Science or Sorcery?

Note: I was surprised when I re-read this article on CAS from 2004, because I didn’t find its prose particularly painful or embarrassing. I’ve made only one big change, restoring the comparison that I originally began the essay with but which I suppressed for publication at the Eldritch Dark for fear of seeming gratuitously offensive. Everything in the essay, including the comparison, is of course intended to be taken with complete seriousness. Tolkien is one of the authors I have most often read, but, as I’ve said before, I wish that someone would translate Lord of the Rings into English.

Science or Sorcery? Interrogating the Supratextual Interface of Klarkash-Ton and the Hobbitual Offender, Simon Whitechapel

The scientific spirit, which cannot leave anything alone and aspires to draw the whole universe of objects, people, ideas and even feelings into its own dull, inhuman empire, was certain, sooner or later, to cast its screwed-up, calculating eyes on the splendour in the grass and the glory in the flower. — Peter Simple, The Stretchford Chronicles (1980).1

Où sont les neiges d’antan? (Where are the snows of yesteryear?) — François Villon, Ballade des Dames du Temps Jadis (1461).

If the Earth were a human body, the United States of America might well be identified as a cancer. There are three strong parallels: growth, greed, and influence. Cancers grow explosively, gobble energy, and spread in their worst forms to every part of the body. Mutatis mutandis, the United States has done the same, growing in a couple of centuries from a tiny colony to a continental superpower that now consumes perhaps a fifth of the world’s resources with only a twentieth of the world’s population,2 and that exports its culture and language to every corner of the world. More and more people outside its borders are growing up to think, act, and talk like Americans, discarding their own histories and cultures as they do so. This American triumph has coincided with, and in part been built on, the triumph of modern science, and like science the United States is based on a rejection of tradition and a belief in the possibility, and even the necessity, of progress.

But as Sir Isaac Newton (1643-1727), one of the founders of modern science, pointed out, for every action there is an opposite and equal reaction. He was talking about physics, but actions have reactions in the mistier world of culture too and simultaneous with the rise of America in the late nineteenth and early twentieth centuries came the rise of the literary genre of fantasy. Like its coeval science fiction, fantasy represents a flight from the present, but where science fiction flies more or less optimistically into the future, fantasy flees more or less pessimistically into the past: it could be defined as an attempt to write as though America did not exist. America offers democracy, science, and rationalism; fantasy rejects them in favor of monarchy, magic, and mystery.

And understandably so: like America itself, democracy, science, and rationalism are profoundly unnatural things, appearing very late in human existence and truly accepted and appreciated by very few of us, for they do not appeal to the irrational and numinous aspects of our nature. America is unnatural because it is deracinated, a conscious, rational experiment in nation-building whose immigrant citizens are cut off from their roots in ancestral history and homeland. The popularity of fantasy in America and the societies its rootless culture has most heavily influenced proves that millions of us feel the loss. Fantasy’s rejection of science and flight from the scientific American present can be summed up by these lines from J.R.R. Tolkien’s The Lord of the Rings (1954-5) in which the wizard Gandalf describes his confrontation with the wizard Saruman, who has recently exchanged his white robes for robes of many colors:

“I liked white better,” I said.
“White!” he sneered. “It serves as a beginning. White cloth may be dyed. The white page can be overwritten; and the white light can be broken.”
“In which case it no longer white,” said I. “And he that breaks a thing to find out what it is has left the path of wisdom.”3

Isaac Newton broke white light in precisely that way with a prism, gaining knowledge as he discarded wisdom. But there was more to Tolkien’s rejection of Newtonian reductionism than simply science: Newton was also a Protestant, and America is a Protestant nation. Like science, Protestantism is based on a rejection of tradition, and because, like America, it is deracinated, it withers very readily: where its offspring rationalist secularism leads, Protestantism sooner or later follows.4 Tolkien (1892-1973) was Catholic, belonging to a church with deep roots, and though his books are early symptoms of her present decadence, they contain all the anti-rational, loss-assuaging ingredients listed above: monarchy, magic, and mystery. One of those books is, after all, called The Return of the King, and the pessimistic, future-fleeing aspects of fantasy are clearly symbolized by the way Tolkien sets his evil empire of Mordor in the east, where the sun rises, and his haven of peace in the west, where the sun sets.

