To Explain the World: The Discovery of Modern Science (10 page)

Astronomy began to be a precise science with the introduction of a device known as a gnomon, which allowed accurate measurements of the Sun’s apparent motions. The gnomon, credited by the fourth-century bishop Eusebius of Caesarea to Anaximander but by Herodotus to the Babylonians, is simply a vertical pole, placed in a level patch of ground open to the Sun’s rays. With the gnomon, one can accurately tell when it is noon; it is the moment in the day when Sun is highest, so that the shadow of the gnomon is shortest. At noon anywhere north of the tropics the Sun is due south, and the shadow of the gnomon therefore points due north, so one can permanently mark out on the ground the points of the compass. The gnomon also provides a calendar. During the spring and summer the Sun rises somewhat north of east, whereas during the autumn and winter it comes up south of east. When the shadow of the gnomon at dawn points due west, the Sun is rising due east, and the date must be either the vernal equinox, when winter gives way to spring; or the autumnal equinox, when summer ends and autumn begins. The summer and winter solstices are the days in the year when the shadow of the gnomon at noon is respectively shortest or longest. (A sundial is different from a gnomon; its pole is parallel to the Earth’s axis rather than to the vertical direction, so that its shadow at a given hour is in the same direction every day. This makes a sundial more useful as a clock, but useless as a calendar.)

The gnomon provides a nice example of an important link between science and technology: an item of technology invented for practical purposes can open the way to scientific discoveries. With the gnomon, it was possible to make a precise count of the days in each season, such as the period from one equinox to the next solstice, or from then to the following equinox. In this way,
Euctemon, an Athenian contemporary of Socrates, discovered that the lengths of the seasons are not precisely equal. This was not what one would expect if the Sun goes around the Earth (or the Earth around the Sun) in a circle at constant speed, with the Earth (or the Sun) at the center, in which case the seasons would be of equal length. Astronomers tried for centuries to understand the inequality of the seasons, but the correct explanation of this and other anomalies was not found until the seventeenth century, when Johannes Kepler realized that the Earth moves around the Sun on an orbit that is elliptical rather than circular, with the Sun not at the center of the orbit but off to one side at a point called a focus, and moves at a speed that increases and decreases as the Earth approaches closer to and recedes farther from the Sun.

The Moon also seems to revolve like the stars each night from east to west around the north celestial pole; and over longer times it moves, like the Sun, through the zodiac from west to east, but taking a little more than 27 days instead of a year to make a full circle against the background of stars. Because the Sun appears to move through the zodiac in the same direction, though more slowly, the Moon takes about 29½ days to return to the same position relative to the Sun. (Actually 29 days, 12 hours, 44 minutes, and 3 seconds.) Since the phases of the Moon depend on the relative position of it and the Sun, this interval of about 29½ days is the lunar month,
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the time from one new moon to the next. It was noticed early that eclipses of the Moon occur at full moon about every 18 years, when the Moon’s path against the background of stars crosses that of the Sun.
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In some respects the Moon provides a more convenient
calendar than the Sun. Observing the phase of the Moon on any given night, one can easily tell approximately how many days have passed since the last new moon—much more easily than one can judge the time of year just by looking at the Sun. So lunar calendars were common in the ancient world, and still survive, for example for religious purposes in Islam. But of course, for purposes of agriculture or sailing or war, one needs to anticipate the changes of seasons, and these are governed by the Sun. Unfortunately, there is not a whole number of lunar months in the year—the year is approximately 11 days longer than 12 lunar months—so the date of any solstice or equinox would not remain fixed in a calendar based on the phases of the Moon.

Another familiar complication is that the year itself is not a whole number of days. This led to the introduction, in the time of Julius Caesar, of a leap year every fourth year. But this created further problems, because the year is not precisely 365¼ days, but 11 minutes longer.

