The Cycloid and Galileo's Science

In the case of the cycloid, it is undeniable that Galileo turned to empiricism precisely because he lacked the mathematical ability to tackle the problem any other way. In physics, this blatant shortcoming has been mistaken for methodological innovation. But in the case ofthe cycloid, we see its true colors. We see that it's a sign of failure rather than of genius. It is not science being born, it is science being down-the-down.