But beside being Catholic and anti-rationalist, Tolkien was, more importantly, a bad writer. His most famous book, The Lord of the Rings, epitomizes what Europeans would see as the worst failings of American popular culture: it is sentimental, shallow, and clumsy.5 His attempt to flee the American present in some ways carries America with it. And that is one of the great ironies of fantasy literature: its most popular, and least subtle, exponent is European, while one of its greatest and most subtle is not merely American but Californian, living and dying in the most “future-crazed”6 state of all: Clark Ashton Smith was born in 1893 in Long Valley, near Sacramento, and died in 1961 a few miles north in Auburn.

But CAS had an English father and did not grow up in any of California’s cities, which may be much more important than it appears. California is one of the youngest states of one of the world’s youngest nations, but its landscape is ancient and its landscape is what CAS was most familiar with: he grew up on his father’s “forty acres” of homestead.7 Straight lines and right angles are rare in nature, ubiquitous in modern cities, and they may have much stronger effects on our psychology than we realize.8 In the old worlds of Europe and Asia, where cities are thousands of years old, streets wind and twist, because the cities of Europe and Asia have grown rather like plants; in the new world of America, streets run in straight lines intersecting at right angles. American cities are planned, rational attempts to conquer and control unplanned, irrational geography, and perhaps the reputation of New Englanders for subtlety and guile rises from their surroundings. Cities like Boston are old enough to have grown in the winding, twisting old world fashion, and perhaps they train their modern inhabitants in the oblique and indirect. CAS’s friend and mentor H.P. Lovecraft (1890-1937) was an urban New Englander: could he have developed his subtle, allusive fiction had he grown up in a city like Chicago or New York, where the streets may train the mind in linearity and directness?9 Could the rural CAS have developed his subtle, allusive fiction had he grown up in a city like San Francisco or Los Angeles?

I would suggest not, but that there is more to an artist’s growth than his physical surroundings is clearly proved by Tolkien, who lived in ancient, alinear England and wrote his crude fantasy amid the winding, twisting streets of Oxford. However, human beings inhabit societies too, and though Lovecraft and CAS may have escaped the stultifying effects of American town-planning, perhaps they benefited from the liberating effects of American politics. The races of Tolkien’s world are clearly based on the English class system: the hobbits, for example, are the rural proletariat and minor bourgeoisie, the orcs are the industrial proletariat, and the elves are the aristocracy whose well-nourished scions Tolkien encountered at Oxford. Compare these passages, the first from Evelyn Waugh’s Oxford novel Brideshead Revisited (1945), the second from Tolkien’s The Hobbit (1937):

About six of them came into my room, the rest stood mouthing outside. My dear, they looked too extraordinary. They had been having one of their ridiculous club dinners, and they were all wearing coloured tail-coats – a sort of livery. ‘My dears,’ I said to them, ‘you look like a lot of most disorderly footmen.’ Then one of them, rather a juicy little piece, accused me of unnatural vices. ‘My dear,’ I said, ‘I may be inverted but I am not insatiable. Come back when you are alone.’10

‘Well, well!’ said a[n Elvish] voice. ‘Just look! Bilbo the hobbit on a pony, my dear! Isn’t it delicious!’ ‘Most astonishing wonderful!’ Then off they went into another song as ridiculous as the one I have written down in full. At last one, a tall young fellow, came out from the trees and bowed to Gandalf and to Thorin.11

Tolkien and Waugh were both snobs and both, as it happens, of below average height. Tall Lovecraft’s and tall CAS’s fiction does not suffer from this snobbery, and although the stories of their friend Robert E. Howard (1906-1936) – who grew up in rural Texas – continually pluck the chords of monarchy, magic, and mystery, his hero Conan becomes a king by brawn and brain, not by birth. But Howard, although a far better writer than Tolkien, is the least interesting of the Weird Tales triumvirate, and CAS’s fiction is aristocratic in more than its mention of kings and emperors. He did not write for the canaille, which is why he used words like canaille:

Yes, indeed, one could write numerous reams on the subject of style. The style – or lack of it – required by nearly all magazine editors, [sic] would require a separate treatise. The idea seems to be that everything should be phrased in a manner that will obviate mental effort on the part of the lowest grade moron. I was told the other day that my “Door to Saturn” could only be read with a dictionary.12

