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Posts Tagged ‘infinity’

Ficciones, Jorge Luis Borges

If you want a good reason to learn Spanish, here’s one: you’ll be able to read Borges in the original. Learning won’t be very difficult, but it would be worth it even if it were. Spanish is a clear and elegant language and Borges is a clear and elegant writer. He puts his stories together like mosaics, using words as chips of coloured stone to create the strangest of worlds and situations.

This collection, which combines El Jardín de Senderos que se Bifurcan (1941) (The Garden of Forking Paths) and Artificios (1944) (Artifices), has the very strange world known as “La Biblioteca de Babel” or “The Library of Babel”, an infinite library of hexagonal rooms whose books are a kind of drunkard’s walk through alphabetic possibility:

Uno, que mi padre vio en un hexágono del circuito quince noventa y cuatro, constaba de las letras MCV perversamente repetidas desde el renglón primero hasta el último.

One book, which my father once saw in a hexagon in circuit 15-94,consisted of the letters M C V perversely repeated from the first line to the last.

Borges was fascinated by concepts like randomness and infinity, which is why he drew on mathematics so often in his stories. “The Library of Babel” is an exploration of those ideas, but amid the abstraction and universality of mathematics there are haunting images like this:

Muerto, no faltarán manos piadosas que me tiren por la baranda; mi sepultura será el aire insondable; mi cuerpo se hundirá largamente y se corromperá y disolverá en el viento engenerado por la caída, que es infinita.

When I am dead, compassionate hands will throw me over the railing; my tomb will be the unfathomable air, my body will sink for ages, and will decay and dissolve in the wind engendered by my fall, which shall be infinite.

That’s both horrible and beautiful. The first words of the quote – “Muerto, no faltarán…” – are an example of how Spanish can be more precise than English. A literal translation would be: “Dead, there shall not lack caring hands to cast me over the railing…” But in English the referent of “dead” hangs in the air and doesn’t settle very readily on “me”. In Spanish, muerto is masculine singular and clearly refers to the speaker.

English has to paraphrase, just as it does with the title of Gautier’s «La Morte Amoureuse» (1836). One of the strange titles in the Library of Babel, Trueno peinado, translates well into English: Combed Thunder. Another title doesn’t: Calambre de Yeso, or Plaster Cramp. I think Sandstone Cramp or Onyx Cramp would work better in English: the translation fails by being too faithful.

But Borges survives translation better than most writers, because his prose is precise and his themes are universal. Or perhaps you could say fundamental. He’s playing with words and ideas, exploring the relationship between language and reality, between reality and imagination, between imagination and mathematics. “The Library of Babel” is an excellent example, which is why it’s perhaps his most famous story.

But there’s a melancholy and even a terror in the story too, which come across more clearly when you’re reading more slowly and with closer attention. That’s one reason it’s good to read in other languages: people whose mother tongue isn’t Spanish can find things in Borges that native speakers can’t.

But that applies to every language: in some ways the natives are trapped by their own familiarity and fluency. Borges was aware of questions like that and in “The Library of Babel” he suddenly throws a door open to an infinity of mirrors. If the relation between symbol and sense is arbitrary, then any combination of letters can have any meaning. That’s why the narrator of the story suddenly asks:

Tú, que me lees, ¿estás seguro de entender mi lenguaje?

You who read me — are you certain you understand my language?

In other stories, like “La Muerte y la Brújula”, or “Death and the Compass”, Borges’ games with symbols and coincidence can begin to seem like self-parody. This is the story of a series of murders committed to form the letters of the Tetragrammaton, or great and unspeakable name of God in Hebrew. I think the title in Spanish is better than the story, because brújula has an enticing echo of brujo, “wizard”, or bruja, “witch”. Borges was a profound writer, not a broad one, and he repeated himself, like a garden of forking paths or an echoing labyrinth. But my Spanish isn’t good enough to appreciate him fully or get the most out of his humour.

