Cutting Down Ockham's Razor
William of Ockham famously argued that the simplest explanation is likely the best one. The idea is appealing, widely believed, and deeply misleading.
By Jim Al-Khalili
Save your razors for shaving hairs. (Credit: Alamy)
We hear all the time that the simplest explanations are usually the right ones. This truth-testing idea—known as Ockham’s razor, after the English medieval philosopher William of Ockham—has been embraced by no less authorities than Isaac Newton and Albert Einstein. Today scientists invoke Ockham’s razor on topics ranging from Covid’s origins to cosmic dark matter, while folks debating a subject on social media regularly invoke it as their final arbiter. After all, why complicate something more than you need to? Isn’t it better to shave ideas down to their essential truths?
Ockham’s razor sounds logical and definitive, which is exactly what makes it dangerous. Not only is the assumption of simplicity often false, but following it blindly can lead to serious misunderstandings, both in science and in everyday life.
A well-known historical validation of the principle of simplicity in science was in the overthrow of the geocentric model of the universe. The ancient Greeks codified a cosmology in which Earth was motionless while the sun, moon, planets, and stars all moved around it in perfect circular paths. That model held sway for nearly 2,000 years, despite becoming increasingly cumbersome as it was modified to account for the observed movements of planets like Mars, which was seen to slow down, speed up, and sometimes even double back on itself.
The Greeks attempted to account for this “retrograde” motion of Mars by assuming that it followed a secondary, smaller circular path, called an epicycle, that was bolted onto its primary circular motion around Earth. Later, improved observations of Mars and the other planets required further tinkering with the geocentric model, such as adding epicycles on top of epicycles and shifting Earth slightly away from the center of all the other bodies’ orbits.
Then, in the 16th century, Nicolaus Copernicus swept away this makeshift model and replaced it with his much simpler heliocentric picture in which the sun, not Earth, is at the center of the universe. In this view, the complicated motions of Mars as seen from Earth could be explained as a consequence of the two planets orbiting the sun at different distances and speeds. Both the Earth-centered and sun-centered models worked, in the sense that they predicted the motions of heavenly bodies reasonably well, but we now know that only one of them is correct: the Copernican model, the one without all the clumsy extras. This, we are told, is Ockham’s razor in action.
But the above account is wrong. Although Copernicus correctly replaced Earth with the sun at the center of the known cosmos, he still believed the planetary orbits to be perfect circles rather than their actual ellipses. As a result, he still needed the epicycles and other unwieldy patch-ups of the old geocentric model to get this heliocentric system to work. Although we now know that Earth does indeed go around the sun, we also know that the true dynamics of our solar system are far more convoluted than anything the ancient Greeks could have imagined. In place of epicycles, we have an ever-shifting system of ellipses whose shapes can never be calculated with perfect precision. It is Ockham’s razor in reverse.
An equally famous example in the history of science is Darwin’s theory of evolution through natural selection. It provides a unifying explanation for the tremendous variety of life we find on Earth, all of which evolved over billions of years from a single origin. Darwin’s theory is based on a few simple assumptions: 1) that individuals within a population of any species vary; 2) that these variations pass down through the generations; 3) that more individuals are born in each generation than can survive; 4) that those with characteristics better adapted to suit their environment are more likely to survive and reproduce. That’s it.
However, wrapped up in these modest assumptions are the mind-bogglingly complex fields of evolutionary biology and genetics, which are among the most challenging areas in all of science. If we are to truly apply Ockham’s razor to life on Earth, then surely the nonscientific theory of creationism—that all life was brought forth as it is today by a supernatural maker—is far simpler than Darwinian evolution.
The lessons here are that the simplest explanation is not necessarily the correct one, and the correct one is often not as simple as it first appears. Ockham’s razor, as applied in science, does not mean that a new theory should replace a previous one just because it is simpler or has fewer assumptions.
I prefer a different interpretation of Ockham’s razor: A better theory is one that is more useful because it makes more-accurate predictions about the world and leads to reproducible results. Simplicity is not always what we should strive for.
In everyday life, too, explanations are often not as simple as we would like them to be. To paraphrase Einstein, we should try to make things as simple as possible, but no simpler. Nevertheless, the idea that simpler is better has become a widely accepted piece of folk wisdom. We are seeing a social trend toward simplistic arguments, particularly in relation to ethical or political issues, that intentionally ignore subtlety and complexity, distilling the issues into memes and tweets in which all nuance is lost.
It is certainly tempting, when trying to make sense of a messy world, to seek out the clarity of a simple and unambiguous viewpoint. Real life is untidy and complicated, and many of us are not prepared to put in the effort to take in the big picture. Keep it simple, people often say, and don’t blind me with details.
And yet, it can be surprising how much clearer and (yes) simpler it becomes to understand an issue if we acknowledge its complexity and examine it more carefully. For example, modern celestial dynamics not only accurately predicts the motions of the planets but also provides a unifying method for understanding asteroids that might hit Earth or planets orbiting other stars—objects completely outside the realm of the old geocentric model.
The challenge is to apply the principle of simplicity thoughtfully and strategically. Simplifying an explanation, description, or argument can be very useful in exposing broad connections. To truly understand a phenomenon, for instance, the scientist will often attempt to strip away the unnecessary detail and expose its bare bones. Laboratory experiments are often carried out under specially controlled conditions to create artificial, idealized environments that make the important features easier to study.
