Monday, September 5, 2016
The Tyranny of Simple Explanations http://www.theatlantic.com/science/archive/2016/08/occams-razor/495332/ The history of science has been distorted by a longstanding conviction that correct theories about nature are always the most elegant ones. Imagine you’re a scientist with a set of results that are equally well predicted by two different theories. Which theory do you choose? This, it’s often said, is just where you need a hypothetical tool fashioned by the 14th-century English Franciscan friar William of Ockham, one of the most important thinkers of the Middle Ages. Called Ockam’s razor (more commonly spelled Occam’s razor), it advises you to seek the more economical solution: In layman’s terms, the simplest explanation is usually the best one. Occam’s razor is often stated as an injunction not to make more assumptions than you absolutely need. What William actually wrote (in his Summa Logicae, 1323) is close enough, and has a pleasing economy of its own: “It is futile to do with more what can be done with fewer.” Isaac Newton more or less restated Ockham’s idea as the first rule of philosophical reasoning in his great work Principia Mathematica (1687): “We are to admit no more causes of natural things, than such as are both true and sufficient to explain their appearances.” In other words, keep your theories and hypotheses as simple as they can be while still accounting for the observed facts. This sounds like good sense: Why make things more complicated than they need be? You gain nothing by complicating an explanation without some corresponding increase in its explanatory power. That’s why most scientific theories are intentional simplifications: They ignore some effects not because they don’t happen, but because they’re thought to have a negligible effect on the outcome. Applied this way, simplicity is a practical virtue, allowing a clearer view of what’s most important in a phenomenon. There’s no easy equation between simplicity and truth. There’s absolutely no reason to believe that. But it’s what Francis Crick was driving at when he warned that Occam’s razor (which he equated with advocating “simplicity and elegance”) might not be well suited to biology, where things can get very messy. While it’s true that “simple, elegant” theories have sometimes turned out to be wrong (a classical example being Alfred Kempe’s flawed 1879 proof of the “four-color theorem” in mathematics), it’s also true that simpler but less accurate theories can be more useful than complicated ones for clarifying the bare bones of an explanation. There’s no easy equation between simplicity and truth, and Crick’s caution about Occam’s razor just perpetuates misconceptions about its meaning and value. The worst misuses, however, fixate on the idea that the razor can adjudicate between rival theories. I have found no single instance where it has served this purpose to settle a scientific debate. Worse still, the history of science is often distorted in attempts to argue that it has. Take the debate between the ancient geocentric view of the universe—in which the sun and planets move around a central Earth—and Nicolaus Copernicus’s heliocentric theory, with the Sun at the center and the Earth and other planets moving around it. In order to get the mistaken geocentric theory to work, ancient philosophers had to embellish circular planetary orbits with smaller circular motions called epicycles. These could account, for example, for the way the planets sometimes seem, from the perspective of the Earth, to be executing backwards loops along their path. It is often claimed that, by the 16th century, this Ptolemaic model of the universe had become so laden with these epicycles that it was on the point of falling apart. Then along came the Polish astronomer with his heliocentric universe, and no more epicycles were needed. The two theories explained the same astronomical observations, but Copernicus’s was simpler, and so Occam’s razor tells us to prefer it. This is wrong for many reasons. First, Copernicus didn’t do away with epicycles. Largely because planetary orbits are in fact elliptical, not circular, he still needed them (and other tinkering, such as a slightly off-center Sun) to make the scheme work. It isn’t even clear that he used fewer epicycles than the geocentric model did. In an introductory tract called the Commentariolus, published around 1514, he said he could explain the motions of the heavens with “just” 34 epicycles. Many later commentators took this to mean that the geocentric model must have needed many more than 34, but there’s no actual evidence for that. And the historian of astronomy Owen Gingerich has dismissed the common assumption that the Ptolemaic model was so epicycle-heavy that it was close to collapse. He argues that a relatively simple design was probably still in use in Copernicus’s time. Theories are distinguished not by making fewer assumptions but different ones. So the reasons for preferring Copernican theory are not so clear. It certainly looked nicer: Ignoring the epicycles and other modifications, you could draw it as a pleasing system of concentric circles, as Copernicus did. But this didn’t make it simpler. In fact, some of the justifications Copernicus gives are more mystical than scientific: In his main work on the heliocentric theory, De revolutionibus orbium coelestium, he maintained that it was proper for the sun to sit at the centre “as if resting on a kingly throne,” governing the stars like a wise ruler. If Occam’s razor doesn’t favor Copernican theory over Ptolemy, what does it say for the cosmological model that replaced Copernicus’s: the elliptical planetary orbits of 17th-century German astronomer Johannes Kepler? By making the orbits ellipses, Kepler got rid of all those unnecessary epicycles. Yet his model wasn’t explaining the same data as Copernicus with a more economical theory; because Kepler had access to the improved astronomical observations of his mentor Tycho Brahe, his model gave a more accurate explanation. Kepler wasn’t any longer just trying to figure out the arrangement of the cosmos. He was also starting to seek a physical mechanism to explain it—the first step towards Newton’s law of gravity. The point here is that, as a tool for distinguishing between rival theories, Occam’s razor is only relevant if the two theories predict identical results but one is simpler than the other—which is to say, it makes fewer assumptions. This is a situation rarely if ever encountered in science. Much more often, theories are distinguished not by making fewer assumptions but different ones. It’s then not obvious how to weigh them up. From a 17th-century perspective, it’s not even clear that Kepler’s single ellipses are “simpler” than Copernican epicycles. Circular orbits seemed a more aesthetically pleasing and divine basis for the