Chapter 1: The Scribes of Babylon

Positional notation: A numeral system in which each position is related to the next by a common multiplier.

As we are much familiar with, as a digit is moved one place to the left in the decimal system, its numerical value is multiplied by ten. The Babylonians are the earliest known culture to have a similar positional notation, however there was one major difference; instead of being multiplied by ten, everytime a digit was moved one place to the left it was multiplied by 60. This system is known as the sexagesimal (base-60) positional numerical system. They of course did not use the same number symbols as we use today. For example, our numbers 1 to 9 were written with tall, thin wedge symbols grouped together to add up to the number. For numbers greater than 9, a sideways wedge was added which symbolized the number 10. Therefore, two sideways wedges would equal 20.

This particular system stopped at the number 59, for a reason we are still unsure of. Rather than having six sideways wedges equal 60, they babylonians went back to the tall thin wedges. One wedge meant "one times sixty", two wedges meant "two times sixty times sixty", and so on. This caused some problems however because there was no way of telling if a wedge meant "1" or "1 x 60" or "1 x 60 x 60" etc. A symbol for zero was then invented by using a pair of diagonal wedges to show that no number occured in a given space. It is believe that the reason why the sexagesimal system is used rather then the decimal system, is because the number 60 is divisible by a large variety of numbers. This may have come in handy when sharing things among the people (grain, land). Also, it was their method of measuring time. They were known to be excellent astronomers so they would have known that a year was almost precisely 365.25 days, although they found it more convenient to divide a year into 360 days. (360=6 x 60)

Today, we can still see this ancient system being used:

• 360 degrees in a full circle; one degree per babylonian day
• 60 seconds in one minute
• 60 minutes in one hour