This article is a preview from the Autumn 2018 edition of New Humanist

There must have been times when Urbain Le Verrier did not believe it himself. How could the pages upon pages of spidery calculations with which he had filled his notebook possibly have anything to do with the messy real world? He persisted because he had faith in Isaac Newton’s universal law of gravitation; because he knew success would bring him not only fame and fortune but immortality; and because, now he had let slip about his quest to one or two people, he had no choice but to front it out.

Le Verrier was on the hunt for a new planet. What convinced him it was out there was the puzzling motion of the outermost world in the Solar System, Uranus.

Uranus had been discovered from a back garden in Bath in 1781. The announcement of its discovery by William Herschel, a freelance German musician from Hanover, created an international sensation.

Uranus was the first planet to be discovered that was unknown to the ancients and it was the first planet discovered in the age of the telescope. Orbiting the Sun in the frigid, dark wastes far beyond Saturn, the planet doubled the size of the Solar System overnight.

But there was a problem. Uranus had actually been observed by English astronomer John Flamsteed back in 1690, who had mistaken it for a star. And others had recorded it too. When the historical observations were combined with observations made after the discovery of the planet, it was possible to deduce the precise path that Uranus was taking in its 84-year journey around the Sun. The trouble was that, each time such an orbit was calculated, within only a few years the planet was found to have strayed from its allotted path.

There could, of course, have been something wrong with Newton’s law of gravity, the means by which the orbit of Uranus was calculated. But the theory had been so amazingly successful in explaining the motion of the planets, the precession of the equinoxes, ocean tides and so on that it had achieved a status comparable to the word of God. So, what was perturbing the orbit of Uranus?

Le Verrier became convinced that there must be another planet even further from the Sun than Uranus, whose gravity was tugging on the planet and causing it to wander from its predicted path. Unfortunately, he knew neither the mass nor the distance from the Sun of such a planet. And it is an annoying feature of Newton’s law of gravity that a small mass nearby can have the same perturbing effect as a big mass further away. It was just one of the many complications faced by Le Verrier as he attempted to calculate the location and properties of a hypothetical planet that could explain the anomalous motion of Uranus.

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Day after day and and late into the night, he worked, bent over his desk at Paris’s École Polytechnique. And, finally, he had an answer. But this was only the beginning of his problems. When he went to see the director of the Paris Observatory to ask for a search of the patch of sky where he believed the planet must be, François Arago fobbed him off. National observatories like the ones in Paris and at Greenwich existed principally to make tables of the locations of planets and stars for navigational purposes. This involved many people carrying out lengthy and painstaking observations. Arago did not want to use up valuable telescope time on a wild goose chase for a planet whose existence seemed to him to be the remotest of long-shots. Besides, nobody in the history of the world had ever before made such a ridiculous prediction.

Fed up and frustrated, Le Verrier wrote letters to astronomers all around Europe asking for help in his quest. One of them was a very junior astronomer at the Berlin Observatory who had sent his thesis to Le Verrier the year before (Le Verrier had ignored it). This astronomer, Johann Galle, would not even have had access to the Berlin observatory’s giant Fraunhofer refractor telescope had not director Joseph Franz Encke taken the night off to celebrate his 55th birthday.

But, on the night of 23 September 1846, Galle and his assistant, Heinrich d’Arrest, began scanning the part of the night sky specified by Le Verrier. And, incredibly, within an hour, they found a tiny fuzzy disk crawling across the sky between the constellations of Capricorn, the goat, and Aquarius, the water carrier. It was exactly the location Le Verrier had specified. (Unknown to him, the location of Neptune had also been predicted independently, though not made public, by Englishman John Couch Adams.)

The discovery of Neptune was an international sensation and Le Verrier became a scientific superstar. Newton’s law of gravity not only explained what we could see, it also predicted what we could not see. Whereas Uranus had been discovered merely because it happened to wander into the field of view of a telescope, Neptune had been discovered by a man with a quill pen sitting at a desk. Le Verrier’s prediction was unprecedented in history.

