What is base sixty?

Welcome to Maths Is Not Boring by Kidopoly.com. I'm Mira. And I'm Finn. A huge hello today to Jack, who is eight, and his five-year-old brother Teddy in Lake Forest, Illinois.

Thanks for listening and doing maths with us every day, Jack and Teddy.

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So, what are we looking at today for Jack and Teddy?

We are looking at a mystery hiding in plain sight. In fact, if you look at a clock right now, you will see it.

A clock? You mean like the numbers on the dial?

I mean the way time works. Why is a minute 60 seconds long? Why is an hour 60 minutes? Why not a hundred? A hundred is so much tidier.

I have literally never thought about that. We count everything else in tens or hundreds. Dollars, centimetres, years. But time gets to be sixty. Why?

Because of an idea that was born almost four thousand years ago. An idea called base sixty.

Okay, base sixty. So normally we count in base ten, right? Zero to nine. And then we bundle them into tens, hundreds, and thousands.

Exactly. 10 is our building block. And it makes sense because we have ten fingers. But long, long before us, around the year 1800 BCE, people in ancient Iraq had a completely different building block. Wait, ancient Iraq? Who lived there back then? The Sumerians first, and then the Babylonians. They were some of the first city builders and astronomers in the world.

And instead of counting in bundles of 10, they counted in bundles of 60. Sixty?

That is a huge building block. Imagine trying to learn your numbers if the base is sixty. Did they have sixty different numbers to memorize?

That is the amazing part. They wrote all their numbers on soft clay tablets using a stylus, which is like a little stick made from a reed. And to write any number up to 60, they only used two shapes. Just two? But how? They used a tool that made a wedge-shaped mark in the wet clay. A vertical wedge shape stood for one, and a sideways wedge shape, like a little hook, stood for ten.

That's it.

Wait, let me picture this. So if they wanted to write the number 32, they would just press three of the sideways ten hooks and two of the vertical one wedges.

You've got it! They built the whole world of numbers out of just those two little wedge marks in the mud.

Okay, but why? I mean, base 60 sounds like such a huge number. 10 is right there on our hands. Why would the Sumerians and the Babylonians choose 60?

Mathematicians still argue about this today. Nobody knows the exact reason for certain. But there is one thing about the number 60 that makes it incredibly special. It is wonderfully friendly. Friendly? How can a number be friendly? Think about sharing. If you have ten things, how many ways can you share them out evenly without chopping any in half?

Uh I can share ten things with two people, they get five each, or I can share with five people, they get two each, or ten people get one each. That's three ways.

Right. But now, imagine you have sixty things. Let's see how many ways we can share those.

Okay, sixty. I could share it with two people, thirty each.

Yes, and you can also share sixty evenly into three parts, or four parts, or five, or six, or ten, or twelve, or fifteen, or twenty, or thirty, or sixty equal parts.

Wait, you can divide it by three and four and five and six.

All of them! Sixty can be shared out evenly in eleven different ways. Ten only has three ways.

Wow. So if I have a pizza cut into sixty slices, I could share it perfectly with three friends, or four friends, or five, or six friends, and nobody gets a weird half slice.

Exactly. It makes fractions and sharing so much easier. When you were doing complicated maths, or trading goods, or mapping the stars, a number that divides that easily is a beautiful tool. That is one very likely reason they loved it.

But still, how do you even start counting to 60 without losing your place? Did they have 60 fingers?

No, but they might have used their fingers in a way we don't. Look at your hand. Do you see the lines on your fingers? The little joints?

Yeah, my fingers each have three little sections.

Right, and you have four long fingers on one hand. Three sections each times four fingers. How many sections is that?

Three, six, nine, twelve. Twelve sections on one hand.

Now, use your thumb on that same hand to point to each section and count them. One to twelve.

Okay, I'm tapping my thumb across the joints of my fingers. Up to twelve.

And now, every time you reach twelve, hold up one finger on your other hand.

Oh! Oh my goodness! My other hand has five fingers. Five fingers, keeping track of twelves. Five times twelve is sixty! I can count to sixty on my hands!

Isn't that beautiful? We don't know for sure if that's how it started, but it's a very famous theory for how they tracked their sixties.

So they figured out how to count to sixty on their hands, and it was perfect for dividing things up. So they just made it their whole math system.

They did. And they used it to map the stars and track the seasons. But here is the most magical part. The Babylonians are gone. The Sumerians are gone, but their 60s are not. Because of the clock! Yes. The Egyptians actually gave us the 24-hour day. But when ancient astronomers needed to slice those hours into smaller, perfect pieces, they reached for the Babylonian 60s, and we never stopped.

So every time I look at my digital watch or the microwave timer, and I see the second ticking up to 59 and then rolling over to zero. I'm actually using Babylonian math.

You are. Every single hour of every single day, you were living inside a 4,000-year-old idea from ancient Iraq. And by the way, its real mathematical name is Sexagesimal.

unknown Haha!

Sexagesimal! That sounds like a magic spell.

It means base 60. And here is a fun fact. For a long time, the Babylonians didn't even have a symbol for zero. They just left an empty space in the clay to show there was nothing there.

A blank space? That would be so confusing. I am very glad we have zeros now. Alright, Finn, it's time for the quiz! Are you ready? I am ready. Bring on the ancient math.

First question. What is the real mathematical name for counting in base 60? Next one. Where did the people who use this system live? Question three. What did they write their numbers on? Here's number four. What were the only two wedge shapes they needed to write their numbers? Last question. What is one place we still use base sixty every single day?

Great job! Let's see how you did. The first answer is sexagesimal, that is the name for base sixty. For question two, they lived in ancient Iraq, the Sumerians and Babylonians. The answer to number three, they wrote their numbers on soft clay tablets. Question four, they just used a one wedge and a ten hook.

And the final answer, we still use it to measure time, like 60 seconds in a minute.

I am never going to look at a clock the same way again. Every time it hits 59, I'm going to think about people pressing wedge shapes into clay.

I know. I love that we still carry their idea with us every minute of the day. Listeners, if you loved seeing this idea with us, please scroll down and leave us a five-star review.

Yeah! Leave five stars for the ancient Babylonians and their beautifully friendly 60. Just scroll down and tap the stars.

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See you next time on Maths is not boring. Bye

What is base sixty?

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