Whatever language you read him in, you’ll probably agree that he is among the greatest writers of the twentieth century. But one of his biggest services to literature may have been to encourage more people to try G.K. Chesterton, one of his own heroes and inspirations. He would certainly have been pleased to do so, because you don’t get ego with Borges. Instead, you get ideas, some of the strangest and most haunting ever set to cellulose. As I said in one of my own attempts at Borgesian weirdness:

Black Aikkos the God is eternally blind,
But he sees with the eyes of the infinite mind… (“The Dice of Aikkos”)

Homer, at the beginning of European literature, is said to have been blind. Borges certainly was, and if he proves to have been at the end of European literature, he is great enough to bear the comparison.

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Physics in Minutes by Giles SparrowPhysics in Minutes: 200 key concepts explained in an instant, Giles Sparrow (Quercus 2014)

In Borges’ story “The Book of Sand” (1975), the narrator acquires a heavy little book that has an infinite number of pages. When he opens it, he can never find the same page twice. The discrepancy between its finite size and its infinite contents begins to prey on his mind. He decides the book is a monstrous thing and wants to get rid of it: “I considered fire, but I feared that the burning of an infinite book might be similarly infinite, and suffocate the planet in smoke.”

It’s a good story, but the central idea doesn’t work, unless you assume magic is at work. A book with an infinite number of pages would be infinitely heavy. In fact, it would instantly become a black hole and start swallowing the universe.

So I assume, anyway. I’m interested in physics but I don’t know much about it. This book is aimed at people like me. It reminded me of Borges’ Book of Sand, partly because it’s small but heavy, partly because of the density of its ideas and the weight of history behind those ideas. Each page of explanation could easily become a hundred or a thousand: physics is daunting in its scope and complexity. Some of the greatest minds in history have put centuries of effort into understanding the behaviour of matter and energy.

That’s how we got astonishing things like electronics, X-rays and the atom bomb. Physics is an intellectual over-achiever, the super-star of the sciences, the most spectacular, powerful and difficult of all. But it’s the most difficult science because it’s also the simplest. Stars and steam-engines are much less complex than societies or brains, which is why you can’t get away with talking nonsense in physics. And although mathematics governs everything, it’s the simpler things – pendulums, light-rays, atoms, stars – that we can mathematize first.

Or some of us can, at least: the highly intelligent and obsessive men, like Galileo and Isaac Newton, who began modern physics by finding ways to extract abstract mathematics from concrete realities. If they’d tried to find maths in psychology or culture, they would have failed, because those things are too complex. They had to look at much simpler things like falling objects, planetary motion and light-rays. Galileo and Newton laid the foundations and later physicists have built on them, so that physics now towers into the scientific skies, the envy and awe of those working with more complex and intractable aspects of existence.

Giles Sparrow takes his readers on a tour of the tower. I suppose you could say he’s operating an express elevator, stopping briefly on the floors and offering a brief explanation of what it contains: elastic and inelastic collisions on one floor, fluid mechanics on another, mass spectrometry, electromagnetic induction and quantum electrodynamics on more. Then the doors snap shut and the elevator shoots up another floor. But one thing is found everywhere: mathematics. Sparrow quotes a lot of equations and uses a lot of numbers. If you want to understand physics, you have to know the maths. If you don’t, there’s no way to disguise your ignorance.

The maths is beyond me, so until brain-modification arrives I won’t be able to understand physics properly. Until then, this book is a good way of glimpsing the glories of the science. It’s also the closest you’ll get to handling Borges’ Book of Sand in real life.

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Numericon by Marianne Freiberger and Rachel ThomasNumericon, Marianne Freiberger and Rachel Thomas (Quercus Editions 2014)

An easy-to-read introduction to some profound and difficult ideas. You can start climbing the foothills of Mount Maths here and train for the icy cliffs and avalanche-scoured slopes above. And perhaps the mountain rises for ever. There may be important mathematical questions that are impossible to answer. But some answers we already have, like the irrationality of √2 and the infinitude of the primes, are astonishing to contemplate. How are finite creatures able to discover facts about infinity? Logic is a lever that can move more than the universe. Euclid described 2,300 years ago how it could be used to prove that primes never ended: for every integer, there is a prime.

