– requires intercalation.

The creation of an accurate tropical or properly intercalated lunar calendar requires an understanding of the mechanics of the solar system, as does the creation of a reliable sundial. The initial developments in Greek astronomy, beginning with Thales and continuing through Callippus, enabled philosophers and the masses alike to better understand, measure, and gauge time.

Initial Evidence of Time

Homer’s Iliad and Odyssey personify and deify notions of time. Frequently, for example, the poems contain such verses as “Now Dawn the saffron-robed was spreading over the face of all the earth,” to describe the start of a new day. But the Homeric texts do not simply relegate the passage of time to divine actions. There exists also in Homer a cognizance of earthly cycles that operate regardless of divine interaction.

In his Elementa astronomiae, the Greek astronomer Geminus refers to a passage in Book X of The Odyssey which belies an appreciation of the differing lengths of a day (hours of daylight) in various regions of the world. The passage explains that in Telepylus of the Laestrygons, one who chooses to forego sleep can work two full-time jobs in a single day, because there, ‘”the out goings of the night and of the day are close together.”

Geminus’ astronomical explanation for this phenomenon, which surely eluded the Mycenaeans, describes the city’s geographical location. Areas close to the north pole, at the solstice, have 24 hours of daylight, due to the earth’s angle in its revolution. Although Homer and his contemporaries did not understand the astronomical reason for differing day lengths, they did recognize them as the product of a geographical or astronomical cycle.

Hesiod’s Works and Days conveys a more sophisticated understanding of astronomy. Rather than relying on inaccurate civil calendars, Hesiod uses natural phenomena– solstices and equinoxes– for delineating periods of time. His instructions on farming recommend planting according to the solstices. Hesiod lacks a scientific understanding of the solar system, but Works and Days demonstrates a clear recognition of the connection between time and astronomy. It also evidences the beginning of a shift from arbitrary civic or lunar calendars to a solar model.

The Presocratics

There is no evidence of scientific/astronomical calendar theory in Greece before the 5th century BC (Samuel 1972: 22), but its eventual development rests heavily on the discoveries of presocratic philosophers a century earlier. Although each of the presocratics had his own theories about cosmology, this section deals specifically with those who contributed most significantly to the Greeks’ ability to understand and measure time: Thales, Anaximander, the Pythagoreans, and Anaxagoras.

Naturally, our discussion of the presocratics begins with Thales of Miletus, whose famous prediction of the eclipse that would terrify General Nicias 170 years later indicates a rudimentary comprehension of solar cycles. Thales had observed that the most recent eclipses fell seventeen years apart, and therefore concluded that eclipses occur at seventeen year intervals. The extension of his logic was that in 170 years the eclipse cycle would repeat another ten times. As luck would have it, he happened to be correct.

Because eclipses depend on a rare alignment of the, sun, earth and moon, however, and because the revolutions of the latter two operate at vastly different rates, there exists no seventeen year cycle, as Thales believed. Thales’ prediction exposes an ignorance of the workings of solar and lunar orbits; but more importantly, it demonstrates an appreciation of their cyclical nature. Diogenes Laertius credits Thales with the discovering the solstices and the obliquity of the zodiac (ecliptic). One should not, however, overstate Thales’ contribution to the Greeks’ understanding of time. His cosmology, which dictates that the earth floats on top of water, hardly makes for a precise understanding of the cosmos. Nevertheless, his exploration of the relationship between stars, the sun, the moon, and the earth, as demonstrated by his studies of navigation, as well as his appreciation of universal cycles, provided an excellent foundation for later discovery.

Some 35 years after Thales, Anaximander of Miletus made several astronomical studies which greatly facilitated the understanding and measuring of time. Diogenes Laertius credits Anaximander with the introduction of the gnomon, which Herodotus claims was originally a foreign invention. The gnomon was merely two pieces of wood attached at a right angle. Ancient astronomers used it to cast shadows, which they could then measure to gauge the passage of time, or predict the coming of solstices and equinoxes.