One of the reasons popular American culture has been so successfully exported is that it has evolved to appeal to the lowest common denominator: it is “phrased” so to “obviate mental effort”, and ideally to bypass the intellect altogether. The simplicity and directness of an American export like rock’n’roll, whose appeal is based on strong rhythms and high volume, are mirrored in the simplicity and directness of American exports like hamburgers and Coca-Cola, whose appeal is based on fat, salt, and sugar. In short, American culture is democratic and inclusive, not aristocratic and exclusive like European culture. And so a second great irony of fantasy literature is that the European Tolkien is far more democratic and far more successfully exported than the Californian Clark Ashton Smith: Tolkien’s writing is crude and strongly flavored, the literary equivalent of hamburger and coke, while the haute cuisine of CAS remains unknown to many of the millions who read and re-read Lord of the Rings – or watch and re-watch its recent translation into film.

And perhaps that is another part of the key to CAS: fiction that can be translated readily and successfully into film, as Tolkien’s has been, tends to be superficial and direct. CAS’s greatest stories could not be successfully translated into film without being transformed in fundamental ways; that is, without being mutilated. This is another way in which CAS is profoundly un-American. America’s most successful and most characteristic export, advertising its culture to the world, has been film, and film, because it is the most powerful of media, is also the most destructive, killing imagination and feeding passivity and voyeurism.13 Cinema’s inbred cousin, television, exaggerates cinema’s failings and commits the additional crimes of trivialization and superficiality: watching a film at the cinema at least has a sense of ritual and occasion, and lasts about as long as a religious service; watching the same film using a television has no sense of ritual or occasion and can be interrupted and postponed at will.

CAS, born blessedly long before television and no movie-goer, was defiantly logophilic and logocentric, and in that sense is far more modern than artists who work in or are influenced by film: vision has existed for many millions of years among animals and the art based on it, appealing to universal simplicities, crosses boundaries of culture and even species with relative ease: recall the Greek tale of Zeuxis’s trompe l’oeil grapes pecked by birds. True language, on the other hand, appeared only with human beings and the art based on it, being far richer and far more subtle, does not cross barriers of culture with ease and without transformation and distortion. And here is a third great irony of CAS’s relation to JRRT. Tolkien, the professional scholar of language in the homeland of English, wrote with far less sensitivity and richness, beating drums and blasting trumpets where CAS played flutes and citheræ. But if fantasy is an attempt to write as though America did not exist, perhaps it took an American to know precisely how best to perform the nullification.


1. The Stretchford Chronicles: 25 Years of Peter Simple, The Daily Telegraph, Purnell & Sons, Bristol, 1980, “A graded land”, pg. 165.

2. A factoid often dragged out (with varying figures – sometimes consumption goes as high as two-thirds) by whining liberals and eco-puritans. The precise ratio is impossible to know, but America certainly out-consumes Europe, just as Europe out-consumes the Third World.

3. The Fellowship of the Ring, Book Two, ch. II, “The Council of Elrond”.

4. “Mark 4:5 And some [seed] fell on stony ground, where it had not much earth; and immediately it sprang up, because it had no depth of earth: 6 But when the sun was up, it was scorched; and because it had no root, it withered away.” Because they have deep roots, Catholic and Orthodox Christianity resist the scorching sun of secularism much more effectively.

5. The Hobbit, with much less ambition, achieves much more.

6. Peter Simple, The Stretchford Chronicles: 25 Years of Peter Simple, The Daily Telegraph, Purnell & Sons, Bristol, 1980, “Let them be left”, pg. 173: “Environmentalists, conservationists, anti-pollutionists: the dull, pseudo-scientific words, endlessly repeated – imports, like so much else, from future-crazed America – can arouse in certain moods a perverse rage to build oil-refineries all over Dartmoor.”

7. “As I Remember Klarkash-Ton”, George F. Haas, from The Black Book of Clark Ashton Smith, Arkham House (see online copy).

8. In one famous psychological experiment, Zulus who lived in round huts and ploughed in curves were found to be much less susceptible to certain optical illusions (e.g. the Müller-Lyer arrow illusion). See, for example, the discussion in R.L. Gregory’s Eye and Brain: the Psychology of Seeing.

