The Ishango Bone is the oldest artifact mentioned in Plimpton 322. Is it really mathematical? Without knowing its context we can’t say for certain. What evidence from the object itself, or what arguments, do you find convincing either way?
http://www.math.buffalo.edu/mad/Ancient-Africa/ishango.html
http://www.naturalsciences.be/expo/old_ishango/en/ishango/introduction.html
The Ancient Roots of Modern Mathematics
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After reading the abpve noted articles I think that the Ishango Bone is not merely decoration, but a mathematical object. The article written by Professor Scott W. Williams states that “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.” From these findings I find it hard to believe that these markings on the Ishango Bone are just coincidental. They appear to be marked and placed in specific groupings in such a way that it seems to me and to the author of the article that it is a mathematical equation. The way the numbers add up and multiply have too many similaries and patterns in order for a person to think this is just a coincidence and call it a piece of decoration.
I’m not convinced about row (c) illustrating the method of doubling. How does it do that?
Well beginning from the right and going left you can see that there are three tallies and right next to it are six tallies. Then after a space there are four tallies and next to that are eight tallies. The pattern then changes slightly, there’s a space followed by ten tally marks and next to that are two sets of five tallies which perhaps shows how the number ten is computed (5+5=10). Although I am not quite sure why the seven tallies are there at the end of the left side.
After reading the article on the website above, i believe that the Ishango Bone was use for mathematic reason. when i was reading the following lines “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)” i made the conclusion that the Ishango bone was mathematical. Row c talks about doubling which was used by the Eygptian hundreds of years after the Ishango bone was writen. Doubling was use to multiply two numbers by the Eygptian and the addition and the subtraction is still being use today. Therefore, i believe that this historical discovery has an impact on mathematical world.
I read what the article says about the markings, but I feel that there isn’t enough proof to what these scholars claim. Writing utensil maybe, but I cant see the mathematics behind the markings. They seem to be random more than sequenced toward something. Maybe to count something but not a formula or sorts. I mean it could be the early signs of a number or counting system but in no form a equation.
It seems amazing that both the rows (a) and (b) add up to 60, given the importance of 60 in the history of math. Could there be any significance to those 60s? Some cultural link between prehistoric sub-Saharan Africa and Mesopotamia 20,000 years later? Surely not — that’s way too long a time and too far away. Or is it?
The Ishango Bone is the oldest mathematical object known to human kind. Being born and raise in a foreign country, I knew about the Ishango bones when I was learning math in High School; it was that important in my country. I believe that it introduces the early stage of multiplication on Row (c) where 3 then 6 and 4 then 8 both examples of multiplication by 2. And also addition with the 5 then 5 which equals 10 that is right next to them. Its known that both row (a) and Row (b) each add up to 60 which shows that there are differents ways that add up to 60. And we all know that 60 is very important in timing, with 60 minutes and 60 seconds. I believe that these are evidence from the object that I find convincing.
In my opinion, the Ishango Bone is a mathematic. It is an ancient baboon with numerical markings on it. The row (a) and (b) ended up with the number 60 which is really important because even the modern society measure the time based on the base 60 ( 60 minutes, 3600 seconds). It might have an astronomic significance also (365 days). In addition, 60 has a lot of factors. I think those two evidences look convincing to me. But I found the row (c) to be confusing.
I think that these three columns of asymmetrically grouped notches imply that the Ishango Bones are the oldest mathematical artifact. The numbers on both the a) and b) rows are all odd numbers (9, 11, 13, 17, 19 and 21). The numbers in the b) row are all of the prime numbers between 10 and 20 plus the summation of both the 1st and the 4th, 2nd and the 3rd equal to 30, while those in the a) row consist of 10 – 1, 20 − 1, 20 + 1 and 20 + 1. The numbers on the rows a) and b) both add up to 60, with the numbers in the c) row are adding up to 48. Booth the sums (48 and 60) are even numbers. On the c) row, the fourth number (10) is a double of the third number (5), the fifth number (8) is the double of the sixth number (4), the seventh number (6) – the double of the eighth number (3). All these facts suggest that the people who made marks on Ishango Bones had some understanding of addition, multiplication, and probably the grouping of numbers into odd and even numbers.