Suda attributes to Anaximander the construction of a sundial in Sparta which observed solstices and equinoxes. Suda makes no mention of the device being used to measure the passage of hours, as it likely did not (Gibbs 1976: 7). The technological development of sundials will be discussed more fully in the “Dawn of the Sundial” section later in this work, but is mentioned here because Anaximander’s introduction of the sundial is representative of his expansive astronomical discoveries.

Anaximander contributed to the ancient study of astronomy the notion that the world is round (not actually a sphere, more like a cylinder, but round nevertheless) and was the first, according to Diogenes Laertius, to argue that moonlight is a lunar reflection of the sun. He also parted from conventional wisdom in his conviction that the sun is larger than the earth, and not vice versa. He established the incorrect but practical (in terms of measuring time) belief that the earth was at the center of the universe, which would be embraced by most of his successors, save the Pythagoreans.

Anaximander’s understanding of the gnomon is undoubtedly due, in large part, to his progress in the study of astronomy. It is also, however, consistent with his philosophical understanding of time. Anaximander viewed the world as a steady state; shifts in one direction were always succeeded by shifts in the other. He reasoned, for example, that the number of hot days are offset by an equal number of cold days. Time, he claimed, ultimately serves as the great equalizer, maintaining the steady state in its due course.

This philosophy of time is cyclical, and is consistent with the notion that time and cosmological phenomena can be observed as operating in cycles. Anaximander’s philosophy gave time a quantifiable, hence measurable dynamic. His notions of astronomy, most notably the roundness of the globe, enabled him to attempt such calculation. The gnomon, which provided an accurate estimation of solstices and equinoxes, further advanced the shift to a tropical calendar. It would later be used to determine the time of day.

…………………………………

The Pythagoreans most revolutionary theory, with respect to time, was unfortunately not embraced by any of their immediate successors. The Pythagoreans were the first to conclude that the sun (De Caelo B13, 293 AI8), and not the earth, is the center of the solar system. Consequently, the Pythagoreans were the first to understand the true cause of an eclipse. More important for our purposes, this superior notion of the solar system would have enabled a more accurate gauging of time.

Anaxagoras’ model of the universe was similar to that of the Pythagoreans, although it was geocentric. He generally shared, but refined the Pythagorean explanation of eclipses, by determining that solar eclipses must occur at the new moon phase. Anaxagoras was the first to explain lunar eclipses as the earth blocking the moon from the sun’s light. The significance of this discovery is that it belies an awareness of the moon’s orbit, precise enough to conclude that its motion brings the moon to a point where blocking was possible only once a month.

The presocratic philosophers’ study of Greek astronomy established the necessary tools and theories for the accurate measure of time in calendars and sundials. Thales’ recognition of the cyclical nature of the solar system, Anaximander’s observations and introduction of the gnomon, the Pythagoreans universal theory, and Anaxagoras’ mastery the lunar model, all set the course for their successors’ advanced studies of chronology. In the following section, we will examine how the further exploration of astronomy and its correlation to chronology continued after the presocratics.

Changing Attitudes Towards Time

As previously noted, the mid-fifth century historian Herodotus was aware of the advances made in astronomy and chronology. In the second book of his histories, he explains in great detail the Greek and Egyptian calendars, indicating that by his time both societies had a strong sense of the relationship between earthly time and the heavens. The Egyptian calendar clearly took into account the lunar cycles, as it, according to Herodotus, “consist[ed] of twelve divisions of the seasons.”

Both societies recognized the limitations of lunar calendars, as they used forms of intercalation to keep the lunar calendar seasonally consistent. “The Greeks add an intercalary month every other year, so that the seasons agree,” writes Herodotus; “but the Egyptians, reckoning thirty days to each of the twelve months, add five days in every year over and above the total, and thus the completed circle of seasons is made to agree with the calendar.” Seemingly, neither society directly incorporated the solar calendar into its calculations of time, but did so at least indirectly in their consideration of the seasons.