Numericon explains his proof, then goes on to describe how the German Georg Cantor (1845-1918) used logic to prove that there is more than one kind of infinity. In fact, there’s an infinite hierarchy of infinities, climbing endlessly into the metaphysical empyrean. That seems like an insane idea and Cantor did end his life in a sanatorium. He’s an extreme example of something Freiberger and Thomas note in their introduction: that mathematicians are often eccentric. It’s a strange subject that doesn’t come naturally to human beings. We can’t escape it, because our brains and bodies are governed by mathematics, but we don’t need to apply it explicitly and consciously to get through life. Those who lift the surface of reality and gaze upon its brilliant mathematical core can find that the light troubles and even subverts their brains.

And some avert their gaze. The German Carl Friedrich Gauss (1777-1855) may have been the greatest mathematician who ever lived, but he declined to publish his revolutionary ideas about Euclid’s fifth axiom: that parallel lines never meet. New geometries arise if the axiom is eliminated, but Gauss didn’t claim the credit for discovering them. As this book describes, it was the younger mathematicians János Bolyai (1802-60) and the Russian Nikolai Lobachevsky (1792-1865). And Bolyai’s mathematician father had tried to warn his son off.

Mathematicians need a sense of adventure. They need recognition and support too, but sometimes even the great ones find both hard to win. Sometimes their greatness is part of the problem, because the work they produce is too new and powerful to be properly appreciated. The Norwegian Niels Henrik Abel (1802-29) died at 26 “from tuberculosis and in abject poverty” (pg. 183). The Frenchman Évariste Galois (1811-32) died even younger, at 21, fatally wounded in a duel. Perhaps it was an affair de cœur, perhaps a plot by his enemies: Galois was revolutionary in both his mathematics and his politics. The Indian Srinivasa Ramanujan (1887-1920) is another great who died young after making discoveries of permanent value.

This book discusses all three and many more, but mathematicians aren’t truly important. Mathematics is necessary; mathematicians are contingent. If advanced civilizations exist on other planets or in parallel universes, their art and literature might be entirely different from our own or might not exist at all. But their mathematics would be recognizable, whatever the nature of the brains that had discovered it. Advanced civilization is impossible to imagine without mathematics and although we can ignore mathematics if we choose, we’re missing something central to existence if we do. As Darwin said: it seems to give one an extra sense. It’s a mind’s eye that can see into infinity – and into infinitesimality.

As though to reflect the importance of mind in maths, this book has relatively few and simple illustrations. Maths can yield gorgeous complexity for real eyes, but the mind’s eye is more important. So this book is eye-candy for the mind. Eye-brandy too: maths can both dazzle you and make you drunk. It’s appropriate that Numericon echoes Necronomicon, because new worlds wait within the pages of both.

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Front cover of Imperial Earth by Arthur C. ClarkeImperial Earth (1976) and Rendezvous with Rama (1972), Arthur C. Clarke

I was a pretty little boy once, before all the drink, drugs and debauchery. Arthur C. Clarke would have been pleased by this, because he liked pretty little boys and in those days he was my favourite writer. Alas, I’m no longer pretty and he’s no longer my favourite writer. I see the flaws in his writing too clearly now and I don’t like his optimistic liberal politics or his piety about One Humanity. But I see the virtues of his writing too: its intelligence, clarity and scientific acumen, for example. If you put aside anthropology and genetics, Clarke knew what he was extrapolating about and his books have aged well. Nothing dates faster than the future, but Clarke’s various futures aren’t wholly ridiculous yet.

