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Humanizing Factorials

Annos-Mysterious-Multiplying-Jar

With The Tower of Hanoi, I had fun with the evil powers of recursion. But I’m not actually learning code to teach my son to become a dictator, even a benevolent one, bearing brownies.   While we’re learning recursion, it’s probably not such a bad idea to bring up the some of the consequences of creating formulas that make work and data collection efficient, but potentially dehumanizing.

A few years back a friend gave Ben a lovely book that shows both ends of the spectrum of rich creativity and mechanistic abstraction. Anno’s Mysterious Multiplying Jar was written and illustraed in 1999 by the Japanese  father and son team, Mitsumasa and Masaichiro Anno.  It tells a simple story of factorial development that starts with a jar,  large enough to contain an ocean.

In this ocean is an island and on this island are two countries:

In each country are three mountains.  On each mountain, four walled kingdoms.  In each kingdom, five villages.  In each village, six houses.  In each house, seven rooms, in each room eight cupboards.  In each cupboard, nine boxes.  In each box, ten jars like the first.

The question at the end of the story is how many jars are contained inside the jar?   The answer is ,of course,  3,628,800  a.k.a.  10 factorial or !10.

The first part of the story is filled with richly illustrated picture of villages, houses, rooms, cupboards, all with their unique, individual characteristics.  The second part retells the story with dots instead.  It goes as far as a two page spread representing !8, or 40,320 dots.   The Annos don’t venture past that, since they’re writing a children’s book, not a heavy tome full of dots.

But the point, so to say, is made.

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2 responses to “Humanizing Factorials

  1. Actually is 9! because there is only 1(one) jar in a box and not 10(ten). and since every jar is the same as the first, we have a fractal, thus an infinity of jars(no exit from the recursive story).

  2. Thanks for pointing that out. I messed up (originally I said there was only 1 jar in each box.) In each box is 10 jars. So the question is how many jars there are all together, which is !10

    But I will stand firm on recursion. There’s nothing in the story that says that all jars necessarily contain mountains. Just the first set of jars. The jars in the boxes, are apparently the last jars. ( the purpose of the book is to have a solution than can be worked out). So it does break there.

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