Luca Mozzati’s Islamic Art (Prestel, 2010) is rather more of a coffee-table book than Lynn Gamwell’s Mathematics + Art, but the text isn’t at all bad. Its main failing is that it concentrates nearly exclusively on Architecture. This at least permits some of the glories of architectural decoration – arabesques, geometric patterns, and calligraphic inscriptions – to be displayed in rich colour, but at the price of leaving out the enormous wealth of carpets, brasswork, wood-carving, glass, and all the rest.
There are to be fair some nice miniatures from Turkey and Mughal India; there are a few details of brasswork and tiles, the occasional wooden casket, and some parchments, but all the same, the book is seriously unbalanced. Perhaps the author simply meant it to be called “Islamic Architecture” and was overruled by his publisher. At least it gives an idea of some of the splendours on offer.
For a book on the principles of at least some Islamic architectural decoration (basically, just girih strapwork), see the review of Eric Broug’s Islamic Geometric Design.
It was cold out today, and I was glad of fleece, warm coat, woolly hat and gloves — not to mention gumboots through the clogging mud, the worst I’ve seen in many walks at Wraysbury Lakes.
But when the sun came out, it was beautiful, and I hope I’ve captured a little of that wintry beauty for you (and some of the puddled paths) with this photo of last year’s dried-out Teasels.
Just as I was about to take the photo, a flash of white from two largish finches caught my eye, and I grabbed my binoculars. Luckily, they landed in a bare thornbush, and showed themselves to be a male and a female Bullfinch, their black caps, red chests and white rumps splendidly visible as they sat a while, occasionally leaning right forwards to peck at the buds. They flew off to another bush, giving me the best views I think I ever had of the male/female differences at rest and in flight. The male really did glow red.
Up on the horse hill, a flock of some 50 Goldfinches flickered overhead. A Green Woodpecker called in the distance, as did two Mistle Thrushes, their loud, monotonous, ringing cries carrying across the wet ground. A solitary Redwing was all that was left of the winter flocks. Two streaky brown Linnets flew across.
A cormorant flapped heavily overhead, quite goose-like in front view but obvious enough in outline as it went by. Down at the nearly birdless lake, 5 Goldeneye brightened up the view, with a few distant Shoveler.
Lynn Gamwell’s Mathematics + Art, A Cultural History (Princeton, 2016) is a beautiful, magnificent, and rather large book. Given its size, its cover price ($50) is very reasonable. The topic is an enormous one, ranging from the ancient to the ultra-modern.
Gamwell makes a serious attempt to cover the ground comprehensively. The book begins with Arithmetic and Geometry (two huge areas in themselves), and a glorious image from a Bible moralisée of 1208-1215 of God the Geometer, measuring out the world – it looks rather like a geode in section, actually – with a pair of dividers.
God the Geometer (Wikimedia Commons)
Page 1 mentions “Mankind’s ape-like ancestors” and talks about the first symmetrical tools; 300,000 years ago, hand axes started to have elegant symmetry. Clearly Gamwell’s intention is to cover the interaction of mathematics + art in the whole span of human history and prehistory: it’s nothing if not ambitious.
The text sweeps rapidly through time, so that on page 3 we reach 3000 BC and the ancient foundations of recorded mathematics, with I, II, III tracking quantities; the Egyptians introduced ∩ for 10, so 12 was ||∩. Soon we are in Ancient Greece and the theorems of Thales (the base angles of an isosceles triangle are equal…), and what the sculptor Polykleitos wrote about the perfect proportions of the human body in the 5th century BC. Attention switches to the elements and the Platonic solids (with a forward reference to Kepler’s depiction in Harmonices Mundi, 1619), Democritus’s mechanical universe, and Euclid’s Elements – all in the first chapter, and I haven’t even mentioned the detailed treatment of the birth of modern physics and Newton’s law of universal gravitation, which Gamwell actually explains with the famous inverse square law equation.
Julia Set detail (Wikimedia Commons / Joshi1983)
The book, in other words, is big, and dares to boldly go where others fear to tread (Steven Hawking wrote in his A Brief History of Time that each equation halved the number of readers: Gamwell has plenty, and explains the symbols of formal logic, too.) She can cover the plans of Gothic cathedrals, the mysteries of perspective from the Italian Renaissance, Zeno’s Paradox (can Achilles catch that tortoise?), modern art from Mondrian to Henry Moore, Bauhaus to Bourbaki. It’s kaleidoscopic, and if you wanted a coffee-table book then you could just flick through it and enjoy the Mandelbrot and Julia sets, gloriously illustrated.
