Give a constructive and a non-constructive explanation to a phenomenon

Thus the task is reversed: you have to find a suitable phenomenon!

Examples:

A famous phenomenon was the chess machine, which was demonstrated at the Viennese court in 1770.
The machine - if it was a machine - played excellent chess. And if it was a machine, I would of course know exactly what the machine was doing - at least in principle. I have no idea what goes on in a person when playing chess, I only have explanations in the form of machines.