In his Memorabilia, Xenophon, a disciple of Socrates, displays a basic understanding of the solar system’s mechanics which implies that the presocratics’ theories were still influential by the mid-fourth century BC. Xenophon describes the sun as on a voyage around the earth, careful never to approach too closely and scorch mankind, but equally prudent to avoid moving too far away, and leaving people to freeze. Although he supports the geocentric universal model, Xenophon’s description demonstrates that he believes the ecliptic to be oblique. This belief manifests itself in an accurate understanding of the seasons– winter is cold because the sun is the farthest away; summers are hot because the sun is close by.

Fourth century astronomers built upon the theories first put forward by the presocratics and reflected in the works of Xenophon. According to Aristotle, Eudoxus explained the motions of all celestial bodes in terms of concentric spheres, with the earth at the center. Each body was connected to the equator of a sphere, which revolved constantly around its own poles. The spheres were all, literally, inside one another, as if layers of one super-sphere. Eudoxus suggested that there were three spheres in total, which carried the sun, stars, moon, and planets.

Eudoxus’ universal model explained the apparent motions of the sun and moon, and enabled astronomers to predict their positions with a great degree of accuracy. By tracking the pace of individual bodies through their respective orbits, one could calculate their velocity and thus determine the lengths of their cycles. As Alan Samuel notes, “It was no longer necessary to depend solely upon the relatively unsophisticated gnomon to determine the lengths of the periods, but mathematical calculation, based on the theory of the spheres, could bring greater precision” (Samuel 1972: 31).

Callippus improved upon Eudoxus’ theory of concentric spheres by adding an additional two layers. The flaw in the Eudoxus model is that it treated the velocities of the “sun” (the velocity of the earth traveling around the sun, but understood by the geocentrists as precisely the opposite) and moon as constant. In reality, however, the moon travels faster when it is closer to the earth, as the earth travels more quickly when it is near the sun. Callippus supported Eudoxus’ theory that the sun and moon’s velocities were constant, but his additional two spheres made solar calculations more accurate, albeit more complex, than under Eudoxus’ model (Samuel 1972: 32).

The Platonic Application

Plato’s astronomy, although less precise than Eudoxus’ and riddled with mythology, was unique because it most boldly asserted and articulated the interrelation between astronomy and time. Plato thought the cosmos not only practical for the measurement of time, but considered them created by god specifically for that purpose. He often used astronomical phenomena, such as solstices and equinoxes, not references to civic calendars, to refer to dates. Moreover, he carefully defined periods of time according to the lunar and solar calendars.

Plato’s astronomy, in short, was somewhat similar to that of Eudoxus and Callippus, in as much that it depicted the various bodies of the universe as layers of a comprehensive whole. Its most fundamental difference from Eudoxus and Callippus’ cosmologies was that the latter treated the layers as spheres, but Plato considered them “whorls,” hollow hemispheres, neatly stacked, one on top of the other.

The moon in Plato’s description of the solar system is rightfully the celestial body closest to the earth. The sun exists in a whorl above the earth and the moon, below another whorl containing the Morning Star and “that which is held sacred to Hermes.” This fourth whorl, claims Plato, rotates at the same speed as the one containing the sun, but in the opposite direction. God placed the remaining planets, according to the Timaeus, in their own orbits. Plato correctly explains that the planets complete their revolutions at different rates, depending on the size of their orbits.

The Timaeus also includes Plato’s conviction that “the sun, the moon, and the five other stars which are called planets were made for defining and preserving the numbers of time.” He defines the units of time beginning with the day and night, which he argues are the product of the earth’s not rotating on its axis. (Dicks 1970: 132-3). “A month,” explains Plato, “has passed when the moon, having completed her own orbit, overtakes the sun.” And a year, “when the sun has completed its own orbit.”

