This week the middle schoolers applied proportions to the 100 meter Olympic competition. As you can see in the picture above, Usain Bolt, in front, is substantially taller than his competitors. We asked if this gives him a competitive advantage. Then we asked if this is an unfair competitive advantage.
Unfair is the key word. There is no objective metric for fairness (this makes economists nuts) so our discussion veered into territory that requires critical thinking (oh no!). And the answer is not clear. On the one hand Usain Bolt did nothing wrong or unethical to become tall. He just has "tall" genes (Our new science teacher Kate is cringing right now if she is reading this). But on the other hand there are sports that do norm by physical characteristics. Wrestling has weight classes. Most sports are divided by gender.
We also delved into some numerical analysis and constructed the following counter-factual. One hundred meters is 51 Usain Bolt body lengths long. What if instead of running 100 meters all other competitors instead ran 51 body lengths. Would Usain Bolt still have won? Ask them.
This week middle schoolers will be running their own races with Karen in physical education. They will record their times and their heights. Will the same person who won the unadjusted race still be the winner if race distances were proportional to their height? We'll find out.
Who is really the fastest? What is the proper and relevant benchmark?
If you are feeling especially adventurous you may want to extend the conversation to other important examples of proportionality.
Should taxes be proportional to income? Are taxes like sales taxes and licenses plate fees fair? Are they properly normed with respect to "ability to pay"?
And, of course, shouldn't the largest person in the family also get the largest piece of pie? I know the other Dads at Kazoo School are with me on this one.
