A
Brief History of Time
(with
apologies to Stephen Hawkings)
From
Thales to Callippus
by:
C.
W.
April 9, 1995
Presented by
Gr.
C.,
email
at
the
Perseus project
Abstract:
A brief
overview of the history of our western time
management. From the perspective of the ancient
greek philosophers are so issues discussed in
the development of our modern time-awareness.
With the old philosophers setting the foundation
for the modern understanding of chronology is
explained that much depended on a calendar
correct for agricultural purposes.
Table
of Contents
Introduction
Initial
Evidence of Time
The
Presocratics
Changing
Attitudes Towards Time
The
Platonic
Application
The
Dawn of the Sundial
Bibliography
Look
at the comments on this paper.
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 his 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 [that
is: the first greek philosopher Greek,
edit.]
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 [to
the
sun- edit.]
. (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.
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.
Comments
on A Brief History of Time.
Kathleen
Norton
says it is excellent :
I think that
this is a well-flowing, comprehensive paper. I
liked that in your introduction you stressed the
importance for the understanding of time. From
then on, I think you made nice transitions into
the different developments of and theories on
the understanding of time. You incorporated
helpful links, including both text and diagrams,
with your own background information when
necessary. Great work!
Tim
Reluga
says it is good :
Nice title our
should be or at the beginning of the second
paragraph Good quote from the timeaus, but a
little streched in wording of paragraph. Nice
diagram of the lunar cycle. Possibly make a link
to the biobliography for the reference at the
bottom, though. Second diagram of connected with
days is confusing because it doesn't illustrate
anything about them, and also implies that the
moon does not orbit in the same plane as the
earth orbits the sun. Associated text is good,
though. Nice definition of intercalation, keeps
the flow going. What is the eclipse diagram
supposed to show? Reference to later part of the
work used very nicely so as not to confuse the
reader. Great! Paper seems to wonder from "time"
theme some and go to pure astronomy. Nice fact
that the egyptians had a 365 day year.
References used very nicely, written very well.
R.
O. says it
is good:
First of all,
I think you've done an excellent job of using
primary sources, which back you up and don't
merely repeat what you've said. The diagrams
could use some explanation at the bottom or in
the text; the "day" diagram was opaque to me. I
think you've fallen into the trap at the
beginning of proving that the subject you're
talking about is important by belittling
something else--in this case telling the seasons
by the weather. Hesiod does NOT recommend
planting by the solstices. He measures time by
the solstices and then waits for the rain or a
sparrow to tell him the proper time to plow and
plant. To me, climate IS season, or rather
weather is season, no matter what the moon says.
If it's cold on St. Patrick's Day (the
traditional day to plant peas), you have to
wait, period. Small things: Suda is not a
person. "Belies" (under Homer) should be
"betrays" or, better, "demonstrates".
Michael
Tirabassi
says it is good :
This project
was well written and presented. The visual aids
were used well, and were somewhat helpful to the
reader. The topic was clearly well researched
and presented in a through manner. good job...
Kristen
says it is good :
There are one
or two typos, but overall this is a very
well-written, comprehensive paper. I like the
reference to New England--it puts things in
perpective. Great links and references, they are
very clear and well-related. You could link to
Kathleen's paper in Thales, or to an account of
the eclipse seen by Nicias. Your diagrams are
great--I think a few more visual aids like this
would be helpful-- maybe picture interpretations
of things you quote in texts. (For example, the
whorl discussion.) Great job.
This
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