Romans lost interest and ability to do technical stuff towards
end of empire (5th cent?)
How dark were the Dark Ages? When I was young I thought the
entire period of the Middle ages was pretty dismal, especially
for the life of the mind. Now the High Middle ages are thought
quite respectable, in the opinions of many producing, as examples,
some of the greatest architecture (Gothic Cathedrals) and one
of the greatest technical inventions (the clock). The High Middle
Ages was both a period of renewal and of creativity. It was a
renaissance before the more famous Renaissance.
Two of the preeminent symbols of the Medieval period, the
tower clock and the European Astrolabe indicate the importance
of time to the Medieval mind. These are both products of the
High Middle Ages. What are their precursors? Did they arise out
of a vacuum? In today's view most of the products of the High
Middle Ages and of the Renaissance were built on a background
of centuries of prior work - they achieved much because the stood
on the shoulders of giants. In this workshop we want to explore
this background and discover just how broad these shoulders were.
Consider how a thirteenth-century scientist/scholar might
view his position. Very loosely, I will take that perspective
for our discussion:
Here in the thirteenth century of our Lord Jesus' reign we
have made much progress in understanding God's work. I would
dare to say, after centuries of ignorance brought on by pagan
invaders and their unenlightened understanding, we now possess
greater knowledge of the world than any in the past. We have
not only regained the knowledge of the Greeks, including that
of the Master (Aristotle), we now are adding to that knowledge
and going beyond it. Today I wish to demonstrate this premise
to you with a review of our knowledge of the calender, time,
and astronomy.
All calenders and time are based on the movement of the Heavens.
In particular the movements of three 'bodies' have been used
to determine time and season: the Sun, the Moon, and the Firmament,
that is the sphere of the fixed stars, itself. Four different
astronomies have been important to determine time and date: the
division of the year by observing the position of the Sun, the
computation of the date of the Easter Full Moon, the determination
of time for prayer by observation of the stars, and the geometrical
astronomy of the ancients, particularly Ptolemy.
To understand these astronomies we will look at the sphere
of the fixed stars, and then at a model of the Earth-centered
Universe known as an armillary sphere.
The sphere of the fixed stars can be represented on a celestial
globe. Here we see a map of the sky with the major visible
stars fixed on a spherical surface. With this model we are viewing
the sphere from the outside - taking a "God's-eye-view,"
if you will. The celestial globe is held in a ring, representing
the meridian. The meridian is a circle passing through
the north and south poles of the sky. It is also the highest
apparent point reached by a celestial body during its orbit.
Because the celestial sphere rotates as a rigid shell, some stars
will reach higher points in the sky, but in each case the peak
will be on the meridian.
The apparent rotation of the sky is also dependent on our
relative position on the Earth, that is our latitude. The latitude
will determine the horizon we see. In our model the meridian
ring fits into a horizon ring (in the case of the model use,
the horizon was formed by the hole in the box in which the celestial
sphere and meridian reside). We can now adjust the celestial
sphere to correspond to our latitude by rotating the meridian
ring within the horizon ring or plate. To adjust the celestial
sphere we take our latitude (the angle of our location above
the equator which is at 0°, while the north pole is at 90°),
and subtract it from 90°. The meridian ring is then turned
until the difference is aligned with the horizon. For example,
for the workshop we can assume a latitude of approximately 40°.
Thus the 60° mark on the meridian ring is set to the horizon.
The planets, which in ancient times included the Sun and
Moon, move in the sky as opposed to the fixed stars (planet is
derived from the Greek meaning wanderer). This does not imply
that they wander all over the sky - all of the planets as well
as the Sun and Moon have paths within the band of the ecliptic.
We can use the armillary
sphere to demonstrate the remaining aspects of the Earth
centered Universe.
The main
sphere in the armillary is defined by three perpendicularly
arranged rings. (Note that these rings are set in the sphere
of the fixed stars, so the armillary and celestial spheres are
readily related to one another.) In the discussion below the
numbers correespond to the numbers on the linked image:
The solsticial colure (2): this ring passes through
the north and south poles as well as the summer and winter solstices
(the points of highest and lowest meridional positions of the
Sun during the year).
The equinoctial colure (1): this ring passes through
the north and south poles as well as the the spring and autumnal
equinoxes (the points of the Sun's passage when the length
of day and night are equal - equal night).
The equator (3): the ring which divides the sphere
into equal northern and southern hemispheres.
A fourth ring, the ecliptic band (4) is set at an
angle of 23.5° to the equator on an axis through the two
equinoxes. The ecliptic defines the annual path of the Sun through
the year. It is marked with the signs of the Zodiac graduated
in degrees so one may find the position of the Sun in the constellations
of the fixed stars on any particular day. As mentioned above
the paths of the Moon and planets also fall within the area defined
by the ecliptic.
Four additional rings, parallel to but above or below the
equator, complete the sphere. Beginning nearest the north pole
we see:
The Arctic circle (5): this defines the latitude above which
the Sun no longer rises and sets on a daily basis.
The tropic of Cancer (6): this circle defines the northernmost
latitude reached by the Sun in its annual cycle, it is the northern
turning point of the Sun's annual journey (thus tropic meaning
turning).
The tropic of Capricorn (7): this circle defines the southernmost
latitude reached by the Sun in its annual cycle, it is the southern
turning point of the Sun's annual journey.
The Antarctic circle (8): this defines the latitude below
which the Sun no longer rises and sets on a daily basis.
An axis (9) passes though the sphere via the poles. A ball
centered on this axis represents the Earth. Small armillary spheres
with the axis terminating in a handle below the south pole demonstrating
the basic arrangement of the Earth-centered Universe, were frequently
used in lectures, and are often represented in art works.
