Models vs. Reality

A little-known change in the attempt to learn about nature happened, in a sense, several hundred years ago. People replaced Natural Philosophy with mathematical Science, in which the attempt to know what nature is was replaced with mathematical models of nature which can predict measurable aspects of nature.

The difference between these two things is that a model may, possibly, tell you about what the underlying reality is. On the other hand, it may not. Models can be accurate entirely by accident.

Trivial examples are always easier, so consider the following model of how often Richard Dawkins is eaten by an alligator, where f is the number of times he’s been eaten by an alligator and t is the time (in the sense of precise date):

f(t) = 0

This model is accurate to more than 200 decimal places. If you conclude from this model that Richard Dawkins is alligator-proof and throw him in an alligator pit to enjoy the spectacle of frustrated alligators, you will be very sadly mistaken. But it’s so accurate!

This is of course a silly example; no one would ever confuse this model or its accuracy for a full description of reality. However, there’s a very interesting story from astronomy where people did exactly that.

I’m speaking, in particular, of the long-running Ptolemaic model of the planets and its eventual overthrow of the Copernican model. The Ptolemaic model was the one where the earth was at the center of the solar system and the planets traveled in cycles and epicycles around it. The thing about this model is that it was actually extremely accurate in its predictions.

(If you’re wondering how it could be so accurate while being so wrong, the thing you have to realize is that Special Relativity actually means that it’s just fine for the earth to be taken as the center of the coordinate. The math just gets harder for some calculations; this is basically what happened. The Ptolemaic model was, basically, a close approximation of that more complicated math.)

However, there is a yet simpler example of incorrect models producing correct results: just consider, for two minutes, that for most of history everyone believed that the Sun orbited the earth and yet they still had highly accurate calendars. Despite not thinking of a year as the time the earth takes to orbit the Sun they nevertheless recorded the years and predicted the solstices with great precision.

Incidentally, if you’re interested in a full history of the shift from the Earth being the center of the solar system to the Sun being at the center, be sure to read the extraordinarily good series of articles by TOF, The Great Ptolemaic Smackdown (originally published in Analog magazine). It is very well worth your time.

One thought on “Models vs. Reality

  1. Mary

    As one of my college professors explained, the Ptolemaic system is basically a Fourier series. And as we had all learned already, ANYTHING can be approximated to any desired (finite) accuracy by a Fourier series.

    Like

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