A theory more pleasing to the mind

For most of human history, the Earth was seen as the stationary center of the universe, with the sun, planets, and starry firmament circling around it at various speeds.  The ancient Greeks quickly managed to work out that the Earth was spherical but struggled to explain the motions of the heavens.

Eventually Eudoxus, a student of Plato, worked out a mathematical model involving concentric spheres, which the planets rode on around the Earth in perfect circles, with the outermost sphere being the firmament.  Aristotle took this model and posited as a physical one, with the spheres being crystalline orbs.

Several centuries later, Ptolemy worked out a fairly rigorous model based on these views that was mostly predictive of astronomical observations.  But while the Ptolemaic system worked, it was widely regarded as problematic, positing a lot of ugly conceptions, such as epicycles, to explain what was happening.

Early on, there were people who pointed out that changing some basic assumptions might simplify the model.  Aristarchus of Samos came up with a heliocentric model way back in the 3rd century BC, with the sun at the center and everything, including the Earth, revolving around it.  But heliocentrism didn’t seem to garner a substantial following among ancient astronomers.

When Copernicus developed his heliocentric model, he was careful to cite Aristarchus and other sources, to make sure that his readers knew there was ancient precedent for the idea, that it wasn’t something completely novel.  At his point in history, in the early 16th century, the completely new remained suspect, even after the discovery of the new world.

Copernicus was a mathematician and his model was rigorous, but it wasn’t without its own problems.  Copernicus retained the spheres and perfect circles, so he had to add his own kludgy anomalies, although these were seen as less severe than the ones in the Ptolemaic model.

In many ways, Copernicus’ model was no better than the Ptolemaic one at making predictions.  His primary justification for it was that the Ptolemaic system was a “monster”, and that his own model was, “more pleasing to the mind.”

Copernicus, fearing the ridicule his theory might provoke, held off publishing it until the end of his life, although he had circulated rough outlines of it earlier.  After publication, there wasn’t much ridicule.  There actually wasn’t much reaction at all.  Astronomers found his mathematics more elegant than Ptolemy’s and were happy to use his system, but most regarded his physics as a convenient fiction.

Throughout the 1500s, it’s estimated that there may only have been about a dozen astronomers in Europe who were convinced Copernicans.  Aside from the reasons noted above, heliocentrism was seen as simply absurd, too much of a departure from common sense.  And that was aside from the issue that it may have contradicted scripture.

And there remained many unanswered questions.  If the Earth moved, why didn’t everyone feel the movement?  Why weren’t birds in flight or clouds affected?  Ancient philosophy held that the element earth fell toward the center of the universe.  But if the Earth wasn’t at the center, then what caused things to fall toward it?  And if the Earth changed position throughout the year, why weren’t the stars seen to shift in relative position, to exhibit parallax?  Not having detectable parallax would mean they were incomprehensibly far away.

There would be weakening of the Ptolemaic system in the later part of the century.  Tycho Brahe, making more rigorous and precise naked eye observations than anyone had ever made before, discovered novas, indicating that the heavens could change, and observed comets that seemed to cross the location of the supposed spheres, implying the spheres didn’t really exist.  But these were issues for Copernicus’ models just as much as they were for Ptolemy’s.

Open minded astronomers continued to note Copernicus’ theory as an interesting, if somewhat bizarre speculation, but only a few adopted it.  The result is that in 1600, 57 years after its publication, Copernicus’ theory seemed in danger of going down the same path as Aristarchus’ earlier proposition, of being little more than a footnote of history.

Then the telescope was invented in 1608, and Galileo took the design, improved it, used it to look at the heavens in 1609, and published his results.  It was only at this point that the different predictions between the models could be tested.  Galileo’s observations were much more compatible with Copericanism.

Galileo would eventually get in trouble with the church for his subsequent advocacy of heliocentrism, but as the observations accumulated, the reality became increasingly undeniable.  Newton would eventually answer many of the lingering questions caused by the new model.  By then, virtually all astronomers were Copernicans.

What interests me about this story is, what could people in the 1500s have done to better assess the Copernican model?  In 1543, when it was published, it amounted to an alternate theory that largely made the same observable predictions as the existing one.  It didn’t really make fewer assumptions than the Ptolemaic one, so parsimony (Occam’s razor) wasn’t much of a guide.

The main thing it seemed to have going for it was it’s more convenient mathematics.  Everyone acknowledged its mathematical elegance early on.  And many astronomers seemed willing to use those mathematics, even while not accepting the implied reality.  A preface added to Copernicus’ book, although not written by Copernicus himself, even suggested that approach.

It wouldn’t be the last time in science that someone said, “Don’t worry.  This is just a mathematical convenience, an accounting gimmick.  It’s not like this crazy thing is true.”  Max Planck used a similar line when he discovered that quantizing energy made his calculations work, which eventually turned out to be the basis for quantum physics.  And I think of Chad Orzel’s recommendation that we not think of Everett’s many worlds as real, just take them as metaphor, an accounting device.

Of course, it’s important to remember the misses as well as the hits.  In recent years we’ve had theories with elegant mathematics that eventually didn’t turn out to be reality.  The LHC reportedly has eaten a lot of such theories.  Although an argument could be made that those theories started much further from empirical motivations than the successful ones above.  Admittedly, this is a subjective standard.

All of which is to say, judging the plausibility of rigorous theories is far from simple.

What do you think?  Was there some standard early modern astronomers could have used to better judge Copernicus’ theory?  Or do we simply have accept that our ability to assess many speculative theories is limited until actual empirical data becomes available?

