Ancient Calendars

Celestial bodies — the Sun, Moon, planets, and stars — have provided us a reference for measuring the passage of time throughout our existence. Ancient civilizations relied upon the apparent motion of these bodies through the sky to determine seasons, months, and years.

The earliest Egyptian calendar [Ref.] was based on the moon's cycles, but later the Egyptians realized that the "Dog Star" in Canis Major, which we call Sirius, rose next to the sun every 365 days, about when the annual inundation of the Nile began. Based on this knowledge, they devised a 365 day calendar that seems to have begun around 3100 BCE (Before the Common Era), which thus seems to be one of the earliest years recorded in history.

Before 2000 BCE, the Babylonians (in today's Iraq) used a year of 12 alternating 29 day and 30 day lunar months, giving a 354 day year. In contrast, the Mayans of Central America relied not only on the Sun and Moon, but also the planet Venus, to establish 260 day and 365 day calendars. This culture and its related predecessors spread across Central America between 2600 BCE and 1500 CE, reaching their apex between 250 and 900 CE. They left celestial-cycle records indicating their belief that the creation of the world occurred in 3114 BCE. Their calendars later became portions of the great Aztec calendar stones. Our present civilization has adopted a 365 day solar calendar with a leap year occurring every fourth year (except century years not evenly divisible by 400).

Early Clocks

Water Clocks

These were stone vessels with sloping sides that allowed water to drip at a nearly constant rate from a small hole near the bottom. Other clepsydras were cylindrical or bowl-shaped containers designed to slowly fill with water coming in at a constant rate. Markings on the inside surfaces measured the passage of "hours" as the water level reached them. These clocks were used to determine hours at night, but may have been used in daylight as well. Another version consisted of a metal bowl with a hole in the bottom; when placed in a container of water the bowl would fill and sink in a certain time

More elaborate and impressive mechanized water clocks were developed between 100 BCE and 500 CE by Greek and Roman horologists and astronomers. The added complexity was aimed at making the flow more constant by regulating the pressure, and at providing fancier displays of the passage of time. Some water clocks rang bells and gongs; others opened doors and windows to show little figures of people, or moved pointers, dials, and astrological models of the universe.

Methods of Counting and Their Uses

As mentioned earlier, primitive people had various ways in which they counted objects. In many cases, the tools used to keep track of various objects depended on the availability and ease of use of different materials. For example, some cultures used collections of shells while others used tally sticks. No matter what aid was used for the counting process, the underlying concept was the same. It was all about making a correspondence between the objects of interest and the counting aids. What is interesting about of this type of counting are the different methods used.

Body Counting

A very common form of counting was by using the hand. The hand was an obvious choice for the use of correspondence counting, or reckoning, as it is an instantly accessible device. As noted by Aristotle, the widespread use of counting to ten is not the result of a calculated choice, but rather the anatomical accident that most humans are born with ten fingers and ten toes. So man learned to count using his fingers and perhaps at this stage, without names for the numbers that he was counting. Nevertheless, this was an effective method of counting that is still used all over the world. Even in schools today, young children are taught to count on their fingers.

Finger counting was such an effective method that it was used by some people to count to numbers greater than ten. For example, there exist certain South African people that employ the use of three people to count to numbers larger than one hundred. This is done by the first person, beginning with the little finger on their left hand, counting continuously until ten is reached. Then when the first person reaches ten, the second person raises their left little finger and the first person starts again. Each time ten is reached, the second person raises a finger. Similarly, when one hundred is reached the third person raises their left little finger and the process continues until the desired number is reached. Therefore, by using three people, the first representing units, the second representing tens and the third representing hundreds, these South African people were able to count to numbers above one hundred

The idea of counting on the fingers was extended by

some cultures to reach numbers higher than ten .For

example, a method used in China and India enabled a

person to count to 28 using the finger joints on each

hand. This can be done as illustrated (right).

This idea of using a part of the body to count was taken

to a different level by other cultures. People from places

like Papua New Guinea and the Torres Straits Islands

used their whole body to count. By taking various points

of their body, for example including the eyes, nose, hips,

etc, as well as the fingers, these people were able to count

to numbers as high as 41. The diagram at right

illustrates one particular method of body counting.

Using the body as a counting tool, people were able to communicate information between tribes. For example, a messenger could be sent to another tribe with the message that they wished to trade 20 baskets of food for 15 pearl necklaces, say. This could have been done by simply indicating the point on his body that corresponded to the correct number of objects.

Unfortunately, counting on any part of the body was not permanent and in many cases permanent records needed to be kept. So while body counting was extremely useful, another method would be needed if any type of permanent record were to be kept.

Collection Counting Another type of method of keeping a record of the number of objects is by having a collection of smaller objects that can be used to make a one-to-one correspondence with the objects to be counted. This method was briefly explained earlier with the example of the shepherd, his sheep and a collection of pebbles. Keeping a record of the number of objects to be counted is as simple as placing one of the smaller objects in a pile for each of the objects to be counted. In this way, as explained earlier, there is one smaller object for each of the counted objects. Now if we were to come back and check our counted objects, all that is required is to repeat this method. It can be quickly seen if there are any objects missing, as there would be some of the smaller objects left over. A slight variation on the example of the shepherd is the following. For each animal let out of the enclosure, place one pebble in a collection. Then at the end of the day, remove a pebble for each animal that returns to the enclosure. This way you quickly see if you have lost or gained any animals throughout the day. Many primitive people in varying ways used this method of keeping tally. Some cultures used collections of shells, pearls, pebbles, elephant teeth, sticks, or even coconuts to keep a tally. These were quite useful methods that were employed frequently by early people; however, in some cases it could be quite impractical. If the shepherd had a very large flock of sheep; it would not be very convenient to be carrying around a large, heavy bag of pebbles. So from this we move to another method of keeping a tally of objects.

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