Joho the BlogPredicting the tides based on purposefully false models - Joho the Blog

Predicting the tides based on purposefully false models

Newton showed that the tides are produced by the gravitational pull of the moon and the Sun. But, as a 1914 article in Scientific American pointed out, if you want any degree of accuracy, you have to deal with the fact that “the earth is not a perfect sphere, it isn’t covered with water to a uniform­ form depth, it has many continents and islands and sea passages of peculiar shapes and depths, the earth does not travel about the sun in a circular path, and earth, sun and moon are not always in line. The result is that two tides are rarely the same for the same place twice running, and that tides dif­fer from each other enormously in both times and in amplitude.”

So, we instead built a machine of brass, steel and mahogany. And instead of trying to understand each of the variables, Lord Kelvin postulated “a very respectable number” of fictitious suns and moons in various positions over the earth, moving in unrealistically perfect circular orbits, to account for the known risings and fallings of the tide, averaging readings to remove unpredictable variations caused by weather and “freshets.” Knowing the outcomes, he would nudge a sun or moon’s position, or add a new sun or moon, in order to get the results to conform to what we know to be the actual tidal measurements. If adding sea serpents would have helped, presumably Lord Kelvin would have included them as well.

The first mechanical tide-predicting machines using these heuristics were made in England. In 1881, one was created in the United States that was used by the Coast and Geodetic Survey for twenty-seven years.

Then, in 1914, it was replaced by a 15,000-piece machine that took “account of thirty-seven factors or components of a tide” (I wish I knew what that means) and predicted the tide at any hour. It also printed out the information rather than requiring a human to transcribe it from dials. “Unlike the human brain, this one cannot make a mistake.”

This new model was more accurate, with greater temporal resolution. But it got that way by giving up on predicting the actual tide, which might vary because of the weather. We simply accept the unpredictability of what we shall for the moment call “reality.” That’s how we manage in a world governed by uniform laws operating on unpredictably complex systems.

It is also a model that uses the known major causes of average tides — the gravitational effects of the sun and moon — but that feels fine about fictionalizing the model until it provides realistic results. This makes the model incapable of being interrogated about the actual causes of the tide, although we can tinker with it to correct inaccuracies. In this there is a very rough analogy — and some disanalogies — with some instances of machine learning.

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