But of course readers expect and deserve more. The chapters cover Arithmetic and Geometry; Proportion; Infinity; Formalism; Logic; Intuitionism; Symmetry; Utopian visions after World War I; The Incompleteness of Mathematics; Computation; Geometric Abstraction after World War II; Computers in Mathematics and Art; and Platonism in the Postmodern Era. This is visibly a huge scope – all of mathematics, all of art, and all of their intersection (to coin a phrase from set theory).
But wait a minute: all of art? It’s certainly all of the time during which art has been created, bone flute (Hohle Fels cave, c. 42,000 years ago) and Lascaux cave paintings (ca 15,000 BC) included. The discussion of art cheerfully scoots about from Iceland to Renaissance Italy; from Russia to China to Japan; from a Hungarian-born Argentine artiss (Gyula Kosice) to the American hand-blown glass and steel sculptures of Josiah McElheny. The reader grapples with fractals and their recursive algorithms; formalist mathematics and constructivism; Klein bottles and the odd behaviour of electrons in quantum mechanics. Gödel, Escher and Bach do their Hofstadter-esque dance of self-reference.
The Elephant in the Room
Missing from the book: Islamic Art. Girih strapwork tiling, Green Mosque, Turkey. (WIkimedia Commons)
So what is missing? The 556 pages barely so much as blink in the direction of Islamic Art, of the dazzling complexity and virtuosity of its geometric designs and decorations, of its centuries-long contribution to mathematics – even the words algorithm and algebra come from Al-Khwarizmi’s name and his book of pioneering mathematics. Nothing. Zilch. Nix. Or as the Arabs would say, Zifr. Well, they invented it.
Did Gamwell simply not know about Islamic tessellations? Of Escher’s inspiration in the Alhambra? Of Girih strapwork all over the minbar pulpits of Egypt, all over the turquoise domes of Persia? Of the dazzling Zellige tilework of Morocco? Of the lustre tiles of Tunisia? Of the inlaid geometric stonework of the Umayyad Mosque in Damascus? Of the airy Jali stone screens of the Mughal palaces of India? It seems not. Her index includes “Arabic numerals”, but she did not follow up that broad clue.
Gamwell has written a fascinating, beautiful, intriguing, and stimulating book. It is sometimes rather too academically picky; sometimes a bit too thorough in explanation, but then you may need more than me on some topics. It is perhaps a bit too much focussed on the twentieth century – after all, why that century, not all the others? Recentism is no reliable guide. But the glaring gap, or as a pretentious art critic would say, the lacuna of all lacunae, is the extraordinary lack of coverage of the whole of the Islamic world. Try a look in the Index – you won’t find Arabia (apart from Arabic numerals), or Morocco, or Syria, or Iran (or even Persia), or Moghul/Mughal. It’s just not there.
I think this matters, and matters terribly. If George Bush and Tony Blair had it in their blood that art, science, mathematics, medicine, poetry, music, pottery, metalwork, masonry, glass, carpets, and gardens all flourished in the Islamic world, for century after century, from the Moroccan Maghreb (“The West”) to Turkey, Egypt, Persia, Afghanistan, all of the Indian subcontinent, Indonesia – would they have acted as ignorantly as they did? And more importantly now, will our future leaders be any better informed, or will they treat Sunni and Shia alike as ignorant savages? For what it’s worth, Daesh / ISIS / ISIL is not Islam, it’s a stupid and wicked splinter group, and has nothing whatsoever to do with a great cultural heritage. Especially, it should not colour our attitudes to Muslims and Islam.
All the same, I felt sufficiently engaged at the lack of coverage to do something about it. I brought two Wikipedia articles, Mathematics and art, and Islamic geometric patterns, to “Good Article” status, pretty much rewriting them from scratch in the process. To make the whole area a bit easier to navigate, I also rewrote the navigation template on Islamic art. Together, these are seen – and perhaps read – by around 100,000 people a year, and of course they help to inform blogs and social media postings, so maybe they will have some effect. If you can suggest ways of reaching more people with this sort of knowledge, I’d be happy to hear from you.
Science proceeds in slow steps, and things far more often become clear gradually than in dramatic Eureka! moments.
After “hours of fun” trying to decipher sheets of paper covered in a mass of footprints, we learnt that most of what we had seen were mouse/vole (indistinguishable as prints), squirrel, cat, and rat. Some of the West London survey sites in London Wildlife Trust’s Vole Patrol had evidence of other mammals, from camera trap shots of foxes and badgers to a fuzzy glimpse of an elusive otter.
Not a Yeti! Double prints of a cat giving a 5-toed look
Huma had been busy visiting all the sites, teaching volunteers, getting people to build mammal nestboxes (like birdboxes, but with the opening round the back!), and inspecting a lot of shrew tubes and sheets of paper covered in footprints.
