HSW – Kepler’s laws are false

by Neil Rickert

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.

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4 Responses to “HSW – Kepler’s laws are false”

  1. “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. ”

    I agree that scientific laws are not “true” descriptions, depending on how we define truth (or at least they can not be known whether or not they are true). Truth is one of those terms that, depending on how we define it, is supposed to have some ideal correlation with the noumenon (as Kant put it), or it may be used within the context of logic, in which case something can be proven to be true depending on our premises, propositions, and exclusion of contradictions. In the case of descriptions, in order to be proven true, the definitions of terms used within the premises have to be agreed upon which is usually not the case.

    I do however see scientific laws as descriptions of the world, even if they are imperfect ones. They are pragmatic descriptions of how we see the world working. Just as I can point to a “chair” and describe its properties (even if those descriptions are incomplete, qualitative, subjective, etc.), I can also point to the world and describe its properties (through approximate laws of motion, etc.). My description of the chair is incomplete and based on pragmatic approximations from our observations, just as my description of the world’s motion may be an approximation based on my observations — they are still both descriptions either way. The chair doesn’t even have a finite number of atoms and is constantly exchanging atoms with the environment (atoms from trees, excretory waste, apples, etc.). Even after this consideration, it is for pragmatic reasons that we use the term “chair”, rather than saying “mostly chair”, etc., and describe its properties with the same pragmatic considerations.

    “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.”

    I still see all scientific theories as a type of description and one that we may say “has some truth”, not that they are objectively true by any means, but simply because they have some correlation with the observations we witness first hand. Just as describing a chair as being “made out of wood” (when it may contain atoms or molecules from things other than wood) isn’t a completely “true” description, we still say that the statement about the chair being “made out of wood” in fact has “some truth” because it does in fact contain mostly wood. It is an approximation, and is just as true a description as scientific theories are (in my opinion). Now this “some truth” claim is merely a pragmatic measure because there is some truth, based on the common way people use the term (i.e. saying the chair is “made out of wood” isn’t completely false because it is mostly made out of wood). When people form scientific laws and theories, the same thing is going on, where the theory and what it tells us isn’t 100% false, that is, those theories generally have SOME correlation with our observations which can make them “true for all practical purposes”. That is a contingency indeed, but a pragmatic one that we can equate with our descriptions of anything in the world around us. So I agree that scientific theories aren’t true descriptions of the world just as I don’t believe that any description of anything is a “true description”. This just means that we can’t describe anything in a true way, not merely that scientific theories are excluded from truth.

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    • I do however see scientific laws as descriptions of the world, even if they are imperfect ones.

      I hope it was obvious that I do not see laws that way.

      When scientists make actual observations (as with measurements), those are descriptions. But why would scientists care about having a broad description (which is what laws would be if they were intended as descriptions)? Wouldn’t scientists leave the broad descriptions to the poets and others?

      I see scientific laws as methodological tools. I perhaps should have cited Nancy Cartwright: “How the Laws of Physics Lie.”

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      • “I hope it was obvious that I do not see laws that way.”

        Yes it was.

        “When scientists make actual observations (as with measurements), those are descriptions. But why would scientists care about having a broad description (which is what laws would be if they were intended as descriptions)? ”

        Measurements are just a more fundamental type of description. For example I could try to measure a chair in terms of all its dimensions, or I could even try to measure what percentage of the woodgrain absorbs particular wavelengths of light. Those are very quantitative and specific descriptions of the chair. On the other hand, if I say that “the chair is brown”, by simply looking at it, this is a much less specific description (it is an approximation of the color or the average color seen), but it is a description nevertheless. One is a more general/broad categorical description of sorts where the other is extremely quantitative and specific. This is why I see observations as specific descriptions of phenomena, and scientific laws as a different type of (as well as broader/ more generalized) description of the same phenomena. I could apply the generalization “all wood from oak trees is a shade of brown”, therefore, all chairs made from this wood can be called brown. It may be the case that “brown” isn’t specific enough to differentiate between one similar looking chair and another, just as Kepler’s laws aren’t correct enough to differentiate between two similar binary star systems, even if their motion is quantitatively different. But “brown” does a decent job describing the chairs made from oak (in one way), just as Kepler’s laws do a decent job describing general planetary motion (in a mathematical way). Kepler’s laws are meant (in my opinion) to describe planetary motion in a general way with which we can apply to many different circumstances. Calling an oak chair “brown” is likewise a decent way of describing the average color of light reflected off of most if not all chairs made of oak.

        “Wouldn’t scientists leave the broad description to the poets and others?”

        When we are talking about scientific laws, we aren’t talking simply about subjective hyperbole, etc. We are talking about a different type of quantitative description. Kepler’s laws are not analogous to calling the Sun “a beautiful shade of yellow”, but rather “the Sun and planet Earth appear to move in this pattern approximately described by these equations”. In line with your perspective, I see that some subjective descriptions do make their way into science and we should be careful not to confuse these with legitimate objective (quantitative) descriptions. It is those subjective descriptions that should be left to the poets and others. But it seems to me that scientific laws, just like the data they help describe (in a broader way), are descriptions. They are just different types of descriptions. Measurements describe specific instances of what we observe, and laws and models approximately describe large amounts of data (and/or patterns seen in that data). Some descriptions are better approximations than others, and some are more useful than others (mathematically or otherwise). This is the way I see it.

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