While my title line might seem dramatic, I want to be clear that this post is not intended as a criticism of Kepler, or of Kepler’s laws. Rather, it is critical of the view that scientific laws are true descriptions of the world. This post is intended as part of my series on how science works. My aim is to describe my own understanding of Kepler’s laws.
The basis of Kepler’s laws
In case some of my readers are not familiar with them, Kepler’s laws are an attempt to account for the motion of the planets in our solar system. Kepler’s laws were preceded by the Ptolemaic idea that the planets moved in cycles and epicycles. Galileo argued, instead for the idea of Copernicus, that the planets traveled in circular paths around the sun. I presume that Kepler was looking for something a little more precise than the Copernican circles.
I am not an historian, so most of what I “know” about Kepler is guess work. He had rather good data about the planets, acquired by Tycho Brahe (and by Kepler himself). My assumption has long been that he plotted the known data, and tried to fit curves to that data.
The under-determination problem
There’s a general problem of under-determination. Given a finite number of data points, there are infinitely many curves that pass through those data points. Of all of the possible curves, why did Kepler pick an ellipse? That has puzzled me since my days in high school. My assumption then, and now, was that it partly a guess by Kepler, and that it was partly the relative mathematical simplicity of the ellipse as a curve. While not quite as simple as the circle, it is not a lot more complex.
These days, we can mathematically derive Kepler’s laws from Newtonian mechanics (including Newton’s law of gravitation). But Kepler did not know that, for Newton’s law of gravity was not known at the time. Newton used Kepler’s laws as part of his motivation for an inverse square law. So if Kepler was guessing, then he made an excellent guess.
Why say that Kepler’s laws are false?
For Kepler’s laws to be true, the motions of actual planets should all be in accordance with those laws. In terms of plotting the observations on a graph, all observations should be exactly on the appropriate elliptic path. They are not. It must have already been obvious to Kepler, that his laws were not an exact fit, that they were at best a pretty good approximation.
Even from a theoretical point of view, we can see that Kepler’s laws are at best an approximation. When we derive Kepler’s laws from Newtonian mechanics, we are solving the two-body problem. That is, we are determining the path of a single planet around the sun, and ignoring the effects of the other planets. So we would naturally expect the results to be not quite right. That is, we would expect them to be technically false, though a good approximation.
Predictions
Kepler’s laws are useful for making predictions of planetary motion. Observations of a planet can determine its Keplerian orbit, and from that we can compute its future path. That the laws are false indicates only that the predictions won’t be perfect. They can still be very good.
The Ptolemaic astronomers used their cycles and epicycles to predict. The Copernican circular paths could also be used for prediction. It was easier to predict using Copernican methods, because of the simpler mathematics. However, it has been argued that the Ptolmaic method made better predictions.
Prediction using Kepler’s laws is only slightly more difficult than using Copernican methods, and is far easier than using the Ptolemaic methods. And prediction with Kepler’s laws give very good results.
Perturbations
Astronomers make observations (or measurements) of planets. And, in those observations, they report the computed Keplerian orbit and the perturbation (or deviation) from that computed orbit. That Kepler’s laws are imperfect does not prevent astronomers from making accurate observations. It merely means that they need to record the perturbations, in addition to the orbital position.
Why does this matter
There’s a tendency of philosophers to look at every statement as if a proposition, and to consider the truth of propositions, viewed as descriptive of the world, as their most important attribute. My aim, in this post, is to point out that descriptive truth is not a requirement for scientific theories. We value theories as tools that we can use in making predictions and in theorizing. We also value mathematical simplicity, even if that simplicity requires some departure from truth. For mathematical simplicity makes laws easier to use.
My own preference is to say that scientific laws are neither true nor false. They are not propositions, they are tools for prediction and theorizing. Our acceptance of laws (and of theories) is based on their pragmatic value, rather than on their truth.
A note on creationism
The creationists and ID proponents are repeatedly claiming to have refuted the theory of evolution. It is a pointless game. If there is horizontal gene transfer (and there does not seem much doubt about that), then common descent is false on a technicality. Biologists are not at all deterred by such nit picking. They value the theory of evolution on pragmatic grounds. If it is false on some technicality, that is no more a problem for evolutionary biology, than is the technical falsity of Kepler’s laws a problem for astronomy.
The Heretical Philosopher 