The five-toed “Yeti” footprint turned out to be a cat (notice the streaks from its furry feet) which had placed one four-toed foot almost in the print of another, so there are two heels of the hand and the middle three toes double-printed. Of such are mysteries made.
Camera trap in position
We all enjoyed looking at what the camera traps had caught. The video clips were much easier to interpret than the still images. Several small children had crept up to the cameras and spent a while peering into the lenses (What? Me? I’m on camera?). Two foxes cavorted with long bushy tails. A badger ambled past like a crotchety old gentlemen on the way to his club. Mice with big round ears, surely wood mice, bounced and scuttled in and out of the field of view: sometimes only the glint of their eyes revealed their presence, and sometimes even that was very small and only at the edge of the frame.
Then we cleared an easily-wiped formica-topped table for … shrew poo analysis. We had up to ten baited tubes from each site. With surgical gloves, dissecting probes, tweezers and hand lenses, we carefully emptied each tube into a Petri dish and looked for mammal pellets. Mice eat seeds and produce solid, compact pellets, round one end, pointed the other. Shrews eat insects and produce pellets of a similar shape, but made of non-stick fragments of insect cuticle, so their pellets tend to crumble. Many of the tubes contained nothing; one or two had been lost in the field; several contained mouse pellets, most likely wood mouse; a few seemed to contain shrew pellets. We dropped the pellets into sealable inch-long plastic tubes labelled with their site, the date, and the shrew tube number, and recorded what we had found in the logbook, to much cheerful banter.
Mammal nestbox: Yes, the hole is meant to be on the back
It will become much easier to determine which wood contains which mammals when we start trapping in a fortnight’s time. Then we have to get up and be at the reserves by 6:30 in the morning for a two-hour stint, to be repeated in the afternoon. My family will be amazed if I manage any kind of early morning.
Here in town, the daffodils are in bloom, the bluebells are coming into fresh green leaf, and the temperature is 10 C, so it might almost be early spring. And this morning I heard the chi-chi-chi / zheeeee! of a singing male Greenfinch, getting into the spring courtship season. But some trees on the same common are full of twittering Redwings, winter visitors from the frozen North, a cheerful and bright winter sight.
Out in the countryside, it looks much more like Winter, the trees as bare as they ought to be in early February, the only flowers a few tufts of snowdrops near the pleasantly lichened reserve signboard at RSPB Otmoor. The reserve has grown steadily better from its early day, with more and more wet scrapes, pools, and reedbeds spanning something like a mile of Otmoor’s wide, flat expanse.
A Kestrel hovered overhead; Bramblings and Chaffinches lurked in the hedges; Redshank called in the distance. Red Kites drifted by over the trees. Seven Snipe jumped up, screeching, from wet grass and zigzagged to a muddy island. A Cetti’s Warbler sang from almost under our feet, invisible.
The luxurious hide revealed numbers of Wigeon, Shoveler, and Teal, and a flock of Linnets with a few Goldfinches feeding on the grass in full view. Yellowhammers, Reed Buntings and more Linnets sat in the bushes. The trees were full of twittering: I soaked up the soundscape with hands cupped to my ears.
Thousands of Golden Plovers (and some Lapwings below)
When a Buzzard came over, some 3,000 Lapwings and a similar number of Golden Plover got up, all glinting gold as they turned together in the sunshine.
Golden Reedbeds from a hide with no roof
Over to the north, a Marsh Harrier dropped into the reeds, got up again and scoured the reedbed for signs of prey, its broad brown wings slightly raised, its broad tail quiet unlike that of the Red Kite that wheeled past it.
Today we all put on waders and got into cold muddy water.
I shovelled silt into an ingenious floating bucket system: the bucket had holes in the bottom to let the water out but it seemed to keep most of the mud in. It was possible to scoop to a depth most of the length of the shovel. Then I towed the silt bucket to the shore (much easier than carrying it) to empty it.
Dragging the silt bucket to land
I also completed the coppicing of the Willow in the background of the photo. It was a stout stump, very dry and hard, and it was quite a task with a small Silkie saw, but better than using a blunt bowsaw!
Meanwhile, the others set about cutting the encroaching Reeds and pulling out a fair number of their long white rhizomes that spread out in the mud. We tried to spare the floating pondweeds, starwort and water mint.
Reed-cutting
A group of Great Tits made a din mobbing a Magpie; and a little later, several Jays spent a while screeching while a pair of Magpies chattered back.
