Within this blog post I will be making a whistle stop tour around three schools of thought on the origins of mathematics.
Maths has been in many people’s lives for as long as they can remember. It features in almost everything that we do and can be interpreted in many different ways. But what was the first ever maths recorded and what did humans use it for?
Mathematics and the Ishango Bone:
According to Zaslavasky, one of the most intriguing mathematical finds to ever be made about the pre-historic world was ‘a carved bone discovered at the fishing site of Ishango’ in Africa (Zaslavosky, 1999, Ch.2). It is said to be from ‘between 23,000 and 18, 000 B.C.’ (Zaslavosky, 199, Ch.2) and is one of the earliest representations of maths known to date.
Here it is ! The Ishango Bone:
Dr Jean Heinzelin:
Dr Jean Heinzelin believes that the bone was ‘used for engraving of writing’ (Q) (Zaslavasky, 199, Ch.2). It can be seen on the bone that ‘there are three separate colunms, each consisting of a set of notches arranged in distinct patterns (Zaslavasky, 1999, Ch.2).
The first column on the right hand side of the right bone, follows a pattern of ‘eleven, thirteen, seventeen and nineteen notches’ (Zaslavasky, 1999, Ch.2) linking to ‘the prime numbers between ten and twenty’ (Zaslavasky,1999, Ch.2).
The second column has a pattern of ‘10+ 1, 20+1, 20-1, and 10-1’ (Zaslavasky, 1999, Ch.2), showing an attempt to relate to a potential base 10 system.
The third shows the numbers to be ordered into ‘eight groups in the following order: 3, 6, 4, 8, 10, 5, 5, 7’ (Zaslavasky, 1999, Ch2). This is suggested to replicate an attempt to double (Zaslavasky, 1999, Ch.2).
This shows the Ishango bone as the first attempt to use a number system to record information and the beginning of an understanding of the way in which numbers work- maths at its most simplistic level.
Alexander Marshack:
Having investigated the bone on a more detailed level, he described the bone as something which ‘represents a notational and counting system, serving to accumulate groups of marks made by different points and apparently engraved at different times’ (Zaslavasky, 1999, Ch2).
His theory depicted the concept of the markings being a simple relation to what we now know as the ‘lunar model’ or lunar calendar (Zaslavasky, 1999, Ch.2).
It was backed-up by plotting ‘the engraved marks on the Ishango bone against a lunar model’ (Zaslavasky, 1999, Ch2). This showed a strong correlation ‘between the groups of marks and the astronomical lunar periods’ (Marshack, p30. The roots of civilization as cited in Zaslavasky, 199, Ch.2).
This is described by Zaslavasky (1999, Ch,2) as ‘evidence of one of man’s earliest intellectual activities, sequential notion on the basis of a lunar calendar, comprising of almost six months’.
Plester and Huylebrouck:
Plester and Huylebrouck support Marshack’s theory in relation to the fact that ‘present day African civilisations use bones, strings and other devices as calendars’ (Plester and Huylebrouck, 1999, p340), proposing the idea that maths was first used to chart the passing of time in monthly cycles.
However, they believe that ‘no awareness of the notion of prime numbers has been discovered before the classical Greek period’ further promoting the idea that Heinzelin is applying a modern approach to mathematics to a more simplistic ancient concept.
Plester however believes ‘that the ancient people of Ishango made use of thee bases 3 and 4 for counting and building further small numbers up to 10’ (Plester and Huylebrouck, 1999, p342) opposed to a system which used a base 10 system. This could mean that humans were able to chart time up to a base 12 system, not base 10.
My interpretation: Marks as symbols of number:
According to Cockburn and Haylock ‘there is a sense in which mathematical symbols…are abbreviations for mathematical ideas or concepts’ (Cockburn and Haylock, 2010, p13). When we are dealing with a number system, for example a base 10 system, each number along the line represents a symbol of measurement much like ‘the point on a number line’ (Q) (Cockburn and Haylock, 2010, p15). Each point on the number line represents one of something. If the Ishango bone was being used as a measurement of the lunar cycle, as highlighted by Marshack, it could be said that each mark (symbol) was a representation of one ‘unit’ (the units in this case being days). One symbol= one day. This would show the Ishango bone as a pre-historic representation of recording numerical information, much like the modern day base 10 system which is used to record information today.
References:
Haylock, D and Cockburn, A (2010) Understanding Mathematics for Young Children. 4th Ed. London: Sage.
Pletser, V and Huylebrouck, D (1999) The Ishango Artefact; the Missing Base 12 Link. Available at: http://www.scipress.org/journals/forma/pdf/1404/14040339.pdf (Accessed 8th November 2015).
Zaslavsky, C (1999) Africa Counts: Number and Pattern in African Cultures. 3rd Ed. Available at: https://books.google.co.uk/books?hl=en&lr=&id=2zanfxcor8UC&oi=fnd&pg=PT12&dq=number+origion+ishango+bone&ots=IT9T78xXM7&sig=iHdv22d_-_CDxRQfYl7tCNDDAgM#v=onepage&q&f=true (Downloaded 8th November 2015)
