Count the gaps between readings, not the readings
- The idea
- Predict
- See it
- Why
- Check
The idea
“Four readings means the change happened four times.”
Each reading feels like a moment when something happened, so counting them seems fair. The first reading is only the starting point, though. Nothing has changed yet.
The short version
The mistake: Four readings means the change happened four times.
What's actually true: A stepwise change happens once per gap between readings, so four readings span only three steps.
- A stepwise change happens between readings. The readings are like fence posts, and the steps are the spaces between them.
- To count the steps, subtract the first time from the last and divide by the step size. From 0 to 60 minutes in 20-minute steps is 3 doublings.
- The same count works for generations, days of drift in a circadian rhythm, or 10 °C steps in temperature. From 15 to 35 °C is two steps.
On the exam: Count the gaps, not the readings. Last minus first, divided by the step size, gives the number of steps.