Babylonian base-60 numeral system - photo

[mklotz]

So how do you know if it's 60 or 1?

The short answer is that it depends on the column in which the number was written.

The Babylonians used a place system like we do. So, the 'one' symbol (let's use the circumflex, ^, here) written in the rightmost column would denote one, while written in the column left of that would denote 60.

|    |  ^ |  = 1
|  ^ |    |  = 60

We would write 60 as ^0 to make it clear that the ^ mark was in the sixties column but the Babylonians didn't develop a written zero symbol until later in their mathematical development. Obviously, the absence of a zero marker can lead to ambiguity in a place number system but they seemed to manage by depending on context to decide what was meant.

It's interesting to note that the form '10' is the base in every place number system...

10 = 2 in base 2 (binary)
10 = 8 in base 8 (octal)
10 = 10 in base 10 (decimal)
10 = 16 in base 16 (hexadecimal)

10 = N in base N