‘inexcusable Pythagorisme’
The Garden of Cyrus
VISITING THOMAS BROWNE in 1671, the diarist John Evelyn called ‘his whole house and garden . . . a paradise and cabinet of rarities, and that of the best collection, especially medals, books, plants, and natural things’. Praise indeed from the renowned author of Sylva, a ‘Discourse of Forest Trees’, translator of French gardening manuals, and author of the first book on salad plants.
The exact boundaries of this town garden are not known. Taking Evelyn’s fulsome description at face value, the garden and the house appear as a contiguous intellectual space, with plants as curious and varied as the precious objects and books indoors. Whatever its extent, it was not enough for Browne’s purposes, as he later leased a small meadow from the Dean and Chapter of Norwich Cathedral.
What did he grow? The keeping of a garden for the pleasure of its flowers was brought to Norwich by the Dutch. The city held Florists’ Feasts and Browne noted the faddism of the ‘tulipists’. More important for a physician was the growing of medicinal plants. During his studies in Montpellier and Padua, Browne had the opportunity to explore the first botanic gardens, the models for later gardens in Oxford and Paris, at Kew, and elsewhere, which all set out with the principal aim of growing and studying plants that might have medical therapeutic effects.
The Chelsea Physic Garden in London, founded in 1673 by the Worshipful Company of Apothecaries, is the garden that is today clearest about these origins, in title at least. I enter through a gateway in a high brick wall overhung with climbing hydrangea, and am immediately disappointed to find that its pharmaceutical garden is not a seventeenth-century replica, but is laid out according to modern medical disciplines – cardiology, gastroenterology and so on. Many of the plants are the ones Browne knew, though. The ‘Anaesthesia and analgesia’ section, for instance, has Mandragora officinarum, the mandrake which was once believed to shriek when pulled from the ground, and whose stout root often bifurcates so that it resembles the figure of a man (especially when a small third rootstalk is present). An active substance in this root, I read on the label, is now made synthetically for use in preoperative anaesthesia. Belladonna, digitalis and the opium poppy are among the plants I find in ‘cardiology’. Liquorice, traditionally used in the treatment of indigestion, has recently been found effective in reducing stomach ulcers. It is favoured as a natural remedy and chemists have derived a synthetic drug from it. Pellitory-of-the-wall, a member of the Urticaceae family, was a remedy for a dry cough, short breath and wheezing. Asparagus was prescribed to stir up lust. It reminds me that the appearance of plants was often taken as a clue to their medical application. Who’s to say this seventeenth-century Viagra doesn’t work even today, innuendo being perhaps as effective as pharmacology? Asparagus still makes regular appearances on lists of supposed aphrodisiac foods.
The botanical garden in Padua, established in 1545, still contains a few of the very same plants that Browne saw growing, notable among them the so-called ‘Goethe palm’, said to be the tree that prompted the German author to write his Metamorphosis of Plants. It had been growing for two centuries when Goethe saw it, and so Browne, too, had surely observed how each leaf, forming as a single blade low down, splits along fine longitudinal creases as it grows and spreads into feathery fronds higher up the tree. Padua’s beds of medicinal plants are more comprehensive than Chelsea’s, and they are less worried about alerting visitors to the poisonous species. A ricin plant, a species often considered as a biological warfare agent, blossoms with comical crimson pompoms at head height. A fruiting red chilli is described as ‘rubefacente’ – restoring redness to the skin – another medicinal prescription based on visual suggestion.
Browne’s own garden surely supplied him with a few of these plants, although as a modern physician he perhaps relied more on apothecaries to make up his preparations. It meant more to him though as a place of contemplation, wonder and enquiry, somewhere that he could observe the ever-changing patterns made by nature. The meadow near Pull’s Ferry on the River Wensum served a more extreme version of this purpose. It was a kind of experiment allowed to run out of control, an early example of Monbiotian ‘rewilding’, as he seems to have let it go simply for the pleasure of seeing what would grow there without cultivation.
Browne’s list of Norfolk birds and fishes was the workmanlike product of a specific request from a fellow scholar. But his botanical work soon opens out into something far more ambitious. This encyclopedia of Norfolk plants – for it is almost entirely from indigenous plants that he draws his inspiration – bears the daunting title The Garden of Cyrus, or the Quincunciall, Lozenge, or Network Plantations of the Ancients, Artificially, Naturally, Mystically Considered. The text is abundant and rhapsodic, even apparently chaotic. But, concerned as it is with patterns of order in nature, it is itself deeply ordered. It purports to be about the ancient Persian custom of planting orchards in a particular design, but Browne quickly abstracts from this idea the geometric form of the quincunx, the X shape made by five points arranged as on the face of a die, and from that launches into a broader exploration of the occurrence and significance of the number five in nature.
This is no work of obscure numerology as you might expect, but one that hovers tantalizingly on the verge of true scientific revelation. The essay unfolds almost literally like a flower, for four short chapters, dealing with this geometry and matters arising from it may be peeled back, as it were, from the long central chapter, the ‘naturally considered’ portion, which holds the essential content, the seed head of the work, a roll call of plants observed by Browne to exhibit a five-fold patterning. While it is the outer chapters that have delighted and puzzled literary admirers, with their bravura displays of Browne’s mature style, it is this central chapter that contains the kernel of science.
