Inventing The Tiring Index

Over the weekend at the PhysTEC conference, I participate in a very fun workshop on using invention tasks to help students engage in proportional reasoning in physics. One of my favorite tasks from the workshop was trying to invent an “inefficiency index” for companies that wash cars, taking a certain amount of people a certain amount of time to wash a single car.

Today, while running with my dog Rudi, I invented the “tiring index”

I was running and getting tired, and started to think, “How tired am I getting?” Anyway, while running, I started to imagine myself running a 5-min mile in the first mile, then a 7-min mile in the next, and then a 9-minute mile in the third. And I wondered if I could quantify how tired that person was getting.

So I invented, the “tiring index”. This person’s tiring index would +2 , or 2 min/mile per mile, because they are taking an extra 2 minute per mile every mile.

Then, I got to thinking about what a negative tiring index would mean. Well, I thought about a person who starts off running a 10-minute mile, but then they run a 9-minute mile, and then a 8-minute mile. This person isn’t tiring at all. In fact, it’s quite the opposite, which is their tiring index would be -1 or  -1 min/mile every mile, or -1 min/mi²

I have learned that inventing indexes is really fun.

Now, I’m thinking about whether the tiring index should be a percentage of the pace rather than a linear rate, and I’m wondering what the “tiring index” is for normal people who run. And I’m really curious… Like, what’s the tiring index for a ball thrown in the air? It can’t be constant. And now I have to eat dinner… ah!

We should all be inventing more indexes… all the time, and being curious about them.