Game of Zones

The Badminton Game by David Inshaw

David Inshaw, The Badminton Game (1972-3)

I first came across this beautiful and mysterious painting in a book devoted to British art. Then I forgot the name of both artist and painting, and couldn’t get at the book any more. Years later, I’ve found it again on the cover of a paperback in a secondhand shop. I like the way it combines zones: the domestic and the dendric, the lunar and the ludic, the terrestrial and the celestial. And it’s full of fractals: the trees, the clouds and, implicitly, the moon and the two girls playing badminton.

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”)

Leaf Brief

Front cover of What A Plant Knows by Daniel ChamovitzWhat a Plant Knows: A Field Guide to the Senses of Your Garden – and Beyond, Daniel Chamovitz (Oneworld 2012)

This is a brief but burgeoning book, covering a lot of science and a lot of scientific history. Plants stay in one place and don’t seem to suffer pain or discomfort, so they’re good experimental subjects, particularly for introverts. That’s why Charles Darwin devoted even more time to plants than he did to worms and barnacles. Chamovitz describes Darwin’s ingenious experiments and the even more ingenious experiments of the researchers that followed him. Over millions of years the world has set problems of survival for plants; in solving these problems, plants have set puzzles for scientists. How do plants know when to flower and prepare for winter? How do they resist attacks by insects? Or prey on insects? Or invite visits from pollinators? And how do they communicate with each other? The answers aren’t just chemical: they’re electrical too, as research on the world’s most famous carnivorous plant has proved:

Alexander Volkov and his colleagues at Oakwood University in Alabama first demonstrated that it is indeed electricity that causes the Venus flytrap to close. To test the model, they rigged up very fine electrodes and applied an electrical current to the open lobes of the trap. This made the trap close without any direct touch to its trigger hairs … (ch. 6, “What A Plant Remembers”, pp. 147-8)

Acoustics is also at work in the plant kingdom:

In a process known as buzz pollination, bumblebees stimulate a flower to release its pollen by rapidly vibrating their wing muscles without actually flapping their wings, leading to a high-frequency vibration. … In a similar vein, Roman Zweifel and Fabienne Zeugin from the University of Bern in Switzerland have reported ultrasonic vibrations emanating from pine and oak trees during a drought. These vibrations result from changes in the water content of the water-transporting xylem vessels. While these sounds are passive results of physical forces (in the same way that a rock crashing off a cliff makes a noise), perhaps these ultrasonic vibrations are used as a signal by other trees to prepare for dry conditions. (ch. 4, “What A Plant Hears”, pg. 107-8)

All of this is mathematical: a plant is a mechanism that processes not just sun, water and carbon-dioxide, but information from its environment too. But then sun, water and CO2 are all part of that information: sunlight signals plants as well as sustaining them. Its strength and duration are cues for the seasons and time of the day. So is its colour:

By the time John F. Kennedy was elected president, Warren L. Butler and his colleagues had demonstrated that a single photoreceptor in plants was responsible for both the red and far-red effects. They called this receptor “phytochrome”, meaning “plant colour”. In its simplest model, phytochrome is a light-activated switch. Red light activates phytochrome, turning it into a form primed to receive far-red light. Far-red light inactivates phytochrome, turning it into a form primed to receive red light. Ecologically, this makes a lot of sense. In nature, the last light a plant sees at the end of the day is far-red, and this signifies to the plant that it should “turn-off”. In the morning it sees red light and it wakes up. In this way a plant measures how long ago it last saw red light and adjusts its growth accordingly. (ch. 1, “What A Plant Sees”, pg. 21-2)

There’s an obvious analogy with a computer automatically turning itself off and on, which would make phytochrome and its associated chemicals a kind of hardware created by the software of the genes. Plants share some of that software with human beings: in one fascinating section, Chamovitz discusses the links between healthy plants and sick people:

The arabidopsis [A. thaliana, mustard plant] genome contains BRCA, CFTR, and several hundred other genes associated with human disease or impairment because they are essential for basic cellular biology. These important genes had already evolved 1.5 billion years ago in the single-celled organism that was the common evolutionary ancestor to both plants and animals. (ch. 4, “What A Plant Hears”, pg. 105)

What a Plant Knows stimulates human minds as it discusses plant senses. It’s one of the best briefest, or briefest best, books on science I’ve ever read, packing a lot of history and scientific information into six chapters. Plants don’t move much, but they’re a very lively topic and botany is a good way to understand and appreciate biology and scientific research better.

Yew and Me

The Pocket Guide to The Trees of Britain and Northern Europe, Alan Mitchell, illustrated by David More (1990)

Leafing through this book after I first bought it, I suddenly grabbed at it, because I thought one of the illustrations was real and that a leaf was about to slide off the page and drop to the floor. It was an easy mistake to make, because David More is a good artist. That isn’t surprising: good artists are often attracted to trees. I think it’s a mathemattraction. Trees are one of the clearest and commonest examples of natural fractals, or shapes that mirror themselves on smaller and smaller scales. In trees, trunks divide into branches into branchlets into twigs into twiglets, where the leaves, well distributed in space, wait to eat the sun.