I myself hate gardens. Or, to be more exact, I hate the duties of a garden; I hate gardening. I can luxuriate in a garden that others have gone to the trouble of creating, and am happy to admire its maker’s talent and skill, and the richness and variety of plant forms that have erupted, consequently or not, from their actions.
But few things dismay me more than my own garden. The very sight of it reproaches me with chores undone. Just an hour of struggling to clear a bed of nettles is enough for me. I can never clear my head of the obvious futility of the task. I rage against the tangle of roots and the stinging. How can it be that so many plants in an English garden scratch and sting? My aversion is partly owing to the fact that the burden of my task is to do with killing – trimming bushes, cutting down dying trees, mowing what we laughingly call the lawn (it is mostly moss, and if it were entirely so, that would be fine by me). I tell myself that this work is essential too, all part of the natural cycle, but it does no good.
There is a deeper annoyance. I have a theory that gardens are a project for people who have given up on intellectual commerce and ideas. The garden is for them what it is so often said to be, a refuge and a solace. Plants may not conform exactly to one’s will, but they may be nurtured or rooted out, and led towards a certain destiny. Our ideas for them determine their prospects – something we cannot enforce in the case of people. It is strange to me that gardeners’ refuge from the chaos of human interaction should be a riot of nature, a mirroring chaos of growth and mindless competition to match the human rat race.
How did Browne feel about gardens? He tells us rather little about this in The Garden of Cyrus. It is notable that many of the plants he describes are those that were, and in many cases still are, to be found in any field or hedgerow. Perhaps he preferred to pass time in his wild meadow than in his tidy physic garden. I would certainly prefer to pass the time in Browne’s meadow. Sadly, I cannot. After Browne died, the land was used as a vegetable garden for the cathedral, then as allotments for residents in the Cathedral Close, until the 1970s, when it was turned into a private car park.
The garden can be a space for philosophy. Limbo, the first circle of hell described in Inferno, is a garden ringed by seven castle walls. Its denizens, Dante tells us, are men of worth, who are not sinners but who, by accident of chronology or geography, have never had the opportunity of baptism. They include Browne’s principal classical sources, not only the philosophers Heraclitus, Empedocles, Socrates, Plato and Aristotle, but also the physicians Galen, Avicenna, and Averroës.
Yet the garden itself and the activity of gardening have, like many popular pastimes, received rather little philosophical attention. Francis Bacon in his Essays of 1625 called gardens ‘the purest of human pleasures’. In a period when sex and even food carried the taint of sin, this is a perhaps expected observation. I am sure many people still believe this, without even taking an ironic pause to note how much this purity is based on the display of plants’ sexual parts. Bacon went on to divulge his rational plan for a garden, basically comprising a hedged square of lawn, the most conventional view of the garden as a symbol of man’s control over nature, and an ideal that still dominates the suburban English imagination.
For many, it is enough that gardens give pleasure, without asking what it is that constitutes the pleasure. Some say a garden is a means of better appreciating nature. But this is not it: the way to appreciate nature must be to get out into nature itself. Others refine this idea. For Bacon, the garden is the ‘first ornamentall Scene of nature’. This is better. But who decides what is ornamental and what is not? Most philosophers of the garden do not really tackle this essential aspect of artifice, the fact that it matters that what one nurtures and trains ultimately looks as if it has been nurtured and trained, at least a little bit. The goal of some of the most admired gardens (Japanese gardens, or the temporary creations of the Chelsea Flower Show, for example) seems to be to improve on nature, to bring it to a state of perfection, but in order to do this they must practically exclude nature altogether. For others, a ‘wild’ garden is more desirable, but this of course may require just as much artful arrangement. In both cases, it is nature and artifice brought together in chosen proportions that matters. The constant tension between these two, between the intention of man and the latent potential for nature to take its independent course (either bringing to full expression man’s intention or gradually, picturesquely, demolishing it), is what distinguishes the garden from the truly wild.
Like Bacon, Browne loves a garden for its own sake as well as for its useful plants. But he is not persuaded by the rigours of the Baconian design. Browne lived before Western civilization developed its sentimental idea of nature as an aesthetic resource. Our concepts of landscape and wilderness were not articulated until the eighteenth century; they would have meant very little to him. Yet he appreciates chaos and chance, the bramble strangling the clipped beech hedge, the blown rose as well as the perfect bud. Again, we find Browne far ahead of the fashion.
He would have enjoyed other things, too. It is notable in the philosophical discussion of gardens today that the actual plants in them seem to play little or no part. The meaning of gardens seems to exist entirely separately from the meanings once ascribed to individual plants. For Browne, almost every plant had a medicinal purpose or an emblematic association. The garden was then a kind of library, a place of half-remembered stories. This allusive, even allegorical, aspect of the garden is now a closed book to most of us.
