Teaching complexity
Almost every subject is complicated if you go deeply enough into it. Where do you stop teaching?
A topic that pops up briefly in secondary school general science courses, and gets slightly more coverage in introductory Astronomy courses, is the tides. The periodic up and down of the sea is connected to the Moon and is normally explained by the weakening of gravity with distance from a mass. That is, the near side of the Earth to the Moon feels a slightly greater gravitational attraction than the center, so water is drawn into a bulge on the Moonward side. Conversely, the anti-Moon side feels a weaker force, so the Earth is drawn away from the water, and again we have a bulge. For most off-earth astronomical applications this is almost all we need, and any complexity comes from the mathematics of treating how objects deform under tidal forces.
But sailors know that it’s not anywhere near that simple. From the picture, any port should have two high tides a (lunar) day, one higher than the other depending on the latitude and declination of the Moon, and high tides should arrive a bit earlier than the Moon is highest overhead, the water being carried around by the rotation of the Earth. Few places fit this picture. Some places have two unequal high tides and two low tides each lunar day; but by no means all. Some only have one of each. And the relationship between the transit of the Moon and the arrival of high tide is highly variable from place to place. As a first step toward predicting the tides (a vital practical problem) mariners worked out the “establishment of the port,” the time difference between transit and high tide.
A great deal of progress was made in tidal predictions during the nineteenth century, not really from any application of the theory of gravity but from a recognition that periodic phenomena were involved. From measurements of the tide at a place over a long enough time, the signal could be broken down into Fourier modes of various frequencies, and then reconstructed into the future. Advanced Physics textbooks of a century ago would give details of the procedure; nowadays it hardly rates a mention, since it’s essentially a solved problem and there’s a lot of new ground to cover.
Such an empirical solution, however, doesn’t really advance our understanding. For instance, why is the Mediterranean Sea almost tideless, while the North Sea (a smaller body of water) has strong and sometimes dangerous tides? The subject quickly becomes that of working out the response of a nonlinear system to several forcing factors, which is hard. Here is an analogy: suppose you have a salad bowl half-full of water in your hands. If you shake it very quickly, you’ll raise tiny waves on its surface but the bulk will not move. If you shift it very slowly, all the water moves with the bowl. In between there is a resonant frequency (maybe more than one) at which most of the water sloshes out onto the floor. Working out the equivalent details for all the ocean basins of the world is challenging, to say the least.
At the moment we teach tides in two incompatible ways. There is the simple lunar-bulge picture, for secondary school science; and the complicated tide tables for each port, for practical use. There’s probably no point in going further, except for a small band of specialists. But how many people along the way have noticed that these don’t agree?