Huma Pearce, mammal expert, in Gunnersbury Triangle
The hut in the Gunnersbury Triangle Nature Reserve, which is managed by London Wildlife Trust, was buzzing with excitement. It was packed full of people on a bitterly cold winter’s day, everyone eager to find out how to map London’s mammals.
You might think that in a metropolis of some ten million people, pretty much everything would be known by now about the city’s wildlife.
But that’s not so. A quick look at the existing maps of some of our mammals – from field vole to otter – tells a simple story. Hardly anything has been published about what lives where in London.
The field is wide open for new discoveries, and those are what we hope to make in the next year as we track down those voles, and maybe some larger animals into the bargain.
London Wildlife Trust has secured £97,000 from the Heritage Lottery Fund to study the distribution and abundance of small mammals in 9 woodland sites in West London. Although the focus will be on small woodland mammals, Huma (the mammal expert employed to co-ordinate and deliver the surveys) also hopes that with the help of volunteers she will be able to collect mammal data from a range of sites of different sizes, scattered across the boroughs of Hounslow, Ealing, Hillingdon and Harrow.
On each of the 9 woodland sites, the project will need to find out which species are present, and to estimate their numbers. But small mammals are shy, inconspicuous and mainly active at night. Tracking them down isn’t easy.
So Huma is getting together and training a “Vole Patrol”, a small army of volunteers, keen to get down and dirty with wildlife. That means us! We need to know how to collect data on the mammals, without hurting them, or disturbing them more than absolutely necessary. That means training.
The first thing you might think of is live trapping, and we’ll do some. Huma showed us a Longworth trap, a light aluminium contraption made of two boxes that lock together. You put some food and bedding inside; a trapdoor falls when little feet venture inside.
But small animals particularly shrews need food all the time. You have to visit all your traps after six hours, to ensure that any animals captured are safe, and to identify the species before they are released. We’ll do some trapping later in the year.
Numbering a hedgehog tunnel
We’re starting, instead, with some baited hedgehog tunnels. Hedgehogs are hibernating at this time of year, so we don’t expect them, but the design is proven, and good for a variety of small mammals too. We assemble them from Correx sheets, like cardboard only waterproof. We fold them into a triangular tube, with a fourth side as an overlap, which we stick down with Velcro. Another sheet of plastic slides inside as a tray.
Clean paper, wet paint, food, paint, paper to slide into hedgehog tunnel
We stick a plastic dish in the middle, and fix masking tape both sides to hold some paint, which we mix up from non-toxic carbon powder and vegetable oil. At either end we pin down a sheet of paper. The dish is baited with special ‘Hog’ biscuits and dried mealworms: it almost looks appetising.
Hundreds of footprints!
We hide the hedgehog tunnels away from likely disturbance. The next day, sure enough, hundreds of footprints are spattered all over the sheets. The small ones are surely mice or voles; the larger ones not so easy to guess.
As well, there seem to be marks of tails dragged through the paint. We have to repeat the process every day for five days, with each tunnel.
Other volunteers will do the same in each of the other survey sites.
As well as the hedgehog tunnels, we take out a boxful of nest tubes. They’re made of yet more Correx sheet formed into square tubes, each with a simple wooden tray that slides in and out; the back is closed with a square of wood.
Fixing a nest tunnel into position
These were to be laid out in a rectangular grid. Easier said than done in a tangled, muddy wood! We push through the brambles, trying not to create more paths than we had to, looking for low branches out of sight of the paths, where we could tie on the nest tunnels. Then we recorded their positions with GPS. We’ll go back later in the year to see which of the boxes have been used.
We also put down some plastic tubes baited with mealworms, low down near a pond, for water shrews to visit, and perhaps to leave a few tokens (in other words, shrew poo) to indicate their visit. Species can be broadly identified from their droppings, but Huma is hoping that we might be able to get these, or little tufts of fur, analysed for DNA to prove which species was responsible.
Cherry Stone opened by vole in Gunnersbury Triangle
We can find out about mammals in other ways too. Different animals open nuts and cherry stones in their own ways: squirrels snap them roughly in half; mice nibble a neat round hole; voles bite into the shell more irregularly. We found a cherry stone near the first hedgehog tunnel: a small mammal had gnawed an irregular hole with sharp tooth-marks along its edge.
A Camera Trap in position for any small mammals in the grass
A glimpse of small mammals can be gained with camera traps, as seen on TV nature documentaries. You tie them onto a tree, overlooking a likely mammal run, and with any luck you’ll see mice, or voles, or who knows, maybe a weasel or an otter. London’s mammals are about to become a lot more famous.
