Imagine you are with your 6-year old niece at the zoo on a sunny summer afternoon. She’s at that age when she insists on counting everything she sees. As you are walking through the parking lot, she wants to count all the tires on the cars. It’s cute, but it really slows you down, so you tell her there’s a trick she can use. She can count just the number of cars and then multiply it by 4 because the number of tires is related in a predictable way to the number of cars. She thinks that’s cool, and you finally manage to get inside the zoo.
Now your niece decides that she wants to count all the legs on the zoo animals. Can you speed things up by having her just count heads and then multiply by a fixed amount to get the number of legs? No, because different animals have different numbers of legs—the lions have 4 legs, the flamingos have 2, and the snakes don’t have any at all. As the number of animals grows, the number of legs doesn’t increase in a steady or predictable pattern. You sigh and buy yourself an extra large box of popcorn to pass the time.