Apart from pretty flowers and the utilitarian satisfaction of growing plants for food (and, in Browne’s case, medicine), what else do we have? What about the activity itself? According to David Cooper, writing in A Philosophy of Gardens: ‘It is symptomatic of a primarily aesthetic approach largely to ignore the practice of gardening.’ Yet there is a benefit to physical health – if all that fresh air can be said to outweigh the effect on the knees and back. And there is a purported benefit to mental health. A spell of ‘gardening leave’ – the genteel euphemism favoured by the British Civil Service when an employee is laid off – has connotations of a sabbatical or nature cure. There is even a charity called Gardening Leave set up to help military veterans with mental health issues through horticultural therapy. A recent piece of research by psychologists at the University of Munich – widely cited by authors of self-help books, though less so by other scientists – even suggests that brief glimpses of the colour green are enough to trigger greater human creativity. The words ‘green’ and ‘grow’ are etymologically linked, according to the paper’s author, Stephanie Lichtenfeld. The meaning we attach to the colour may stretch ‘from the concrete notion of vegetative growth and life to the more abstract, psychological notions of development and mastery’. Rory Stuart finds more spiritual answers in his book What Are Gardens For? He believes gardening inculcates virtues of care, self-discipline and humility (a word that derives, as he points out, from the Latin humus, meaning earth). ‘We gardeners,’ he writes, ‘feel the tranquillity of being among living things that do not move and make little noise, that obey a cyclical rhythm that is not our own, and over which we have limited influence.’
I understand in an obscure way that all these virtues – even the mutually contradictory ones of taking care and letting go – are present in the activity of gardening. I well up without fail at the end of Candide, when Candide and Cunégonde sing the final number, ‘Make Our Garden Grow’. Is this emotional release entirely an effect of the music, or do the words have something to do with it? I feel all of a sudden that keeping a garden is a profoundly moral thing to do. In the original Voltaire, the line is: ‘Il faut cultiver notre jardin.’ It is a metaphorical as well as horticultural envoi: we should stick to our knitting, we should keep calm and carry on, because there’s always work to do in a garden.
But then my unease returns, because being asked simply to ‘carry on’ immediately prompts the rejoinder: ‘What’s the alternative?’ I am reminded of the opening lines of the monologue in Samuel Beckett’s novel The Unnamable: ‘Keep going, going on. Call that going? Call that on?’ I am back where I started. I’m with Franz Kafka, from whose diary Beckett pulled out this dyspeptic quote: ‘Gardening. No hope for the future.’
Browne’s near-contemporary Andrew Marvell was preoccupied with the meaning of gardens, and wrote many poems on the subject. In ‘The Garden’, he is savage about our tendency to congratulate ourselves on growing what nature might grow anyway without our help:
How vainly men themselves amaze
To win the palm, the oak, or bays,
And their uncessant labours see
Crown’d from some single herb or tree.
Though Browne admires Cyrus (the Younger, a prince of Persia in the fifth century BCE) as ‘Not only a Lord of Gardens, but a manuall planter thereof’, it is doubtful that he did much spadework himself. He sought out rare seeds and made careful notes of where they were planted and whether they came up, but he still considers that he ‘was never the master of any considerable garden’. Nor I.
Perhaps I can overcome my aversion and even find illumination if I plant a garden for myself. I will make a square bed. In the autumn, I will plant four trees in the corners and one in the centre to make a quincunx. Now, though, it is spring, and I will seek out some of the smaller plants that Browne celebrates in The Garden of Cyrus. Many I find growing – by accident or by design – in my garden already. The walnut, hazel and alder all have catkins that display the lozenge patterning that Browne describes. The sycamore and the fig have new palmate leaves made up of five fingers. Later in the year I will see the ‘squamous heads’ of scabious and knapweed, artichoke and teasel. Always there high on the wall if I need a quincunxial reference point are clusters of Sempervivum, ‘Jupiters beard, or houseleek; which old superstitions set on the tops of houses, as a defensative against lightening’. I know from personal experience that the plant is no defence against lightning, but I can see that its tight rosettes of succulent leaves do provide durable evidence of the occurrence of the number five in plants. I twist one away from the wall and label the leaves in sequence as they spiral out from the centre. When I have done, I have five distinct whorls, and every leaf is accounted for.
I scan seed catalogues searching for some of the rarer plants Browne names, but find few matches. Perhaps his examples are now considered to be weeds, or have become unfashionable, or else the names have changed over the years. I am especially disappointed not to be able to track down the ‘man Orchis of Columna ’, an orchid whose flower has no five-fold property but the shape of a man – ‘well made out, it excelleth in all analogies,’ says Browne. Eventually, I order seeds of salsify and asphodel, the flower said to carpet the meadows of the underworld.
Then I select a neglected patch of turf and begin to clear a square of earth in readiness.
‘Gardens were before Gardiners, and but some hours after the earth,’ Browne concludes in the opening paragraph of The Garden of Cyrus. It’s a slick phrase, another quotable quote. What does he really mean? In the first book of Genesis, God creates the plant kingdom – grass and the herb yielding seed and the tree yielding fruit – three days before he introduces man. This is how there can be a garden before gardeners, although Genesis 2 immediately contradicts this version by implying that it needed both rain and man to till the ground before Eden could be made.
A garden is not just grass and herbs and trees, however. It must also display evidence of artful arrangement. The garden of the third day, then, must have God’s design upon it, which means that each and every plant carries within it evidence of God’s creation.