Huma is keen to involve as many people from the local community in the project. So, if you would like to volunteer on some mammal surveys, I suggest you contact her by email: hpearce@wildlondon.org.uk
After the bitter cold of the New Year, down to a surprising -12C in London, suddenly spring (as it were) is back in the air, and the Daffodils are resuming their progress towards full bloom in gardens and on roadsides.
The warmth and sunshine tempted me out to Wraysbury. With the heavy rain and perhaps also the rapid changes of temperature, a large Poplar had fallen across the river, forming a minor weir.
Muntjac print
On the path, a Muntjac deer had left its tiny prints in the soft mud. Unlike a lot of other mammals, at least this one is readily identifiable from its print, the two small sharp slots of its slim feet not mistakable for anything else.
The lake, which had been full of birds as big as Swans last time I visited, was almost empty: a few Coots, some Great Crested Grebes, a Black-Headed Gull, a few roosting Cormorants, a few Tufted: and happily two of the area’s specialities, three pairs of Goosander, and nine Goldeneye (including three males).
A Kestrel hovered and dropped slowly after a small mammal in the long grass. A Redwing flickered away around a corner. A Song Thrush sang sweetly from a thicket. One or perhaps two Bullfinches gave their distinctive “Deu” call from the middle of a bush. Half-a-dozen Fieldfares chattered and skittered about from the top of one bare thornbush to another. A few Wood pigeons and Crows looked out warily.
One of the real difficulties in nature conservation is the basic fact that humans have short lives and shorter memories.
We instinctively assume that the way the countryside “should” look is … how it looked when we were young. Obviously, it had been that way since time immemorial, at least since the year 1 B.M. (where B.M. means “Before Me”). In Feral, George Monbiot calls this “Shifting Baseline Syndrome” – each new generation sets the baseline to the time of its own youth: we imagine our childhood landscape to have been just right, good, and natural.
Only it wasn’t. Our limited time horizon obscures the fact that the countryside has been changing continuously since Roman times, indeed since the Stone Age. Forests have been felled, making way for fields, towns, and roads. Already by 1000 AD, most of Britain’s forests had disappeared, and our larger forest animals like bear, wolf, lynx and wolverine were disappearing with them.
But even in a single lifetime, the loss of once-familiar species is shockingly evident. I had a small reminder when I found one of my birdwatching notebooks from my schooldays. We had been on a Natural History Society trip to Portland Bill, where we stayed in the old lighthouse, a bird observatory in a fine location for counting (and trapping and ringing) arriving and departing migrants. A group of us walked out in the bright sunshine on 1 September 1972, and I listed what we saw.
Portland Bill Bird List 1 Sept 1972
I was pleased to see a Raven, a Garden Warbler, and a Kittiwake, as I would be today, though all these species are doing well. I was reasonably pleased to hear a Little Owl, something that would now be rather special. I was quite unsurprised to see 20 House Sparrows, and I don’t seem to have found the Turtle Dove or the Redstart at all remarkable. Either of those would now be close to the highlight of the year: and the Song Thrush too, once a regular garden bird, has become really rather uncommon. Then there are the Skylark and Whinchat, which I gave no more notice to than the Linnet, Jackdaw and Stonechat; and the Sand Martin too is declining alarmingly. The 39 Goldfinches, on the other hand, were somewhat remarkable to me then, but I see nearly as many in flocks around the quieter streets in town. I didn’t think the presence of 5 warblers worth noting, though at least that isn’t too terribly difficult to achieve today – just a matter of going to a reasonably decent nature reserve, as there won’t be many species on farmland (you’re lucky to get Chiffchaff and Blackcap, really). The mixture of farmland species, birds of open moorland (Meadow Pipit, Wheatear), and coastal species (Shag, Kittiwake, Rock Pipit) is far more remarkable than I realised at the time, and is probably characteristic of those headlands where migrants congregate.
It would be interesting to repeat the walk early in September (or in the spring migration) and see what we’d see. I think there would be fewer species. And a lot fewer sparrows.
A fine cloudless day, with the jackdaws chasing about in the southwesterly breeze, the edge of Storm Eva that is blowing into the already flooded Northwest of Britain. A few winter ducks on the Pen Ponds – a Wigeon or two, a few dozen Gadwall – but the main surprise was the number of Common Gulls – at least thirty – in little flocks on both of the ponds. They can be seen here to have pale legs and ‘windows’ of white in their black wingtips, unlike the smaller Black-Headed gulls (there are one or two sitting in the water towards the left of the photo) which have very pale backs, no windows, and a black spot behind the eye (when they don’t have their chocolate-brown breeding hood, that is). Perhaps they have come down from the chilly North of Scandinavia to enjoy the very mild weather here.
The English seem unemotional … except for their passion for nature
