07. Babylona/Maya/China/Binacci – Philippe Leblanc

Philippe Leblanc (BE)

Babylonacci 20 Mini P (2018)
Mayanacci 25 Mini G (2017)
Chinacci 20 Mini S (2018)
Binacci 20 Mini O (2021)

Texts by Philippe Leblanc & Raoul Sommeillier

A written form of numbers – born from the need to organise harvests and commerce, and for time-keeping purposes – appeared at the same time as writing in general. 

Numeration is a method of numbering, or representing numbers. Whether concrete or material, or abstract through words, gestures and symbols, such representations have helped different populations to express, mimic and write numbers. A system of numeration, or numeral system, sets forth the numeration rules to use such words, gestures and symbols.

In addition, systems of numeration can be directly bound to a specific number writing system. The current decimal (base 10) and positional number system, known as the Arabic numeral system or the Hindu–Arabic system, is widespread. In the past, however, multiple and diverse systems were adopted by civilizations such as the Mayans, the Babylonians, or the Chinese. In addition, because of their efficiency, certain systems are used in specific fields; the binary numeral system is ubiquitous in computer science and electronics.

Through his collection of four oeuvres, Leblanc aims to show how the depiction of numbers can be complex through different writing systems: symbolic representations and numeral systems that are typical of cultures with divergent geographic and temporal characteristics.

Each work depicts a different way to represent a sequence of numbers. The artist did not just choose any sequence, he chose the Fibonacci sequence:

0  1  1  2  3  5  8  13  21  34  55  89  144 …

The following section focuses on the numeration rules in each work of art.
1. Mayanacci 25 Mini G
2. Chinacci 20 Mini S
3. Babylonacci 20 Mini O
4. Binacci 20 Mini O

Click on the up and down arrows to move from one work to another.

1. Mayanacci 25 Mini G

The laser perforations in watercolour paper correspond to the 25 first terms in the Leonardo Fibonacci sequence. A famous 13th century Italian mathematician, he is mainly known for having introduced the Hindu-Arabic numeral system in Europe.

Here, the mathematical sequence in which each term is equal to the sum of the two previous terms, is written in a Mayan numeral system dating back to the 4th century BCE. One of the world’s oldest known North American civilizations, the Maya lived in prehistoric times and their first constructions date to the third millennium BC. Their numeral system appeared around 300 BC.

In addition to their complex calendar, the Maya used a positional base 20 numeral system. It consisted of three types of symbols: a shell shape, dots and lines. As shown here in a stylised fashion, the three symbols are all that is needed to write every number, since the position of each symbol gives it a value. It is a so-called positional system, as is our decimal system.

Dots indicate units. Numbers from 1 to 4, are written using 1 to 4 dots. Number five is a line. Adding all the dots and lines gives 19.

For 20 and beyond (201), they used two rows of writing. 400 and beyond (4001) required three rows. Writing beyond 8,000 (203), required four rows, etc. The figure below shows some examples of large Mayan numbers.

Number zero, which the Maya represented by a shell, is not included in Mayanacci 25 Mini G, since it is not one of the first 25 terms in the sequence. The sequence should be read from left to right and from top to bottom.

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