Seven hundred years ago in a commentary on a religious tract, William of Ockham, a Franciscan friar, wrote that “plurality must never be posited without necessity.” Such is Occam’s razor.
A bit gnomic, you might think. A bit hard to see at first how it earned its status as one of the most prized intellectual tools in scientific endeavour. But in his new book Life is Simple, Johnjoe McFadden proclaims it world-changing, “cutting through the thickets of medieval metaphysics to clear a path for modern science.” In short, this is a book of hero-worship, and just possibly McFadden has a point.
For most of us, Occam’s razor is like a country we can’t quite place on the map; we know it’s something to do with simplicity, but we’re not sure exactly what. Cited widely in science, but often misunderstood, for some it’s invaluable, hinting at profound truths about the nature of knowledge. For others it’s worse than useless. The old line attributed to HL Mencken has it that for every complicated question there is an answer that is clear, simple and wrong.
At its heart is the idea that simplicity can in some way help us decide between competing theories, all else being equal. “It is futile to do with more what can be done with fewer,” as William put it elsewhere. Perhaps the most persistent of the confusions is that this means simpler wins every time, against any alternative. A more accurate paraphrasing might be “don’t add complications if you don’t have to.” That still leaves plenty of room for interpretation, not least about whether all else is ever really equal between two competing theories, giving us one of the most debated—and for my money intriguing—heuristics around. Mental shortcut or philosophical thicket? Questions about the razor’s true use and meaning abound.
However, McFadden initially puts them aside, and begins with the man behind the metaphor, helping Occam to emerge as William, a fearless free-thinker who slashed even Aristotle down to size with cut-the-crap bravado; a bolshie radical whose afterlife as a vague abstraction means his impact is taken for granted, but who inspired the mother of all intellectual revolutions. We discover that he has been named as a plausible model for the character William of Baskerville, played in The Name of the Rose by an ex-James Bond, Sean Connery and, on this telling, that sounds about right. The Pope, who William accused of heresy, summoned him to Avignon for trial and fancied to burn him at the stake, only for Bond—I mean William—to be smuggled from under the papal nose in the dead of night onto a ship to who knows where, to flash his razor again.
We look on as intellectual shibboleths are brutally simplified by being cut out altogether. Take the universal essences that Aristotle said existed in all things—cherries with their essence of cherry-ness, fathers with some shared but elusive quality of father-ness. This metaphysical theory, like the related theory of forms posited by Plato, has provoked philosophical debate for millennia. Still, Slash goes William: a father has no universal essence of fatherhood; a father’s just a man with kids, and that’s all the definition we need.
In any case, if God is omnipotent, he can make cherries any way he likes; “cherry” is just the name people have chosen for them, says William, thus helping to distinguish the world of God from that of ordinary mortals—one the province of faith and the unknowable truth, the other of human thought—and slash, liberating science to think what it can, free from the binds of old religion.
Aristotle’s insistence that each thing was only of its kind meant that not even lines and circles could be thought connected, and that maths must stand apart from life. Slash goes William, pointing out that you can uncoil a circled rope to make a line, thus smoothing the incorporation of maths into science, with the former eventually pervading and guiding the latter.
“Really?” you ask as McFadden piles up William’s intellectual credits, “can we honestly attribute so much to one man?” But you suspend your doubts to enjoy the ride, as William despatches received wisdoms like villains in the alleyways of thought.
The bulk of the 350 pages tells the many stories of how various architects of different scientific breakthroughs are indebted to William, with a succession of names and discoveries that verges at times on the encyclopaedic: Copernicus, Kepler, Galileo, Boyle, Newton, Mendel, Einstein… and more, all cutting through old errors, discovering new and elegant laws, unifying the universe in some simplifying way—a fil rouge through the history of science from a practising scientist who is clearly comfortable with his vast material.
Here’s William in 1320, anticipating by more than 500 years, says McFadden, the theory that reduces nature’s variety to a simple process of natural selection acting on random variation: “The necessity of nature brings it about that the parts in some animals are conveniently arranged for the health of the whole. For example, the front teeth are sharp and apt for dividing food and the molars are flat and apt for mashing food… these parts do not exist because of such uses. Rather, when they come to be then the animals survive. The reason is this… these parts become apt for conserving the animal by chance.”
“Confusion over whether Occam’s razor implies a fundamentally simple universe has dogged the idea for much of its long life”
It is hard not to marvel. But afterwards, the slight unease returns: a feeling that the all-encompassing story of William’s simplifying genius sounds a little too marvellous to be true. This is partly because McFadden has so far avoided most of the philosophical argument. The reader is asked instead to trust the historical examples of the razor’s efficacy, even though some have wondered if all these examples truly exemplify simplification.
