Occam's Razor

 

On the night of May 26th, 1328, three Franciscan friars slip out of the papal city of Avignon and ride south to the Crusader port of Aigues-Mortes. Two were senior members of the order whereas the third was a little-known English scholar, William of Occam. If captured, they could face excommunication, imprisonment or even a slow death on a burning pyre.
 
We know little of William’s early years, only that he was born in the Surrey village of Occam and given to the Franciscan order as a child. The Franciscans sent him to the University of Oxford to study the science of theology. That there was such a discipline seems very odd today, but throughout most of human history, there hadn’t really been a distinction between the natural and supernatural.
 
More than a thousand years earlier, Aristotle attempted to pull a thread of science out of observations such as “everything that moves is moved by another” But he also drifted into his metaphysics by arguing that, to avoid an infinite regress of movers, there had to be a first cause or prime mover. He also believed that some causes lay in the future, in the form of the purpose of objects or actions. So, the purpose of trees was to provide wood, the purpose of wood was to provide fire, the purpose of fire was to warm humans. He again capped this otherwise infinite regress with the prime mover.
 
Aristotle was also keen on categorising and provided the first stab at biological taxonomy by dividing plants and animals into categories. However, he based his categorisation on the notion of invisible but real universals, which are kind of invisible essences of objects. So cats became cats because they were filled with a feline universal, dogs with a canine universal and so on. He extended the universal idea into every category of being, so universals of redness, roundness, chairness, fatherness and so on was what made objects red, round, fathers or chairs.
 
Aristotle’s prime mover was more of an it than a him, but was nevertheless enthusiastically incorporated into Christianity by the greatest theologian of the Middle Ages, Thomas Aquinas. Aquinas imported Aristotle’s framework to construct a kind of scientific theology whose closest parallel today might be the “experimental theology” in Philip Pullman’s His Dark Materials novels. Its cornerstone was five proofs of God constructed with Aristotle’s chains of reasoning but the Christian God replacing both the prime mover and final cause. Aquinas also imported Aristotle’s universals as ideas in God’s mind so their study became a route to the divine, so theology became a science. By a clever manipulation of the universal idea, Aquinas even claimed to have incorporated the Eucharist miracle into his theological science.
 
Aquinas’s theology came to dominate Christianity. If its fusion with science had survived then science in the West might have suffered the same stagnation under the weight of dogma that it suffered in so many other parts of the world. Fortunately, William of Occam had a tool sharp enough to sever the link.
 
William of Occam is most famous for insisting that “entities should not be multiplied beyond necessity”. Occam’s razor advises that we should only accept the simplest solution to a problem, as long as it works. He used his razor to argue first that universals are entities beyond necessity because “fathers are fathers [simply] because they have sons”, dogs because they bark etc. With universals dismissed, scientific theology and its route to God tumbled. It collapsed completely after Occam went on to demolish all five of Aquinas’s so-called proofs of God. For example, he argued that final causes or purposes are also entities beyond necessity writing that “why does the fire heat the wood … it is its nature”.
 
 
Occam maintained that the only route to God is through faith, not reason, whereas reason, rather than faith, is the path to science. To assure the independence of science, he advised that “assertions, especially in physics, which do not pertain to theology should not be officially condemned or prohibited by anyone because in such things everyone should be free so that they may freely say what they please”.
 
As far I am aware, William is the first person in the history of the world to so clearly separate science from religion. Nearly all the greatest scientists up to the 20th century embraced Occam’s separation and his razor.
 
Back in the 14th century, William’s radical ideas caused consternation within the cloisters of Oxford. A former chancellor argued that his elimination of universals threatened the Catholic faith by knocking holes in Aquinas’s interpretation of the Eucharist miracle. About two centuries later, this same issue would precipitate the Reformation. Early in 1324, it precipitated a summons that arrived in Oxford, charging William to attend trial at the papal seat in Avignon to face charges of teaching heresy.
 
William reached Avignon probably early in the summer of 1324. His trial was lengthy and, in 1327, Pope John XXII issued a bull charging Occam with having uttered “many erroneous and heretical opinions”. However, by this time William had become embroiled in an even more dangerous conflict between the Pope and the Franciscan order.
 