For example, Imperial Earth was published in 1976 and is set in the twenty-third century, but it’s still possible to suspend disbelief while you’re reading the book. It’s getting harder, however, and one thing must have been hard to accept even in 1976. The novel is about the Makenzie clan, who live in an underground city on Saturn’s moon Titan and are unique because of two allegedly uncorrectable errors. First, a computer has accidentally altered their surname and second, a photon has adventitiously ended their lineage:

The fault lay in Malcolm’s genes, not Ellen’s. Sometime during his shuttling back and forth between Earth and Mars, a stray photon that had been cruising through space since the cosmic dawn had blasted his hopes for the future. The damage was irreparable, as Malcolm discovered when he consulted the best genetic surgeons of four worlds. (ch. 1, “A Shriek in the Night”)

So Malcolm Makenzie has to clone himself to produce his son Colin, and Colin has to clone himself to produce Malcolm’s grandson Duncan. Rubbish! Men have colonized the solar system and can produce clones, but can’t repair simple damage to sex-cells? And the clones, produced from somatic cells, have the same defect? That Malcolm, Colin and Duncan are all black-skinned isn’t incredible, just irritating: like Ursula Le Guin’s fantasy, Clarke’s future is a Star-Trekkian, rainbow-of-races one and he likes being ironic about racism and prejudice. It’s also a disenchanted future: there’s nothing supernatural in it and man’s power over nature is increasing all the time.

But Clarke still wants to invoke old emotions. So where is sublimity – awe, mystery and wonder – to come from in a universe without God or gods? This problem has existed for a long time: the German sociologist Max Weber (1864-1920) identified the phenomenon of Entzauberung, or disenchantment, at the beginning of the twentieth century, as science advanced and God retreated. Where do atheists find awe?

The poet A.E. Housman (1859-1936) faced the same problem in the same era and Arthur C. Clarke was familiar with Housman’s solutions. Clarke even took the title of a novel, Against the Fall of Night (1948), from one of Housman’s poems:

Smooth between sea and land
Is laid the yellow sand,
And here through summer days
The seed of Adam plays.

Here the child comes to found
His unremaining mound,
And the grown lad to score
Two names upon the shore.

Here, on the level sand,
Between the sea and land,
What shall I build or write
Against the fall of night?

Tell me of runes to grave
That hold the bursting wave,
Or bastions to design
For longer date than mine.

Shall it be Troy or Rome
I fence against the foam,
Or my own name, to stay
When I depart for aye?

Nothing: too near at hand,
Planing the figure sand,
Effacing clean and fast
Cities not built to last
And charms devised in vain,
Pours the confounding main.

(XLV in More Poems, 1936)

Housman uses the sea as a metaphor for time, which conquers all things and all men. We are dwarfed by time just as we are dwarfed by the sea. Both can invoke awe even in atheists. Housman also sought awe in the ungovernable chances that rule our lives and in the thought of death being the final and irrevocable end. But Clarke, a much more optimistic and cheerful character than Housman, did not dwell so much on death. It appears in his work occasionally, not obsessively:

Grandma had met Captain Kleinman only a year after the final parting with Malcolm; she may have been on an emotional rebound, but he certainly was not. Yet thereafter the Captain had never looked at another woman, and it had become one of those love affairs famous on many worlds. It had lasted throughout the planning and preparations for the first expedition to Saturn and the fitting-out of the Challenger in orbit off Titan. And as far as Ellen Makenzie was concerned it had never died; it was frozen forever at the moment when the ship met its mysterious and still inexplicable doom, deep in the jet streams of the South Temperate Zone. (ch. 5, “The Politics of Space and Time”)

Mysterious and inexplicable dooms are very old themes, but Clarke still wanted to use one, despite his optimism and belief in science and reason. But he preferred Housman’s awe-by-dwarfing and awe-by-chance. In Imperial Earth, communication is by hyper-scientific, unenchanted “viddyphone”. But one day, by “pure chance”, Duncan Makenzie finds a “magic number”, accidentally misdialling when he is trying to call his step-grandmother. The circuit is “live immediately”, but there is “no ringing tone” and “no picture”:

Then he noticed the sound. At first, he thought that someone was breathing quietly into the microphone at the far end, but he quickly realized his mistake. There was a random, inhuman quality about this gentle susurration; it lacked any regular rhythm, and there were long intervals of complete silence. As he listened, Duncan felt a growing sense of awe. Here was something completely outside his normal, everyday experience, yet he recognized it almost at once. In his ten years of life, the impressions of many worlds had been imprinted on his mind, and no one who had heard this most evocative of sounds could ever forget it. He was listening to the voice of the wind as it sighed and whispered across the lifeless landscape a hundred meters above his head.