9. See Lovecraft’s short story “Haunter of the Dark” (1936), set in the New England city of Providence but with a protagonist from the straight-lined, right-angled Wisconsin city of Milwaukee: “As Blake climbed higher, the region seemed stranger and stranger, with bewildering mazes of brooding brown alleys leading eternally off to the south. … Twice he lost his way …”

10. Op. cit., Book One, “Et in Arcadia Ego”, ch. 2

11. Op. cit., Chapter 3, “A Short Rest”.

12. Clark Ashton Smith: Letters to H.P. Lovecraft, Necronomicon Press, West Warwick (Rhode Island), 1987, pg. 23, “c. mid-December 1930” (see online copy).

13. In fantasy’s sister genre, horror, England and America again provide the most successful writer and one of the greatest, but this time England wins: the American Stephen King (1947-     ), the most successful writer of horror, is a cinematic writer weaned on film and has nothing of the subtlety and depth of the English M.R. James (1862-1936) (see CAS’s appreciation “The Weird Works of M.R. James”).

© 2004 Simon Whitechapel

Sward and Sorcery

Watership Down by Richard Adams with cover by Pauline BaynesWatership Down, Richard Adams (1972)

A book is a magical thing. Black marks on white paper create words; words conjure worlds. But the sorcery of Watership Down is remarkable even by literary standards. The world conjured here defies expectation and suspends disbelief. Richard Adams took a seemingly ludicrous subject – the adventures of a group of rabbits – and made it something that could grip the imagination and stir the emotions of readers at any age.

He did this by combining two distinct traditions of writing about animals: the realism of Jack London’s Call of the Wild (1903) and White Fang (1906) with the fantasy of Wind in the Willows (1908) and Beatrix Potter (1866-1943). Jack London’s animals are real and don’t speak, but Grahame and Potter turned animals into miniature humans, bringing them into our world, taming and civilizing them. Adams does the reverse: he takes us into the world of animals. He kept his rabbits wild and on all fours, sworn to the sward that they create with their teeth, but he used one piece of anthropomorphism. Hazel, Fiver, Bigwig and the other rabbits can all talk. They have a language, Lapine, and communicate with other animals using a “very simple, limited lingua franca of the hedgerow and woodland” (Part II, ch. 20).

How else could there be a proper story? But that one piece of anthropomorphism is actually an umbrella sheltering many other things: intelligence, memory, planning, persuasion, story-telling, the ability to lie, and so on. With language, the rabbits become like a tribe of primitive humans, pre-literate, almost innumerate:

Rabbits can count up to four. Any number above that is Hrair – ‘a lot’ or ‘a thousand’. Thus they say U Hrair – ‘The Thousand’ – to mean, collectively, all the enemies (or elil, as they call them) of rabbits – fox, stoat, weasel, cat, owl, man, etc. There were probably more than five rabbits in the litter where Fiver was born, but his name, Hrairoo, means ‘Little thousand’, i.e. the little one of a lot, or, as they say of pigs, ‘the runt’. (Part I, “The Journey”, ch. 1, “The Notice Board”)

At the beginning of the book, Fiver is the unacknowledged shaman of Sandleford Warren and foresees the doom that approaches it. Unfortunately, few rabbits believe him, which is why Adams heads the first chapter with a quote from Aeschylus, Cassandra’s warning that “The house reeks of death and dripping blood.” Every other chapter has its apposite quote, ancient or modern, poetry or prose, whimsical or serious: Aeschylus, Shakespeare, Tennyson, Napoleon, W.H. Auden, Dr Johnson, Clausewitz, Walter de la Mare and so on. The quotes stitch Watership Down deftly into the literary canon and into history, because the book is, in part, a celebration of story-telling and the possibilities of language.

That celebration is echoed inside the book, because the narrative is broken up by stories of El-ahrairah, the rabbits’ trickster-prince and protector. He’s like Odysseus and Watership Down is like the Odyssey. It’s a cycle of folk-tales in the making. Like Odysseus, the rabbits have to rely on their cunning and their speed, tricking monsters, not directly confronting them. Their own adventures will, in time, be attributed to El-ahrairah. Without writing, they have no history and sooner or later real events will melt into myth. But that’s the natural way: writing is a mysterious and evil thing to those rabbits who can intuit its purpose:

In the livid, foggy twilight, Fiver stared at the board. As he stared, the black sticks flickered on the white surface. They raised their sharp, wedge-shaped little heads and chattered together like a nestful of young weasels. The sound, mocking and cruel, came faintly to his ears, as though muffled by sand or sacking. ‘In memory of Hazel-rah! In memory of Hazel-rah! In memory of Hazel-rah! Ha ha ha ha ha ha!’ (Part II, ch. 26, “Fiver Beyond”)

