Mathematics with Friends - The Second Episode

# Mathematics with Friends - The Second Episode

First counting

Blog by Ioanna Georgiou and illustrated by Asuka Young

The section in red comes from Season 10, Episode 4 of the TV series “Friends” created by Marta Kauffman & David Crane, and broadcasted by NBC between 1994 and 2004 and readily available on streaming channels. We use the everyday mathematical themes mentioned as our starting point, to explore the fascinating world of mathematics further.

Chandler is excited to show Emma how to hold one finger out, on her first birthday, indicating she is one year old!

Chandler: Guys you have to see what Emma just did. How old are you? How old are you today? (Holds one finger out)

Emma: o…i…s (Holds one finger out)

Rachel: Oh! Emma that's right! You are that many!

Thinking time

What symbols do we use to represent numbers? Is there a way that transcends cultures but is still meaningful? How have the symbols been changing through time? What remains timeless?

People have used various symbols to represent numbers, including times before writing was even invented. We know this from artefacts such as the Lebombo bone. You can see what this looks like here. This baboon’s fibula is around 40,000 years old. It is considered the oldest mathematical artefact because it has 29 notches that have been deliberately carved on it.

These 29 notches are believed to represent the duration of a lunar cycle. A lunar cycle is how long it takes for the moon to go through its different phases – as seen from the earth (the moon itself stays the same!) We now know that it takes 29.5 days from a New Moon to the next New Moon - read more about phases of the moon here.

This carving of 29 notches must have helped pre-historic people to measure time. The duration of a lunar cycle is very close to our calendars nowadays, which each month lasting around the same as a lunar cycle. Once we count the days in a lunar cycle and then how many lunar cycles in a year, we can estimate change in seasons. This is super important as we need to know when rain is coming, when to harvest, and plan for our sustenance!

Another very popular way of keeping count is our fingers. Not quite as permanent as notches on bones, counting on our fingers is how we learn not only to count but also to perform calculations.

So, our little heroine, Alexandra, from our first maths episode, would be able, just like Emma in the dialogue above, to hold one finger up when she turned one, and two when turned two or when she turned eight and wanted to make bunny ears in the photo with her BFF.

How about three? How do you show three with your fingers? Just stop reading for a moment and hold up three fingers. Weird request? Not quite. Whilst one or two are more uniform across cultures – one is shown with the index finger and two is shown with the index and middle fingers held up together (like bunny ears, or the victory sign), three in some cultures includes the ring finger in addition to the index and middle, making the total three of course, but in some other cultures, the third finger to be held up would be the thumb. There is yet another less common variation, where three is shown holding up the middle, ring and pinkie fingers. Read more about this here.

See the note at the bottom of this piece if you over 18...

Using our fingers so extensively makes it easier for us to do calculations. Our fingers are a bit like an abacus we carry around all the time. This can lead to us considering how it is so easy for us to count in fives. Try count in ones, like normal counting, and then try counting in fives. Same speed pretty much! Isn’t that spectacular? Having five fingers on each hand is the reason why five and ten are so hard wired in our brains, and so natural to think in fives and tens.

Let’s do one last trick. Let’s show how to count to twelve on just four fingers.

Each finger has three sections, called phalanges. By taking the thumb to touch iteratively against each of those phalanges, we are counting all the way to twelve on a single hand. That’s one of the reasons why quantities such as a dozen, or twelve inches in a foot, twelve hours in a clock have been widely used for centuries. See this article if you want to know more.

Next steps

Look out for the next time someone needs to use their fingers for sums or just to show a number. What other symbols have you come across for depicting numbers?

More on different number systems in another “maths with friends” episode!

Spoiler alert: In the Quentin Tarantino’s 2009 film “Inglourious Basterds” (which Alexandra is strictly not allowed to watch until she is 18, so please follow the  same if under 18) the British undercover spy reveals his identity accidentally not because of his accent in German, but rather for when he orders three beers and holds up the index, middle and ring finger. Germans would hold up their index and middle fingers and their thumb. But this is not only a huge spoiler for the film but also to say that it was maths that changed the plot of that story!

#### More about the Author and Illustrator - and Preorder the Book

Asuka Young, the amazing illustrator I collaborated with for Mathematical Adventures! and Peculiar Deaths of Famous Mathematicians has livened up the dialogues with her illustrations! And we can’t wait to see this material transforming into a book in the end of this series. You can even pre-order it at a special price if you’d like! See here for more details.