Countless efforts, far too many to go into here, have been made throughout history to construct calendars that take account of these complications. A fundamental contribution was made around 432 BC by Meton of Athens, possibly a partner of Euctemon. Perhaps by the use of Babylonian records, Meton noticed that 19 years is almost precisely 235 lunar months. They differ by only 2 hours. So one can make a calendar covering 19 years rather than one year, in which both the time of year and the phase of the Moon are correctly identified for each day. The calendar then repeats itself for every successive 19-year period. But though 19 years is nearly exactly 235 lunar months, it is about a third of a day less than 6,940 days, so Meton had to prescribe that after every few 19-year cycles a day would be dropped from the calendar.

The effort of astronomers to reconcile calendars based on the Sun and Moon is illustrated by the definition of Easter. The Council of Nicaea in AD 325 decreed that Easter should be celebrated on the first Sunday following the first full moon following the vernal equinox. In the reign of Theodosius I it was declared
a capital crime to celebrate Easter on the wrong day. Unfortunately the precise date when the vernal equinox is actually observed varies from place to place on the surface of the Earth.
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To avoid the horror of Easter being celebrated on different days in different places, it was necessary to prescribe a definite date for the vernal equinox, and also for the first full moon following it. The Roman church in late antiquity adopted the Metonic cycle for this purpose, but the monastic communities of Ireland adopted an older Jewish 84-year cycle. The struggle in the seventh century between Roman missionaries and Irish monks for control over the English church was largely a conflict over the date of Easter.

Until modern times the construction of calendars has been a major occupation of astronomers, leading up to the adoption of our modern calendar in 1582 under the auspices of Pope Gregory XIII. For purposes of calculating the date of Easter, the date of the vernal equinox is now fixed to be March 21, but it is March 21 as given by the Gregorian calendar in the West and by the Julian calendar in the Orthodox churches of the East. So Easter is still celebrated on different days in different parts of the world.

Though scientific astronomy found useful applications in the Hellenic era, this did not impress Plato. There is a revealing exchange in the
Republic
between Socrates and his foil Glaucon.
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Socrates suggests that astronomy should be included in the education of philosopher kings, and Glaucon readily agrees: “I mean, it’s not only farmers and sailors who need to be sensitive to the seasons, months, and phases of the year; it’s just as important for military purposes as well.” Socrates calls this naive. For
him, the point of astronomy is that “studying this kind of subject cleans and re-ignites a particular mental organ . . . and this organ is a thousand times more worth preserving than any eye, since it is the only organ which can see truth.” This intellectual snobbery was less common in Alexandria than in Athens, but it appears for instance in the first century AD, in the writing of the philosopher Philo of Alexandria, who remarks that “that which is appreciable by the intellect is at all times superior to that which is visible to the outward senses.”
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Fortunately, perhaps under the pressure of practical needs, astronomers learned not to rely on intellect alone.

7

Measuring the Sun, Moon, and Earth

One of the most remarkable achievements of Greek astronomy was the measurement of the sizes of the Earth, Sun, and Moon, and the distances of the Sun and Moon from the Earth. It is not that the results obtained were numerically accurate. The observations on which these calculations were based were too crude to yield accurate sizes and distances. But for the first time mathematics was being correctly used to draw quantitative conclusions about the nature of the world.

In this work, it was essential first to understand the nature of eclipses of the Sun and Moon, and to discover that the Earth is a sphere. Both the Christian martyr Hippolytus and Aëtius, a much-quoted philosopher of uncertain date, credit the earliest understanding of eclipses to Anaxagoras, an Ionian Greek born around 500 BC at Clazomenae (near Smyrna), who taught in Athens.
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Perhaps relying on the observation of Parmenides that the bright side of the Moon always faces the Sun, Anaxagoras concluded, “It is the Sun that endows the Moon with its brilliance.”
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From this, it was natural to infer that eclipses of the Moon occur when the Moon passes through the Earth’s shadow. He is also supposed to have understood that eclipses of the Sun occur when the Moon’s shadow falls on the Earth.

