Part 3/6:
Fermat's insight was that nature does not simply minimize distance, but rather minimizes the time it takes for light to travel. The constant n in Snell's Law turned out to be the ratio of the speeds of light in the two media.
The Principle of Least Action
Around 40 years after Bernoulli's solution, one of his students, Pierre Louis de Maupertuis, proposed an even more fundamental principle - the "principle of least action." Rather than time, Maupertuis claimed that nature minimizes a quantity he called "action," defined as mass times velocity times distance.