Browne approaches the plants of Norfolk quite differently from the way he considers its animals. The animals are curiosities, to be described and listed, foolish misunderstandings about them to be cleared up as he goes. The plants warrant deeper enquiry. It is as if they hold the key to something. Browne of course already has every reason to believe that they do, as so many of them are the basis of medical cures. While delighting in his powers of scientific observation, he hopes to discern signs of the original garden, Eden, amid the chaotic undergrowth of East Anglia.
In doing this, he anticipates his own desired sight of Paradise. For Browne, the aspects of gardening that we tend to gloss over – the cutting back, the rotting vegetation – are to be celebrated as much as any blossom. The autumn of decay and dying is the prelude to nature’s regeneration in the shoots of spring and to man’s own resurrection. The garden is a lifelong place of religious inspiration. Through study of its regenerative powers, he writes in Religio Medici: ‘no true Scholler becomes an Atheist, but from the visible effects of nature, growes up a reall Divine’.
Our lives are spent distinguishing between order and disorder. We are adapted to recognize order in nature because a disruption of that order may be key to our survival – it may indicate prey moving through the long grass or fruit hidden among the leaves. We discern visual order when the repetition of similar units (blades of grass, leaves) forms an array or pattern. The essential components of a pattern are space and number. The interplay of these two factors is formally described by the language of symmetry (the mirror symmetry of a face, the rotational symmetry of many flowers, the translational symmetry of a row of vines, say).
According to Browne, ‘nature Geometrizeth, and observeth order in all things’. For him, order in nature is a clue to the ways of the innocent world before the Fall, and patterns of growth and repetition are auguries of renewal, rebirth and resurrection. (Order is an ambiguous word, of course, encompassing social and moral order as well as visual order in nature, a thought that cannot be far from Browne’s mind, writing The Garden of Cyrus during the later years of Cromwell’s Protectorate.)
Number is an index of this natural order. ‘I have often admired the mysticall way of Pythagoras, and the secret magicke of numbers,’ Browne writes. But he is no numerologist who believes that certain numbers have significance in themselves. He follows a number if it leads somewhere, but not beyond the point of reason. When he explores the supposed significance of man’s ‘climacterical’, or sixty-third, year, he is led naturally to that number’s factors, seven and nine, and from there notes the traditional division of human life into seven-year stages of maturity, for example. But he is careful to add the sceptical note that at one time or another ‘all or most’ numbers have been ‘mystically applauded’. He cites one, for the unity of God; three, for the mystery of the Trinity; four, the number of the elements as well as the number of letters in the name of God in Hebrew and various other ancient languages; six, which is a perfect number (its factors add up to itself) as well as the number of days of the creation; and ten, which we use as our number base for counting.
It is notable that Browne’s reasons for the significance of these numbers are drawn from human culture. If he had included nature in his argument, he would have been able to add the missing numbers, the two of bilateral animals, the eight of the octopus and spider, and above all the five of the starfish and so many flowers.
Yet in The Garden of Cyrus, paradoxically, Browne’s gallery of specimen plants doesn’t really serve his ostensible rhetorical purpose of persuading us that the number five is special. It leaves us instead with the delicious feeling that he could just as easily have done the same for any number. The work is a vehicle for Browne’s typical genius of weaving an entertaining distraction from any ‘bye and barren Theme’.
This casualness is all the more tantalizing because we know now that the number five really is a key to the secret of natural growth. In 1202, the mathematician Leonardo of Pisa, known as Fibonacci, published a book of number puzzles called Liber Abaci, which included one conundrum about rabbit-breeding. The problem was this: starting with one pair of rabbits, how many pairs will you have after so many generations? Conveniently, the rabbits live for ever, and breed when they are exactly a month old and monthly after that, producing a pair of male and female young each time. The number of pairs each month is given by the sequence that now bears Fibonacci’s name, in which each number is the sum of the two immediately preceding numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and so on. As the series advances, the ratio of adjacent terms (1:1, 2:1, 3:2, 5:3, etc.) approaches the proportion known as the golden ratio: 1.618034 . . . Both the numbers of the sequence and the forms that can be constructed based on the golden ratio are abundant in nature.
Fortunately, the numbers of the sequence often emerge in natural patterns that don’t bounce around as much as rabbits. They surface, for example, in the angular spacing between successive leaves on a stem, the constant angle being one of the fractions of a circle given by the Fibonacci sequence: one half, one third, one fifth, and so on. They appear more obviously in the tighter arrays of pine-cone scales and clustered florets of composite flowers, where adjacent numbers in the series govern the way they spiral out from the centre where they are formed (and where the biological process of cell division takes the place of replicating rabbits as the generating process behind the numbers). I saw five spirals of leaves in my Sempervivum. Returning to my cutting, I find that these run anticlockwise out from the centre of the rosette. Looking closely, I now see that there is a second, steeper set of spirals running clockwise. I count them; there are eight, the number after five in the sequence.