Founded by St Francis, the Franciscans insisted that the surest way to holiness was to follow Jesus’s example of abandoning wealth to live in a state of apostolic poverty. The wealthiest man in Christendom, Pope John XXII, who was busy building the magnificent Palais de Papes in Avignon, disagreed. The dispute was pinned onto the seemingly trivial issue of whether Jesus owned a purse. The Franciscans were scandalised whereas Pope John insisted that Jesus not only owned a purse but, as the son of God, one filled with ownership of the world.
 
This was a pivotal notion in the Middle Ages because the papacy claimed that, on his death, Jesus had bequeathed ownership, or dominion – considered to be another universal – to St Peter who bequeathed it to succeeding popes, who bestowed it on Christian kings, who divided it out amongst their nobles. Nearly 200 years later and Pope Alexander VI claimed this same divine dominion to divide South America between the Spanish and Portuguese crowns.
 
Despite the heresy charges, as the cleverest scholar at their disposal, the Franciscans gave William the job of deliberating on John XXII’s arguments. Occam concluded that not only was the Pope wrong, but his writings proved him to be a heretic. This is what provoked the Franciscans’ flight, chased by a posse of Vatican soldiers. They escaped to board a ship which took them to Italy and the protection of the Holy Roman Emperor, who happened to be crowning a rival Pope in Rome at the time.
 
William spent the rest of his life under the protection of the Holy Roman Emperor. He continued to attack papal authority and was pursued by agents of several popes, one of whom threatened to burn down the town of Tournai in modern-day Belgium to capture the fugitive.
 
On the vexed question of apostolic poverty vs papal dominion, William upended the entire medieval world order by insisting that God has given everyone the same natural right to sustenance, safety and shelter. These rights were real, but money, property and dominion were entirely human inventions that, like the universal of fatherhood, only existed in the minds of people who believed in them. So, the Pope’s claim for worldly dominion was as empty as Jesus’s purse.
  
William also insisted that the authority of rulers derived from the ruled “from God through his people” and that “power should not be entrusted to anyone without the consent of all”. Since pagans and infidels were also descended from Adam and Eve, they had inherited the same natural rights as Christians.
 
William of Occam was excommunicated after fleeing Avignon, but this was rescinded by Pope Innocent VI in 1359. His razor, insisting on the simplest solutions, remains central to science and is an invaluable adversary against pseudoscience, dogma, conspiracy theories or general baloney.
 
As a fearless defender of natural rights against institutional authority and the first to clearly separate science from religion, he is a worthy contender for the title of patron saint of our secular world.
 
 
William of Occam: the patron saint of the modern secular world. By Johnjoe McFadden.  The Irish Times,  September 9, 2021.

It’s May 1964 and, on a low hillside in New Jersey, the physicists Robert Woodrow Wilson and Arno Allan Penzias are listening in on the Universe. They are standing beneath what looks like a gargantuan ear trumpet attached to a garden shed: the Holmdel Horn Antenna, built by Bell Laboratories to investigate microwaves as an alternative to radio waves for telecommunication. When interest in microwave communication waned, Bell lent out the Holmdel horn to interested scientists.
 
Penzias and Wilson were interested. Both aged around 30, they planned to map the sky with microwaves. But they were baffled: when they pointed the horn at a dark region beyond the galaxy and only sparsely populated with stars, instead of the silence they expected, they detected a kind of background hiss – a hiss that filled the entire sky.
 
Meanwhile, the physicist Robert H Dicke was working on a related puzzle. Two decades earlier, Dicke had invented the microwave detector. Now he and his lab were trying to develop sensitive instruments to test the cosmological predictions that emerged from Albert Einstein’s general theory of relativity, particularly how it related to Edwin Hubble’s astonishing discovery that the Universe is expanding. The reigning, steady-state theory claimed that the Universe had always been expanding, balanced by a continuous creation of new matter. The rival theorists, including Dicke, took expansion at its face value, running it backwards in time to propose that, about 14 billion years ago, the Universe burst into existence in a cataclysmic explosion from a very tiny point.
 
An exploding universe should have left a uniform faint cloud of microwave radiation, which Dicke’s team was determined to find. News of the group’s efforts reached Penzias and Wilson, prompting Penzias to give Dicke a call. Over a brownbag lunch, Dicke’s colleagues recall him picking up the receiver, repeating phrases such as ‘horn antenna’ and nodding. After hanging up, he turned to his group and said: ‘Well boys, we’ve been scooped.’ Dicke realised that Penzias and Wilson had discovered the Big Bang.
 