On the shape of the Earth, the combination of reason and observation served Aristotle very well. Diogenes Laertius and
the Greek geographer Strabo credit Parmenides with knowing, long before Aristotle, that the Earth is a sphere, but we have no idea how (if at all) Parmenides reached this conclusion. In
On the Heavens
Aristotle gave both theoretical and empirical arguments for the spherical shape of the Earth. As we saw in
Chapter 3
, according to Aristotle’s a priori theory of matter the heavy elements earth and (less so) water seek to approach the center of the cosmos, while air and (more so) fire tend to recede from it. The Earth is a sphere, whose center coincides with the center of the cosmos, because this allows the greatest amount of the element earth to approach this center. Aristotle did not rest on this theoretical argument, but added empirical evidence for the spherical shape of the Earth. The Earth’s shadow on the Moon during a lunar eclipse is curved,
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and the position of stars in the sky seems to change as we travel north or south:

In eclipses the outline is always curved, and, since it is the interposition of the Earth that makes the eclipse, the form of the line will be caused by the form of the Earth’s surface, which is therefore spherical. Again, our observation of the stars make[s] it evident, not only that the Earth is circular, but also that it is a circle of no great size. For quite a small change of position on our part to south or north causes a manifest alteration of the horizon. There is much change, I mean, in the stars which are overhead, and the stars seen are different, as one moves northward or southward. Indeed there are some stars seen in Egypt and in the neighborhood of Cyprus that are not seen in the northerly regions; and stars, which in the north are never beyond the range of observation, in those regions rise and set.
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It is characteristic of Aristotle’s attitude toward mathematics that he made no attempt to use these observations of stars to give a quantitative estimate of the size of the Earth. Apart from this, I find it puzzling that Aristotle did not also cite a phenomenon that must have been familiar to every sailor. When a ship at sea is first seen on a clear day at a great distance it is “hull down on the horizon”—the curve of the Earth hides all but the tops of its masts—but then, as it approaches, the rest of the ship becomes visible.
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Aristotle’s understanding of the spherical shape of the Earth was no small achievement. Anaximander had thought that the Earth is a cylinder, on whose flat face we live. According to Anaximenes, the Earth is flat, while the Sun, Moon, and stars float on the air, being hidden from us when they go behind high parts of the Earth. Xenophanes had written, “This is the upper limit of the Earth that we see at our feet; but the part beneath goes down to infinity.”
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Later, both Democritus and Anaxagoras had thought like Anaximenes that the Earth is flat.

I suspect that the persistent belief in the flatness of the Earth may have been due to an obvious problem with a spherical Earth: if the Earth is a sphere, then why do travelers not fall off? This was nicely answered by Aristotle’s theory of matter. Aristotle understood that there is no universal direction “down,” along which objects placed anywhere tend to fall. Rather, everywhere on Earth things made of the heavy elements earth and water tend to fall toward the center of the world, in agreement with observation.

In this respect, Aristotle’s theory that the natural place of the heavier elements is in the center of the cosmos worked much like the modern theory of gravitation, with the important difference that for Aristotle there was just one center of the cosmos, while today we understand that any large mass will tend to contract to a sphere under the influence of its own gravitation, and then will attract other bodies toward its own center. Aristotle’s theory did not explain why any body other than the Earth should be a sphere, and yet he knew that at least the Moon is a sphere, reasoning from the gradual change of its phases, from full to new and back again.
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After Aristotle, the overwhelming consensus among astronomers and philosophers (aside from a few like Lactantius) was that the Earth is a sphere. With the mind’s eye, Archimedes even saw the spherical shape of the Earth in a glass of water; in Proposition 2 of
On Floating Bodies
, he demonstrates, “The surface of any fluid at rest is the surface of a sphere whose center is the Earth.”
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(This would be true only in the absence of surface tension, which Archimedes neglected.)