The systematic investigation of these arrangements did not really get going until the nineteenth century, when it was named phyllotaxis (from the Greek words for leaf and arrangement). The revelation that the plant kingdom contained a hidden law of numbers prompted works of wonder, such as John Hutton Balfour’s Botany and Religion, or Illustrations of the Works of God in the Structure, Functions, Arrangement, and General Distribution of Plants of 1859, but scientists were left puzzled as to how this could aid their efforts to understand botanical structures. It turns out that it is in fact possible to classify every plant species in terms of two adjacent numbers of the Fibonacci sequence. Many plants display this underlying mathematics in the disposition of leaves around their stems, or more obviously in flower petals and seed heads. But there is more. Scientists have recently found that it is possible to produce the same spiral patterns in entirely physical systems, for example when magnetic droplets take up positions in a suitable magnetic field. The Fibonacci sequence turns out to be not the exclusive property of biology but something linked to fundamental physical laws. Yet it seems that this exciting empirical observation still awaits the theory that will fully explain it.
Throughout his catalogue of plants, Browne seems to be on the verge of discerning the Fibonacci sequence. But he is not a mathematician and nowhere uses mathematics to assist his argument, as Descartes was able to do in his description of the logarithmic spiral, or as the architect Inigo Jones did in his design for the beautiful spiral staircase of the Queen’s House, Greenwich, both of which rely on the golden ratio.
And Browne is, besides, fatally distracted from this course by the lure of the quincunx.
At the end of May, the first frail tendrils of salsify appear in the modules I have seeded. It is supposedly one of those moments when the pleasure of gardening is made manifest. You are given something back for your efforts, a reward, a new creation. I am moderately pleased, but more frustrated at the complete non-appearance of my asphodels. Plants either grow or they do not. In truth, I feel I have had little to do with their progress. My greatest happiness so far has come from preparing a perfect bare square of earth.
Now it is time to plant out. I have bought some asphodelines to replace the failed asphodels, and a species of sunflower. The sun is hot and it is almost still. I quickly develop a sweat as I dig holes for them. I find the tools less than ideal for the task and end up scooping earth with cupped hands. None of it is a joy. I bed the plants in and water them. A few days later I check on them. They seem to have taken well, but my main satisfaction is to see that my square is still free of weeds.
From time to time through the summer I monitor progress. The sunflowers bloom, and I count their petals. Each flower has thirteen petals – another Fibonacci number – and their seed heads radiate in thirteen nested arcs. One morning in September, I find that although the bees are enjoying the sunflowers, deer have also been enjoying my salsify. They have chewed off all the tops in the night and now I must re-bed the disturbed roots and hope they regenerate.
My efforts in the garden are less dogged than those of Gustave Flaubert’s Bouvard and Pécuchet, but I notice that my reactions are similar. Like them, I find myself exclaiming at what has grown: ‘They took pleasure in naming aloud all the vegetables: “Look, carrots! Ah, cabbages!” ’ This is the conventional response to the ‘miracle’ of growth, or, more particularly, to the miracle that (as we kid ourselves) we have grown these plants, our hubris there in the twisting of the verb into the transitive form.
Elsewhere in my garden, the number five is conspicuously recurrent. I have many of the plants that Browne lists as ‘pentagonally wrapped up’, from bindweed to roses, both wild ones with simple, five-petal flowers and fancy breeds, which have many more petals, but which, as Browne finds, still reveal their allegiance to the five-fold in their ‘calicular leaves’ or sepals. The five-fold seems special because it is odd, odd in both the phenomenal and the numeral sense. It lacks the more obvious natural symmetry that flowers with even numbers of petals have.
In Timaeus, Plato’s description of the world, the philosopher aligns the four simplest Platonic solids, the tetrahedron, the cube, the octahedron and the icosahedron, with the four elements, fire, earth, air and water. The fifth and most complex solid, the pentagon-faced dodecahedron, represents the ether that suffuses the universe. It turns out that he wasn’t far off the truth. Many molecules are built around pentagonal rings of bonded atoms, including my favourite, buckminsterfullerene. I found out that five-fold symmetry arises at many scales in nature. It is in the starfish and sea urchins that Thomas Browne knew, but also in the marine microorganisms known as radiolaria and in viruses that he did not know. It is perhaps even present at the atomic scale in the symmetry of the clouds of charge around atomic nuclei.
Five-fold symmetry was long thought to be absent from the mineral world of crystals because it is impossible to produce a space-filling array using repeating units based only on pentagonal geometry. Proper crystals are constrained to have two-, three-, four- or six-fold symmetry. However, in 1984, ‘quasicrystals’ with five-fold symmetry were observed in certain metal alloys, and many more have been discovered since. They have similarities with the tiling patterns mathematically described by Roger Penrose not long before, which incorporate star and pentagon tiles among other shapes to produce arrays that may be infinitely extended, but which, unlike a floor of square or hexagonal tiles, does not incorporate periodic repetition. In 2013, physicists at the University of Nice even managed to produce standing waves based on stars and pentagons in vibrating pools of oil, something previously thought impossible. Browne might still exclaim today ‘how nature delighteth in this number’.
