Thursday, March 4, 2010

Spatial Scarcity in a Knapsack

Back when I was working for the Powell Center for Economic Literacy, we frequently did workshops for elementary teachers. One of the favorites for illustrating the concept of scarcity was one titled Spatial Scarcity.

The lesson was aimed at early elementary students, and asked them to make choices when packing their backpack. They could assemble all the things they would like to bring to school and decide what would fit into their backpack. The assumption was that there are many things we want, but we have limited resources (the pack and our strength), so we must choose. It's very visual, but lacks sophistication for older grades.

Imagine my surprise when watching television (very) early one morning I happened upon an episode of NUMB3RS. For those of you unfamiliar with the series, it's a drama on CBS about an FBI agent and his mathematician brother. The academic uses math to help the law enforcer recognize patterns and otherwise solve crimes.

In episode 324 (sorry, I haven't been able to find the video or clip on the CBS site), the mathematician brother mentions a knapsack algorithm designed to help people choose what to put into a knapsack. Each item has a weight (total weight in the example is not to exceed 30 pounds) and a value assigned. The algorithm allegedly makes it easier to make an optimal selection. I followed some links and found that the knapsack problem was somewhat different from what was presented (surprise).

The variable that could be pursued in an economics course (when and if CBS puts the clip up) would be the assignment of values to the various items. As we know, individuals value things differently. As a result, your "optimal" knapsack may be different from mine. Certain items may be similar, but the final mix can differ from person to person. And that brings us to the whole issue of values in making choices. In the end, you may decide this is too sophisticated.  Nevertheless, it's an interesting extension of a classic elementary lesson.

Has anyone else seen the show/episode? What are your thoughts?

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