Science Puzzle
The Puppy That Would Outgrow the House
Sam weighs their new Labrador puppy. At 8 weeks old it weighs 6 kg; at 16 weeks it weighs 15 kg. It's putting on just over a kilogram a week.
Sam draws a straight line through the two points and carries it on. By the dog's 10th birthday, the line reaches about 580 kg, heavier than most horses. Sam's arithmetic is correct. So what's wrong with the prediction?
The Answer
Sam has extrapolated: stretched a pattern far beyond the data it came from and assumed it carries on unchanged.
The straight line fits the two weigh-ins perfectly, but it only describes how the puppy grew between 8 and 16 weeks. Puppies, like people, grow fastest when they're young. Growth then slows and stops. A Labrador reaches its adult weight, usually around 25 to 36 kg, by about a year to 18 months old. After that its weight stays roughly steady. A graph of real growth rises steeply and then levels off into a flat line.
Extrapolation causes trouble wherever a trend is pushed past its data. The writer Mark Twain once joked that because the lower Mississippi River had been getting shorter, a steady trend would mean it had once stuck out over the Gulf of Mexico like a fishing rod. In 2004, researchers drew straight lines through Olympic 100 metre winning times and predicted that women would overtake men in 2156. Critics pointed out that the same lines, followed far enough, would have sprinters finishing before the starting gun.
A trend is a good guide close to the data it came from. The further you push it, the more you need a reason to believe nothing will change.
The principle: The danger of extrapolation. A pattern found within a range of data may not hold outside it, so predictions far beyond the measurements need extra evidence that the pattern continues.