122 5. COUNTING20, and there is a cowrie-shell figure standing for zero. The second vigesimal digit
in a Maya number should normally represent units of 20 · 20 = 400. However, in the
Haab calendar, discussed below, it represents 360. The reason probably comes from
the objects being counted, namely days. Even today a "business year" is 360 days
(twelve 30-day months), and this cycle was also important to the Maya. Beyond
this point the unit for each place value is 20 times the value of its predecessor.4. What was counted?
People have counted an endless list of things since time immemorial. But if we were
to name three items whose count was of most importance, these would be days,
years, and new moons. One of the earliest uses of both arithmetic and geometry
was in the construction of reliable calendars. Calendars have a practical economic
value in organizing the activities of nomadic and agricultural peoples; this value
is in addition to the social value associated with the scheduling of religious rites.
For these reasons, calendars have been regarded as both sacred lore and applied
science. At the base of any calendar must lie many years of record keeping, simply
counting the days between full moons and solstices. Only after a sufficient data
base has been collected can the computations needed to chart the days, weeks,
months, and years be carried out. We know that such observations have been made
for a long time, since the prominent lines of sight at many megalithic structures
such as Stonehenge mark the summer and winter solstices. It does not require very
acute observation to notice that the sun rises and sets at points farther and farther
north for about 182 or 183 days, then begins to move south for the next 182 or 183
days. Once that observation was made, setting up posts to keep track of the exact
location of sunrise and sunset would not have taken very long. This progression
of the sun could also be correlated with the star patterns (constellations) that rise
at sunset, marking the cycle we call a tropical or sidereal year. These two years
actually differ by about 20 minutes, but obviously it would require a long time for
that discrepancy to be noticed.4.1. Calendars. The first broad division in calendars is between what we may
call (for purposes of the present discussion only) linear and cyclic calendars. In a
linear calendar the basic unit is the day, and days are simply numbered (positively
or negatively) from some arbitrary day to which the number zero or 1 is assigned.
Such calendars are highly artificial and used mostly for scientific purposes. For
civil use, calendars attempt to repeat cycles after a month or a year or both. In
traditional calendars, years were counted within the reign of a particular ruler and
began with 1 as each new ruler came to power, but in the Gregorian calendar the
year number does not cycle. Days and months, however, do cycle; they have their
names and numbers repeated at fixed intervals. Cyclic calendars may be classified
as solar, lunar, and lunisolar.
Ancient Egypt. The Egyptians observed the world about them with considerable
accuracy, as the precise north-south orientation of some of the pyramids shows.
Anyone who observes the sky for any extended period of time cannot help noticing
the bright blue-green star Sirius, which is overhead at midnight during winter in
the northern hemisphere. According to Montet (1974), it was recorded on the
outside wall of the Temple of Ramesses III at Medinet Habu that the first day
of the Egyptian year was to be the day on which Sirius and the Sun rose at the
same time. To the Egyptians Sirius was the goddess Sopdit, and they had a special