The Microscope Equation

Abstract

If we are in a car and we look at the speedometer and it says we are traveling 60 mph, then about how far will we travel in the next minute? 30 seconds? Two minutes? Traveling at 60 mph is the same as a rate of 1 mile per minute and we would answer one mile, a half a mile, and two miles, but we should recognize that in our responses we are assuming the speed is constant. These answers are approximations as we might speed up or slow down, but unless our change in speed is drastic, say slamming on the breaks, the results are likely reasonably close or, in other words, a good estimate. On the other hand, if we wanted to estimate how far we travel over the next hour we would say 60 miles, but we would recognize that this response may not be great as our speed may well change over the course of an hour. Our reasoning here is formalized as the microscope equation in M-Box 7.1.