universe, so Kepler adduced them only with hesitation. (Mindful of this, even Galileo refused to accept Kepler’s ellipses.) It’s been said also that Darwinian evolution, by allowing for a single origin of life from which all other organisms descended, was a simplification of what it replaced. But Darwin was not the first to propose evolution from a common ancestor (his grandfather Erasmus was one of those predecessors), and his theory had to assume a much longer history of the Earth than did those which supposed divine creation. Sure, a supernatural creator might seem like a pretty complex assumption today, but it wouldn’t have looked that way in the devout Victorian age. Even today, whether or not the “God hypothesis” simplifies matters remains contentious. The fact that our universe sports physical constants, such as the strength of fundamental forces, that seem oddly fine-tuned to enable life to exist, is one of the most profound puzzles in cosmology. An increasingly popular answer among cosmologists is to suggest that ours is just one of a vast, perhaps infinite, number of universes with different constants, and ours looks fine-tuned purely because we’re here to see it. There are theories that lend some credence to this view, but it rather lacks the economy demanded by Occam’s razor, and it is hardly surprising if some people decide that a single divine creation, with life as part of the plan, is more parsimonious. What’s more, scientific models that differ in their assumptions typically make slightly different predictions, too. It is these predictions, not criteria of “simplicity,” that are of greatest use for evaluating rival theories. The judgement may then depend on where you look: Different theories may have predictive strengths in different areas. Another popular example advanced in favor of Occam’s razor is the replacement of the phlogiston theory of chemistry—the idea that a substance called phlogiston was released when things burn in air—by the chemist Antoine Lavoisier’s theory of oxygen in the late 18th century. However, it’s far from obvious that, at the time, the notion that reaction with oxygen in air, rather than expulsion of phlogiston, was either simpler or more consistent with the observed “facts” about combustion. As the historian of science Hasok Chang has argued, by the standards of its times, “the old concept of phlogiston was no more mistaken and no less productive than Lavoisier’s concept of oxygen”. But as with so many scientific ideas that have fallen by the wayside, it has been deemed necessary not just to discard it but to vilify and ridicule it so as to paint a triumphant picture of progress from ignorance to enlightenment. I can think of only one instance in science where rival “theories” contend to explain exactly the same set of facts on the basis of easily enumerable and comparable assumptions. These are not “theories” in the usual sense, but interpretations: namely, interpretations of quantum mechanics, the theory generally needed to describe how objects behave at the scale of atoms and subatomic particles. Quantum mechanics works exceedingly well as a mathematical theory for predicting phenomena, but there is still no agreement on what it tells us about the fundamental fabric of reality. The theory predicts not what will happen in a quantum experiment or observation, but only what the probabilities of the various outcomes are. Yet in practice we see just a single outcome. How then do we get from calculating probabilities to anticipating definite, unique observations? One answer is that there is a process called “collapse of the wavefunction,” through which, from all the outcomes allowed by quantum theory, just one emerges at the size scales that humans can perceive. But it’s not at all clear how this putative collapse occurs. Some say it’s just a convenient fiction that describes the subjective updating of our knowledge when we make a measurement—rather like the way all 52 probabilities for the top card of a shuffled pack collapse to just one when we look. Others think wavefunction collapse might be a real physical process, a bit like radioactive decay, which can be triggered by the act of looking with human-scale instruments. Either way, there’s no prescription for it in quantum theory; it needs to be added “by hand.” A theory is not “better” if it is simpler—but it might well be more useful. In what looks like a more economical interpretation, first proposed by the physicist Hugh Everett III in 1957, there is no collapse at all. Instead, all the possible outcomes are realized—but they happen in different universes, which “split” when a measurement is made. This is the Many Worlds Interpretation (MWI) of quantum mechanics. We only see one outcome, because we ourselves split too, and each copy can only perceive events in one world. It’s a testament to scientists’ confusion about Occam’s razor that it has been invoked both to defend and to attack the MWI. Some consider this ceaseless, bewildering proliferation of universes to be the antithesis of William of Ockham’s principle of economy. “As far as economy of thought is concerned … there never was anything in the history of thought so bluntly contrary to Ockham’s rule than Everett’s many worlds,” the quantum theorist Roland Omnès writes in The Interpretation of Quantum Mechanics. Others who favor the MWI wave off such criticisms by saying that Occam’s razor was never a binding criterion anyway. And still other advocates, like Sean Carroll, a cosmologist at the California Institute of Technology, point out that Occam’s razor is meant only to apply to the assumptions of a theory, not the predictions. Because the Many Worlds Interpretation accounts for all the observations without the added assumption of collapse of the wavefunction, says Carroll, the MWI is preferable—according to Occam’s razor—to the alternatives. But this is all just special pleading. Occam’s razor was never meant for paring nature down to some beautiful, parsimonious core of truth. Because science is so difficult and messy, the allure of a philosophical tool for clearing a path or pruning the thickets is obvious. In their readiness to find spurious applications of Occam’s razor in the history of science, or to enlist, dismiss, or reshape the razor at will to shore up their preferences, scientists reveal their seduction by this vision. But they should resist it. The value of keeping assumptions to a minimum is cognitive, not ontological: It helps you to think. A theory is not “better” if it is simpler—but it might well be more useful, and that counts for much more. ABOUT THE AUTHOR • PHILIP BALL is a writer based in London. His work has appeared in Nature, The New York Times, and Chemistry World. He is the author ofThe Water Kingdom: A Secret History of Chinaand Critical Mass: How One Thing Leads to Another.
Posted by DG at 5:42 AM