Tuesday, November 18

Amish Friendship Bread and Exponential Growth

If you're not familiar with Amish Friendship Bread, here's how it works. You receive a ziplock back with a mixture of flour, water and sugar in it, presumably from a friend. Over a 10 day period you squish the bag around, and add more flour, water and sugar. Then, on day 10, you pull out 4 portions of the mixture, and give it to friends. You then add more stuff (eggs, oil, baking soda, etc.) and bake the bread (which is more like cake if you ask me). So 4 of your friends now have the stuff, and repeat the process over the next 10 days. It's tasty stuff.

In the last 2 weeks, Shannon and I have gone through that whole cycle, which lead to a brief study of what this 4 fold growth means for the world, as well as our supply of flour, water, sugar and ziplock bags.

Basically, it comes down to this: buy stock in Ziplock. And their competitors. Anyone making an airtight bag.

After 10 days, 4 people have the bread. By the end of a month, we're up to 64 people (roughly the population of my street). Not that impressive. By two months it's 4,096 (small part of town), and by 3 months its 262,144 people (all of southern utah). And, like all exponential growth problems, this is when it starts getting fun. One more month reaches over 16 million people, or the population of a whole pile of western states (UT, NV, ID, MT, WY, CO, NM, ND, SD). At the conclusion of 5 months and pass one billion people, and at 6 months we have about 10 bags of Amish Friendship Bread for every person on earth.

From here, the problem repeats itself, in a way. Once everyone has a bag, start the growth over again but after a month it's not 64 of your friends that have a bag, it's you that has 64 taking over your kitchen. By the end of the year, there are about 4,700,000,000,000 billion bags of Amish Friendship Bread in the world. (And you're rich, because you bought stock in Ziplock, remember?)

Clearly, this does not describe reality. Shannon and I received some friendship bread a few years ago, and since it hasn't taken over the world yet, people must not be passing it on. If only 25% of the people who received the bread passed it on, it would just barely remain in existance. If the rate went up to 30% growth would be small, with my one loaf of bread growing to about 600 over the course of a year. In reality, the survival rate of the bags is probably somewhat lower than 25% which would not be sustainable for the friendship bread population, and would require certain individuals to create the bread from nothing occasionally to start up new chains.

Ok, I think I finally got all this out of my system and I can go on with my life.

7 comments:

Sabrina said...

I wish the Amish bread would spread through the earth. That stuff is tasty!

Cheryl said...

It IS tasty. But after about 8 times of the cycle, will you still have people who call YOU friends??

Melissa said...

I wish I knew how to start my own bag of slop. I think I have the recipe and instructions, I just don't know how to get it going. I had it when we were in Provo and I would only give away three of them and keep one for myself so that every ten days we would get to eat it. So yummy.

Adam Lowe said...

That's why multilevel marketing/pyramid schemes don't work. If everyone filled up their "downlines" with new people, after not very many levels everyone on the planet would be involved.

People forget that in those models, people can't be repeated. You don't just have to find a million people to fill up the next level, you have to find a million new people who haven't been involved yet.

Clark said...

This isn't to disagree with Adam, but luckily with the Amish Friendship Bread scheme, people can be repeated. My set of instructions actually tells me to keep 1 of the 4 bags for myself, so I can continue eating the bread every 10 days forever. The AFB market won't be 'full' until people are consuming the bread at their maximum, which might be something like 1 loaf every 5 days. (It makes quite a bit.)

Melissa: You can google various AFB starter recipes. They are basically the same flour/sugar/milk (I think it's milk, not water, as my post said) that you add to the mix yourself, but also with some yeast. The initial starter can only contain additional ingredients that a reproducing, as the only thing that is ever added to that is the flour/sugar/milk mix. Yeast is the only thing I can think of that you could want in your mixture that is capable of reproducing. Anyway, google should provide the answers you need.

Ben said...

question... wouldn't you only have after you get this thing divided about 10 times a bunch of yeast alchohol and a tiny bit of milk flour and sugar (since they don't reproduce)? Yuck.

Shanny said...

You get a mixture. Then you add some milk sugar and flour and then you divide it. That keeps things balanced out. It also keeps the amount of mixture from dwindling to nothing in just a few generations.