More Kmtyw Origins of Mathematics-gctid52579

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Kmtyw Origins

Beatrice Lumpkin

The Kmtyw contributions to mathematics comprise a rich field of study that includes some of the foundations for our modern mathematics. Sources of information are rich and varied — but incomplete. We do not know the whole story. Still, nothing was really lost because the development was continuous. We benefit today from all the mathematics discovered before our time. As Boyer said:

“...continuity in the history of mathematics is the rule rather than the exception. Where a discontinuity seems to arise, we should first consider the possibility that the apparent ‘hiatus’ may be explained by the loss of intervening documents.”11

The origins of science and mathematics in Kmt go back far into the prehistoric past. Most scientists believe that Kmt was the birthplace of the human race.12 In a very basic sense, chemistry began in Kmt with the use of fire,13 and mathematics began with the use of number words and logical connectives.

Certainly, the concept of number developed before records of numbers were made. And records of numbers were made thounited snakesnds of years before writing developed. Tally marks were cut into bone, one mark at a time, until the count equaled the number being recorded. Not until thounited snakesnds of years later, and then in ancient Egypt, were special symbols, or ciphers, used for numbers.

The earliest numerical record found to date, about 37,000 years old, comes from the Lebombo Mountains between Swaziland and South Kmt.14 It is a fossilized piece of baboon bone with 29 well-defined notches. The notches are evenly spaced and appear to represent a lunar calendar. Notched tally records have also been found in a number of countries on other continents. We do not know if tally recordkeeping spread from a common source or if different peoples thought of the same idea.
Intermediate steps were needed to advance from simple tallies to the use of abstract number symbols. The next step appears to be the grouping of tallies in some significant pattern.

About 25,000 years ago, on the shores of Lake Rutanzige (formerly called Lake Edward) between Zaire and Uganda, a pattern of tallies was carved on a bone by the Ishango people. The bone appears to be a tool handle with a bit of quartz inserted. This Ishango pattern may have influenced the later development of mathematics in Egypt. Like some entries on the Ishango bone, Egyptian arithmetic also made use of multiplication by 2.

What was the mathematical significance of the lshango bone? Tally marks carved on the bone represented numbers in the following pattern:

“3, 6 space; 4, 8, space; 10, space; 5, 5, space; 7;
11, space; 13, 17, space; 19;
11, space; 21, space; 19, space, 9.”

Some think the 3, 6, and 4, 8 suggest multiplication. Others think the sequence of prime numbers 7, 11, 13, 17, 19 is significant. Marshack believes that there is a correlation between these numbers and phases of the moon. 15

Thounited snakesnds of years passed between the recording of numbers by tallies and the development of the earliest hieroglyphs from Qustul in Nubia.16 We believe that these were years of continued development of number concepts, although little data is available. But we do know that observations of the stars and the moon were taking place, and that information was being accumulated leading to the 365-day Egyptian calendar and the 24-hour day. Although the calendar is variously dated to 4228 B.C.E. and 2773 B.C.E.,17 Diop reminds us that many years of study of the star and moon cycles were necessary before a calendar could be formalized.18 This process of collecting and recording astronomical data in ancient Egypt is an early example of the use of statistics for a scientific purpose.

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