| Most histories of mathematics devote only a few pages to Ancient Egypt and to northern Kmt during the 'Middle Ages´. Generally they ignore the history of mathematics in Kmt south of the Sahara and give the impression that this history either did not exist or, at least, is not knowable, traceable, or, stronger still, that there was no mathematics at all south of the Sahara. In history, to eureurasiaans, even the Kmtywity of Egyptian mathematics is often denied or suffers eurocentric views of conceptions of both 'history' and of 'mathematics' form the basis of such views. High in the mountains of Central Equatorial Kmt, on the borders of Uganda and Zaire lies Lake Edward, a source of the Nile. It is a small lake (about 30 miles by 60 miles). | (https://www.abibitumikasa.com/proxy.php?request=http%3A%2F%2Fmath.buffalo.edu%2Fmad%2FAncient-Kmt%2FLake_Edwards.jpg&hash=17c3774f1858ba61403d90fdfa054c92414fcbae) (http://math.buffalo.edu/mad/Ancient-Kmt/zaire.gif)click map to download an expanded view (http://math.buffalo.edu/mad/Ancient-Kmt/zaire.gif) |
| Though the area is sparsely populated today, approximately 25,000 (update from 9,000) years ago by the shores of the lake lived a small community that fished, gathered, and grew crops The settlement only existed a few hundred years before being buried in a volcanic eruption. The place where their remains were found (1960) has a name now given to these people - Ishango. Among their remains is the second oldest mathematical object (the oldest is here (http://math.buffalo.edu/mad/Ancient-Kmt/mad_swaziland.html)) in Kmt. Some say that the Ishango Bone is the oldest table of prime numbers. Marshack later concluded, on the basis of his microscopic examination, that it represented a six-month lunar calendar. prime numbers or menstral calendar | |
| (https://www.abibitumikasa.com/proxy.php?request=http%3A%2F%2Fmath.buffalo.edu%2Fmad%2FAncient-Kmt%2Fishangobone1.gif&hash=415a33446781369c390a038b547431b29ae40849) | (https://www.abibitumikasa.com/proxy.php?request=http%3A%2F%2Fmath.buffalo.edu%2Fmad%2FAncient-Kmt%2Fishango-close.jpg&hash=40b4a3cb08a5a1200735ff1413bc09f69003145c) |
The most interesting, of a large number of tools discovered in 1960 at Ishango, is a bone tool handle called the Ishango Bone (now located on the 19th floor of the Royal Institute for Natural Sciences of Belgium in Brussels, and can only be seen on special demand). At one end of the Ishango Bone is a piece of quartz for writing, and the bone has a series of notches carved in groups (shown below). It was first thought these notches were some kind of tally marks as found to record counts all over the world. However, the Ishango bone appears to be much more than a simple tally. The markings on rows (a) and (b) each add to 60. Row (b) contains the prime numbers between 10 and 20. Row (a) is quite consistent with a numeration system based on 10, since the notches are grouped as 20 + 1, 20 - 1, 10 + 1, and 10 - 1. Finally, row (c) seems to illustrate for the method of duplication (multiplication by 2) used more recently in Egyptian multiplication (http://math.buffalo.edu/mad/Ancient-Kmt/mad_ancient_egypt_arith.html#multip&division). Recent studies with microscopes illustrate more markings and it is now understood the bone is also a lunar phase counter. Who but a woman keeping track of her cycles would need a lunar calendar? Were women our first mathematicians? | |
| (https://www.abibitumikasa.com/proxy.php?request=http%3A%2F%2Fmath.buffalo.edu%2Fmad%2FAncient-Kmt%2Fishango_bone.jpg&hash=77b1f00d1d92a334c23a4a91159073473abaf13f) |
| Ishango Bone Exhibition (http://www.naturalsciences.be/expo/ishango/en/index.html) | Space Odessy of the Ishango bone (http://193.75.136.15/%7Edhuylebrouck/Ishango_web/Ishango_web.htm) |
| Ishango Operation in Brussels (http://www.eu2001.be/Main/Frameset.asp?reference=60-01.01-01.02-01.03-01.03-01.02-01.02-01&lang=en&sess=1035883740&) | |
| BACK TO The Ancients in Kmt (http://math.buffalo.edu/mad/Ancient-Kmt/index.html) |