Talk:Ishango bone
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[edit] Egyptian Multiplication?
This article claims that the bone is an example of Egyptian multiplication. Could someone please point it out more explicitly to me? I don't see what's being multiplied, or what the result is. And yes, I understand the concept of Egyptian multiplication. -Rwv37 18:10, 13 November 2005 (UTC)
[edit] Age of Artifact
I believe the modern scholarly concensus dates this bone to approximately 6,500 BC. I've changed the date.
- The reference used for this article states that it's 20,000 years old. --Sean Brunnock 12:09, 31 March 2006 (UTC)
[edit] Age of Artifact 2
See the following paper for the age. The "consensus" is false. Brooks A.S. and Smith C.C., 1987 "Ishango revisited: new age determinations and cultural interpretations" The African Archaeological Review, 5 : 65-78.
[edit] Ishango Bone
The Ishango bone is a tally stick, made of bone, which contains 3 sequences of grouped carvings. The bone was found in the area of what are now the headwaters of the Nile River. The bone has three rows of notches, with the row a) below having 2 sets of numbers in excess-one format, base 10: 9,19, 21,11. Row b) is a descending series of prime numbers from 19; row c) continues the series of prime numbers, down to 5; row c) then contains multiples of 3, 4 and 5, in an example of Egyptian multiplication.
- Rows of tally notches below:
| (a) | 9 | 19 | 21 | 11 | ||||
| (b) | 19 | 17 | 13 | 11 | ||||
| (c) | 7 | 5 | 5 | 10 | 8 | 4 | 6 | 3 |
Originally from Africa, this artifact now resides at the Royal Belgian Institute of Natural Sciences, Brussels, Belgium. The bone is dated to around 18,000 BC. [1]
The middle column begins with 3 notches, and then doubles to 6 notches. The process is repeated for the number 4, which doubles to 8 notches, and then reversed for the number 10, which is halved to 5 notches. These numbers then, are not purely random and instead suggests some understanding of the principle of multiplication and division by 2. The bone may therefore have been used as a counting tool for simple mathematical procedures.
Furthermore, the number of notches on either side of the central column indicate more counting prowess. The numbers on both the left and right column are all odd numbers (9, 11, 13, 17, 19 and 21). Furthermore, the numbers on the left column are all prime numbers, demonstrating some mathematical knowledge. The numbers on each side column add up to 60, with the numbers in the central column adding up to 48. Both of these numbers are multiples of 12, again suggesting an understanding of multiplication and division.
[edit] References
[edit] Removed speculation
I removed the following, from a sentence beginning with - The Ishango grouping may have been used to construct a number system "which is speculated to have spread north to Egypt and contributed to the development of mathematics". We would definitely need a reliable source on this, this speculation seems highly unlikely to me. This number system from 20,000 years ago is speculated to have spread to egypt, appearing over 10,000 years later in the egyptian mathematics? Given the gap of many millennia, one would need serious evidence to make this claim. --Xyzzyplugh 13:59, 26 November 2006 (UTC)