Writers must make choices, or long books become longer. But the relative lack of philosophy is the price paid—because after all this is an idea—and you could be forgiven frustration when McFadden lobs in, in isolation, the sentence: “Not even simplicity is as simple as it might appear,” with a footnote pointing to another book, Elliott Sober’s Ockham’s Razors.
Indeed, his title Life is Simple topped of my list of provocations, since not even McFadden believes that’s what William meant. Occam’s razor, he writes in one of the few, brief forays into the thickets of its meaning, “contrary to many of its detractors, does not insist that the world is simple, only that in reasoning about it we should not multiply entities beyond necessity. If the existing entities cannot do the job, then you have free rein to add as many entities as needed, so long as they are not ‘beyond necessity.’”
If you’re now wondering how we’re supposed to tell how much complexity is necessary in judging or postulating a scientific theory, you’re not alone. Confusion whether Occam’s razor implies a fundamentally simple universe has dogged the idea for much of its long life. McFadden seems clear that it implies no such thing. The science writer and Prospect contributor Philip Ball agrees: “Occam’s razor was never meant for paring nature down to some beautiful, parsimonious core of truth.” So where is McFadden going with his title—apparently so at odds with his hero’s rule?
All becomes clear. If Occam’s razor emphatically does not insist that the universe is simple, McFadden, it turns out, emphatically does. He believes it really is innately “parsimonious,” or even “lazy,” taking the most direct route to achieving life and a viable universe. He calls this “strong Occam,” in contrast to the “weak Occam” William himself had in mind.
It’s bracing stuff. Simplicity becomes the fabric of life and the guiding principle of science, even if we may never know whether science has arrived at the final, definitive description of that simplicity. Weak Occam works, McFadden thinks, because it pecks at this deeper truth. For support, he leans partly on arguments from probability: simpler is simply more likely.
Is he right? No idea. Again, the case in the book is mostly sold, not weighed. But it’s an arresting thought. The question that will bother general readers, I think, remains one which has often haunted Occam. What do we do with this vision of simplicity? How do we use it? Does it strengthen the case for generally preferring simpler explanations? Or only under certain conditions?
“A clean, sleek theory holds undoubted aesthetic appeal, but there is a certain exquisite beauty to complexity”
One prominent statistician—Andrew Gelman, working in social science—hates Occam, finding it useless for practical inquiry. When McFadden speaks of “life,” he means fundamental physics and biology. Gelman is interested in social life and politics. Does Occam work for one but not the other? Since the temptation to extend ideas of simplicity across the whole caboodle can end up feeding totalitarianism, some sense of the limits seems essential.
Practical life is evidently not simple at all and trying to simplify it can do harm. Afghanistan, climate change, Covid? Even physics can quickly hit complexity. Consider the humble snowflake. Is that simple? Yes and no. Its hexagonal pattern apparently derives from nature’s most efficient way of joining H2O molecules. But as Ken Libbrecht has written: “The growth of snowflakes is a highly nonlinear, nonequilibrium phenomenon, for which subtle processes at the nanoscale can profoundly affect the development of complex patterns at all scales. Understanding their formation requires a rich synthesis of molecular dynamics, surface physics, growth instabilities, pattern formation and statistical mechanics.”
The upshot is that we cannot say how even a single damn snowflake will turn out. Even simple mechanisms, stuck together, quickly form a path to unfathomable complexity— which, by the way, can be as aesthetically seductive as simplicity. A sleek theory holds undoubted aesthetic appeal, but there can be exquisite beauty in complexity too, which makes life interesting, renders nature more mysterious and saves us from predictability.
This complexity is perfectly consistent with McFadden’s argument. A set of simple rules can have Byzantine, unpredictable consequences. But it does mean in the end that the book invites as many questions as it offers answers, especially as there’s so little space for doubters, or for real consideration of counter arguments. And you do wonder at times if McFadden has been on a rampant confirmation-bias trip, seeking any reference anywhere that suggests a loose affinity with William’s thought to claim that he was father to just about every great scientific idea since the 14th century.
But McFadden’s love for William is hard to resist. If you are at all interested in the history of ideas, this is a fabulous read. Even after you’ve taken a few detours through other material to become better oriented in the controversy over what exactly he’s good for, William plausibly still stands as a daring, original figure who deserves a place in the Pantheon, and McFadden has done a great service in bringing the whole William and his influence to wider attention. In short, Life is Simple is enthralling. But whether life is simple, and how or whether Occam can help, is another book.