The uniformity of the cosmic microwave background (CMB) tells us that, at its birth, ‘the Universe has turned out to be stunningly simple,’ as Neil Turok, director emeritus of the Perimeter Institute for Theoretical Physics in Ontario, Canada, put it at a public lecture in 2015. ‘[W]e don’t understand how nature got away with it,’ he added. A few decades after Penzias and Wilson’s discovery, NASA’s Cosmic Background Explorer satellite measured faint ripples in the CMB, with variations in radiation intensity of less than one part in 100,000. That’s a lot less than the variation in whiteness you’d see in the cleanest, whitest sheet of paper you’ve ever seen.
 
Wind forward 13.8 billion years, and, with its trillions of galaxies and zillions of stars and planets, the Universe is far from simple. On at least one planet, it has even managed to generate a multitude of life forms capable of comprehending both the complexity of our Universe and the puzzle of its simple origins. Yet, despite being so rich in complexity, some of these life forms, particularly those we now call scientists, retain a fondness for that defining characteristic of our primitive Universe: simplicity.
 
 
The Franciscan friar William of Occam (1285-1347) wasn’t the first to express a preference for simplicity, though he’s most associated with its implications for reason. The principle known as Occam’s Razor insists that, given several accounts of a problem, we should choose the simplest. The razor ‘shaves off’ unnecessary explanations, and is often expressed in the form ‘entities should not be multiplied beyond necessity’. So, if you pass a house and hear barking and purring, then you should think a dog and a cat are the family pets, rather than a dog, a cat and a rabbit. Of course, a bunny might also be enjoying the family’s hospitality, but the existing data provides no support for the more complex model. Occam’s Razor says that we should keep models, theories or explanations simple until proven otherwise – in this case, perhaps until sighting a fluffy tail through the window.
 
Seven hundred years ago, William of Occam used his razor to dismantle medieval science or metaphysics. In subsequent centuries, the great scientists of the early modern era used it to forge modern science. The mathematician Claudius Ptolemy’s (c100-170 CE) system for calculating the motions of the planets, based on the idea that the Earth was at the centre, was a theory of byzantine complexity. So, when Copernicus (1473-1543) was confronted by it, he searched for a solution that ‘could be solved with fewer and much simpler constructions’. The solution he discovered – or rediscovered, as it had been proposed in ancient Greece by Aristarchus of Samos, but then dismissed by Aristotle – was of course the solar system, in which the planets orbit around the Sun. Yet, in Copernicus’s hands, it was no more accurate than Ptolemy’s geocentric system. Copernicus’s only argument in favour of heliocentricity was that it was simpler.
 
Nearly all the great scientists who followed Copernicus retained Occam’s preference for simple solutions. In the 1500s, Leonardo da Vinci insisted that human ingenuity ‘will never devise any [solutions] more beautiful, nor more simple, nor more to the purpose than Nature does’. A century or so later, his countryman Galileo claimed that ‘facts which at first seem improbable will, even on scant explanation, drop the cloak which has hidden them and stand forth in naked and simple beauty.’ Isaac Newton noted in his Principia (1687) that ‘we are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances’; while in the 20th century Einstein is said to have advised that ‘Everything should be made as simple as possible, but not simpler.’ In a Universe seemingly so saturated with complexity, what work does simplicity do for us?
 
Part of the answer is that simplicity is the defining feature of science. Alchemists were great experimenters, astrologers can do maths, and philosophers are great at logic. But only science insists on simplicity. Many advances of modern science involved a succession of simplifications, either through unifying previously disparate phenomena or by eliminating superfluous entities. Probably the greatest simplification was provided by Newton, who unified trillions of motions, both on Earth and in the heavens, into just three laws of motion and one of gravity. Then in the late 19th century, Ludwig Boltzmann extended Newton’s laws into the microscopic realm to provide an economical explanation of heat as a measure of the motion of atoms. Einstein achieved perhaps the most radical simplification by unifying space and time within a single entity, spacetime. Charles Darwin and Alfred Russel Wallace had brought the entire natural world under a single law of natural selection; while the work of Louis Pasteur, Gregor Mendel, Hugo de Vries, James Watson, Francis Crick and many others dispensed with the vital principle to extend simple scientific laws into biology. Each scientist considered their advance to deliver a simplification that eliminated superfluous complexity. As Wallace, the co-discover of natural selection, put it: ‘The theory itself is exceedingly simple.’

