Coding classes in Norfolk

Suppose a turbine slows the wind passing through it by a fraction a. The standard formula for the share of the wind's power an ideal rotor can capture is 4a(1 − a)². Slow the air too little and most of it passes straight through; slow it too much and it backs up. Somewhere between 0 and a half is a sweet spot, and the learner's job is to find it by trying values of a, counting every try. Calculus gives the answer as a third, with a share of 16/27, about 59.3 per cent, known as the Betz limit. The program should reach the same answer without it.

The simple approach tries a value every so often across the range and keeps the largest. It works, but each extra digit of precision multiplies the work by ten. Ternary search is smarter: it tries two points, throws away the third of the range that cannot contain the top, and repeats. Golden-section search does the same but places its two points at the golden ratio, about 0.618, so that one of them can be reused next round. It needs only one new try per step, and it found a = 0.333333 and a share of 0.592593 after 30 tries, against 500,001 for the list of guesses.

Now the trap. Both clever searches assume the curve has a single peak. The learner draws an invented curve with two hills, a lower one of height 1.0 near 0.2 and a higher one of 1.3 near 0.75, and runs golden-section search over the whole range. It returns 0.2, the lower hill, and reports it with complete confidence. Nothing in the answer warns that a better peak exists. The fast method is only as good as the assumption behind it, and checking that assumption is part of the job.

So a young person in Norfolk should learn to code in 2026 to understand when a fast answer can be trusted. The longer argument is in why teenagers should still learn to code in 2026.