Like Tolkien in The Hobbit (1937) and Lord of the Rings (1954-5), Adams is writing against the evils of technology and modernity; unlike Tolkien, he lists writing among those evils. A book that condemns writing is a paradox, but Adams is adopting a rabbit’s perspective. Tolkien’s books were, I’d suggest, a strong hidden influence on Watership Down. Rabbits are hole-dwellers like hobbits and the band of rabbits who set out from Sandleford Warren are rather like the Company of the Ring. Adams treats Lapine the way Tolkien treats his invented languages, using it to make us aware of the gulf across which the story comes to us:

With them was a third rabbit, Hlao – Pipkin – a friend of Fiver. (Hlao means any small concavity in the grass where moisture may collect, e.g. the dimple formed by a dandelion or thistle-cup.) (Part 1, ch. 4, “The Departure”)

Meriadoc was chosen to fit the fact that this character’s shortened name, Kali, meant in the Westron ‘jolly, gay’, though this was actually an abbreviation of the now unmeaning Buckland name Kalimac. (Lord of the Rings, Appendix F, “On Translation”)

But I think Adams is more linguistically creative and subtle than Tolkien, whose invented languages still seem like real ones: Welsh, Finnish, Old Norse and so on. Lapine isn’t reminiscent of anything familiar and some of its words – pfeffa, “cat”, and hrududu, “motor vehicle” – are cleverly simple, just the sort of onomatopoeias you can imagine a talking rabbit would use.

Cover of a recent edition of Watership Down

Cover of a recent edition of Watership Down

Lapine is also like Nadsat, the teen-speak invented by Anthony Burgess for A Clockwork Orange (1962). Adams leaves some words of Lapine untranslated at first, letting context give them meaning, sprinkling them through the text and allowing them to sink slowly into the reader’s mind. By the end of the book, you’ll find that you can understand basic Lapine: “Siflay hraka, u embleer rah,” says Bigwig to General Woundwort and the line doesn’t need translation.

General Woundwort is the Polyphemus or Sauron of Watership Down: a rabbit almost as big as a hare, the cunning and vicious megalomaniac who leads the slave-warren Efrafra. His wickedness is on a much smaller scale than Sauron’s, of course, but that makes it more credible and so more powerful. Lord of the Rings is more ambitious than The Hobbit, which is admirable, but also less successful, which was inevitable. Bilbo sets out to slay a dragon, not save the world. The rabbits in Watership Down are unwilling refugees who want to found a permanent warren of their own. It’s a small thing within the wider world, where humans rear giant metal pylons, span rivers with bridges, and speed to and fro in hrududim, but then human affairs are small within the wider universe.

It doesn’t matter: significance is not determined by size, purpose doesn’t have to be blunted by futility. The rabbits’ instincts drive them on and their ambitions are big enough for their abilities. They don’t need more. It’s General Woundwort’s desire to be great that prevents him from being so. He’s the most human of the rabbits and so the most evil: “All other elil do what they have to do and Frith moves them as he moves us. They live on the earth and they need food. Men will never rest till they’ve spoiled the earth and destroyed the animals.” (Part II, ch. 21, “For El-ahrairah to Cry”)

Man’s restlessness and meddling are a theme Adams took up again in The Plague Dogs (1977), a novel about two dogs that escape from a research laboratory in the Lake District. It’s a weak book set beside Watership Down, written more self-consciously and less coherently. Adams doesn’t stitch literary allusions into the story: he nails them in like corrugated iron. But his sympathy for animals is still there and so is his ability to describe the world through their sharper and subtler senses. The rabbits of Watership Down are like a primitive tribe of humans, but you never forget that they aren’t actually human:

A robin on a low branch twittered a phrase and listened for another that answered to him from beyond the farmhouse. A chaffinch gave its little falling song and farther off, high in an elm, a chiff-chaff began to call. Hazel stopped and then sat up, the better to scent the air. Powerful smells of straw and cow-dung mingled with those of elm-leaves, ashes and cattle-feed. Fainter traces came to his nose as the overtones of a bell sound in a trained ear. Tobacco, naturally: a good deal of cat and rather less dog and then, suddenly and beyond doubt, rabbit. He looked at Pipkin and saw that he too had caught it. (Part II, ch. 24, “Nuthanger Farm”)