 
Just why do simpler laws work so well? The statistical approach known as Bayesian inference, after the English statistician Thomas Bayes (1702-61), can help explain simplicity’s power. Bayesian inference allows us to update our degree of belief in an explanation, theory or model based on its ability to predict data. To grasp this, imagine you have a friend who has two dice. The first is a simple six-sided cube, and the second is more complex, with 60 sides that can throw 60 different numbers. Suppose your friend throws one of the dice in secret and calls out a number, say 5. She asks you to guess which dice was thrown. Like astronomical data that either the geocentric or heliocentric system could account for, the number 5 could have been thrown by either dice. Are they equally likely? Bayesian inference says no, because it weights alternative models – the six- vs the 60-sided dice – according to the likelihood that they would have generated the data. There is a one-in-six chance of a six-sided dice throwing a 5, whereas only a one-in-60 chance of the 60-sided dice throwing a 5. Comparing likelihoods, then, the six-sided dice is 10 times more likely to be the source of the data than the 60-sided dice.
 
Simple scientific laws are preferred, then, because, if they fit or fully explain the data, they’re more likely to be the source of it. With more knobs to tweak, arbitrarily complex models such as Ptolemy’s astronomical system could be made to fit any dataset. As the mathematician John von Neumann once quipped: ‘with four parameters I can fit an elephant, and with five I can make him wiggle his trunk’.
 
Is there more to simplicity than probability? Many of the greatest scientists and philosophers were devotees of what might be called a strong version of Occam’s Razor. This claims that the world is about as simple as it can be, consistent with our existence. The theoretical physicist and Nobel Laureate Eugene Wigner’s influential paper ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences’ (1960) argued that the extraordinary ability of mathematics to make sense of the world is a puzzle. An analogous case can be made for the success of simplicity in science. Why is Occam’s Razor so unreasonably effective? Why does simplicity work so well?
 
Consider how, when Einstein first attempted to incorporate gravity and acceleration into relativity, he eschewed any considerations of ‘beauty and simplicity’. Instead, he favoured what is called completeness: the incorporation of the maximum amount of available information into a model. Yet a decade of struggling with complex equations met with failure. He eventually changed tack to embrace Occam’s Razor, accepting only the simplest and most elegant equations, and later testing them against physical facts. This time, Einstein struck gold, unearthing his general theory of relativity in 1915. Thereafter, he insisted that ‘equations of such complexity … can be found only through the discovery of a logically simple mathematical condition that determines the equations completely or almost completely.’
 
But could it be simpler still? Why are there 17 particles in the Standard Model of particle physics when we are composed of only a handful? If the Universe is maximally simple, why are trillions of almost massless and electrically neutral neutrinos passing through our bodies every second? Surely neutrinos are entities beyond our necessity? Another candidate for an entity beyond necessity is the mysterious dark matter, of which our Universe appears to be chiefly composed. Why does a simple universe harbour so much apparently superfluous stuff?
 
In fact, both dark matter and neutrinos are essential for our existence. Neutrinos are a necessary byproduct of the stellar nuclear-fusion reactions that fuse protons to make helium nuclei, plus the heat and light that make life possible. One of physics’ laws of conservation demands that the total number of leptons (electrons, muons, tau particles and neutrinos) must remain constant. This can be satisfied in the stellar fusion reaction only through the release of massive numbers of neutrinos. Similarly for dark matter. In the early Universe, it acted as a kind of cosmological clotting agent that helped to coalesce the diffuse gas that emerged from the Big Bang into the lumpy clouds that became galaxies, stars, planets and eventually us. Haloes of dark matter at the edge of galaxies also act as galactic guardians, deflecting high-speed supernovae remnants rich in the heavy elements essential for life, from shooting off into the vast empty reaches of intergalactic space.
 
In my latest book, I propose a radical, if speculative, solution for why the Universe might in fact be as simple as it’s possible to be. Its starting point is the remarkable theory of cosmological natural selection (CNS) proposed by the physicist Lee Smolin. CNS proposes that, just like living creatures, universes have evolved through a cosmological process, analogous to natural selection.
 