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Beginning many millennia ago, priests and rulers had struck awe in their subjects by predicting astronomical events such as eclipses of the Sun and Moon. But this form of prediction involved merely recording observations of the night sky and spotting any recurring patterns. Science, in marked contrast, finds the universal laws behind the patterns. And those laws not only represent a deeper level of understanding but are also portable. They can be applied in entirely different domains. So, for instance, Newton’s law of gravity – formulated to explain the motion of planets around the Sun – can be used to predict the arrival of two tides every 25 hours.

Le Verrier, in deducing the location and properties of an unseen planet, had revealed the central magic of science: its ability to predict things never before suspected, which then turn out to actually exist in the real universe. As the biologist and philosopher Jean Rostand would say one day: “Science has made us gods even before we are worthy of being men.”
But Le Verrier’s discovery of Neptune was merely the first striking instance of this god-like power. In 1863, in a scientific tour de force, Scots physicist James Clerk Maxwell distilled all known electrical and magnetic phenomena into one small set of equations. “Maxwell’s equations” predicted the existence of an “electromagnetic field” that permeates empty space, and the possibility that a disturbance might ripple through it. According to the equations, such a wave would travel at precisely the speed of light in a vacuum. Incredibly, light was a ripple of electricity and magnetism.

This was not all that Maxwell’s theory predicted. It was possible for such an “electromagnetic wave” to oscillate at any of an infinity of different frequencies. Visible light spanned only a tiny range. But there could exist oscillations that were both more rapid than visible light and more sluggish. The universe, it turned out, was permeated by invisible light. By convention, we talk of the seven colours of the rainbow but in reality, beyond the range of what we can see, there lie millions of other colours.

I always remember this (unattributed) poem quoted by Arthur C. Clarke in his book Report on Planet Three:

A being who sees me tapping
The five-sensed can of mind
Amid such greater glories
That I am worse than blind.

In 1888, the German physicist Heinrich Hertz, in his laboratory in Karlsruhe, succeeded in both generating and detecting one form of invisible light: radio waves. In doing so, he made possible the ultra-connected world of the 21st century in which billions upon billions of voices, emails and web pages continually fly though the air all around us. “From a long view of the history of mankind – seen from, say 10,000 years from now – there can be little doubt that the most significant event of the 19th century will be judged as Maxwell’s discovery of the laws of electrodynamics,” said American Nobel prize-winner Richard Feynman.

And, in the 20th century, scientists have continued to exercise the god-like powers demonstrated by Le Verrier and Maxwell. In 1930, English physicist Paul Dirac wrote down a quantum mechanical equation describing the electron which was compatible with Einstein’s special theory of relativity of 1905. Much to his surprise, he noticed that the equation predicted the existence of a “mirror universe”. A mere two years later in California, American physicist Carl Anderson was studying “cosmic rays” – high-energy subatomic particles from space – when on a photographic plate he spotted the track of the first particle of “antimatter”: a positively charged counterpart of the electron, soon christened the “positron”.

In 1930, to explain an anomaly of radioactive “beta decay”, the Austrian physicist Wolfgang Pauli out of “desperation” predicted the existence of a subatomic particle so mind-blowingly antisocial that it could travel through light years of lead before being stopped. “I have done a terrible thing,” he declared. “I have postulated a particle that cannot be detected.” However, in 1956, H-bomb scientists Frederick Reines and Clyde Cowan achieved the impossible. They detected the “neutrinos” emerging from a military reactor at the Savannah River facility in South Carolina. (Hold up your thumb. 100 billion neutrinos are passing through your thumbnail each second. Eight and a half minutes ago they were in the heart of the Sun.)

