Coding classes in Cheshire

Jodrell Bank's Crab Pulsar Monthly Ephemeris is a plain text file anyone can download. Each line gives a date and the pulsar's spin rate in turns per second, measured to ten decimal places, plus the observatory's own figure for how fast that rate is falling. The learner reads the 482 dated lines from 15 May 1988 to 24 July 2026, then, for each neighbouring pair, subtracts the spin rates and divides by the seconds between the dates. That is a finite difference, the simplest possible estimate of a derivative, and it can be checked, because Jodrell publishes the answer.

The first result is reassuring: a one-line calculation, done by a learner, agrees with a world-class observatory to about one part in a hundred thousand. The fourth is the interesting failure. For one week in November 2017 our finite difference disagrees by 6.6 per cent, because the pulsar abruptly sped up, an event astronomers call a glitch. A derivative estimated across a sudden jump is not a derivative at all, and a learner who plots the differences sees the glitch stand out like a spike.

The last two rows are the deepest lesson. Astronomers use a simple formula, spin rate divided by twice the spin-down rate, to estimate a pulsar's age from its slowdown alone. For the Crab it gives 1,279 years. But NASA records the supernova that made it in 1054, only 972 years ago. The formula assumes the star was born spinning far faster and has always braked in one particular way; the mismatch says at least one assumption is wrong. Even stranger, the estimate got older by 24 years during a 38-year record. A model is useful exactly when you know where it fails.

So a Cheshire teenager should learn to code in 2026, a short drive from the Lovell Telescope, to be able to test a formula against reality rather than repeat it. The longer argument is in why teenagers should still learn to code in 2026.