(An Unconventional Guide to Computers) Copyright Information
The Ancient Egyptians |
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| Number systems with bases other than ten have sprouted up throughout history. For example, the ancient Egyptians spent a lot of time experimenting with duo- decimal (base-12) systems, because they counted finger- joints instead of fingers. | Each of our fingers has three joints (at least they do in my branch of the family), so if you use your thumb to point to the joints of the other fingers on the same hand, you can count one-two-three on the first finger, four-five-six on the next, and so on up to twelve on your little finger. | |
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| If a similar technique is used with both hands, you can represent values from one through twenty-four. This explains why the ancient Egyptians divided their days into twenty-four periods, which is, in turn, why we have twenty-four hours in a day. Strangely enough, an Egyptian hour was only approximately equal to one of our hours. This was because the Egyptians liked things to be nice and tidy, so they decided to have twelve hours of daylight and twelve hours of nighttime. Unfortunately, as the amount of daylight varies throughout the year, they were obliged to adjust the lengths of their hours according to the seasons! | ||
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| One of the methods that the Egyptians used to measure time was the water clock, or Clepsydra, which consisted of a container of water with a small hole in the bottom through which the water escaped. Units of time were marked on the side of the container, and the length of the units corresponding to day and night could be adjusted by varying the distance between the markings or by modifying the shape of the container; for example, by having the top wider than the bottom (see also The first self-striking water clock). (The term "Clepsydra" is derived from the Greek klepto, meaning "thief", and hydro, meaning "water". Thus, Clepsydra literally means "water thief".) | In addition to their base-twelve system, the Egyptians also
experimented with a sort-of-base-ten system. In this system the numbers 1 through 9 were
drawn using the appropriate number of vertical lines; 10 was represented by a circle; 100
was a coiled rope; 1,000 a lotus blossom; 10,000 a pointing finger; 100,000 a tadpole; and
1,000,000 a picture of a man with his arms spread wide in amazement. So to represent a number like 2,327,685, they would have been obliged to use pictures of two amazed men, three tadpoles, two pointing fingers, seven lotus blossoms, six coiled ropes, eight circles, and five vertical lines. It only requires a few attempts to divide tadpoles and lotus blossoms by pointing fingers and coiled ropes to appreciate why this scheme didn't exactly take the world by storm. |
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| Actually, it's easy for us to rest on our laurels and smugly criticize ideas of the past with the benefit of hindsight (the one exact science), but the Egyptians were certainly not alone. As an example we might consider Roman numerals, in which I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000, and so forth. Now try to multiply CCLXV by XXXVIII as quickly as you can. In fact Roman numerals were used extensively in England until the middle of the 17th century, and are still used to some extent to this day; for example, the copyright notice on films and television programs often indicates the year in Roman numerals! | ||
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| These notes are abstracted from the book Bebop BYTES Back (An Unconventional Guide to Computers) Copyright Information |
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