That’s describing a raid on a farm that keeps pet rabbits. Hazel wants to find some does for the warren at Watership Down, where he and his fellow hlessil – “wanderers, scratchers, vagabonds” – seem to have finally found sanctuary. They’ve come a long way through strange country, but they’ll go further and see stranger before the end of the book. Watership Down is first and foremost an adventure story, but it’s also a celebration of the English countryside: its flowers, trees, birds, streams and rivers; its sounds, scents, shapes; its delights and dangers. The rabbits have their place there, naming themselves from nature, and unlike man, with his stinks and cacophonies, they don’t desire dominion over it.

The raucous gull Kehaar, their ally in their struggle with General Woundwort and Efrafra, brings word of far-off places and the mysterious sea, but their world is room enough. It fills their senses, challenges their cunning and ingenuity, sustains them, in the end will slay them. The countryside is the biggest character, as the title suggests, and rabbits were the best way to bring that character into a book. They’re social animals, mostly warren-dwelling, occasionally wandering, and if Adams could suspend disbelief and give them language, he could conjure a world of wonders through their eyes, ears, noses and mouths.

He could and did exactly that with the help of R.M. Lockley, who wrote The Private Life of the Rabbit, the “remarkable book” on which he drew for a “knowledge of rabbits and their ways” (“Acknowledgments”). Rabbits are in fact remarkable animals, but most people won’t realize that until they read the remarkable book called Watership Down. It’s a microcosm that mirrors the macrocosm, both reflecting man and reflecting on our ways. Rabbits “don’t name the stars”, Adams tells us, but in truth they don’t name anything, because Lapine doesn’t exist. It was his great achievement to make that impossibility plausible, turning sward-munchers into adventurers, mystics and dynasts with the sorcery of words:

A few minutes later there was not a rabbit to be seen on the down. The sun sank beneath Ladle Hill and the autumn stars began to shine in the darkening east – Perseus and the Pleiades, Cassiopeia, faint Pisces and the great square of Pegasus. The wind freshened, and soon myriads of dry beech leaves were filling the ditches and hollows and blowing in gusts across the dark miles of open grass. Underground, the story continued. (Part IV, ch. 50, “And Last”)

Spiral Archipelago

Incomplete map of Earthsea

Incomplete map of Earthsea

Ursula K. Le Guin, creatrix of Earthsea, is a much better writer than J.R.R. Tolkien, creator of Middle-earth: much more subtle, skilful and sophisticated. But for me Middle-earth has one big advantage over Earthsea: I can imagine Middle-earth really existing. I can’t say that for Earthsea, an archipelago-world of fishermen, goatherds and wizards. There’s something dead and disconnected about Earthsea. I’m not sure what it is, but it may have something to do with Le Guin’s dedicated political correctness.

For example, despite the northern European climate and culture on Earthsea, a sea-faring world with lots of rain, mist, snow and mountains, most of the people are supposed to have dark skins. The ones that don’t – the white-skinned, blond-haired Kargs – are the bloodthirsty baddies of A Wizard of Earthsea (1968), the first book in the series. Balls to biology, in other words: there’s propaganda to propagate. So it’s not surprising that Le Guin’s father was a famous and respected figure in the mostly disreputable discipline of anthropology. Earthsea is fantasy for Guardian-readers, in short.

But I still like the idea of an archipelago-world: sea and islands, islands and sea. As Le Guin herself says: “We all have archipelagos in our minds.” That’s one of the reasons I like the Ulam spiral: it reminds me of Earthsea. Unlike Earthsea, however, the sea and islands go on for ever. In the Ulam spiral, the islands are the prime numbers and the sea is the composite numbers. It’s based on a counter-clockwise spiral of integers, like this:

