Coding classes in Dorset

A radioactive clock works by halving. After one half-life, half the original atoms are left; after two, a quarter; after n half-lives, one half raised to the power n. The International Atomic Energy Agency's LiveChart database publishes the half-lives: carbon-14 5,700 years, potassium-40 1.248 billion years, uranium-235 704 million years, uranium-238 4.468 billion years. The learner writes one function and asks what fraction of each would remain in a rock 150 million years old, an age we chose for teaching.

Carbon-14 is the first surprise. After 26,316 halvings, the fraction left has almost eight thousand zeros after the decimal point, and Python's ordinary floating-point numbers cannot store anything that small: they give up after roughly a thousand halvings and print exactly 0.0. The answer is not zero, but the computer says it is. Working with logarithms instead keeps the true size of the number. It also makes the geology obvious: carbon-14 falls to one part in a thousand after 56,805 years, so it cannot date anything older than that, let alone a rock from the age of the dinosaurs.

The second surprise is about the other clocks. Suppose a laboratory measures the fraction left but gets it 1 per cent wrong. Working backwards from uranium-238, the age of our 150-million-year-old rock would come out anywhere from 86 to 215 million years, because so little of it has decayed that a small error in the fraction is a huge error in the age. Uranium-235, which has gone through about a fifth of a half-life, gives 140 to 160 million years for the same 1 per cent error. The most useful clock is the one whose half-life is not too far from the age being measured.

So a Dorset teenager should learn to code in 2026 to know when a computer's exact-looking answer is really just the edge of what it can represent. The longer argument is in why teenagers should still learn to code in 2026.