The base that tells time...

When we talk about numbers we understand how our number system is setup. We have negative numbers, we have zero, and we have as many positive numbers as we can conjure up. What we work in everyday is the Arabic number system or what is known as base 10. When we looked at bases we were all comfortable working within our base system.  We can do operations easily and estimate answers because we know this:

0,1,2,3,4,5,6,7,8,9

These are our whole numbers and they make up the majority of the numbers that we deal with on a daily basis. When we get to 9 everyone know that we go to 10. But the simplistic nature of these shouldn’t be overlooked. Essentially this is just grouping by tens.  When we have a group of ten we have “filled” up a place value therefore we need to create a new category. We use this concept every day and every time we interact with numbers; and for the most part we don’t appreciate the usefulness of this concept.

So what would happen if we weren’t in base ten, well I’m glad you asked. How about if well look at a base that was invented by the ancient Sumerians in the 3rd millennium BC, base 60. And what if I told you that you, yes you, interact with it every day, would you believe me?

We should first define what base 60 is. Base 60 is commonly referred to as the sexagesimal system. The ancient Babylonians invented this trivial. They choose the number 60 because of this highly composite nature. Remember a composite number is a number that can be divided by a number other than 1 and itself. 60 can be divided by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. When we talked above about how when we have nine of something we regrouped into another group similarly in base 60 when we have a grouping of 59 things we have but if we have 60 things we have one grouping of 60 and zero groups of one and we recognize this number: 10. Now we have to add the sub notion which helps us distinguish between our base 10 and base 60. So if we have 60 things in base 60 that number would be: 10_base60.

So your probably asking well then what if we had 72 items then the number should be broken down by saying we have 1 grouping of 60 and we have 12 things left so the number should be 140_base60 right? Wrong. Instead when we go above 9 we have to use symbols to represent numbers, the easiest way to do this is to use the alphabet. So once we go above 9, A=10, B=11, C=12 … and so on. So the number 72 in base 60 should be written like so: 1C_base60. 

Now I mentioned before that we actually use this in our everyday lives. But when? Lets think about when we group things in terms of 60 things…. We do it all the TIME! When we tell time we use the sexagesimal system; 60 secs is a 1 minute, 60 mins is 1 hour. We also use it in relation to circles in a specific type of math, trigonometry. So the next time you overlook the simplistic nature of base 10 and say its hard, just remember that we also work in base 60 and could you imagine not only writing very large number but also incorporating numbers as well to represent a number? Talk about confusing!