#### Kepler and the Art of Astrophysical Inference

I recently discovered iTunesU, and I have to confess, I find it utterly fascinating. By golly, it is everything that they promised us that the internet would be. Informative, entertaining, *and* educational. What are the odds?!? Anyway, while poking around the myriad lectures, courses, and talks that are now online, I came across a popular Physics lecture series at UMichigan which listed a talk by one of my favorite speakers, Owen Gingerich. He had spoken about The Four Myths of the Copernican Revolution last November. It was, how shall we say, *riveting*.

Owen talks in detail about how the Copernican model came to supplant the Ptolemaic model. In particular, he describes how Kepler went from Ptolemaic epicycles to elliptical orbits. Contrary to general impression, Kepler *did not* fit ellipses to Tycho Brahe’s observations of Mars. The ellipticity is far too small for it to be fittable! But rather, he used logical reasoning to first offset Earth’s epicyle away from the center in order to avoid the so-called Martian Catastrophe, and then used the phenomenological constraint of the law of equal areas to infer that the path must be an ellipse.

This process, along with Galileo’s advocacy for the heliocentric system, demonstrates a telling fact about how Astrophysics is done in practice. Hyunsook once lamented that astronomers seem to be rather trigger happy with correlations and regressions, and everyone knows they don’t constitute proof of anything, so why do they do it? Owen says about 39 1/2 minutes into the lecture:

Here we have the fourth of the myths, that Galileo’s telescopic observations finally

provedthe motion of the earth and thereby, at last, established the truth of the Copernican system.

What I want to assure you is that, in general, science does not operate by proofs. You hear that an awful lot, about science looking for propositions that can be falsified, that proof plays this big role.. uh-uh. It is

coherenceof explanation, understanding things that are well-knit together; the broader the framework of knitting the things together, the more we are able to believe it.

Exactly! We build models, often with little justification in terms of experimental proof, and muddle along trying to make it fit into a coherent narrative. This is why statistics is looked upon with suspicion among astronomers, and why for centuries our mantra has been *“if it takes statistics to prove it, it isn’t real!”*

## hlee:

Replying to the last sentence, not to exaggerate, but to amuse, astronomers care best fits and error bars more than statisticians and the statement seems to imply all the efforts to get best fits and errors are unrealistic. The idea of proving is interpreted in different ways, I guess. What I go against is using a statistic to prove empirical laws like the law of equal areas without comprehending the fundamentals of the statistic, which explains astronomers’ suspicion if we change the direction of our view points. In my opinion, it is not a fault of statistics but the people who use it inappropriately. Speaking of best fits and error bars, from the tree growing point of view, the method of growing trees receives more attention than estimating errors. Statisticians do care finding laws (best ways to grow a tree) that represent the truth of the nature. (Note: tree = classification tree or regression). Not knowing detailed history (haven’t listened Prof. Gingerich’s talk but I will soon), I’m very opinionated but one thing I’m sure is that in migration, adaption happens but not necessarily it reflects its origin. Selective mutation is what I’m afraid of.

04-17-2008, 3:42 pm## vlk:

Oh I definitely did not mean to imply that hypothesis tests and principled statistical calculations and the like are useless. Without a rigorous assessment of whatever-it-is, there is no science, and everything becomes an opinion. The point that Owen was making is simply that astronomers (and scientists in general) tend to make progress based on a coherent “story” without waiting for a formal Kuhnian revolution, and usually when a final proof of a worldview does arrive, it is rather anti-climactic (he refers to Foucalt’s pendulum as an example). Think of it as continuously updating your priors to make it narrower and narrower until at long last it becomes a delta function. So you can see how a marginal result along the way has little effect on the believability of the model.

04-17-2008, 4:26 pm## aneta:

I like the VLK image of the priors becoming a delta function! this is then certainty! do we have such things in astronomy?

04-17-2008, 9:55 pm## vlk:

Good point, Aneta. I was going to respond, using the original example, that now we know with certainty that the Earth rotates, so that is an example of a prior that has become a delta function. But of course it is conditional on Newtonian mechanics and Einsteinian relativity, so strictly speaking it isn’t a prior! Oh well, like they say, if you push an analogy, it can fall off the edge of the world!

04-17-2008, 11:55 pm