Duncan forgot all about Grandma, and turned the volume up to its highest level. He lay back on the couch, closed his eyes, and tried to project himself into the unknown, hostile world from which he was protected by all the safety devices that three hundred years of space technology could contrive. (ch. 1, “A Shriek in the Night”)

Safety devices disenchant; the wind’s randomness re-enchants. Wind combines both power and chance: it’s a chaotic and sometimes destructive phenomenon. But there’s more to come for Duncan on the “magic number”:

As luck would have it, the wind must have slackened at about the time he [began to record its sounds], because there was a long, frustrating silence. Then, out of that silence, came something new. It was faint and distant, yet conveyed the impression of overwhelming power. First there was a thin scream that mounted second by second in intensity, but somehow never came any closer. The scream rose swiftly to a demonic shriek, with undertones of thunder – then dwindled away as quickly as it had appeared. From beginning to end it lasted less than half a minute. Then there was only the sighing of the wind, even lonelier than before.

The shriek conveys “overwhelming power” and sounds “demonic”, but Duncan doesn’t believe in demons and the overwhelming power turns out to be wielded by man: the shriek was made by a “ram-tanker” scooping hydrogen from Titan’s atmosphere to use as fuel. Clarke’s future runs partly on Promethium, which would have pleased Marx:

I was standing on a beach in Siberia when this book [Leszek Kołakowski’s Main Currents Of Marxism, Vol I, II and III, (1978)] was recommended to me. The wavelets of a small artificial ocean made by damming the river Ob were splashing on the sand, and I was wondering out loud about the roots of the Soviet passion for making grand modifications to nature. “You need to read Kolakowski,” said the person I was with. “He’s got a great chapter about what he calls ‘the Promethean motif’ in Marxism – the idea that it’s the destiny of humanity to steal fire from the gods and make the world whatever we want it to be.” (“Book Of A Lifetime”, Francis Spufford)

The Promethean impulse in incompetent communism led to horrendous pollution and a world that people didn’t actually want. In capitalism, it hasn’t been as destructive so far, but the world it creates still leaves people wanting sublimity. Housman taught Clarke some ways of invoking that, but Clarke had his own way too: mathematics. In Imperial Earth, Duncan’s grandmother introduces Duncan to pentominoes, or shapes made by fitting five squares together edge-to-edge. Only twelve pentominoes are possible and they can arranged to make a ten-by-six rectangle. But it’s not as easy to make the rectangle as it looks:

For a long time, Duncan stared at the collection of twelve deceptively simple figures. As he slowly assimilated what Grandma had told him, he had the first genuine mathematical revelation of his life. What had at first seemed merely a childish game had opened endless vistas and horizons – though even the brightest of ten-year-olds could not begin to guess the full extent of the universe now opening up before him. This moment of dawning wonder and awe was purely passive; a far more intense explosion of intellectual delight occurred when he found his first very own solution to the problem. For weeks he carried around with him the set of twelve pentominoes in their plastic box, playing with them at every odd moment. […] And once in a sort of geometrical trance or ecstasy which he was never able to repeat, he discovered five solutions in less than an hour. Newton and Einstein and Chen-Tsu could have felt no greater kinship with the gods of mathematics in their own moments of truth… (ch. 7, “A Cross of Titanite”)

The gods are gone from Clarke’s universe, but he still uses them as a metaphor for the way mathematics dwarfs man. Note the final ellipsis too: it’s Clarke’s own, because he likes trailing dots and leaving things unsaid. In mathematics, trailing dots are used to represent indefiniteness or infinity: 1, 2, 3… Infinity is another source of the sublime and Clarke invokes it regularly in Imperial Earth. This is Duncan looking at the strange mineral Titanite under a microscope:

A hexagonal corridor of light, dwindling away to infinity, outlined by millions of sparkling points in a geometrically perfect array. By changing focus, Duncan could hurtle down that corridor, without ever coming to an end. How incredible that such a universe lay inside a piece of rock only a millimetre thick! (ch. 7, “A Cross of Titanite”)

This is Duncan hearing the engine that powers the space-ship taking him to Earth:

From an infinite distance came the thin wail of the [Asymptotic] Drive; Duncan told himself that he was listening to the death cry of matter as it left the known universe, bequeathing to the ship all the energy of its mass in the final moment of dissolution. Every minute, several kilograms of hydrogen were falling into that tiny but insatiable vortex – the hole that could never be filled. (ch. 15, “At the Node”)

And this is Duncan actually on Earth:

It was even worse when he looked up at the sky, so utterly different from the low, crimson overcast of Titan. He had flown halfway across the Solar System, yet never had he received such an impression of space and distance as he did now, when he stared at the solid-looking white clouds, sailing through a blue abyss that seemed to go on forever. It was useless to tell himself that they were only ten kilometres away – the distance a spaceship could travel in a fraction of a second. Not even the starfields of the Milky Way had yielded such glimpses of infinity. (ch. 19, “Mount Vernon”)

In the main hall of the Administration Building, Duncan paused for a moment before the giant, slowly rotating DNA helix which dominated the entrance. As his gaze roamed along the spokes of the twisted ladder, contemplating its all-but-infinite possibilities, he could not help thinking again of the pentominoes that Grandma Ellen had set out before him years ago. There were only twelve of those shapes – yet it would take the lifetime of the universe to exhaust their possibilities. And here was no mere dozen, but billions upon billions of locations to be filled by the letters of the genetic code. The total number of combinations was not one to stagger the mind because there was no way whatsoever in which the mind could grasp even the faintest conception of it. The number of electrons required to pack the entire cosmos solid from end to end was virtually zero in comparison. (ch. 42, “The Mirror of the Sea”)

So it’s too awesome to be awesome. Which is awesome. Duncan is dwelling on DNA because he’s at the cloning-centre, overseeing the fourth generation of Makenzies. Because a clone is a copy, the possibilities of recombination are over, but there will be a twist at the end of Imperial Earth whereby possibility is renewed and life comes out of death in a way it never did in Housman. There’s also a clever link in Imperial Earth between Clarke’s two great alien loves: the sea and the heavens. Something apparently small and earth-bound turns out to be gigantic and otherworldly. Clarke used marine and extra-terrestrial themes in all his books, but there’s another clever link in Rendezvous with Rama, where the sea is actually waiting in the heavens. Or a sea is waiting, at least.

And it’s a cylindrical sea, extending right around the interior of a gigantic alien space-craft whose ultimate purpose and destination are never discovered. Or not in this first novel of the Rama series, at least. I haven’t read any of the other books, which Clarke wrote in collaboration with Gentry Lee, and I don’t want to. I don’t want answers to the questions raised by Rendezvous with Rama, just as I don’t want answers to the questions raised in H.P. Lovecraft’s At the Mountains of Madness (1931):

Some of the Old Ones, in the decadent days, had made strange prayers to those mountains — but none ever went near them or dared to guess what lay beyond. No human eye had ever seen them, and as I studied the emotions conveyed in the carvings, I prayed that none ever might. There are protecting hills along the coast beyond them — Queen Mary and Kaiser Wilhelm Lands — and I thank Heaven no one has been able to land and climb those hills. I am not as sceptical about old tales and fears as I used to be, and I do not laugh now at the prehuman sculptor’s notion that lightning paused meaningfully now and then at each of the brooding crests, and that an unexplained glow shone from one of those terrible pinnacles all through the long polar night. There may be a very real and very monstrous meaning in the old Pnakotic whispers about Kadath in the Cold Waste. (At the Mountains of Madness, 1931)