11 thoughts on “A theory more pleasing to the mind

  1. It wasn’t a standard that was missing, it was engaged minds communicating. What many people who ask questions that start “Why hasn’t science …” fail to realize is that the numbers of people engaged in any type of scientific endeavor were quite few and mostly isolated. I few communicated via written letters and through published books.

    When Newton published his magnus opus, there were very few people who could read it first, and understand it second. Same was true for Einstein, but by then the number of people engaged in any scientific pursuit had expanded greatly.

    The early astronomers who were productive all had wealthy patrons and the desire to attract such drove most of these early scientists as much as the science itself. Same is true today: scientists have to eat. (This is an argument in support of publicly funded science because in its absence all of the science will be owned by the wealthy.)

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  2. Heh. I just mentioned that reality is like entropy — it always wins in the end.

    Without data, it’s just metaphysics and arguments. About the only argument I can think of that might parse Copernicus from Ptolemy is an appeal to external realism and rejection of self-centric models. (Which, BTW, is why I tend to reject idealism. I see it as Ptolemaic.) Call it kind of an early version of the anthropic argument.

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    1. I actually meant to note the self-centric aspect in the post. Dang!

      But definitely. If the reason a theory appeals to us is that it affirms our importance, we need to be on guard. Likewise, if the reason we’re resistant to a theory is it seems to make us less significant. we also need to be on guard. That doesn’t mean the self affirming option is guaranteed to be wrong, but in the absence of other evidence or logic, it probably is.

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  3. Why is “the element earth is attracted to Earth” any less plausible than “…to the center of the universe”? You don’t even have to invent gravity. Or you could posit “the element earth is attracted to other chunks of earth” in which case you sort-of, but not quite, have invented gravity.

    Given two theories that are on a par of complexity, and both include ugly kludges, but one of which has significantly *smaller* kludges, I think that one should be preferred. The prior probability of neatly explaining away the kludges is higher, the smaller they are. So you’re not exactly preferring Coperican theory as such, just betting that it is more likely to lead to an improved successor.

    Reality is the ultimate arbiter, but in the long run we’re all dead. Meanwhile there’s Bayes.

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  4. “Why is “the element earth is attracted to Earth” any less plausible than “…to the center of the universe”?”

    For an Aristotelian, “gravity” meant the attraction of earth and water to the center of the universe. (“Levity” meant the tendency of air and fire to rise away from it.) For us, the idea that matter attracts other matter is obvious, but it wasn’t to them. Prior to Newton, there were people who did take the example of magnetism and try to come up with something. Newton’s contribution was really in finding the mathematical structure of it.

    But that was only after observations had forced the issue. Which indicates that the real barrier was psychological. People preferred geocentrism. After all, the universe seems much more about us if we’re at the center of it. Us being off to the side was unpleasant to think about. The idea we might be a speck in an infinite universe was intolerable.

    I do think you’re right though. The lower kludginess, represented primarily by the more elegant mathematics, was a clue. But I don’t know that anyone prior to 1609 could feel justified in being certain about either model.

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  5. Interesting question! Assuming you have two models that “save appearances” equally well and seem internally equal in most other respects, maybe there’s nothing you can do except choose the one that jives most with your worldview. In which case it’s not surprising that the geocentric model was hard to overthrow. And it IS hard to wrap one’s mind around the earth moving. Why doesn’t it move out from under my feet when I jump up? The heliocentric model must’ve seemed pretty nutty when you take that stuff into consideration.

    That said—and it’s been a long time since I read about this stuff—didn’t the Copernican model explain retrograde motion internally (for lack of a better word) without having to rely on ad hoc epicycles? And didn’t the planets have an interconnectedness that was absent in the Ptolemaic model? In other words, when you say, “It didn’t really make fewer assumptions than the Ptolemaic one, so parsimony (Occam’s razor) wasn’t much of a guide.” But I’m wondering…didn’t it make fewer assumptions? Wasn’t it more falsifiable? It’s a shame I really don’t remember this stuff…

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    1. Interestingly enough, Copernicus was actually not able to eliminate epicycles from his model, although they were smaller, and he renamed them “epicyclets”. The reasons show just how many conceptual hurdles people in his time had to overcome. He kept the idea that all heavenly movements had to be composed of perfect circles, a notion that went back to Plato. He also kept the crystalline spheres to keep everything moving correctly.

      Tycho Brahe later observed comets passing through what we supposed to be the spheres, so empirical data forced him to dismiss them. But it was someone he trained, Johannes Kepler (a convinced Copernican), who would finally eliminate the epicycles. He did it by letting go of the perfect circle notion, and accepting that planetary movements followed ellipses instead. (That move seems simple and obvious to us, but we aren’t embedded in the paradigm they were.)

      The fall of the spheres and circles created the mystery of how the planets “knew” where to go. “Gravity” in the 16th century meant the attraction of elemental earth and water to the center of the universe. The idea that all matter might be attracted to other matter was hinted at by similar magnetic phenomena, but no one could work out the mathematics until Newton. And of course, no one really knew what gravity was until Einstein.

      Still, Copernicus’ model was simpler and the mathematics easier to work with. That mathematical elegance was really the primary clue for someone in the 1500s. But it was easy to accept them without accepting the implications, and that’s apparently what most astronomers did.

      I think the most a rational person could do in 1550 was be open to the possibility that Copernicus’ model was reality. It would be easier after Tycho, easier still after Kepler, but only locked in with Galileo after 1610.

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