The most recent examples of this magical predictive power of science are the fabled Higgs boson – whose parent “Higgs field” is responsible for endowing all other subatomic particles with mass – and gravitational waves. Peter Higgs, hiking in the Cairngorms in 1964 (actually, there were four other physicists involved too), used powerful symmetry arguments to predict the existence of a hitherto unsuspected subatomic particle. In 2012, 40 years later and after tens of billions of euros spent on constructing the Large Hadron Collider, there it was: the Higgs particle. Albert Einstein, in Berlin at the height of the First World War, predicted the existence of ripples in the fabric of space time. Almost a century later, in September 2015, they were detected on Earth by Laser Interferometric Gravitational-Wave Observatory, or LIGO. They had come from two merging black holes which have briefly put out 50 times more power than all the stars in the Universe combined.

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Einstein highlights something interesting about this ability of science to predict the existence of things never before suspected, which are then found to be real things in the real universe. It is extremely hard for the practitioners of science to believe this is really possible. Einstein himself did not believe in two major predictions of his theory of gravity of 1915: black holes and the Big Bang. Even in the case of gravitational waves he vacillated, predicting their existence in 1916, un-predicting them a year later, before predicting them again in 1936.

There are countless other examples of this. The central magic of science is so magical that the scientists themselves can scarcely believe it can be true. This was something pondered by the American Nobel prize-winner Steven Weinberg in his popular 1977 book about the Big Bang, The First Three Minutes. Why, he wondered was the prediction of the heat of the Big Bang fireball, published in the science journal Nature in 1948, totally ignored, and the “cosmic background radiation” discovered only by accident in 1965? “The problem”, he concluded, “is not that we take our theories too seriously but that we do not take them seriously enough.”

And this is the crux of it. It is incredibly difficult, if not impossible, for physicists to truly believe that the abstract mathematical equations they scrawl across whiteboards and blackboards actually represent real things that exist in real world. Famously, the Austrian physicist Eugene Wigner remarked on the “unreasonable effectiveness of mathematics in the physical sciences”. Mathematics, it turns out, is a perfect analogue for physics. Why the Universe should have such a twin nobody knows.

There have been some brave speculations in recent years, however. Swedish-American physicist Max Tegmark has proposed that the reason maths is so good at representing physics is that maths is physics. In other words, every mathematical entity is actualised. Tegmark imagines a vast “multiverse” of universes. In some of these domains, there exists only basic maths such as geometry or Boolean algebra. These are not complex enough to create anything of interest. However, in a few domains of the multiverse, there exists mathematics at least as complex as the fabled “theory of everything”. In such domains – and we live in one of them – the maths is capable of generating the complexity of galaxies and stars, planets and people.

* * *

The English physicist Stephen Wolfram takes a different view, however. Just as a drunk who loses their keys at night will look for them under a streetlight because it is not possible to see anything anywhere else, Wolfram maintains, physicists apply maths to the part of the universe where it is applicable because, obviously, there is no point it applying it to places where it is not applicable. The places where maths is applicable are the simple parts. There, it is possible to capture behaviour in a mathematical formula, which has predictive power. In the complex parts – turbulent interstellar gas clouds, biological systems and so on – however, it is not. They are fundamentally unpredictable.

Wolfram thinks that most of what the Universe is doing is complex and cannot be modelled with mathematics. In fact, he wrote a book, A New Kind of Science (Wolfram Media, 2002), about how to illuminate the bulk of the processes going on in the universe – not with mathematical equations but with simple recursive computer programmes.

The fact remains, however, that physicists are just as gobsmacked as they were in Le Verrier’s day about the incredible predictive power of science. The central magic remains as magical as ever. In 1971, the English astronomer Paul Murdin discovered Cygnus X-1, the first black hole candidate in our Milky Way. The existence of such an entity had been predicted in 1916 by the German astronomer Karl Schwarzschild, dying on the Eastern Front of an auto-immune disease that covered his skin in ugly and painful blisters.

Murdin, like every other scientist who has ever confirmed a scientific prediction, expressed amazement at his discovery. “The surprising thing is that black holes turn out to be real objects,” says Murdin. “Incredibly, they actually exist!”