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A Simple Way to Navigate Life’s Complexity

 

A Simple Way to Navigate Life’s Complexity

Ockham’s razor can help anyone evaluate the odds that distinguish sense from nonsense.

October 20, 2022

Ockham’s razor is the principle that the most economical way of looking at the world is probably the correct one: Given a choice of solutions to a problem, we should opt for the simplest one that works. It sounds convenient, but is it useful? A young Franciscan friar called William (1287–1347), from the village of Ockham, England, certainly thought so. He risked his life to wield his razor as a force of reason against the religious philosophy of his age.

Seven hundred years later, Ockham’s razor ranks among the most influential ideas in the history of science, yet it remains widely misunderstood. It does not mean that reality is simple, nor that valid scientific explanations should seem simple to us. Fundamentally, it is a rule for understanding probabilities, distinguishing likely scenarios from unlikely ones. Applied in a knowing way, Ockham’s razor can help us see through falsehoods, conspiracy theories, and sloppy reasoning.

William of Ockham developed his razor to cut away at the intricate worldview he encountered when he arrived at the University of Oxford around 1320. The predominant belief then (as in most cultures in most times) was that there was no separation between science and religion. Supernatural forces could be invoked at will to explain observed phenomena. Gods or angels pulled the sun, moon and planets across the sky; evil spirits unleashed illness or famine. Further complicating matters, every object was also considered to possess an invisible final cause, or telos. For instance, the telos of wood was to make fire, the telos of fire was to warm humans, and the telos of humans was to worship God. The unknowable mind of God was the final cause of it all.

An abundance of spirits and causes could explain anything, Ockham realized, so they actually explain nothing. He used his conceptual razor to dismantle this cluttered medieval metaphysics and replace it with a search for simplicity that formed the foundation of what we now regard as science. In Ockham’s words, “Numquam ponenda est pluralitas sine necessitate” (“Plurality should never be posited without necessity”). Supernatural forces can produce any imaginable result, but natural law can lead only to natural outcomes.

The need for Ockham’s razor has far outlasted the age in which it was conceived, in large part because the flaws in human nature remain unchanged. We are still drawn to magical thinking and custom-made explanations for the things that matter to us. More than ever, we need the razor to separate sense from nonsense in a confusing, complicated world.

In exploring the history of Ockham’s razor, we retrace key steps in the emergence of modern, rationalist thinking. William of Ockham started by discarding the medieval concept of universals (essences that supposedly defined the intrinsic properties of people and objects) along with the notion of final causes. Instead, he proposed that a fire is hot because that is its nature, not because it is operating to some greater end.

With these twin rejections, Ockham demolished the road from science to God. He went on to argue that science and religion are incompatible because religion is based solely on faith whereas science is based solely on reason. As far as I know, William of Ockham was the first person in the history of the world to record this distinction, which earned him a summons to trial on charges of heresy in Avignon. It did not go well. Ockham accused the pope of being a heretic himself and then fled Avignon. He was excommunicated and pursued across Europe by successive popes but never caught. He died in Munich in 1347.

Despite papal disapproval, Ockham’s ideas spawned a medieval underground movement known as the via moderna, which was adopted by a new generation of European scholars who valued reason above dogma. Jean (John) Buridan, a 14th-century philosopher at the University of Paris, notably applied Ockhamist philosophy to the heavens. The ancient Greeks believed the stars move across the night sky because they are pinned to a rotating celestial sphere. Drawing on Ockham’s writings about the nature of perspective, Buridan argued
that the rotation of Earth could more reasonably account for their apparent motion: “Just as it is better to save the appearances through fewer causes than through many, . . . it is better that the Earth (which is very small) is moved most rapidly and the highest sphere is at rest than to say the opposite.” This insight was a jumping-off point for what we today call “science.”

If a simpler theory existed, scientists would have adopted it. That’s what separates science from pseudoscience and sheer baloney.

Long after Ockham’s death, via moderna
books were copied, then published and circulated widely in major
European cities. That is likely how the famed Polish polymath Nicolaus
Copernicus picked up Buridan’s argument, starting in 1498, and concluded that the planets revolve around the sun rather than the Earth.