Smolin came up with CNS as a potential solution to what’s called the fine-tuning problem: how the fundamental constants and parameters, such as the masses of the fundamental particles or the charge of an electron, got to be the precise values needed for the creation of matter, stars, planets and life. CNS first notes the apparent symmetry between the Big Bang, in which stars and particles were spewed out of a dimensionless point at the birth of our Universe, and the Big Crunch, the scenario for the end of our Universe when a supermassive black hole swallows up stars and particles before vanishing back into a dimensionless point. This symmetry has led many cosmologists to propose that black holes in our Universe might be the ‘other side’ of Big Bangs of other universes, expanding elsewhere. In this scenario, time did not begin at the Big Bang, but continues backwards through to the death of its parent universe in a Big Crunch, through to its birth from a black hole, and so on, stretching backward in time, potentially into infinity. Not only that but, since our region of the Universe is filled with an estimated 100 billion supermassive black holes, Smolin proposes that each is the progenitor of one of 100 billion universes that have descended from our own.
 
The model Smolin proposed includes a kind of universal self-replication process, with black holes acting as reproductive cells. The next ingredient is heredity. Smolin proposes that each offspring universe inherits almost the same fundamental constants of its parent. The ‘almost’ is there because Smolin suggests that, in a process analogous to mutation, their values are tweaked as they pass through a black hole, so baby universes become slightly different from their parent. Lastly, he imagines a kind of cosmological ecosystem in which universes compete for matter and energy. Gradually, over a great many cosmological generations, the multiverse of universes would become dominated by the fittest and most fecund universes, through their possession of those rare values of the fundamental constants that maximise black holes, and thereby generate the maximum number of descendant universes.
 
Smolin’s CNS theory explains why our Universe is finely tuned to make many black holes, but it does not account for why it is simple. I have my own explanation of this, though Smolin himself is not convinced. First, I point out that natural selection carries its own Occam’s Razor that removes redundant biological features through the inevitability of mutations. While most mutations are harmless, those that impair vital functions are normally removed from the gene pool because the individuals carrying them leave fewer descendants. This process of ‘purifying selection’, as it’s known, maintains our genes, and the functions they encode, in good shape.
 
However, if an essential function becomes redundant, perhaps by a change of environment, then purifying selection no longer works. For example, by standing upright, our ancestors lifted their noses off the ground, so their sense of smell became less important. This means that mutations could afford to accumulate in the newly dispensable genes, until the functions they encoded were lost. For us, hundreds of smell genes accumulated mutations, so that we lost the ability to detect hundreds of odours that we no longer need to smell. This inevitable process of mutational pruning of inessential functions provides a kind of evolutionary Occam’s Razor that removes superfluous biological complexity.
 

Perhaps a similar process of purifying selection operates in cosmological natural selection to keep things simple. Instead of biological mutations, we have tweaks to fundamental constants of universes as they pass through black holes. Let’s imagine that our Universe contains two black holes that are the proud parents of two baby universes. When the constants (the masses of particles, the charge of an electron and so forth) pass through the first black hole, they remain unchanged. As a consequence, a universe very like our own evolves, which we will call the 17P universe, reflecting the fact that it possesses 17 fundamental particles. However, in the second black hole, a tweak (mutation) to the fundamental constants generates a universe with one extra particle. This particle plays no role in black-hole formation, nor in the formation of stars or life, but instead merely hangs around, perhaps in intergalactic clouds. The 18th particle is an entity beyond necessity in this 18P universe.
 
Let’s additionally suppose that 18P’s extra particle has average mass and abundance for fundamental particles, so that it accounts for about one-18th of total mass in that universe. This locking away of mass in the intergalactic clouds of particle 18 will diminish the amount of matter/energy available for black-hole formation. As a consequence, the presence of particle 18 will reduce the number of black holes by one-18th, or about 5 per cent. Since black holes are the mothers of universes, the 18P universe will generate around 5 per cent fewer progeny than its sibling, the 17P universe. This difference in fecundity will continue into succeeding generations until, by about generation 20, descendants of the 18P universe will be one-third as abundant as descendants of the more parsimonious 17P universe. In the natural world, mutations that lead to just a 1 per cent reduction in fitness are sufficient to drive a mutant into extinction, so a 5 per cent decrease in fitness is likely to eliminate, or at least drastically reduce, the abundance of 18-particle universes, relative to their more parsimonious 17-particle universes.
 