Lovecraft was another writer who faced a Godless universe and the dilemma of disenchantment. He invoked sublimity and dwarfed the puny ambitions of man by mixing astronomy with biology and inventing sky-spanning, dimension-demolishing monsters. Clarke was familiar with Lovecraft – he wrote a Lovecraftian pastiche called “At the Mountains of Murkiness” – but his optimism kept him from imitating Lovecraft’s monstrous, quasi-supernatural solutions. All the same, the giant alien artifact of Rama is reminiscent of the vast alien city discovered by Antarctic explorers in At the Mountains of Madness. That is perhaps Lovecraft’s best and most successful book, just as Rendezvous with Rama is perhaps Clarke’s best and most successful. There’s much less reference to infinity in Rendezvous than in Imperial Earth, probably because Clarke has enough on his hands as it is. When Rama originally appears in the solar system, it is so large that it is mistaken for an asteroid:

The object first catalogued as 31/439, according to the year and the order of its discovery, was detected while still outside the orbit of Jupiter. There was nothing unusual about its location; many asteroids went beyond Saturn before turning once more towards their distant master, the sun. And Thule II, most far-ranging of all, travelled so close to Uranus that it might well have been a lost moon of that planet.

But a first radar contact at such a distance was unprecedented; clearly, 31/439 must be of exceptional size. From the strength of the echo, the computers deduced a diameter of at least forty kilometres; such a giant had not been discovered for a hundred years. That it had been overlooked for so long seemed incredible.

Then the orbit was calculated, and the mystery was resolved – to be replaced by a greater one. 31/439 was not travelling on a normal asteroidal path, along an ellipse which it retraced with clockwork precision every few years. It was a lonely wanderer between the stars, making its first and last visit to the solar system – for it was moving so swiftly that the gravitational field of the sun could never capture it. It would flash inwards past the orbits of Jupiter, Mars, Earth, Venus and Mercury, gaining speed – as it did so, until it rounded the sun and headed out once again into the unknown. (ch. 2, “Intruder”)

The year of discovery is 2131, so it’s easier to suspend disbelief in Rendezvous than in Imperial Earth, set in 2276. Rama keeps getting curiouser and curiouser: originally thought to be asteroidal, it’s soon discovered to be artificial on a scale far beyond man’s wildest ambitions. Furthermore, it’s hollow and when a spaceship called Endeavour is sent to investigate it, the crew discover an air-lock and can get inside. And “air-lock” is the word: Rama is full of air that men can breathe. Because it’s cylindrical and spinning on its long axis, it also has gravity and the crew of Endeavour are able to set up camp in the interior.
Rendezvous with Rama by Arthur C. Clarke
What they see when the lighting comes on is well-captured by the cover-artist of the first edition. However, the clouds are artistic licence, inspired by the section in which Clarke describes how the frozen interior of Rama and the ice of the Cylindrical Sea begin to thaw. There’s a scientific team on Earth called the Rama Committee, which is overseeing the exploration of Rama, and one of its leading lights is an exobiologist called Carlisle Perera. He is able to predict something others have missed. The crew of Endeavour have to abandon Rama while his prediction works itself out. On their return, they make more unexpected discoveries, sail the Cylindrical Sea, and fly to the far end of Rama, which is otherwise inaccessible because of the cliff on the opposite side of the Sea. Or one of the crew flies to the South Pole, at least:

Lieutenant James Pak was the most junior officer on board Endeavour, and this was only his fourth mission into deep space. He was ambitious, and due for promotion; he had also committed a serious breach of regulations. No wonder, therefore, that he took a long time to make up his mind. (ch. 24, “Dragonfly”)

He’s breached regulations by smuggling a “sky-bike” on board as “Recreational Stores”. A sky-bike is a man-powered flyer and he intended to use it in the Lunar Olympics. Now, he suggests to Captain Norton that he fly along Rama instead to the mysterious horns at the South Pole. Gravity will be lower near the axis of Rama and he’ll easily be able to keep aloft. This is an example of how Clarke, having imagined Rama, is able to add scientific detail to his creation: he can see how things might really be. But part of how things might really be, inside a giant alien spacecraft, is a lot that human beings can’t understand, like the structures Jimmy Pak flies to on his sky-bike Dragonfly:

In almost every way the southern and northern ends of Rama differed completely. Here was no triad of stairways, no series of narrow, concentric plateaux, no sweeping curve from hub to plain. Instead, there was an immense central spike, more than five kilometres long, extending along the axis. Six smaller ones, half this size, were equally spaced around it; the whole assembly looked like a group of remarkably symmetrical stalactites, hanging from the roof of a cave. Or, inverting the point of view, the spires of some Cambodian temple, set at the bottom of a crater… (ch. 26, “The Voice of Rama”)

Again the ellipsis is in the original: Clarke is trailing off into mystery, because no-one can understand what the spikes are for. But they become charged with electricity and produce giant bolts of lightning, which cripple Dragonfly and force Jimmy into a crash-landing on the southern half of Rama. He encounters more mysteries here and makes a startling discovery:

Not until he was only a few metres away could he be completely sure that life as he knew it had intruded into the sterile, aseptic world of Rama. For blooming here in lonely splendour at the edge of the southern continent was a flower. (ch. 30, “The Flower”)

This is part of the revelation that Rama is a kind of space-ark and not as lifeless as it originally seemed. But the flower is inside “a trellis of wires and rods”, so when Jimmy decides to pick it, he has to travel light:

He stripped off all his clothes, grasped the smooth metal rods, and started to wriggle into the framework. It was a tight fit; he felt like a prisoner escaping through the bars of his cell. When he had inserted himself completely into the lattice he tried backing out again, just to see if there were any problems. It was considerably more difficult, since he now had to use his outstretched arms for pushing instead of pulling, but he saw no reason why he should get helplessly trapped. (Ibid.)

Jimmy is “the most junior officer” on Endeavour, remember, so I think Clarke’s Housmanesque, paederastic tastes were guiding his imagination there. But a Housman character wouldn’t be called “Jimmy” and wouldn’t survive his misadventure. Clarke raises the possibility of death, but doesn’t realize it: Jimmy is able to escape the southern half of Rama and return to his crewmates. Then there are more startling discoveries, more mysteries, and more touches of scientific verisimilitude, including “tidal waves” on the Cylindrical Sea, which is actually fitted with:

Anti-slosh plates, Norton told himself. Exactly the same as in Endeavour’s own propellant tanks – but on a thousand-fold greater scale. There must be a complex pattern of them all around the Sea, to damp out any waves as quickly as possible. (ch. 32, “The Wave”)

Rama has its own propulsion system, you see, and is starting to manoeuvre as it approaches the sun, so the Cylindrical Sea is starting to slosh about. As he describes Rama’s final hours in the solar system, Clarke comes up with some clever twists and misdirections and the last line of the novel is one of the best in science-fiction. You should have been expecting it, but you probably won’t have been, because it suddenly switches scale from the micro to the macro. Rendezvous with Rama is an admirable novel in a number of ways: easy and enjoyable to read, minutely imagined, cleverly plotted and plausibly detailed. I find its Star-Trekkian, rainbow-of-races, free-and-easy-sexuality society irritating nowadays, but that’s Clarke being Pollyanna or Pangloss.

It’s also Clarke being adolescent: if he’s your favourite author, you might be intelligent or an adult but you probably won’t be both. If the human race is still recognizably human in 2131 or 2276, I doubt it will take him seriously as a writer, but it might honour him as a prophet for his physics and astronautics, if not for his anthropology. There isn’t only one human race: there are lots and Clarke, like many other science-fiction writers, missed exploring a very interesting and complex world by being piously obtuse about humanity and its genetic variability.

But he explored other interesting and complex worlds, extrapolating and imagining and introducing millions of readers to the wonders of space, science and the sea. Rendezvous with Rama is about a giant and mysterious space-ark carrying a mysterious cargo to an unknown destination. It may also be an ark for Arthur C. Clarke’s reputation, carrying it down the decades until his hopes are realized or his creations confounded. He’s not my favourite writer any more but I still admire him and I’m grateful for the pleasure his books have given me.

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