The most powerful force in the universe is compound interest.— Albert Einstein
Last week-end, the parent network in our town was buzzing. A teen in a neighboring town had invited friends over for a party while her parents were away. Before the teen knew it, 10 friends had turned into 90. The party got out of control. Crystal glasses were broken. Drawers were ransacked. Guests vomited throughout the house. The police were called.
In the end, 22 teens were arrested.
As the parent talk led to how could this happen and who was to blame, my mind turned to another question: What can we learn from this? As a systems educator, I heard a familiar pattern: small numbers escalating in unexpected and explosive ways, like invasive species, fads and epidemics. In the story of the party, one invitation turned into two texts turned into four forwarded messages turning into eight new “friends” and so on. Sounds like exponential growth.
Most of us learn about exponential growth in a math class, somewhere between the ages of 14 and 16. We learn that exponential growth means doubling, like this: 1, 2, 4, 8, 16, 32. We learn that it’s important to know if you want your bank account to grow or if you want to understand population dynamics.
And we forget it.
So I grab a chess board, a big bag of Cheerio’s (jelly beans would be better) and my two boys.
We read the letter-to the-editor (page 2) written by the mother of the girl who threw the party.
And we talk about the numbers. How was it that one or two invitations could lead to 80 uninvited party guests?
To make it real, I put one Cheerio on the chessboard and say: “Pretend these are jelly beans. You win a bet and as your prize I have to pay you one jelly bean on the first day. For the next 63 days, I give you double the jelly beans I gave you the day. Sounds like a good deal? There’s only one requirement: you have to agree to eat the jelly beans you get each day. Deal?”
My younger son rolls his eyes. Like, who wouldn’t accept that deal? He accepts my deal and then we walk through it:
“On the first day, you get one jelly bean, the second day you get two and on the third day you get four. So far so good.” Now he takes over. “On the fourth day I get eight jelly beans and on the fifth I get 16 and then I get 32!”
Things are looking good. The squares are too small and the Cheerios are too big so we pull out a piece of paper and calculate that on the 10th day though, he has 512 jelly beans to eat. He’s still not phased. Double that number on the 11th day. That would be 1,024 jelly beans.
His eyes start to widen. By the 20th day, the number is over 500,000 jelly beans. On the last day, the 64th day, he would have 18,446,744,073,709,551,616 jelly beans. He starts to look queasy. I’d DIE if I had to eat all of those jelly beans!
We draw a graph like this:
We talk about how sneaky doubling can be. And how once it gets going, in the case of the party, it can be unstoppable. “So”, I ask, trying to mask the hope in my voice: “if you understand how texting can double, could that help you avoid trouble down the road?”
Here are a few of their answers:
Well, now I wouldn’t forward the text.
If I don’t know who the text came from in the first place, then it could already be blowing up out of control.
Of course, we also talked about not going to a party if the parents aren’t home.
My sons are 13 and 11. Will they remember this conversation when the party invitations come in as they get older? I can only hope so. Check back with me in five years and I’ll let you know.
Here are some resources for teaching kids about exponential growth:
Stories are a great way to learn about anything, even exponential growth. Here’s a system-based review I wrote about One Grain of Rice by Demi (good for young and old) for the Waters Foundation.
For a similar story, try “Sissa and the Troublesome Trifles. See I. G. Edmonds, Trickster Tales (Philadelphia: J. P. Lippincott Co.,1966) pp. 5-13.
This youtube clip by Dr. Albert Bartlett of U Colorado is worth every minute, more for teens and adults.
There are also some wonderfully clear examples of exponential growth on the Khan Academy site that explore compound interest and bacteria.
Really good explanations, visuals and video clips on these two blogs:
Zimblog: Understanding Exponential Growth
Growth Busters: check out the documentary film and the blogLook for Part II of this blog in the coming weeks: Why do most of us profoundly underestimate the effects of exponential growth?