![\"Ishango](\"http:\/\/kalamu.com\/neogriot\/wp-content\/uploads\/2013\/08\/ishango_bone.jpg\")
<\/a>Ishango Bones<\/strong><\/span><\/p><\/div>\n <\/p>\n The Ishango Bone:<\/span><\/strong><\/span><\/p>\n <\/p>\n Today, I would like to talk about the\u00a0Ishango bone<\/span><\/a>, or rather the first evidence of a calculator in the world. \u00a0Named after the place where it was found in theDemocratic Republic of Congo<\/span><\/a>\u00a0(DRC), the Ishango bone is what is called a bone tool or the craddle of mathematics.\u00a0 Dating as far back as\u00a022000 years ago, in the\u00a0Upper Paleolitic era, the Ishango bone is a\u00a0dark brown\u00a0bone\u00a0which happens to be the\u00a0fibula of a baboon, with a\u00a0sharp piece of quartz affixed to one end for engraving.\u00a0\u00a0It is the oldest attestation of the practice of arithmetic in human history.\u00a0<\/span><\/p>\n The Belgian geologist\u00a0Jean de Heinzelin de Braucourt<\/span><\/a>\u00a0uncovered the bone buried in layers of volcanic ashes on the shores of\u00a0Lake Edward<\/span><\/a>\u00a0in the Ishango region in DRC, near the border with\u00a0Uganda<\/span><\/a>.\u00a0 The Ishango bones are actually\u00a0two (2) bones\u00a0of baboon,\u00a010 to 14 cm long, with several incisions on each faces.\u00a0 The smallest of the two bones was the first to be exposed at the\u00a0Royal Belgian Institute of Natural Sciences<\/span><\/a>\u00a0in Brussels; it carries several incisions organized in groups of\u00a0three\u00a0columns.<\/span><\/p>\n The\u00a0left column<\/strong>\u00a0can be divided in\u00a04 groups, with each group possessing\u00a019, 17, 13,\u00a0and\u00a011 notches.\u00a0 The sum of these being\u00a060.\u00a0 Those are the\u00a04 successive prime numbers\u00a0between\u00a010\u00a0and\u00a020. \u00a0This constitutes a quad of prime numbers.<\/span><\/p>\n The\u00a0central column<\/strong>\u00a0is divided in groups of\u00a08.\u00a0 By an approximate count, one can find (in the parenthesis, is the maximum number):\u00a07 (8), 5 (7), 5 (9), 10, 8 (14), 4 (6), 6, 3.\u00a0 The minimal sum is\u00a048, while the maximal sum is\u00a063.<\/span><\/p>\n The\u00a0right\u00a0column<\/strong>\u00a0is divided into\u00a04 groups, where each group has\u00a09, 19, 21, and\u00a011 notches.\u00a0 The sum of these 4 numbers is\u00a060.<\/span><\/p>\n The\u00a0second bone\u00a0has not been well-studied.\u00a0 However, we know that it is composed of 6 groups of\u00a020, 6, 18, 6, 20, and\u00a08 notches.<\/span><\/p>\n The first bone has been subject to a lot of interpretation.\u00a0 At first, it was thought to be just a\u00a0tally stick\u00a0with a\u00a0series of tally marks, but scientists have demonstrated that the groupings of notches on the bone are indicative of a mathematical understanding which goes beyond simple counting.\u00a0 In fact, many believe that the notches follow a mathematical succession. The notches have been interpreted as a\u00a0prehistoric calculator, or a\u00a0lunar calendar, or aprehistoric barcode.<\/span><\/p>\n Jean de Heinzellin was the first to consider the bone as a vestige of interest in the history of mathematics.\u00a0 For instance, he noted that the numbers in the left column were compatible with a numeration system based on\u00a010, since he saw that:\u00a021 =\u00a020 + 1,19 = 20 \u2013 1,\u00a011 = 10 +1, and\u00a09 = 10 -1.\u00a0 These numbers are also prime numbers between\u00a010 and 20:\u00a011, 13, 17, 19.<\/span><\/p>\n The Ishango bones with the notches<\/strong><\/em><\/span><\/p><\/div>\n Some other scientists such as the Belgian physical engineer\u00a0proposed that the bones were probably a slide rule. While\u00a0Alexander Marshack<\/span><\/a>\u00a0has indicated that the bones could refer to the\u00a0oldest lunar calendar on earth.\u00a0\u00a0Claudia Zaslavsky<\/span><\/a>\u00a0thinks that\u00a0the\u00a0author\u00a0of the Ishango bone must have been a\u00a0woman\u00a0following the lunar phases to calculate her menstrual cycle. \u00a0However, the\u00a0second bone\u00a0completely rules out the lunar calendar theory, and favors more the numeration system.<\/span><\/p>\n All said, it is amazing to realize that\u00a0there were mathematicians 20,000 years ago on the African continent<\/strong>. \u00a0It is so great to realize that my ancestors, on the shores of Lake Edouard, were actually brilliant scientists playing with prime numbers.\u00a0\u00a0Whether it was a\u00a0woman calculating her menstrual cycle, or some brilliant tribe astronomer, it feels so good to know that the paleo-mathematicians of Ishango already knew prime numbers.\u00a0 They were a great civilization long before the pharaohs of Egypt. Thus, in reality, the Ishango bone is the oldest table of prime numbers in the world.\u00a0<\/strong>To read more, check outMathematicians of the African Diaspora,<\/span><\/a>,\u00a0the Prime Glossary<\/span><\/a>,\u00a0<\/strong>and\u00a0Wolfram Mathworld<\/span><\/a>.<\/strong><\/span><\/p>\nCraddle of Ancient\u00a0Mathematics<\/span><\/h2>\n
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