Five-fold symmetry is mysteriously pervasive in human culture. It occurs as a decorative device on prehistoric pottery, and in Minoan and Mycenaean seals. It was a symbol first to the Pythagoreans, then to medieval astrologers and alchemists. It is associated with witchcraft: Goethe’s Faust exorcises Mephistopheles using a pentagram (Goethe had also noted the prevalence of five-fold design in nature). Then there is the Pentagon itself, a building designed for the efficient circulation of staff, but which inevitably invites theories of more sinister symbolism. The design echoes the symmetry of earlier defensive structures, including many seventeenth-century forts, such as the Landguard Fort at Harwich, which Browne may have known.
The same symmetry is equally favoured on our own proletarian plane. A pentagon inscribed with a star forms the logo of the Chrysler car manufacturer, for example. Almost all modern office chairs possess five equally disposed feet. At what point was four no longer enough? Geoff Hollington, a friend who has designed such chairs, informs me that the change was prompted by safety regulations introduced in the 1970s with the aim of making it harder to fall over while sitting on chairs that now had the new hazard of castors on their feet. The geometry shows that one extra leg buys a considerable increase in the tipping force. But Geoff believes it is also a visual preference. ‘Maybe we prefer this because it’s familiarly what happens in nature.’
Another design commonplace, the car hubcap, supports this argument. These wheel covers obviously must have a basic circular symmetry. But they usually sport a decorative lower order of symmetry, too. Unlike chair legs, there is no mechanical reason to prefer five-fold symmetry, and yet this does seem to be the most common pattern.
The number five is equally pervasive in aural experience. The pentatonic scale – five notes so harmoniously spaced that they may form a pleasing tune no matter in what order they are played – forms the basis of folk music around the world. One work that makes conspicuous play of it is by the Japanese composer T
ru Takemitsu. His orchestral piece A Flock Descends into the Pentagonal Garden, composed in 1977, is based on a dream of his in which a flock of birds alights in the said garden, which turns out to be the curiously shaved head of the artist Marcel Duchamp as captured in a famous photograph by Man Ray.
‘To enlarge this contemplation unto all the mysteries and secrets, accomodable unto this number, were inexcusable Pythagorisme,’ writes Browne at the head of the fifth and final chapter of The Garden of Cyrus. He is showing some neck here, for he has already digressed far and wide, and now goes on to point out that five is the number of the senses and of the conic sections, and that, as it is written in Leviticus, the sinner who takes something that is not his must pay back one fifth extra above its value. For my part, I observe merely that VAT today stands at 20 per cent.
To anybody mathematically minded, the quincunx clearly has little to do with five-fold symmetry or the number five at all, although it turns out in the end, most surprisingly, that the gardeners of the ‘network plantations of the ancients’ and nature’s phyllotaxis are chasing after the same goal.
Browne’s quincunx is the diamond trellis he shows us in the frontispiece of The Garden of Cyrus. It is a pattern seen, as he tells us, in catkins and pine cones and leaded windows and iron gratings and fishing nets. It is present singly in the X frame of Roman chair supports and in the way beds are lashed together. Above all, though, the quincunx is the template of the ‘sacred Plantations of Antiquity’, and perhaps even the Garden of Eden, which we know had at least the central tree of knowledge.
Quincunxes are out of fashion these days, but I find a grand remnant of some near Capel St Andrew in Suffolk along a straight mile or so of a road bordering the northern edge of Rendlesham Forest, a place haunted by Britain’s most notorious UFO sighting. The trees are known as the Butley Clumps. According to one local story, they were planted in 1805 to celebrate Nelson’s victory at Trafalgar, quintets chosen perhaps because of the year. All that remains of most of the quincunxes are one or two massive beech stumps, but in a few cases all four stumps survive, clearly disposed to the corners of a square, with a central trunk – this always a pine – also present. Here and there, an effort has been made to replant the missing clusters, with quadrates of sturdy beeches planted around their central Scots pines, all protected by rabbit-proof plastic mesh.
But the stumps are better. They have a memorial potency. I cannot tell how long ago the trees died or were felled, but they still serve as symbolic markers in the landscape. Walkers have worn a pathway along the verge of the road from quincunx to quincunx, passing through the middle of each, dodging round the central pine where necessary, threading them onto a continuous ley line.
Browne’s diagram of a quincunx is in fact nothing more than the simplest of two-dimensional lattices. Its unit cell – the minimum module from which the array may be built and extended to infinity – is a square (or a rhombus, in Browne’s elegant drawing). Each corner – the site of a tree in a quincunxial orchard – is equivalent. Each unit cell thus contains a quarter of a tree at each corner. When arrayed together, these unit cells form a simple orchard with trees in equally spaced rows in two directions.
So where is the number five? Perhaps some visual elaboration would have helped here, but Browne announces in his dedicatory epistle that he does not wish to ‘affright the common Reader with any other Diagramms’. However, it is possible to superimpose a slightly larger ‘unit cell’ at forty-five degrees to the first, with one central tree and a quarter share of four new trees at each corner, that does begin to look like a quincunx. But this leads to the same simple orchard when it is repeated.
