The role of beauty and simplicity in scientific theories

In the post on Copernicus earlier this week, I noted that his heliocentric theory, right from its initial publication, was hailed as far more mathematically elegant than the Aristotelian / Ptolemaic system, which was taken as the canonical model of the universe at the time.  But while everyone hailed Copernican mathematics, virtually no one accepted its ontology.  The idea that the Earth moved around the Sun was simply too radical for most people.

It’s easy to forget today the searing shift in perspective that took place between Copernicus’ publication of his theory in 1543, and Newton’s publication of his theory of gravitation and mechanics in 1687.  In that period, we went from being the center of creation, with the universe literally revolving around us, to an insignificant speck in an incomprehensibly vast darkness.  It’s probably not an coincidence that the first modern atheists and deists arose in the 17th and 18th centuries.

In retrospect, the mathematical elegance of Copernicanism was a major clue.  But as I noted in that post, we have to be careful with generalizing from that.  This morning, Aeon highlighted an article by Massimo Pigliucci from earlier this year (which I apparently completely missed at the time), pointing out that Richard Feynman often asserted that truth could be recognized by its beauty and simplicity.  Massimo’s thesis is that, given the failure of things like supersymmetry and other related theories,  Feynman was wrong.

I think Massimo, along with similar critics such as Sabine Hossenfelder, Peter Woit, and Jim Baggott are right, to an extent.  No theory should be accepted purely on the basis of its beauty, simplicity, or elegance, on its aesthetics.  But given the Copernican story, it also seems excessively hasty to completely dismiss such theories.

On the one hand, if Copernicus had held to such a philosophy, he might have avoided engaging in what, in his time, amounted to metaphysical speculation.  Eventually telescopic observations would have forced the matter, and a new model would have needed to be developed in the 17th century.

On the other hand, Copernicus’ theory arguably spurred decades of discussion, setting up the intellectual atmosphere that inspired figures like Tycho Brahe,  Kepler, and Galileo.  All observation is theory laden.  How much longer would science have taken to reach the same conclusions without Copernicus’ theoretical work?  There’s probably no way to know.

In addition, we have to admit the fact that no theory, even one with a long history of successfully predicting observations, is ever the only explanation for those observations.  There are always alternate models.  We can say we use Occam’s razor to select one, but “simplicity” is often just another name for the aesthetic aspects that are really used in that selection.

I think the right middle ground then, is that logical or mathematical elegance are fine for admitting a theory into the candidate for reality category.  If it gets falsified, then we can dismiss it.  If it’s the simplest theory and racks up predictive success, then we can accept it as the best explanation, until a better one comes along.  That appears to be as much certitude as anyone’s going to get.

Unless of course I’m missing something?

12 thoughts on “The role of beauty and simplicity in scientific theories

  1. For me it’s more that theories that have proven themselves experimentally usually turn out to have a beauty or elegance. At the same time, many elegant beautiful ideas turn out to be false, so it’s not an exclusive property.

    The meta-question is, perhaps, more interesting. Why do we find some theories “elegant” or “beautiful”? What is the underlying basis for the almost universal appreciation of, for example, Euler’s Identity?

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    1. Definitely on many elegant ideas turning out to be false. In the end, observations always trump elegance. Einstein would have had a hard time convincing people to move from Newton’s relatively simple mathematics to his far more complicated ones if there hadn’t been anomalies that couldn’t be handled without it.

      On why we find some theories elegant, it might be that working with them is just easier. That was reportedly the case with Copernicus’ model over Ptolemy’s. It might only be that it takes less mental energy to contemplate it. Of course, I’m sure often it’s just because it flatters our biases.

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      1. I suspect there is a strong correlation between our perceptions of “elegant” and what is simple. Engineers sometimes define elegant to mean the simplest solution that fully accomplishes the task, although there is still something ineffable about “elegance” — it includes the idea of perfection in addition to simplicity.

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        1. For scientific theories, it might be that elegance is the ratio of components to explanatory benefit, a sort of epistemological cost / benefit ratio. In that sense, it’s similar to Occam’s razor, but including an assessment of how difficult some assumptions are to work with compared to others.

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          1. There may be something similar with engineering elegance. Repairing your radiator hose with duct tape is simple, but not elegant. An elegant engineering solution has, I think, an element of being obvious in hindsight but not in foresight. There is a sense of surprise to an elegant engineering solution, a sense of, “Oh, I should have thought of that!”

            In a way that feeling involves something simple doing a complex or clever job almost out of proportion to how simple it is. (Whereas duct tape is just doing what it does.)

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  2. I don’t know if the simplicity and beauty of a theory mean that it’s right, but I do think if a theory starts to seem really ugly and complicated, that might be a sign that something’s wrong. Excessive complexity might just mean someone had to keep adding ad hoc solutions to the theory to keep it working.

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    1. I think it was Thomas Kuhn who said that theories are almost never discarded when they’re initially falsified. At first someone simply modifies the theory. It may not be dropped even if the modifications start getting excessive, until a simpler theory comes along, which if it’s a major theory, may require a paradigm shift like the one from the Aristotelian to the Newtonian worldview.

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  3. Beauty lies in the eye of the beholder. It is the human view, which has to be upgraded to find beauty in the complexity of truth.

    For example, surd numbers were earlier considered ugly in contrast to Pythagoras’s harmony of rational numbers. Later mathematicians found immense beauty in the Golden irrational ratio.

    Simplicity is a measure of ease with which a calculator reduces complicated expressions.

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    1. “It is the human view, which has to be upgraded to find beauty in the complexity of truth.”

      Excellent point. I think about all the physicists who find the Shrodinger equation beautiful. I can’t say beauty is the thing that jumps out at me when I look at it. But I’m not schooled enough in the details to see that beauty.

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