Writing and the Sexagesimal System as a tool of time measurement
On the international stage we all know of the horrendous crimes against humanity committed in the Middle East, principally in Iraq and Syria. Beyond this, disgracefully almost unreported and unknown to the public, for more than ten years havoc has been and is still being wreaked on a historical stage which belongs to all of us, in the lands where the Sumerian, Babylonian and Assyrian civilizations were born, the ancient Mesopotamia.
The looting of the National Museum of Baghdad in 2003 was the tragic prelude to the destruction and irreversible breaking up of a cultural heritage of priceless value. Indiscriminate and inexpert excavations have been carried out in Iraq and Syria in order to find archaeological treasures to be smuggled out as a means of financing mobs of so-called soldiers and jihadists.
Thousands of tablets of cuneiform writing have thus been purloined from these countries and gone to enrich private collections and even public cultural institutions. All this will have very negative consequences for the preserving ancient civilizations, which have created valuable tools for the progress of knowledge and science of mankind.
Approximately 5000 years ago the Sumerians, a people of uncertain ethnic and geographical origin who lived in modern Southern Iraq, invented a system of writing.
As the Etruscans passed their knowledge of the world and engineering inventions on to the Romans before disappearing completely from the stage of history, so did the Sumerians with their semitic neighbours and conquerors: Akkadians, Babylonians and Assyrians.
The Sumerians were the first people in history to write numerals.
They used two basic symbols: one (a sort of nail with a conic head ) and ten ( a sign similar to: < ).
This writing was called cuneiform from the Latin word cuneus for ‘wedge’, owing to its wedge-shaped style. In the course of several centuries the development of representation of numerals related to the development of counting led to the conceptualisation of quantity and thence to the expression of reality in abstract form. This in turn stimulated the development of writing.
In other words by combining the symbols used in their record-keeping the Sumerians gradually came to giving them also have a phonetic meaning. Around 85% of the hundreds of thousands of cuneiform tablets found in the archaeological excavations in Mesopotamia deal with economic computing. This evolution was completed by 2400B.C. creating the full cuneiform script, used throughout the centuries to write a large variety of languages without any known linguistic affiliation. In the same way it also occurred in recent times with the transcription of the Turkish language from Arabic to Latin characters.
The great American Assyriologist S.N. Kramer said that history begins at Sumer, since writing is the characteristic that separates history from prehistory. The Sumerians recorded on their clay tablets facts of everyday life, historical events, laws such as the Hammurabi Code and legendary epics, as Gilgamesh, where an account of the Deluge occurs for the first time.
It is also known that the decimal system had originated from the number of the fingers of our hands, whilst the one with basis 20, is from the number of the fingers of our hands and feet.
Instead, the Sumerian numerical system had a sexagesimal basis.
It has been often asked why this ingenious people after having already marked the number 10 had not based their system on it. The Hellenistic mathematicians in the III century B. C. gave a quick answer: the sexagesimal basis is much easier to handle when coping with division operations than the decimal one.
But we do not learn to divide before we can count. The rationale must be quite different.
The Latin numerical system, much less sophisticated than the Sumerian one, had a symbol for one hundred, C, and another for one thousand, M. Sumerians and their epigones, Babylonians and Assyrians, had marked these numbers by combinations of ten’s and sixty’s. In their first and subsequent exercises on counting Sumerians, the forerunners of modern experimental mathematics, had stopped adding ten’s to ten’s as soon as they had arrived at 60. As a matter of fact they marked this number by a bigger one. Since it was from 60 that they had to start counting and multiplying again. Thus the number 70 was marked as sixty-ten ( same way the French still do: soixante-dix ), and 80 as sixty-two ten’s, 90 as sixty-three ten’s and 100 as sixty-four ten’s.
In cuneiform Sîn, the God of Moon has the attribute of number 30, equivalent to 29,5 days, one lunar month, or lunation, whilst Anu, the God of the Sky had the number 60, twice a lunation.
These mythological clues show how the sexagesimal system had sprung up from measurements of time. This numerical system was intertwined with astronomical cycles, which were very important for societies flourishing on agriculture and trade of their products.
Therefore as twice the number of a hand fingers gives ten, twice a rounded up lunation gives sixty.
According to the Babylonian calendars used in the ancient Rome until the reform imposed by Julius Cesar one year consisted of 360 days. Similarly in the sky the zodiac was rooted in the full angle of 360 degrees, since time and space had the same measurement system. For the Mesopotamian civilizations the word beru did not mean merely two hours, but two hour’s walk.
Later on the Greek genius for abstractions gave a much wider significance to the empirical mathematical solutions found by Sumerians. Pythagoras’ s theorem is the most known case.
By converse from Greek mathematicians sprang up the fracture of the Mesopotamian numerical consistency. Pythagorean Arithmetic was based on ten, considered as the perfect number, whilst Geometry remained to be rooted on sexagesimal standards.
Our time computing is still based on the sexagesimal system: seconds, minutes, hours, days, months, up to the full year. A second is then subdivided in tenths, hundredths and thousandths of a second, whilst a year is replicated in decades, centuries and millennia. As soon as we slide into the infinitely we deviate from a system of measurement and turn again to counting with the fingers of our hands.