It’s unclear whether the kind of multiverse envisaged by Smolin’s theory is finite or infinite. If infinite, then the simplest universe capable of forming black holes will be infinitely more abundant than the next simplest universe. If instead the supply of universes is finite, then we have a similar situation to biological evolution on Earth. Universes will compete for available resources – matter and energy – and the simplest that convert more of their mass into black holes will leave the most descendants. For both scenarios, if we ask which universe we are most likely to inhabit, it will be the simplest, as they are the most abundant. When inhabitants of these universes peer into the heavens to discover their cosmic microwave background and perceive its incredible smoothness, they, like Turok, will remain baffled at how their universe has managed to do so much from such a ‘stunningly simple’ beginning.
 
The cosmological razor idea has one further startling implication. It suggests that the fundamental law of the Universe is not quantum mechanics, or general relativity or even the laws of mathematics. It is the law of natural selection discovered by Darwin and Wallace. As the philosopher Daniel Dennett insisted, it is ‘The single best idea anyone has ever had.’ It might also be the simplest idea that any universe has ever had.
 
Why Simplicity Works. By Johnjoe McFadden. Aeon, October 11, 2021. 

What is Occam’s Razor?
 
Johnjoe McFadden, Professor of Molecular Genetics at the University of Surrey, joined  Seán Moncrieff on The Moncrieff Show. Newstalk, October 21, 2021. 

Astonishing where an idea can lead you. You start with something that 800 years hence will sound like it’s being taught at kindergarten: fathers are fathers, not because they are filled with some ‘essence of fatherhood’, but because they have children.
 
Fast-forward a few years, and the Pope is trying to have you killed. Not only have you run roughshod over his beloved eucharist (justified, till then, by some very dodgy Aristotelian logic-chopping); you’re also saying there’s no ‘essence of kinghood’, either. If kings are only kings because they have subjects, then, said William of Occam, ‘power should not be entrusted to anyone without the consent of all’. Heady stuff for 1334.
 
How this progression of thought gave birth to the very idea of modern science is the subject of what may be the most sheerly enjoyable history of science of recent years.
 
William was born around 1288 in the little town of Ockham in Surrey. He was probably an orphan; at any rate he was given to the Franciscan order at about the age of 11. He shone at Greyfriars in London, and around 1310 was dispatched to Oxford’s newfangled university. All manner of intellectual, theological and political shenanigans followed, mostly to do with William’s efforts to demolish almost the entire edifice of medieval philosophy.
 
It needed demolishing, and that’s because it still held to Aristotle’s ideas about what an object is. He wondered how single objects and multiples can co-exist. His solution: categorise everything. A cherry is a cherry is a cherry, and all cherries have cherryness in common. A cherry is a ‘universal’; the properties that might distinguish one cherry from another are ‘accidental’.
 
The trouble with Aristotle’s universals, though, is that they assume a one-to-one correspondence between word and thing, and posit a universe made up of a terrifying number of unique things — at least one for each noun or verb in the language. And the problem with that is that it’s an engine for making mistakes.
 
Medieval philosophy relied largely on syllogistic reasoning, juggling things into logical-looking relations. ‘Socrates is a man, all men are mortal, so Socrates is mortal.’ So he is, but — and this is crucial — this conclusion is arrived at more by luck than good judgment. The statement isn’t ‘true’ in any sense; it’s merely internally consistent. Imagine we make a mistake. Imagine we spring from a society where beards are pretty much de rigueur (classical Athens, say, or Farringdon Road). Imagine we said: ‘Socrates is a man, all men have beards, therefore Socrates has a beard’? Though one of its premises is wrong, the statement barrels ahead regardless; it’s internally consistent, and so, if you’re not paying attention, it creates the appearance of truth. But there’s worse: the argument that gives Socrates a beard might actually be true. Some men do have beards. Socrates may be one of them. And if he is, that beard seems — again, if you’re not paying attention — to confirm a false assertion.
 
William of Occam understood that our relationship with the world is a lot looser, cloudier and more indeterminate than syllogistic logic allows. That’s why, when a tavern owner hangs a barrel hoop outside his house, passing travellers know they can stop there for a drink. The moment words are decoupled from things they act as signs, negotiating flexibly with a world of blooming, buzzing confusion.
 
Once we take this idea to heart, then very quickly — and as a matter of taste more than anything — we discover how much more powerful straightforward explanations are than complicated ones. Occam came up with a number of versions of what even then was not an entirely new idea: ‘It is futile to do with more what can be done with less,’ he once remarked. Subsequent formulations do little but paint this lily.
 
