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Three rows of up to 3 small 1s (written like Ys with some shortened tails) or 10s (a 10 is written like <) appear clustered together.

The 10, described as an arrowhead, looks like a bit like < stretched out. The wedge may or may not have a tail, drawn by pulling the cuneiform-writing stylus along the clay after imprinting the part triangle form. Because of the tool used to draw the lines, there is a limited variety. Remember the form of writing is cuneiform or wedge-shaped. There are a few separate symbols (all based on the wedge and the line), but all other numbers are formed from them. Unfortunately, the Y also represents a 50. The symbol for a one is a wedge or Y-shaped form. Since we grew up with a different system, Babylonian numbers are confusing.Īt least the numbers run from high on the left to low on the right, like our Arabic system, but the rest will probably seem unfamiliar. The table appears to be astronomical, based on the categories of Babylonian years.Īll photos come from this online scanned version of a 19th century edition of George Rawlinson's The Seven Great Monarchies Of The Ancient Eastern World.Ĭuneiform Table of Squares. *George Rawlinson (1812-1902), Henry's brother, shows a simplified transcribed table of squares in The Seven Great Monarchies of the Ancient Eastern World. What do you think? Would it have been harder to learn the number basics as a Babylonian school child or as a modern student in an English-speaking school? Still no tie-breaker: It's not necessarily any easier to learn squared and cubed year terms derived from Latin than it is one-syllable Babylonian ones that don't involve cubing, but multiplication by 10. Nick Mackinnon refers to a tablet from Senkareh (Larsa) from Sir Henry Rawlinson (1810-1895)* for the units the Babylonians used and not just for the years involved but also the quantities implied: I don't know of any higher term than that, but those are not the units the Babylonians used. We have a decade for 10 years, a century for 100 years (10 decades) or 10X10=10 years squared, and a millennium for 1000 years (10 centuries) or 10X100=10 years cubed. We talk about periods of years using decimal quantities. I will go into the positions of the Babylonian system on further pages, but first there are some important number words to learn. Learning the Babylonian left to right (high to low) positional system for one's first taste of basic arithmetic is probably no more difficult than learning our 2-directional one, where we have to remember the order of the decimal numbers - increasing from the decimal, ones, tens, hundreds, and then fanning out in the other direction on the other side, no oneths column, just tenths, hundredths, thousandths, etc. The two systems do it differently, partly because their system lacked a zero. The Babylonian system uses base-60, meaning that instead of being decimal, it's sexagesimal.īoth the Babylonian number system and ours rely on position to give value. In 'Homage to Babylonia', writer-teacher Nick Mackinnon says he uses Babylonian mathematics to teach 13-year-olds about bases other than 10. Still, having to learn Base 60 is intimidating. Base 60 also has various useful factors in it that make it easy to calculate with. They were accomplished astronomers and so the number could have come from their observations of the heavens. In part they used Base 60, the same number we see all around us in minutes, seconds, and degrees of a triangle or circle. The Babylonians used this Base 10, but only in part. We actually have 20, but let's assume we're wearing sandals with protective toe coverings to keep off the sand in the desert, hot from the same sun that would bake the clay tablets and preserve them for us to find millennia later.

We use a Base 10, a concept that seems obvious since we have 10 digits. The next step throws a wrench into the simplicity department.

Whether this is harder or easier to learn to handle than a pencil is a toss-up, but so far they're ahead in the ease department, with only two basic symbols to learn.

What they wrote with was a tool one would use in sculpture, since the medium was clay. They didn't have our pens and pencils, or paper for that matter. That's basically all the ancient people of Mesopotamia had to do, although they varied them here and there, elongating, turning, etc. Imagine how much easier it would be to learn arithmetic in the early years if all you had to do was learn to write a line like I and a triangle. Three Main Areas of Difference From Our Numbers Number of Symbols Used in Babylonian Math

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With this table of squares you can see how to put Base 60 put into practice. Here is an example of Babylonian mathematics, written in cuneiform.