The armillary sphere, like the celestial sphere may also
be held in a meridian ring (10) by the shaft of the axis above.
The sphere is then generally set in a stand with a horizon
ring so it can be set to the local latitude as described
above for the celestial sphere. The horizon ring is commonly
marked with the four compass points, a degree scale, a calender
scale, and a zodiac scale. The calendar and zodiac scales enable
the user to correlate the day of the year with the Sun's position
on the sky. (Note that the sky and the calendar drift relative
to one-another on an approximately 23,000 year cycle - thus a
conversion table is needed for the years of the instrument's
intended use. Gradually the scales will drift out of sync and
new conversion tables will be required. The basic armillary sphere
however will be accurate for many millions of years.)
We can now set our armillary sphere to the local latitude
as was done with the celestial sphere above, and follow the path
of the Sun for any given day of the year. We may determine times
of sunrise and sunset, meridian height of the Sun, etc. With
this model of the Universe in hand, we can continue our discussion
of the calendar and time.
The use of the Sun to monitor the seasons is both fundamental
and ancient. The seasons after all determine times of planting,
harvest etc. Of course pagans monitored the Sun's position from
time immemorial, celebrating solstices and equinoxes, planting
and harvesting festivals, etc. As the Church established its
position during the early Middle ages, it took over these celebrations
with Saint's Days to help the people overcome their pagan past.
Another mode of astronomy practiced in the Medieval period
is the use of the stars to tell time.* This was long a tradition
in Monasteries for determining the time for prayers. Of course
one can only use stars to tell time at night. Telling time by
the stars requires only the determination of a particular stars
altitude, and knowing what its altitude should be at different
hours. The pre-eminent instrument for telling time by the stars
was the planispheric
astrolabe.** (CR pp 66-9)
Let's now look at the lunar astronomy used to compute Easter.
First, to bring perspective, Easter is the most important Holy
day of the Christian calendar. It is the date for "reestablishing
the time of Creation, the time of salvation in which humankind
is renewed, to be once again at that time, in illo tempore.
(SM, p 80, top) Remember that Jesus arose on the sunday following
the Paschal meal. But the time of the Paschal meal is determined
using the Hebrew lunar calendar. Christians wanted to express
Easter in terms of the civil, not the Hebrew calendar.
In order to accomplish this we need to consider the determination
of the dates of the spring equinox and the full Moon. (For a
modern version of these calculations see CR pp 26-7.) This may
seem simple. However, there are 365 1/4 days in one Julian year,
while there are 12 lunar months of 29 1/2 days, giving a lunar
year of 354 days. So our first task is to determine how frequently
these two cycles will come into agreement. A little calculation
will show that the full moon will fall on the same date approximately
every 19 years (see Table 2, SM, p 83). *** Unfortunately we're
not finished, Easter must also fall on a sunday, so we have another
cycle to bring day of the week and day of the month into agreement,
which occurs every 28 years. Combining these two cycles give
a fully recurring system with a period of 532 years. Now the
computus, or computation of the date of Easter using these cycles
is fairly simple, requiring only arithmetic, but a table encompassing
532 years is a bit much. It is not only a lot to compute, it
is a lot to copy! So, many early tables only covered a sequence
of 5 x 19 years = 95 years (other cycles were also used***).
The 95 year cycle almost gives an Easter cycle. Now you
might say, wait a minute, its not that difficult to note when
the full moon is, and figure out when Easter will be on the Sunday
following. But keep in mind how important this Holy day is, and
then recall that one also needed to know when to begin the Lenten
Fast (40 days before Easter) as well as Ash Wednesday which is
also linked. In fact, to get out the word etc. the date of Easter
had to be known almost by Christmas! Finally, it was also felt
important that all of Christendom should celebrate Easter on
the same date! Thus the long time-line tables, and passionate
theological disputes. (SM p84)
* The stars may also be used to monitor the seasons. One
can look for the appearance and disappearance of stars near the
southern horizon. This is really an indirect measure of solar
altitude. That is the stars positions are fixed, but you can't
see them in the daylight, so as the Sun goes down earlier in
the winter, additional stars become visible. Noting the heliacal
rising and setting of these southern stars can therefore provide
another measure of time of year. This can be an important consideration
in areas where clouds and overcast obscure viewing and one must
use every available signal to accurately determine the solstices
and equinoxes.
** This was made slightly more complex in Medieval times
because of the use of unequal hours in time keeping, while
the fixed stars keep equal time. Prior to the invention of the
mechanical clock most cultures used systems of unequal hours,
where the day is broken up into the same number of divisions
summer or winter. Thus at European latitudes summer hours are
about 1 1/4 hr long and winter hours would be about 3/4 hr long.
Only at the equinoxes are unequal hours of the same length as
equal hours. (CR pp 22-3)
***A very thorough discussion of the Lunar computus and the
various cycles and bringing them into congruence is given in
chapter 5 of McClusky (SM).
References: Much of this workshop is derived
from McClusky. If you want to further pursue the concepts of
astronomy and the calendar in the Middle Ages read McClusky.
The astronomy books by Lippincott and by Ronan are written for
beginners, but have much to offer even those familiar with observing
the night sky. Both use historical examples, are profusely illustrated,
and demonstrate historical instruments and modes of observing.
Ronan is particularly interesting for the many home-made instruments
he describes.
KL = Lippincott, Kristen. Eyewitness Science Astronomy.
DK Publishing, New York (1994);
SM = McClusky, Stephen C. Astronomies and Cultures in
Early Medieval Europe. Cambridge University Press, Cambridge
(1998).
CR = Ronan, Colin A. The Practical Astronomer. Macmillan
publishing Co. Inc., New York (1981).
Medieval Science & Scientific
Instruments