Coding classes in Clackmannanshire

The model is invented, not the Fishcross engine. A 10 metre beam pivots at its middle and is cast thicker at one end, so its mass per metre rises steadily from 1 to 2 tonnes. The learner finds its centre of mass two ways: by slicing it into 100,000 thin pieces and adding up each piece's mass times its position, and by the exact formula from calculus. Both give a total of 15 tonnes balancing at 5.5556 metres from the lighter end. A numerical answer and an exact one that agree to four places is a good sign both are right.

Now the loads: 12 tonnes hanging half a metre from one end, where the pump rods would be, and 3 tonnes half a metre from the other. Each load turns the beam with a moment, its mass times its distance from the pivot, and the moments do not cancel: the pump end is heavier by 32.2 tonne-metres. Where should a 4 tonne counterweight go to balance it? The formula answers instantly: 13.04 metres from the pump end. But the beam is only 10 metres long.

The lesson is about checking answers against reality. Algebra happily returned a position that does not exist. A search method did something worse: bisection, which halves a range until it finds where the moments cancel, was told to look between the pivot and the end of the beam and quietly returned 10 metres, the end itself, because the moments never changed sign in that range. A program that reports "10 metres" with no warning is more dangerous than one that crashes. Good code checks that a solution exists before trusting the number it prints.

So a young person in Clackmannanshire should learn to code in 2026 to check that an answer can actually happen before trusting it. The longer argument is in why teenagers should still learn to code in 2026.