counting up

I am fascinated by the use of the number zero as a relative quantity as opposed to an absolute quantity. Following a recent unit on operations with integers, I engaged my seventh graders in a discussion about ways in which we use zero not to signify the absence of any thing, but rather to simply assign a starting point for counting.

One familiar example involves temperature: 0 degrees Fahrenheit, 0 degrees Celsius, and 0 Kelvin. How confusing is this: three different temperatures, each having a zero point, mean different things!* For those students working with quadratic equations, it's not uncommon to set some nonzero height equal to zero in order to simplify the problem.

Time provides yet another case: we use zero to indicate the commencement of some event (t=0). We often think of the seconds leading up to a rocket launch as a count-down: ten, nine, eight.... However, this is actually shorthand for T-minus-ten, T-minus-nine, T-minus-eight, ... , in which T, representing the time of launch, takes place at T=0. The engineers are actually counting up, using negative numbers leading up to zero!

As I discussed the count-down (which is actually a count-up) with my students, I made a connection that I had never noticed before. In our daily lives, we count up all the time! How do we indicate to everyone that it's time to starting singing "Happy Birthday" to the party honoree? One, two, three. Happy birthday... How do we coordinate a group's efforts to lift a heavy object? One, two, three. Lift.

Contrary to intuition, we decide to start our event at four in these two cases! How did this practice evolve, such that our count-down actually involves a count-up, the event taking place when we reach an arbitrary number that we never consciously consider a starting point?

* This example of temperature differs from other cases in which we deal with a change of units. With length, weight, volume, etc., zero indicates nothingness across all units.