This does not appear to be the arrangement of trees in Cyrus’s garden as described by the Greek historian Xenophon, which Browne paraphrases as having ‘the rows and orders so handsomely disposed; or five trees so set together, that a regular angularity, and through prospect was left on every side’. This could still be a simple square grid spaced so as to leave good orthogonal and diagonal sightlines, but Browne’s description does suggest something more complicated that would give a sense of the trees being laid out in distinct sets of five as well. For a true quincunx to be the repeating unit cell, it turns out that the trees must be set out in rows that cross at every third tree.
The justification for quincunxial plantation is that it supposedly gives trees more light. In the simple square grid all trees receive the same light, although of course they shade one another if they are too closely planted. If the trees are set out at the same spacing in their rows but with the intersections only at every second tree rather than every tree, the trees at the intersections receive less light than the trees in between. The same goes for the array based on repeating quincunxes, in which the intersections happen at every third tree. Some trees are better off in these arrangements, but some are relatively more shaded. The only answer to planting an orchard to give every tree equal light is to follow the simplest arrangement and to increase the spacing sufficiently. The quincunx is no more than an ornamental conceit.
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November has come, and it is time for me to plant my own quincunx. I have no plans for a commercial orchard, and so the question of how best to arrange rows of trees for maximum yield does not arise. I buy four bare-root apple trees of interesting varieties and a young pine. I check the dimensions to make sure I have a perfect square and then dig the holes, one in each corner and one in the centre. I tease out the roots of each tree and place it gently in the appropriate hole, filling it with earth and pressing it down as I go. Finally, I stake the trees and lash them together so that they will not be blown over in the next storm. I step back to inspect my naive handiwork. They are not the first trees I have ever planted, but it is the first time I have tried to impose a regular design on nature. I am not sure I like the pattern I have made in a garden that is frankly governed by randomness. I wonder for how long my little plantation will read as a quincunx.
I feel Browne’s focus on the quincunx may be a case of ‘visual editing’ on his part in order to extract maximum interest from the apparently unpromising starting point of the simplest of geometric arrays. It serves him well as he embraces the five-fold in plants and the grid-like patterns on pine cones and catkins. But in essence there is nothing to be explored here except the connections that he imagines. Browne does not give us diagrams or, as he also says, ‘mathematicall truths’ because he prefers the ambiguous richness of text, the impressed array of words on the page and their infinite possibilities of meaning.
What Browne did not know is that the quincunxial orchard and the five-fold arrangements produced by phyllotaxis do in fact share common cause in a scientific sense. Both are directed towards the same end – that of supplying plants most efficiently with the light and energy they need in order to grow. He might have been disappointed to understand that there is nothing paradisiacal or even biological about this. It is solely the battle between physical forces that governs the emergence of these patterns. He would be consoled, though, to recognize that this in no way removes God from the garden.
I am beginning to think part of my aversion to the garden is based on an unwillingness, inculcated in me by science, to find easy ‘wonder’ there. If, as Browne claims, the observation of nature in a garden is inimical to atheistic thinking, then perhaps this is the root of my discomfort.
Although he operated on the scientific fringe, Browne’s speculations as a ‘botanologer’ on symmetry and pattern in plants are pertinent again today, and are now taken further by the new geometry of fractals, in which similar patterns are found to repeat on different scales, for example in the tapering leaves of familiar plants such as ferns as well as in the seed heads studied by Browne.
Phyllotaxis, according to the science writer Philip Ball, ‘contains a hidden mathematical pattern for which we are unlikely to find an explanation by rooting around in the genetics of plant developmental biology’. There is something reassuring about this, not so much because it is a poke in the eye for reductionism and the apparently inexorable tendency for discoveries to be made at scales smaller than the visible, as because it restores the idea that simply looking at things in the right way might still have much to teach us. Assisted by computer visualizations, plant biologists are once again finding that observation of the growth and form of plants may be as instructive as analysing their component genes and proteins.
I find a man who I am tempted to characterize as Browne’s spiritual successor just outside Norwich at the John Innes Centre. Professor Enrico Coen is a plant geneticist who has made his name in science for a new understanding of what controls the development of flowers, work for which he was awarded the Darwin Medal of the Royal Society. He also has a fine disregard for the artificial boundaries erected between science and the arts. He is an accomplished portrait painter, often persuading visiting scientists to sit for him. Furthermore, he has just written a visionary book that is sure to provoke more cautious colleagues to critical apoplexy. In Cells to Civilizations, Coen aims to identify common factors that organize life at every scale, from the division of biological cells during the growth of organisms to the statelier pace of evolution and the development of human civilization. It is a book of Brownean scope and daring, an attempt to provide the ‘theory of everything’ that biology seems to lack. Enrico seems to share with Browne the ability to step aside from the trudge of the scientific project and take in a bigger view. He understands that some of his peers may be sceptical or worse, but he is confident that his book will connect nevertheless. ‘People who want to see unifying ideas – it will appeal to them,’ he says. ‘The question is how you do these things in a critical way, and not end up in mystical pondering. I feel I’m doing it in a way that’s very grounded in science.’
