Amish Friendship Math

Ever gotten a start for Amish friendship bread? It’s kind of like sourdough: you have a container of fermented “starter,” you use it to make the bread, then you replenish it so it keeps growing. After you’ve nursed the starter along for ten days, you make yourself a batch of yummy bread using part of the starter, then you divide up the starter into 4 bags, keep one for yourself, and give three away. That’s presumably why they call it “friendship bread.”

(Disclaimer: Wikipedia says "There is no reason to think that the bread has any connection to the Amish people." The Amish are much wiser than this. And I can’t imagine them using Jell-O pudding mix as an ingredient in anything.)

It sounds so innocent and…friendly. But friendship bread is really a terrifying exercise in exponential growth.

If I have a cup of starter, that’s

4⁰=1 (Don’t ask me why. Anything to the zero power is one). So far so good. The original starter yields 4 new bags, including the one I keep, for

4¹=4

If each neighbor takes good care of the starter and gives three neighbors a bag, we have

4²=16

A bag takes 10 days to mature, so another 10 days later we have

4³=128 bags of starter after about a month. In another month or so, we’re up to

4⁶=8,192 If you estimate that every home in my town has about 4 people in it, that’s one bag per house. In another month, we’re up to

4⁹=524,200, or enough bags to cover about 2 million households of 4 people. Another month later, we have

4¹²=33,544, 432 bags.

Only two more rounds after that, we’ve got a bag of starter for every household in the U.S.:

4¹⁴=268,440,000.

After sixteen rounds, we don’t have quite enough Amish friendship bread starters for everyone in the world:

4¹⁶=4,295,000,000, but everyone in the world can have about three bags after the next round (if we haven’t run out of Zip-loc bags by then):

4¹⁷=17,180,000,000 after a little less than 6 months since my original bag of starter.

But wait! There’s more! These numbers are vastly underestimated, since the bag I kept goes on to spawn four more bags, as does each one of the other bags, leading much more quickly to the downfall of humankind as we know it. If everyone obeyed the instructions on the bag, we’d already have international ordinances and relief agencies dedicated to eradicating the friendship bread menace.

Fortunately, my neighbors are deeply aware of the Amish friendship bread threat, and they declined my Zip-loc bags. Friendship bread went no farther than my house, where I made 5 batches and threw away the instructions.

Oh, and if you didn’t read past “yummy bread,” here are some instructions for starting your own Amish friendship bread (this recipe yields only three starts). Just don’t give me a bag.