a lot of knotted strings all tied together.

Image: Wikimedia Commons/Pi3.124 CC-BY-SA 4.0

People record numbers in lots of different ways. This method was used by the Inca people and many others who lived near the Andes Mountains of South America.

You will need

  • Pieces of string

A bit of background

The numbers we’re looking at are written in knots on a string! They were used in quipu, which were complex recording devices made from string.

Experts aren’t sure how to read all the information from a quipu, but certain patterns keep turning up. Marcia and Robert Ascher have decoded some patterns into numbers. Here is the method they have for reading quipu strings.

A simple knot

  1. Take a piece of string.
  2. Make a loop and pass the end through it – this is the simplest knot you can tie, called an overhand knot. It’s also how the Inca wrote 10.
  3. Purple string with 3 evenly spaced knots.To write 20, make two overhand knots close together, but not touching. You can add more knots to make 30, 40, all the way up to 90.


What about single digits?

  1. Single digits are a bit trickier to tie than tens.
  2. A purplee string wrapped loosely around someones fingersTo make the number 2, start by making two loops of string. Then pass the end through both of them. Be neat and careful as you tighten the knot.
  3. A purple string with an elaborate knot. To make larger single-digit numbers, add more loops before you pass the end through. So to write 5, make five loops and then pass the end of the string through all of them.
  4. A purple string with a loosely tied figue of 8 knot.To write 1, you need a knot known as a figure eight. To tie this knot, make a loop. Before you feed the end through, twist the loop 180 degrees. If you’ve twisted it the right way, you should get a figure eight. (If not, you might not get any knot at all!)


Putting it together

By combining different knot patterns, quipu experts could write a whole range of numbers.

  1. A purple string with four knots in it.The ones digit is placed near the end of the string, then after a large gap, put the tens digit.
  2. A purple string with several knots in it.A hundreds digit is written using the same knot patterns as the tens digit, but a large gap up from the tens. So 123 is written with an overhand knot, gap, two overhand knots, gap, one knot with three loops.
  3. To write a zero, no knot is tied. On a single string this can be confusing, because it might just be a long gap. But on a quipu, many strings run next to each other, and the digits line up from string to string. You can easily tell when one string has no knots and other strings do have them.


More about quipu

We can read numbers in quipu, but there’s plenty more that this activity doesn’t cover. Here are a few more feature you might find in a quipu.

• Quipu often contained different-coloured strings, and some strings were even striped.
• Some strings branch, with other strings coming off from them.
• Some knot patterns don’t match the numbers described in this activity.

It’s clear that there’s a lot more information in a quipu than a simple list of numbers. A quipu might also be able to tell you what is being counted (maybe people, or distances, or days). Or it might tell you where that thing is located.

Some experts believe that stories could be written in quipu. Right now, there is no accepted way to read those stories. Luckily, archeologists keep finding more and more quipu. With enough examples and the right clues, we might be able to untangle more of their secrets!

Related activities

Maya numbers
Decoding binary numbers

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