When deciduous, or leaf-dropping, trees go hungry during the winter, this fractal structure is laid bare. And when you look at a bare tree, you’re looking at yourself, because humans are fractals too. Our torsos sprout arms sprout hands sprout fingers. Our veins become veinlets become capillaries. Ditto our lungs and nervous systems. We start big and get small, mirroring ourselves on smaller and smaller scales. Fractals make maximum and most efficient use of space and what’s found in me or thee is also found in a tree, both above and below ground. The roots of a tree are also fractals. But one big difference between trees and people is that trees are much freer to vary their general shape. Trees aren’t mirror-symmetrical like animals and that’s another thing that attracts human eyes and human artists. Each tree is unique, shaped by the chance of its seeding and setting, though each species has its characteristic silhouette. David More occasionally shows that bare winter silhouette, but usually draws the trees in full leaf, disposed to eat the sun. Trees can also be identified by their leaves alone and leaves too are fractals. The veins of a leaf divide and sub-divide, carrying the raw materials and the finished products of photosynthesis to and from the trunk and roots. Trees are giants that work on a microscopic scale, manufacturing themselves from photons and molecules of water and carbon dioxide.

We eat or sculpt what they manufacture, as Alan Mitchell describes in the text of this book:

The name “Walnut” comes from the Anglo-Saxon for “foreign nut” and was in use before the Norman Conquest, probably dating from Roman times. It may refer to the fruit rather than the tree but the Common Walnut, Juglans regia, has been grown in Britain for a very long time. The Romans associated their god Jupiter (Jove) with this tree, hence the Latin name juglans, “Jove’s acorn (glans) or nut”… The wood [of Black Walnut, Juglans nigra] is like that of Common Walnut and both are unsurpassed for use as gunstocks because, once seasoned and worked, neither moves at all and they withstand shock particularly well. They are also valued in furniture for their good colour and their ability to take a high polish. (entry for “Walnuts”, pg. 18)

That’s from the first and longer section, devoted to “Broadleaved Trees and Palms”; in the second section, “Conifers”, devoted to pines and their relatives, maths appears in a new form. Pine-cones embody the Fibonacci sequence, one of the most famous of all number sequences or series. Start with 1 and 1, then add the pair and go on adding pairs: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… That’s the Fibonacci sequence, named after the Italian mathematician Leonardo Fibonacci (c.1170-c.1245). And if you examine the two spirals created by the scales of a pine-cone, clockwise and counter-clockwise, you’ll find that there are, say, five spirals in one direction and eight in another, or eight and thirteen. The scales of a pineapple and petals of many flowers behave in a similar way. These patterns aren’t fractals like branches and leaves, but they’re also about distributing living matter efficiently through space. Mitchell doesn’t discuss any of this mathematics, but it’s there implicitly in the illustrations and underlies his text. Even the toxicity of the yew is ultimately mathematical, because the effect of toxins is determined by their chemical shape and its interaction with the chemicals in our bodies. Micro-geometry can be noxious. Or nourishing:

The Yews are a group of conifers, much more primitive than those which bear cones. Each berry-like fruit has a single large seed, partially enclosed in a succulent red aril which grows up around it. The seed is, like the foliage, very poisonous to people and many animals, but deer and rabbits eat the leaves without harm. Yew has extremely strong and durable wood [and the] Common Yew, Taxus baccata, is nearly immortal, resistant to almost every pest and disease of importance, and immune to stress from exposure, drought and cold. It is by a long way the longest-living tree we have and many in country churchyards are certainly much older than the churches, often thousands of years old. Since the yews pre-date the churches, the sites may have been holy sites and the yews sacred trees, possibly symbols of immortality, under which the Elders met. (entry for “Yews”, pg. 92)

This isn’t a big book, but there’s a lot to look at and read. I’d like a doubtful etymology to be true: some say “book” is related to “beech”, because beech-bark or beech-leaves were used for writing on. Bark is another way of identifying a tree and another aspect of their dendro-mathematics, in its texture, colours and patterns. But trees can please the ear as well as the eye: the dendrophile A.E. Housman (1859-1936) recorded how “…overhead the aspen heaves / Its rainy-sounding silver leaves” (A Shropshire Lad, XXVI). There’s maths there too. An Aspen sounds like rain in part because its many leaves, which tremble even in the lightest breeze, are acting like many rain-drops. That trembling is reflected in the tree’s scientific name: Populus tremula, “trembling poplar”. Housman, a Latin professor as well as an English poet, could have explained how tree-nouns in Latin are masculine in form: Alnus, Pinus, Ulmus; but feminine in gender: A. glutinosa, P. contorta, U. glabra (Common Alder, Lodgepole Pine, Wych-Elm). He also sums up why trees please in these simple and ancient words of English:

Give me a land of boughs in leaf,
A land of trees that stand;
Where trees are fallen, there is grief;
I love no leafless land.

More Poems, VIII.

The Four Treasons

Each year the patient hand of time
Plucks bare the oak, the ash, the lime,
And sharp against the Autumn sky
The subtle branches soothe the eye.

When Winter’s spell is fast on earth
The trees await the sun’s rebirth,
And pearled in frost, they stand and seem
Designed for beauty in a dream.

Then Spring revokes the spell and wills
The early leaves, the silver rills:
And symbol’d songs, more sweet than words,
Fill air with urgence of the birds.

Last, Summer’s lion roars his heat:
And pollen drifts and leaves compete
To drink the golden tide of light
Ere fall the sable drought of night.

In Memoriam A.E.H.