We meet in one of the gardens slotted in among the John Innes Centre laboratory buildings. It is a hot day and Enrico is wearing a light short-sleeved shirt with a checked pattern that reminds me of Browne’s grid of lozenges. The sun glints off his tanned bald head until we take shelter under a rose bower. Everywhere are blossoms. I fear for the stooks of ripe artichoke that stand nearby: ‘artichoke omelette’ has been written up on a whiteboard as one course of a feast planned for the end of an interdisciplinary seminar of biologists and computer scientists.
Enrico offers welcome evidence to refute the ‘two cultures’ view of the arts and sciences that has historically bedevilled British education and academia. ‘It’s all a false dichotomy,’ he insists. ‘Science tells us important things, but it’s also a human activity. We can’t separate that.’ As if in proof, his oil sketches line the stairwells of the John Innes Centre. One of his portraits is of Jonathan Miller, the physician and theatre director, perhaps the most conspicuous refutation of the two-cultures doctrine at work in Britain. Although Enrico was born in Liverpool, his own breadth of learning must be something to do with his Italian heritage. Both his parents are half-Italian, and both are scientists, but there is an echo of the Renaissance spirit that allows art and science to occupy the same space. ‘We used to go to Italy every summer holiday,’ he says. ‘They would take me to art galleries. I never really grew up with a sharp divide.’
One of Enrico’s favourite models for investigating flower shape is the Antirrhinum or snapdragon. The snapdragon, as it happens, already has a special connection with the city of Norwich. A snapping dragon was once a feature of medieval religious processions linked to the Guild of St George, although by the time of Thomas Browne it had been incorporated into mayoral ceremonies, where it still makes its appearance today.
It is the asymmetric arrangement of its petals that causes the flower to resemble a dragon’s mouth. Exactly how the snapdragon, or any flower, actually develops its distinctive shape is hard to figure. But the regularity of that shape is at the heart of the matter. Pollinating insects – bees in the case of snapdragons – must find the experience of visiting the flower memorable in order to seek out others like it. If its petals vary too much in number, shape or size, the approaching bee may not recognize it or may not be able to gather pollen successfully. Number is especially important, it seems. ‘There is an evolutionary tendency for flowers to become more consistent in the numbers of features such as petals,’ Enrico tells me.
Before genes were known, naturalists had little option but to classify plants according to the shapes of their leaves and flowers, but they could not say how or why they take the wide variety of forms that they do. Snapdragons are easy to grow and were once a popular model organism in plant breeding experiments, but fell out of fashion when attention turned to crop plants. Later, though, they were found to possess a type of gene that can jump to different positions in the genome and thereby produce mutations. Enrico had a hunch that these genes might be useful tools for investigating flower shape.
In the snapdragon, one gene is responsible for the symmetrical folding back of the petals that happens in most flowers. Another gene breaks that symmetry so that the flower morphs into the familiar dragon’s-mouth shape. One of the petals becomes the dragon’s ‘tongue’ and the landing platform for the bee, while the others curl back to make the dragon’s ‘head’. Without these genetic components, the snapdragon would develop without the petals folding back or with five symmetrical petals like so many other flowers, and it would lose its exclusive appeal to bees. ‘The asymmetry of the snapdragon relates to the asymmetry of the bee,’ Enrico explains. ‘It reflects the fact that it’s visited by an animal.’ This understanding demanded knowledge of the mechanism of individual genes but also relied on the traditional naturalist’s skill of observation. ‘It’s relating different perspectives. That’s how you arrive at understanding.’
Enrico’s research today involves a powerful combination of the latest knowledge of plant genetics and the use of computer models to visualize patterns of growth. Members of his team work at large computer screens; there are few growing plants in the lab. But there is beauty. On one of the screens, I see astonishing high-speed sequences of the inner structure of plants taking shape as they grow. They are so perfect and bright that I assume they are computer graphics. But I am corrected: they are assembled from natural images. On other occasions, though, Enrico’s team do create entirely artificial visualizations of plant growth. These are based solely on data describing the behaviour of the individual cells that make them up, with no information about overall morphology. The visualizations are beautiful – Enrico’s painter’s eye is obvious in some of the illustrations in the team’s scientific papers – but also highly instructive. They are a vital aid to help fellow scientists grasp the basic algorithms of growth and a salutary reminder that there’s no substitute for seeing. The images are uncannily close to what we see in the garden: they demonstrate in the most graphic way the power of nature to develop complex organisms using a very few, simple rules. Perhaps it is this power that we sense when we observe the splitting of a palm leaf or the lozenges on a catkin.
But actual gardening? ‘It’s not something I get,’ says Enrico.
botanologer (GC, 1658) / botanist (Miscellany Tracts, 1684): Browne was aware of the need to explain what it was that he and his peers were doing, and this is one of many words he coined to give names to emerging scientific disciplines. Phytology, the study of plants, also makes its debut in The Garden of Cyrus. In Religio Medici, Browne thinks there may be something also in phytognomy, the art or science of deducing the qualities of a plant from its appearance (hence the prescribing of asparagus as seventeenth-century Viagra). Other new disciplines or their practitioners include mineralogist, ichthyology, zoographer and cryptography, as well as a notable pseudoscience, rhabdomancy, meaning divining by means of a rod. Around 1682, in a late note on garlands and the kinds of flowers and plants used in them, Browne improved on botanologer by adding the word botanist to the English language.
