(Roughly) Daily

“Nature is pleased with simplicity”*…

As Clare Booth Luce once said, sometimes “simplicity is the ultimate sophistication”…

… 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…

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.

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…

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.

Does the existence of a multiverse hold the key for why nature’s laws seem so simple? “Why simplicity works,” from JohnJoe McFadden (@johnjoemcfadden)

* “Nature does nothing in vain when less will serve; for Nature is pleased with simplicity and affects not the pomp of superfluous causes.” – Isaac Newton, The Mathematical Principles of Natural Philosophy


As we emphasize the essential, we might spare a thought for Martin Gardner; he died on this date in 2010. Though not an academic, nor ever a formal student of math or science, he wrote widely and prolifically on both subjects in such popular books as The Ambidextrous Universe and The Relativity Explosion and as the “Mathematical Games” columnist for Scientific American. Indeed, his elegant– and understandable– puzzles delighted professional and amateur readers alike, and helped inspire a generation of young mathematicians.

Gardner’s interests were wide; in addition to the math and science that were his power alley, he studied and wrote on topics that included magic, philosophy, religion, and literature (c.f., especially his work on Lewis Carroll– including the delightful Annotated Alice— and on G.K. Chesterton).  And he was a fierce debunker of pseudoscience: a founding member of CSICOP, and contributor of a monthly column (“Notes of a Fringe Watcher,” from 1983 to 2002) in Skeptical Inquirer, that organization’s monthly magazine.


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