Contrary to common misconception, Copernicus’s heliocentric
(sun-centered) system was not a physically realistic model of the solar
system. Rather, it was a more economical model, integrating
Ockham’s razor into the order of the cosmos. At the time, the Church
adhered to a geocentric cosmology developed in the 2nd century CE by the
Greek astronomer Claudius Ptolemy,
in which the sun, moon, stars, and planets were affixed to a system of
nested spheres. To account for the irregular motions of the planets,
Ptolemy had them pinned not only to their spheres but also suspended
from combinations of secondary circles, or epicycles—a kind of Ferris
wheel of circles within circles. It was a very complicated system.

Copernicus had been educated at the University of Kraków, a center for via moderna scholars, so it is not surprising that he was inspired
to discover whether the heavenly motions “could be solved with fewer
and much simpler constructions than were formerly used.” His first step
was, like Buridan’s, to allow Earth to spin. Then he made things simpler
still by placing the sun, not Earth, at the center, transforming our
view of the order of nature.

Losing centrality in the cosmos was a shattering blow to humanity’s
ego, yet Copernicus’s heliocentric model was enthusiastically adopted by
nearly all the giants of the Scientific Revolution, including Johannes Kepler, Galileo Galilei, and Isaac Newton.
This embrace is particularly puzzling because the Copernican
heliocentric model was no better at predicting the motions of the
planets than was the Ptolemaic system. The new model even required its
own epicycles. Copernicus knew this, but he claimed that his system was
superior because it was fundamentally simpler. His followers agreed,
ushering in the science-based, sun-centered solar system as we know it
today.

The heliocentric model is often regarded as a notable validation of Ockham’s razor. Surprisingly, it is also cited as a critique. Some prominent historians of science, including Thomas Kuhn
and Arthur Koestler, have insisted that the simplicity criterion that inspired Copernicus was mostly subjective. Kuhn wrote, “Judged on purely practical grounds, Copernicus’ new planetary system was a failure; it was neither more accurate nor significantly simpler than its Ptolemaic predecessor.” Kuhn argued that scientific advances are based not solely on reason but also on cultural bias, irrationality, and aesthetic preference. His charge remains highly relevant today. It has been enthusiastically picked up by postmodernist philosophers who insist that science has no more claim on objective truth than witchcraft, folk belief, or astrology.

That line of attack misses the significance of Ockhamist simplicity. Copernicus, Kepler, and Galileo were not counting epicycles. They were interested in the simplicity of underlying causes. As the Danish astronomer Tycho Brahe wrote, heliocentricity “circumvents all that is superfluous and discordant in the system of Ptolemy.” In the Ptolemaic system, each planet has an epicycle whose period exactly matches the Earth year, for no apparent reason, to account for the occasional retrograde (backward) movement of the planets in the sky. In the Copernican system, though, retrograde motion makes simple sense. It is caused by Earth either overtaking, or being overtaken by, another planet in its orbit around the sun—merely an effect of perspective.

The importance of finding a simpler solution is apparent from what happened next. In the early 1600s, Kepler found he could further simplify Copernicus’s model by discarding epicycles and describing each planet’s orbit as a unique, elegant ellipse—impossible in Ptolemy’s system. Around the same time, Galileo (who had referred to William of Ockham in his notes) found a simple set of laws describing motion on Earth. With his theory of universal gravitation, Isaac Newton delivered, arguably, the biggest simplification in the history of science, discerning a common cause underpinning Copernicus’s model, Kepler’s ellipses, and Galileo’s laws of motion. It swept away a role for gods and angels in running the cosmos.

Another common criticism of Ockham’s razor misinterprets the principle of simplicity as a claim that the world is simple. (Many current dabblers in pseudoscience are drawn to this misinterpretation, maintaining that their ideas must be right because they are easier to understand than mainstream science.) That is not Ockham’s razor. Ockham insisted that entities should not be multiplied beyond necessity. Those two words allow us to add as much complexity as is needed, but no more.

General relativity and quantum mechanics are not what most people would call simple, but they are hardly refutations of Ockham’s razor. Is there a simpler law than general relativity that can account for the equivalence of acceleration and gravity? Is there a simpler explanation of the photoelectric effect than quantum mechanics? If a simpler theory existed, scientists would have adopted it. That’s what separates science from astrology, religion, magic, mysticism, pseudoscience, conspiracy theories, and sheer baloney.

