Mechanical Monkey

An orange mechanical monkey in front of a purple background.
A large rectangular green and purple exhibit with an orange monkey on the left behind glass and coloured buttons on the right information panel.

Certain numerical operations create much larger numbers than other numerical operations.

How it works

Move the mechanical monkey’s feet to numbers along the baseline and watch the monkey’s hands reveal the answer on the screen to your chosen mathematical operation. The monkey can perform operations such as addition, multiplication and exponentiation (indices) if it’s given enough bananas and time.

Things to try or ask around the exhibit

  • Which operation generates the largest numbers: addition, multiplication or exponentiation?
  • What geometry can you see in how the monkey moves across the screen?
  • What pattern can you pick up in the numbers on the screen?

Background

When the monkey performs addition and multiplication, the order of the numbers doesn’t matter: 2 + 3 = 3 + 2. It is the same for multiplication: 2 × 3 = 3 × 2.

When the monkey performs exponentiation (long chains of multiplication), the ‘powers’ or ‘indices’ are a shorthand way of writing that multiplication. For example, you can write 1 × 2 × 2 × 2 × 2 × 2 as 25 (or ‘two to the power of five’), which equals 32. However, 52 (or 'five to the power of two') is shorthand for 1 × 5 × 5, which equals 25 (which is smaller than 32). Therefore, AB hardly ever equals BA. Can you use the monkey to find an exception this rule?