Sumerian Numerals

Chronicles of Computation — The Early Mechanisms

In the fertile crescent of Mesopotamia, nestled between the Tigris and Euphrates rivers, the ancient civilization of Sumer thrived around 4500 BCE. The Sumerians, a people of remarkable ingenuity and curiosity, laid the foundation for many aspects of modern society. Among their many contributions, one stands out for its profound and lasting impact: the development of a numerical system, the precursor to the mathematics we know today.

The Sumerians were the first civilization to develop a counting system. Unlike the base-10 decimal system we use today, the Sumerians used a base-60, or sexagesimal, system. This choice was not arbitrary but was likely influenced by the Sumerians’ astronomical observations and their calendar, which was based on the lunar cycle. The number 60 is a highly composite number, divisible by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30. This made calculations and divisions more straightforward and less prone to error.

Photo by Sanni Sahil on Unsplash

Another reason for employing a base divisible by 12 is the ability to use the thumb as a pointer. You can do that touching the three finger bones of each finger sequentially, starting with the outermost bone of the little finger, allowing for counting up to 12 using just one hand. This counting system, still prevalent in many regions of Asia, could account for the existence of numeral systems based on 12 and 60, in addition to those based on 10, 20, and 5.

The Sumerians recorded their numbers on clay tablets, using a stylus to make wedge-shaped marks in the soft clay. These marks, known as cuneiform, represented different numbers based on their orientation and arrangement. For example, a single vertical wedge represented the number 1, while a single horizontal wedge represented the number 10.

Let’s take a look at how this system works in Python:

# Sumerian Numerals in Python
def decimal_to_sumerian(decimal_number):
    sumerian_numerals = {
        1: '|',  # Vertical wedge
        10: '<',  # Horizontal wedge
        # Add more Sumerian numerals as needed
    }
    sumerian_number = ''
    for numeral in sorted(sumerian_numerals.keys(),
                          reverse=True):
        while decimal_number >= numeral:
            sumerian_number += sumerian_numerals[numeral]
            decimal_number -= numeral
    return sumerian_number

print(decimal_to_sumerian(32))

This code takes a decimal number as input and converts it to its Sumerian numeral representation. It does this by iterating over the Sumerian numerals in descending order, subtracting the current numeral from the input number until it can’t be subtracted anymore, and then moving on to the next numeral. The result is a string of Sumerian numerals that represents the input number.

Save the previous file as sumerian_numerals.py and run it using Python. Here’s the output:

<<<||

Try to change the number to convert and see how that affects the result.

The Sumerian numerical system had a profound impact on their society, enabling them to engage in complex trade agreements, develop architectural plans, and even chart the stars. It was the cornerstone of their civilization’s technological and cultural advancements.

Interestingly, the echoes of the Sumerian base-60 system can still be heard today. We divide an hour into 60 minutes and a minute into 60 seconds, a direct legacy of the Sumerians’ sexagesimal system. The next time you glance at your watch or clock, remember that you are looking at a piece of history that stretches back over 6000 years.

The Sumerians’ contribution to mathematics is a testament to their innovative spirit and intellectual prowess. Their base-60 numerical system, etched into clay tablets with a simple stylus, was a revolutionary development that shaped the course of human history. It is a powerful reminder of the enduring impact of ancient civilizations on our modern world.

Recent research continues to shed light on the intricacies of the Sumerian numerical system and its applications. As we continue to uncover the secrets of the Sumerian numerical system, we gain not only a deeper understanding of this ancient civilization but also a greater appreciation for the mathematical concepts that underpin our modern world. The Sumerians’ legacy, etched into clay tablets thousands of years ago, reminds us of our enduring fascination with numbers.

This story is part of the Chronicles of Computation book. The next section is The Abacus: An Ancient Calculator.