Q1.
Suppose you ride a bicycle from your school to your home. You want to model the time it takes to go home from school. What details would you keep? What details could you ignore? Suggest why ignoring some details may actually be useful.
Answer
The model only has to produce one number — the time t — so keep every quantity that changes t by more than a minute or two, and drop the rest.
| Keep | Effect on the time | Ignore |
|---|---|---|
| Distance from school to home | t grows in direct proportion to it | Colour and make of the cycle |
| Your average cycling speed | t is inversely proportional to it | What you are wearing |
| Number and length of stops (signals, level crossing) | Adds a few minutes directly | Each individual pothole |
| Slope of the road, strong headwind | Changes the average speed by 10–20% | Songs playing in your head |
A worked model for a 3 km ride at an average 12 km h⁻¹ with two signals of about 90 s each:
riding time = distance / average speed
= 3 km / 12 km h⁻¹ = 0.25 h = 15 min
waiting time = 2 × 90 s = 180 s = 3 min
total time t = 15 min + 3 min = 18 min
= 3 km / 12 km h⁻¹ = 0.25 h = 15 min
waiting time = 2 × 90 s = 180 s = 3 min
total time t = 15 min + 3 min = 18 min
Why ignoring details is useful: three reasons, and all three matter.
- You can actually measure what is left. Distance and average speed can be found with an odometer and a watch. The exact wind at every metre of the road cannot be — a model that needs unmeasurable inputs gives no answer at all.
- The ignored details are smaller than the natural scatter. Your own riding time varies by two or three minutes from day to day. A detail that changes the answer by ten seconds is buried inside that scatter, so including it cannot make the prediction better.
- A simple model can be tested and corrected. Time yourself for a week. If the real time is always 22 min and not 18 min, you know exactly one thing is wrong — most likely the assumed speed — and you can fix it. In a model with twenty inputs you would not know which one to blame.
Try this: ride the same route on a holiday, when there is no traffic. If your time falls to about 15 min, the stops term in the model is confirmed. That is a model being tested against observation — the same procedure a scientist uses.