ON MY daily drive into work at the University of Surrey, I pass a road sign to Ockham. Perhaps a slight difference in spelling is one reason why it took me a surprising while to realise the English village鈥檚 connection to one of the most fundamental concepts in science 鈥� I would argue, in my now more enlightened state, perhaps its most fundamental concept.
I am talking about Occam鈥檚 razor. The creation of a 14th-century theologian with a racy life story, this is a principle often quoted as 鈥渆ntities should not be multiplied beyond necessity鈥�. It urges us to choose the simplest explanations or models for any phenomenon we observe. If you see moving lights in the night sky, say, think of known existing entities such as aeroplanes, satellites or shooting stars before considering flying saucers.
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It has been a tool for scientific progress, not to mention a guiding principle for our own thoughts, right up to the present day. But I believe that modern science has rather lost sight of the simple fact that simplicity is the sharpest guide to greater truths.
Ockham is linked to Occam鈥檚 razor by virtue of William of Ockham. Born in the village around 1285, William went to a local Franciscan school before being sent to Oxford to study theology, then known as 鈥渢he Queen of Sciences鈥�. This title was largely due to the influence of Italian theologian Thomas Aquinas, who had recently Christianised the work of the greatest scientist of ancient Greece, Aristotle.
That mind-meld had supplied five scientific 鈥減roofs鈥� of the existence of God, a variety of metaphysical essences of reality known as 鈥渦niversals鈥�, and diverse accounts of objects in terms of their ultimate purpose or telos. The purpose of acorns was to feed pigs, for example, while the purpose of pigs was to feed humans and the purpose of humans was to worship God.
Religious scholars of the time were assiduously dissecting the world into its plethora of universals, but when William arrived in Oxford, he was having none of it. He wielded his razor for the first time as he claimed these were all entities multiplied beyond necessity. He went on to insist that science and religion should never be mixed, because science is based on reason, whereas religion derives from faith. He was, I believe, the first person to so clearly separate science from its religious tethers, a move crucial to science鈥檚 subsequent secular development.
These weren鈥檛 universally popular innovations. They earned William a charge of teaching heresy and a summons to be tried before Pope John XXII in Avignon, in present-day France. His trial lasted about four years, but was never completed. William was forced to flee, chased by a posse of papal soldiers, after countercharging that the Pope himself was a heretic. He accepted the protection of the Holy Roman Emperor Louis IV of Bavaria, then in bitter dispute with the Pope, and spent much of the rest of his life writing what might be interpreted as mildly snarky treatises about the nature of political and religious authority.
His razor, meanwhile, acquired many devotees. Nicolaus Copernicus was one early adopter. Confronted with the 鈥渕onstrous鈥� complexity of the dominant idea that other astronomical bodies circled our planet, he declared in his Commentariolus of 1543 that the planetary motions 鈥渃ould be solved with fewer and much simpler constructions鈥�. That hunt for greater simplicity led him to the model of planets orbiting the sun. Johannes Kepler later discerned an even greater simplification, finding three mathematical laws of planetary motion applicable to all orbiting bodies 鈥� laws later explained in terms of Isaac Newton鈥檚 laws of motion and gravity that were as valid on Earth as in the heavens. That confirmed William鈥檚 own speculation some 350 years earlier that 鈥淚t appears to me鈥� that the matter in the heavens is of the same kind as the matter here below. And this is because plurality should never be posited without necessity.鈥�
The history of science is littered with similar stories of scientists allowing simplicity to guide them to greater understanding. But Occam鈥檚 razor seems to have gone rather out of fashion in today鈥檚 world of large data sets. That is even though it is embedded in one of our most powerful tools for dealing with them, one that is increasingly seen as fundamental to data-driven science: Bayesian inference.
Invented by Thomas Bayes 鈥� another religious man, this time a Presbyterian minister 鈥� in the 18th century, Bayesian inference is a tool that allows us to update a prior belief in a model, theory or explanation as new information comes in. Think of two dice, one six-sided and the other 60-sided. Suppose I throw one of these. I don鈥檛 tell you which, but reveal that it landed on a 4. You still don鈥檛 know which die I threw, but Bayesian inference provides a mathematical framework through which you can state that it is far more likely to have been the six-sided die (10 times as likely, in fact) 鈥� purely because there are many more other numbers that the 60-sided die could have produced.
Simple theories or models, such as Copernicus鈥檚 heliocentric solar system, are like the six-sided die: they make sharp predictions. Complex theories or models, such as Ptolemy鈥檚 model of everything orbiting our planet, are like the 60-sided die, making looser predictions that can fit a wider range of data. When we acquire information that fits with both simple and complex models, Bayesian inference, a mathematical embodiment of Occam鈥檚 razor, urges us to accept the simpler option because it is more likely to be the source of the data.
That goes against a grain in my own field of systems biology, which deals with modelling complex biological systems. The discipline has come of age since 2000, when the first draft of the human genome sequence was unveiled. At first, the promised new era of medicine informed by the knowledge of our genome seemed slow in coming. The finger of blame was pointed at the way biologists treated genes in isolation, rather than as components of complex, dynamic systems. My field galloped to the rescue by providing complex mathematical models of multiple genes and their innumerable interactions. But a problem then arose: where do you stop? Should models include 10 genes, 100, 1000, 10,000 鈥� or the entire human genome?
My own interest in Occam鈥檚 razor was piqued about 10 years ago, when one of the founders of systems biology, my colleague and friend Hans Westerhoff, presented a seminar at Surrey entitled 鈥淣o Occam鈥檚 razor for systems biology鈥�. He argued that models of life鈥檚 workings needed to be as complex as possible to capture the high-level emergent properties that depend on interactions between genes and their products.
鈥淥ccam鈥檚 razor isn鈥檛 just a tool of science 鈥� it is science鈥�
I have come to disagree. Although complex pathways and interactions certainly exist in living cells, unless we have evidence that their presence is needed to account for the data we see, we should eliminate them from our models: otherwise, we risk filling them with experimental noise. Together with my colleagues Katharina N枚h and Axel Theorell at the J眉lich Research Centre in Germany, I am part of a team developing tools that apply the razor to slice through millions of candidate models of metabolism to find the simplest that work.
Truth in simplicity
My debate with Westerhoff and others continues, but my exploration of the impact of William鈥檚 logic has convinced me that Occam鈥檚 razor isn鈥檛 just a tool of science 鈥� it is science. Whether we are building bridges using Newtonian mechanics or employing our understanding of the genetic code to make covid-19 vaccines, science is essentially the search for the simplest models. To find them, and develop concepts and technologies from them, we use additional tools, such as experimentation, mathematics and logic.
But none of these tools is unique to science. Cooks experiment with new recipes, just as musicians experiment with harmonies, while mathematics and logic are as essential to accountants as they are to physicists. And using the tools doesn鈥檛 make something a science. Despite centuries of experimentation, alchemy didn鈥檛 develop into a science because its 鈥渢heories鈥� were junkyards of entities beyond necessity. Astrologers have wasted centuries using mathematics to make useless predictions.
Some people cite Karl Popper鈥檚 鈥渇alsifiability鈥� criterion 鈥� that scientific theories can be disproved 鈥� as what distinguishes science from, say, religion. But as well as being equally applicable to many human activities, such as law, falsifiability doesn鈥檛 work. It is as impossible to disprove as to prove a hypothesis. The best we can do is compare the probabilities of rival hypotheses. And it is with that sort of thing that simplicity, as embodied in Occam鈥檚 razor, has always provided the best way.
Johnjoe McFadden is the author of Life Is Simple. To buy a copy, go to