Unfortunately, people often seek simplicity well beyond the point of usefulness. There is a well-known joke (to us physicists, at least) about a dairy farmer who wants to find a scientific way to increase the milk production of his cows, so he seeks the help of a team of theoretical physicists. After carefully studying the problem, the physicists finally tell him they have found a solution—but that it works only if they assume a spherical cow in a vacuum.
Several years ago, I interviewed Peter Higgs, the British physicist after whom the famous particle is named, for my BBC radio program, The Life Scientific. I asked him if he could explain in 30 seconds what the Higgs boson was. He looked at me solemnly and, I have to admit, not particularly apologetically, and shook his head. He explained that it had taken him many decades to understand the physics underlying the Higgs mechanism in quantum field theory, so how could people expect such a complex subject to be condensed into a short sound bite?
Despite the well-documented failings of Ockham’s razor, it is hard to fight the human impulse to look for the simplest account of something we don’t understand. If we do find a simple explanation, we tend to hang on to it because of its strong psychological appeal over more complicated explanations that may require considerable effort to fully understand. Scientists, even the best of us, are no different from anyone else.
Soon after Einstein completed his general theory of relativity, in 1915, he applied its equations to a description of the evolution of the universe as a whole. To his consternation, he found that his equations predicted a universe that was collapsing in on itself due to the mutual gravitational pull of all the matter it contains. Einstein knew that the universe didn’t appear to be collapsing, and the simplest assumption he could make was that it had to be stable. He then accommodated that assumption with the simplest possible mathematical fix: He modified his equations with a “cosmological constant,” a term that counteracted the part describing the cumulative attractive gravitational pull of matter. In this way, he stabilized his model of the universe with a single number.
But it didn’t take long for other scientists to suggest a different interpretation of general relativity. What if the universe wasn’t stable after all? What if it was getting bigger, and all gravity was doing was slowing down its expansion rather than causing it to collapse? This explanation was confirmed by the astronomer Edwin Hubble in the late 1920s. Einstein realized then that there was no longer any need for his “fix.” He got rid of his cosmological constant, reportedly calling it the biggest blunder of his life. The story does not end there, however. In 1998, astronomers discovered not only that the universe is expanding but that the expansion is accelerating. Something is counteracting the gravitational pull of matter.
This is a good example of how our scientific understanding can grow as new evidence accumulates. Einstein introduced the cosmological constant based on the simple assumption that the universe was static—which was soon contradicted by new observations. His successors rejected the cosmological constant on the simple assumption that the expanding universe was steadily winding down—and that, too, was eventually falsified by the evidence. The thing causing the universe to accelerate is generically called “dark energy,” but its true identity is unknown. It might resemble Einstein’s cosmological constant, but that might be yet another oversimplification. What we do know is that the universe is far more complex than Einstein thought.
Sometimes, acknowledging the role of complexity is vital for understanding the properties of a system. Even simple systems following deterministic physical laws can behave in highly unpredictable ways, as when a kitchen faucet abruptly switches from smooth (laminar) to turbulent flow. Conversely, seemingly random behavior can reveal meaningful patterns when we zoom out and embrace complexity. This realization has sparked entire areas of scientific research—from statistical mechanics in the 19th century to chaos theory in the 20th and complex systems in the 21st—influencing disciplines as diverse as biology, artificial intelligence, and economics.
Scientists therefore try not to be seduced by Ockham’s razor. In my preferred formulation: The simplest explanation is not necessarily the most useful one, and ideas that appear simple often fall apart in the face of new evidence.
It is a lesson we should all embrace. We live in an age of sound bites, slogans, and instant access to news and opinion. Information overload easily leads people toward strident, simplifying opinions. Ockham’s razor has become a tool of political identity. Those daring to point out that an issue is more complicated than either side wishes to admit can find themselves attacked by both sides: If you’re not 100 percent with me, you are against me.
We would do well to apply anti-Ockham scrutiny to our political and social discourse, just as scientists attempt to apply it to their research. Practically speaking, we cannot go around digging into every issue or rejecting every explanation just because it seems too easy. But we can train ourselves to be wary of making up our minds on a matter as soon as we’ve found a simple narrative. We should try to question whether that simple narrative is accepted by people who have put in the effort to study it more deeply than we have, or than we can.
If we are prepared to dig a little deeper, we are likely to be rewarded. Not only will our view of the world become richer, but our outlook on life will be more fulfilling. That’s a huge benefit in exchange for a small loss of simplicity.
September 8, 2022
Popular accounts of the history of science are full of just-so stories. There is an inevitable progression from ancient superstitions to modern discoveries, and those discoveries are so self-evidently true that they merely needed someone (usually a Great Man) to come along and clear away the confusion. Thus we have Galileo sweeping aside the mumbo-jumbo of the Church’s geocentric cosmology, or Darwin neatly tying up the biological world with his idea of evolution through natural selection. Just-so stories send a message that simplicity is the life-blood of scientific progress, which is doubly wrong. It misrepresents both the scientific method and the actual history of how great discoveries occur: in fits and starts, typically, blending insights from many different people and blurring new ideas with old conceptions. Abandoning the clichéd narrative of simplicity does more than lead us to better explanations of the world around us. It also reveals a much richer, more complete, and more honest account of how our modern ways of thinking came to be.
— Corey S. Powell, co-editor