His idea proved so powerful that three centuries later the French theologian Libert Froidmont coined the term ‘Occam’s Razor’, to describe how we arrive at good explanations by shaving away excess complexity. As Johnjoe McFadden shows, that razor’s still doing useful work.
 
Life is Simple is primarily a history of science, tracing William’s dangerous idea through astronomy, cosmology, physics and biology, from Copernicus to Brahe, Kepler to Newton, Darwin to Mendel, Einstein to Noether to Weyl. But McFadden never loses sight of William’s staggering, in some ways deplorable, influence over the human psyche as a whole. For if words are independent of things, how do we know what’s true?
 
Thanks to William of Occam, we don’t. The universe, after Occam, is unknowable. Yes, we can come up with explanations of things, and test them against observation and experience; but from here on in, our only test of truth will be utility. Ptolemy’s 2nd-century Almagest, a truly florid description of the motions of the stars and planetary paths, is not and never will be wrong; the worst we can say is that it’s overcomplicated.
 
In the Coen brothers’ movie The Big Lebowski, an exasperated Dude turns on his friend: ‘You’re not wrong, Walter,’ he cries, ‘you’re just an asshole.’ William of Occam is our universal Walter, and the first prophet of our disenchantment. He’s the friend we wish we’d never listened to when he told us Father Christmas was not real.
 
The great disrupter: how William of Occam overturned medieval thought. By Simon Ings. The Spectator, August 28, 2021.

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.” 
 
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?  

 
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.
 
Occam’s razor and the limits of simplicity. By Michael Blastland. Prospect,  September 15, 2021

William of Ockham is the medieval philosopher who gave us what is perhaps the world's only metaphysical knife. Raised by Franciscan friars and educated at Oxford in the late 13th century, he focused his energies on what can only be described as esoterica, topics spanning theology and politics. In service of this occupation, he clashed with Pope John XXII and was excommunicated by the Catholic Church.

 Ockham's exploration of the philosophical concept of nominalism and his preference for parsimony in logical arguments gave rise to the concept of Ockham's Razor (sometimes spelled "Occam"). Stated plainly, the Razor asserts that if two models equally explain a scenario, the simpler of the two is more likely.

 Remarkably, this principle has been applied and contested for seven-hundred years, though the metaphor of the Razor itself surfaced after Ockham's death. Yet the boundaries of science have expanded into the territories of quantum mechanics, human behavior, and artificial intelligence — complicated fields, where "simplicity" may not always apply. To that, one might reasonably ask if Ockham's Razor is still a useful principle when it comes to science. In other words: Is the Razor still sharp?

 The Value of the Razor

  In his book "The Demon-Haunted World," the late Carl Sagan introduces a thought experiment of a dragon in his garage. When Sagan convinces someone to come look at the dragon, the visitor opens the garage door and finds nothing there. Sagan then counters that "she's an invisible dragon," and, naturally, cannot be seen. The visitor suggests setting up an infrared camera to catch the thermal emissions from the dragon's breath, but Sagan's dragon gives off no heat. The visitor then suggests layering the floor with flour to detect the movement of the dragon, but Sagan's dragon floats serenely, leaving no footprints nor stirring the air. At this point, most would agree with the visitor's logical conclusion: Sagan's invisible, floating, thermally-neutral pet dragon is a fiction. Ockham's Razor cuts through the chaff of Sagan's dubious explanations to suggest that given the state of the evidence – an empty garage – the most prudent interpretation is that there is no dragon.

 For those who think the example above is far-fetched, consider instead some of the more outlandish conspiracy theories circulating on the internet. To their adherents, any rational challenge to them is met with a further amendment to the original theory. The theory becomes increasingly baroque and convoluted to respond to each subsequent challenge to its initial thesis.

 If conspiracy theories are often characterized by a surplus of cobbled together amendments to shore up the original thesis, the challenges of many modern scientific research studies are more akin to a criminal investigation. The researcher finds an empty garage, looks inside, and attempts to infer what has transpired. The imaginative can concoct many stories to explain what they find, but each explanation will be subject to the biases of the investigator.