You don’t need to understand why Ockham’s razor works in order to use it, but it is even more powerful when you know the important statistical insights it embodies. The principle of simplicity succinctly expresses Bayesian inference, a type of deduction that is fundamental to science and statistics because it provides a rigorous way to estimate the probability that a particular belief is valid.

Here’s an illustration of Bayesian inference in action. Let’s say I have two dice, one conventional 6-sided and the other 60-sided. Out of sight, I throw one of them. Your task is to guess which die I’ve thrown. It could be either, so you assign each die a probability of 1/2. Now I call out the number I rolled: 38. To decide which die is more likely, you multiply the first probability by the likelihood that your model has generated the observed data. For the 6-sided die, the probability is zero, since it has no number 38. Multiplying your first probability of 1/2 by zero gives you a final probability of zero.

Now the 60-sided die has a 1/60 chance of throwing a 38. Multiplying 1/2 by 1/60 gives you a 1/120 probability of the 60-sided die being the source of the data. To compare the two models, we simply divide the larger final probability by the smaller one. 1/120 divided by zero is infinity. That is, the 60-sided die is infinitely more likely to be the source of the data than the 6-sided die. You can confidently conclude that the 60-sided die is the right one.

That example is easy. But let’s say that after my next throw, I call out the number 5. Which die is it now? It could be either, but Bayesian reasoning says that the two are not equally likely. Once again, both have a first probability of 1/2. Then the 6-sided die has a 1/6 likelihood of throwing a 5, giving a final probability of 1/12. The more complex 60-sided die has a 1/60 likelihood of throwing a 5, giving a final probability of 1/120. To compare the two models, we again divide the bigger final, or posterior, probability (1/12) by the smaller, or prior, one (1/120). Bayesian reasoning tells us that the simpler, 6-sided die is 10 times as likely as the 60-sided die to have produced the 5 that I rolled.

If science were taught as the means we use to find the simplest solutions to the most complex problems, it might make more sense.

Note that Bayesian inference delivers probabilities, not certainties.
Sometimes 60-sided dice do come up 5! But Bayesian inference favors the
sharper predictions made by simpler models. That is the statistical
underpinning of Ockham’s razor.

The brilliance of Ockham’s razor is that it allows anyone to apply
Bayesian principles to daily life without having to consult arcane
principles of statistical inference. And the razor is universal,
relevant to all kinds of situations for which there are multiple possible
causes. As William of Ockham argued in his original formulation, it
even explains why scientific explanations are much simpler and more
economical than invoking God.

Scientific theories may look complicated, but they can play by only one set of rules: natural law. There are no limits on
God, however. So you can opt for a single origin of life plus natural
selection, or you can opt for a trillion separate divine creations of
every species on Earth. An omnipotent God could do anything, including
making an infinite number of universes, each with its own set of laws.
The Bayesian likelihood of God being the source of this particular
universe is therefore one divided by infinity, or zero. From a Bayesian
perspective, God isn’t simple. God is maximally complex and should be
eliminated from all rational analysis.

Ockham’s razor also shows why conspiracy theories are overwhelmingly unlikely. Tall tales tend to be long
tales, so an easy way to assess the relative likelihood of alternative
explanations is to compare their length. Were doctors, scientists,
public health officials, vaccine manufacturers, and distributors all
complicit in a plot by Bill Gates to engineer and release a
computer-chipped Covid-19 virus to gain control of the world, or did a
regular virus come from a bat? Did election officials, politicians,
voting-machine manufacturers, police, and justice departments conspire
against Donald Trump, or did he lose the 2020 election? In a world of
social media feedback loops that deliver only the news and opinions that
people choose to hear, we need to hold tight to Ockham’s razor and go
with the simplest sufficient explanation and solutions.

Last, with the rise in popularity of pseudoscience and mysticism, we
should be asking if there is a better way to teach science in the
classroom. Bombarding students with theories, equations, and long lists
of facts can make science seem overwhelming. We might do well to look
back to William of Ockham for guidance. If science were taught as the
means we use to find the simplest solutions to the most complex
problems, it might make more sense.

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