Plato also defines the Perfect Year, a concept which has since been renamed, in his honor, the “Platonic year.” He describes an occurrence of the perfect year as, “when the relative speeds of all the eight revolutions accomplish their course together and reach their starting point.” Since Plato did not have calculations for the velocities of every planet’s orbit, he did not estimate the duration of a Perfect Year, but as one could imagine, such an occurrence would be infrequent. In a Perfect Year, all of the celestial bodies reach their starting point (whatever that is) simultaneously. Since the bodies all move at different speeds, they could all go around their orbits tens of thousands of times before achieving such a level of synchronicity.

Although the Perfect Year is hardly a convenient standard by which to measure time, Plato’s consideration of it is evidence of his commitment to exploring all the connections between the passage of time and astronomy. This commitment manifests itself in Plato’s own usage of astronomical phenomena as a practical mean of denoting time. In The Laws, he calls for officials to assemble at the temple the day before their new term in office, “which comes with the month next after the summer solstice.” In this quotation, he employs both the solar calendar, by referring to the solstice, and the lunar, in his use of months, but makes no reference to any existing civil calendar, or official names for months. Likewise, Plato demands that the whole state must come together annually, “after the summer solstice.” Here Plato defines the year by the sun, conveying his conviction that only solar calendars are accurate.

Dawn of the Sundial

The bulk of this undertaking has focused on the correlation of astronomy and calendars in ancient Greece, but with the exception of the treatment of Anaximander, it has not discussed in any great deal the impact of astronomical progress on the construction of sundials. The chief explanation for the discrepancy in treatments is that there exists much more information on the study of solar years than on the use of the gnomon for measuring the passage of time. Nevertheless, the scientific exploration begun by Thales enabled astronomers to build more effective sundials. It would be a shame not to grant the gnomon at least cursory consideration in a document chronicling Greek conceptions of time. According to Sharon Gibbs of Yale University, author of Greek and Roman Sundials, despite Anaximander’s fabled sixth century construction of a dial in Sparta, “there were few, if any, sundials, marking the seasons and seasonal hours in Greece before the third century BC” (Gibbs 1976: 7-8). Consequently, it is not surprising that there are few literary references to sundials between the ages of Anaximander and Callippus. However, in Aristophanes’ Ecclesiazusae, a character notes that he determines dinner time by the length of a gnomon’s shadow, suggesting that by the fourth century BC, Greeks were already familiar with the device.

Gibbs notes that sundials worked as both crude clocks and calendars. Three day curves on the dial enabled one to trace the gnomon shadow’s path at solstices and equinoxes The dial was also divided by eleven hour lines, the first hour beginning at sunrise; the last one ending at sunset.

As an understanding of the solar orbit facilitates the creation of good calendars, it also enables the better construction of sundials. To the philosophers who mapped the “sun’s” orbit and advanced the use of astronomy to measure time, the third century sundial architects owe a great debt of gratitude.

Within the origins of science lies the fountainhead of time. The presocratics, Eudoxus and Callippus, and most notably Plato, by mapping the solar system and measuring astronomical cycles, set the foundation for the modern understanding of chronology. As seasonal accuracy was indispensable for attaining material prosperity in ancient societies, the ability to measure periods of time has been of increasing importance ever since. Indeed, many scientific advances rest ultimately upon the ancient discovery of such concepts as the oblique zodiac, the spherical earth, or the prediction of solstice.

7. Bibliography

Dicks, D.R., Early Greek Astronomy; Cornell University Press, Ithaca, New York, 1970.

Gibbs, Sharon L., Greek and Roman Sundials; Yale University Press, New Haven, CT, 1976.

Heath, Thomas, Greek Astronomy; Dover Publications, New York, NY, 1991.

Kirk, G.S., Raven, J.E., and Schofield, M., The Presocratic Philosophers; Cambridge University Press, New York, NY, 1983.

Samuel, Alan E., Greek and Roman Chronology; Beck’sche Verlagsbuchhandlung, Munich, Germany, 1972.

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3jpeg-1.gifReprinted from playingwith time.org

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