It is widely believed, and taught in Physics courses, that two high tides of equal magnitude occur daily. In reality, the tides are a complicated sloshing of the oceans with three main periods: M2 (12.82h) due to the Moon, S2 (12h) due to the Sun, and K1 (23.93h) due to both and to the tilt of the Earth's axis. Following Newton, one can compute the magnitude of the tidal forces, but an understanding of tide dynamics, based on the work of Laplace and Lord Kelvin, is incomplete even today. Over most coastlines M2 is dominant, but in New Orleans, for instance, there is only one high tide each day. In the North Atlantic, the M2 tide runs up the European coast and down the American coast, circling a mid-Ocean point of zero amplitude. This "amphidromic" behavior is seen in many basins, and is due to the Coriolis force acting on tidal currents. Thus, the ocean tides are a direct proof of the Earth's rotation, as Galileo maintained. In fact, his kinematic theory of the "ebb and flow of the waters", based on the Copernican motions of Earth, Sun and Moon, is basically correct, although incomplete. An accurate global picture of tidal amplitudes (but not yet of tidal currents) has been obtained by GPS satellites, and is in turn relevant to space age science and technology.