Islamic Geometric Design by Eric Broug (with Moroccan Zellige tilework)
Eric Broug’s Islamic Geometric Design (Thames and Hudson, 2013) is as big and beautiful as Luca Mozzati’s Islamic Art. Like that book, it goes some way towards correcting the bias – the total blind spot to be frank – in Lynn Gamwell’s otherwise splendid Mathematics + Art on all things Islamic.
Broug’s focus is sharply on how to create such designs: both, how the Islamic craftsmen who made them did their job centuries ago, and how you can do it today. The book ends, indeed, with an Appendix of some 50 pages on “How to create designs”. The body of the book looks at Basic Design Principles, Grids and Polygons, and then 4-fold, 6-fold, 5-fold, and Combined Geometric Design. The focus is thus on geometry pure and simple, referring from there briefly to the history of each object covered.
Unfortunately, although the cover shows a fine example of Moroccan “zellige” tilework, the book is almost entirely devoted to the more rule-based geometric strapwork called girih, which one may guess was more interesting to someone like Broug, who plainly likes a tough geometric puzzle to solve. Girih can, it seems, be constructed either as was traditionally supposed simply with a ruler and compasses, or, intriguingly, with a small set of “tiles” (conceptual rather than ceramic), which can be assembled and arranged in an almost infinite variety of ways, including aperiodically (a fascinating aspect if you’re a mathematical physicist).
Many of the objects analysed in the book are walls, ceilings or domes of buildings, such as mosques, medersas and mausoleums. Happily, however, many other examples are taken from woodwork including minbars (pulpits), bronze doors, tiles and screens, with the occasional plate. Broug is mainly interested in the very strictly geometric Girih strapwork designs, which can be analysed rather thoroughly with geometry; he is less interested in the far less mathematical Zellige of Morocco, arabesques, or calligraphy, which are all important forms of Islamic decoration; and he does not concern himself with the making of artefacts such as glass, ceramics, paintings, or metal objects except insofar as they are geometrically patterned.
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.
The English seem unemotional … except for their passion for nature