 ↓                                               ↑
146 101←100←099←098←097←096←095←094←093←092←091 132
 ↓   ↓                                       ↑   ↑
147 102 065←064←063←062←061←060←059←058←057 090 131
 ↓   ↓   ↓                                  ↑   ↑
148 103 066 037←036←035←034←033←032←031 056 089 130
 ↓   ↓   ↓   ↓                       ↑   ↑   ↑   ↑
149 104 067 038 017←016←015←014←013 030 055 088 129
 ↓   ↓   ↓   ↓   ↓               ↑      ↑   ↑   ↑
150 105 068 039 018 005←004←003 012 029 054 087 128
 ↓   ↓   ↓   ↓   ↓   ↓       ↑   ↑   ↑   ↑   ↑   ↑
151 106 069 040 019 006 001002 011 028 053 086 127
 ↓   ↓   ↓   ↓   ↓   ↓           ↑      ↑   ↑   
152 107 070 041 020 007→008→009→010 027 052 085 126
 ↓   ↓   ↓   ↓   ↓                   ↑   ↑   ↑   ↑
153 108 071 042 021→022→023→024→025→026 051 084 125
 ↓   ↓   ↓   ↓                           ↑   ↑   ↑
154 109 072 043→044→045→046→047→048→049→050 083 124
 ↓   ↓   ↓                                   ↑   ↑
155 110 073→074→075→076→077→078→079→080→081→082 123
 ↓   ↓                                           ↑
156 111→112→113→114→115→116→117→118→119→120→121→122
 ↓                                                   ↑

The spiral is named after Stanislaw Ulam (1909-84), a Polish mathematician who invented it while doodling during a boring meeting. When numbers are represented as pixels and 1 is green, the spiral looks like this – note the unique “knee” formed by 2, 3 (directly above 2) and 11 (to the right of 2):

Ulam spiral

Ulam spiral (animated)

(If the image above does not animate, please try opening it in a new window.)

Some prime-pixels are isolated, like eyots or aits (small islands) in the number-sea, but some touch corner-to-corner and form larger units, larger islands. There are also prime-diamonds, like islands with lakes on them. The largest island, with 19 primes, may come very near the centre of the spiral:


Island 1 = (5, 7, 17, 19, 23, 37, 41, 43, 47, 67, 71, 73, 79, 103, 107, 109, 113, 149, 151) (i=19) (x=-3, y=3, n=37) (n=1 at x=0, y=0)

Here are some more prime-islands – prIslands or priminsulas – in the Ulam-sea that I find interesting or attractive for one reason or other:


Island 2 = (281, 283, 353, 431, 433, 521, 523, 617, 619, 719, 827, 829, 947) (i=13) (x=6, y=-12, n=619)


Island 3 = (20347, 20921, 21499, 21503, 22091, 22093, 22691, 23293, 23297, 23909, 23911, 24533, 25163, 25801, 26449, 27103, 27767, 28439) (i=18) (x=-39, y=-81, n=26449)


Island 4 = (537347, 540283, 543227, 546179, 549139, 552107, 555083, 558067, 561059, 561061, 564059, 564061, 567067, 570083, 573107, 573109) (i=16) (x=375, y=-315, n=561061)


Island 5 = (1259047, 1263539, 1263541, 1268039, 1272547, 1277063, 1281587, 1286119, 1290659, 1295207, 1299763) (i=11) (x=-561, y=399, n=1259047)


Island 6 = (1341841, 1346479, 1351123, 1355777, 1360439, 1360441, 1365107, 1365109, 1369783, 1369787, 1369789, 1374473, 1379167) (i=13) (x=-585, y=-297, n=1369783)


Island 7 = (2419799, 2419801, 2426027, 2426033, 2432263, 2432267, 2438507, 2438509, 2444759, 2451017, 2457283, 2463557) (i=12) (x=558, y=780, n=2432263)


Island 8 = (3189833, 3196979, 3196981, 3204137, 3204139, 3211301, 3211303, 3218471, 3218473, 3218477, 3225653) (i=11) (x=-894, y=858, n=3196981)

C.A.S. Lewis

C.S. Lewis (1898-1963) was from Ulster, Clark Ashton Smith (1893-1961) from California. The two men wrote fantasy fiction, distrusted science, and rejected modernism. They had two initials in common too, but not much else. Like his friend J.R.R. Tolkien, Lewis believed in angels but, again like Tolkien, he didn’t write like one. CAS didn’t believe in angels, but did write like one. There is less literary magic in the whole of the Narnia series (1950-6) or Lord of the Rings (1954-5) than in a single of CAS’s Zothique stories, like “The Dark Eidolon” (1935) or “Empire of the Necromancers” (1932). If the English language is a harp, Lewis and Tolkien rarely plucked its sweetest strings. CASean notes do sound now and then in Lord of the Rings, like “The Mirror of Galadriel” and “The Pyre of Denethor”, but the prose of these chapters doesn’t match their titles. CAS, by contrast, could have written prose worthy of the titles. Elsewhere in Lord of the Rings, it’s the prose of a chapter that’s CASean rather than the title. But not very CASean, and not for very long:

The long journey from Rivendell had brought them far south of their own land, but not until now in this more sheltered region had the hobbits felt the change of clime. Here Spring was already busy about them: fronds pierced moss and mould, larches were green-fingered, small flowers were opening in the turf, birds were singing. Ithilien, the garden of Gondor now desolate kept still a dishevelled dryad loveliness. (The Two Towers, Book IV, chapter 4, “Of Herbs and Stewed Rabbit”)

Kings made tombs more splendid than houses of the living, and counted old names in the rolls of their descent dearer than the names of sons. Childless lords sat in aged halls musing on heraldry; in secret chambers withered men compounded strong elixirs, or in high cold towers asked questions of the stars. And the last king of the line of Anárion had no heir. (Ibid., chapter 5, “The Window on the West”)

Queen Jadis rides a hackney-cab in nineteenth-century London

Lewis does better, or at least longer: he sustains a flight of CASean invention over two chapters of The Magician’s Nephew (1955). As usual, Pauline Baynes’ drawings are better than his writing, but the prose is conjuring something unusual for Lewis: a genuine sense of antiquity, mystery and desolation. The two young protagonists of the book, Digory and Polly, have been tricked into a “Wood between the Worlds” by the book’s magician. The wood is full of magic pools. Jump into one of them and you’ll be transported to another world. Digory and Polly jump into a pool and find themselves in an ancient abandoned palace lit by a “dull, rather red light”. They begin to explore:

Every now and then they thought they were going to get out into the open and see what sort of country lay around the enormous palace. But each time they only got into another courtyard. They must have been magnificent places when people were still living there. In one there had once been a fountain. A great stone monster with wide-spread wings stood with its mouth open and you could still see a bit of piping at the back of its mouth, out of which the water used to pour. Under it was a wide stone basin to hold the water; but it was as dry as a bone. In other places there were the dry sticks of some sort of climbing plant which had wound itself round the pillars and helped to pull some of them down. But it had died long ago. And there were no ants or spiders or any of the other living things you expect to see in a ruin; and where the dry earth showed between the broken flagstones there was no grass or moss. (Op. cit., chapter four, “The bell and the hammer” (sic))

The prose plods, but one’s aesthetics nods: Lewis is invoking a strange and powerful world. Then the children find a room full of richly dressed men and women frozen like statues. Some look kind and wise, some proud and cruel, some evil and despairing. One woman, the most richly dressed of all and, to Digory, the most beautiful, has a “look of such fierceness and pride that it took your breath away.” There is magic in the room and Digory triggers it, thereby breaking the spell that holds the beautiful woman in suspended animation. She is both a queen and a witch – the witch Jadis. Her name in French means “of old, in olden times”, but the children are not in France, as they discover when Jadis guides them out of the palace:

Much more light than they had yet seen in that country was pouring in through the now empty doorway, and when the Queen led them out through it they were not surprised to find themselves in the open air. The wind that blew in their faces was cold, yet somehow stale. They were looking from a high terrace and there was a great landscape spread out below them.

Low down and near the horizon hung a great, red sun, far bigger than our sun. Digory felt at once that it was also older than ours: a sun near the end of its life, weary of looking down upon that world. To the left of the sun, and higher up, there was a single star, big and bright. Those were the only two things to be seen in the dark sky; they made a dismal group. And on the earth, in every direction, as far as the eye could reach, there spread a vast city in which there was no living thing to be seen. And all the temples, towers, palaces, pyramids, and bridges cast long, disastrous-looking shadows in the light of that withered sun. Once a great river had flowed through the city, but the water had long since vanished, and it was now only a wide ditch of gray dust.

“Look well on that which no eyes will ever see again,” said the Queen. “Such was Charn, that great city, the city of the King of Kings, the wonder of the world, perhaps of all worlds…” (chapter five, “The Deplorable Word”)

Jadis and the city of Charn are Lewis’s most successful invocations of CASean themes like female beauty, sorcerous evil, and dying (or dead) worlds. But the prose is weak and insipid beside that of Clark Ashton Smith – as you can see for yourself by following the links below:

“The Dark Eidolon”

“Empire of the Necromancers”

“The Charnel God”