 In his classic article, "Why Most Published Research Findings Are False" John Ioannidis explains why research that examines a "greater number and lesser preselection of tested relationships" is prone to this problem. Stated another way: "seek and ye shall find." Particularly in observational studies that capture vast numbers of predictor variables, it becomes quite possible that one or more of these many variables appears to have a relationship with the outcome due to chance alone. Preselection is important, as in the absence of a conjecture of what factors matter prior to the research, it is easier to concoct a story that links variables that may simply be random noise. This problem is compounded by modern statistical software packages that make it easy to test hundreds of variables against an outcome, even when the researcher has prior reason to believe that a given variable would be linked to the outcome.

 Ockham's Razor is useful in these situations by challenging research where "everything but the kitchen sink" is tested against one or more outcomes. Sometimes, the simplest explanation of unlikely results is that the study in question is inconclusive, and any apparent relationships are more noise than signal.

 The challenge of knowing where to cut

 In physics, Ockham's Razor has long been associated with aesthetics. Simplicity and parsimony as formulated by Ockham become elegance and truth among Einstein and his contemporaries. It is said that Einstein was indifferent when told that experimental findings found evidence to support his theory of General Relativity. The theory had to be correct, he reasoned, as it was simply too elegant to be wrong. Or, in his own words, "the only physical theories that we are willing to accept are the beautiful ones."

 But defining what is "beautiful" in science is as contentious as it is in art. Though Einstein's aesthetics were prescient, it is hard to build a scientific enterprise around such intuitions.

 The essayist and science writer Philip Ball points out that Ockham's Razor has been used both to advance the "Many Worlds" interpretation of quantum mechanics as well as to critique it. (The Many World interpretation posits that there are numerous parallel universes in which all possible outcomes of binary quantum mechanical measurements are realized.)The simplicity and elegance of the theory are contingent on how we define the terms. The assumptions of the Many Worlds hypothesis may be simple, but its predictions and implications are vast and complex. So which way should the Razor cut?

 It is also easier to apply the Razor when examining past paradigm changes in science than when using it to evaluate current scientific disputes. Take the renewed debate on whether COVID-19 began as a natural zoonotic illness or emerged from a lab. To apply Ockham's Razor we have to first be much more specific about what constitutes a simple explanation. We then have to ask an even more challenging question of which theory best fits the existing data. Such a question involves determining how hard it would be for COVID-19 to naturally evolve, examining both the molecular as well as the epidemiological evidence. The point being, invoking the Razor is often easier than applying it.

 Nicks in the blade

 Ironically the preservation of Ockham's Razor over the centuries may be due to its own internal simplicity. Simply by uttering the phrase "Ockham's Razor," it is possible to challenge everything from an interpretation of a new physics experiment, to the explanation of a social movement, to a possible account for a crime scene. The Razor has broad utility in pushing back against explanations that appear to be overly complicated or continue to amend their original thesis by layering secondary and contingent explanations in response to new challenges.

 Yet in science, the Razor is just one concept that researchers might use in considering a theory. How predictive is the theory? Is it falsifiable? How well does it align with other explanations that we believe are correct? How internally consistent is it? These and many more questions all are part of the discourse of science. Ockham's Razor in and of itself is not the sole criterion for finding the truth — and applying the Razor outside of the narrow realm of statistical model selection is not so simple.

 For scientists that would equate the Razor with beauty and elegance, this only sparks the question of who gets to define beauty? Past scientific revolutions have a habit of diminishing the centrality of humans; the heavens do not revolve around us, we were not created separate from the rest of nature, our minds are not perfectly rational in their function. Believing that the universe must accord with our own sense of the beautiful seems another case of hubris and unwarranted human exceptionalism.

 A close shave

 Let's revisit the dragon in the garage. Imagine you are told that this invisible dragon can induce fatal burns without the heat and smoke of fire. You investigate further and conclude that since there is no evidence of a beast, neither the dragon nor its deadly force can exist. Hours later, you succumb to radiation burns from your exposure in the garage.

 Though Okham's Razor may not be well suited to all types of knowledge, at the boundaries of scientific knowledge it offers a rubric to test hypotheses. The Razor continues to demonstrate utility to whittle down chaff at the margins. It would be convenient if the Razor alone was sufficient to settle all scientific debate. But the world, it turns out, is not so parsimonious.

  

As science advances, does Ockham’s Razor still apply? By Luke Shors and Amit Chandra. Salon, June 13, 2021.