n – n2 + 41 is prime for all values of n for 0 to 40.
n – n2 + 41 is prime for all values of n for 0 to 40.
If I were asked to nominate a great work of 21st-century art, I would not choose anything by the likes of Damien Hirst or the architect Frank Gehry (responsible for the giant metal midden in Bilbao known as the Guggenheim Museum). Instead, I’d put forward something by Klaas-Douwe B. Dijkstra, Richard Lewington, and British Wildlife Publishing of Gillingham in Dorset. They’re not big names like Hirst and Gehry and they’re not earning big money or exercising big influence. And they’re unlike Hirst and Gehry in another way: they’ve created a genuinely beautiful and intellectually stimulating piece of art.
The art-work is called the Field Guide to the Dragonflies of Britain and Europe (2006). Dijkstra oversees the detailed, expert, and fascinating text, Lewington supplies the detailed, accurate, and beautiful drawings, complemented by photographs of dragonflies and damselflies in the wild. Lots of people don’t know the difference between these two suborders of the Odonata, but their common names reflect their appearance: the Zygoptera, or damselflies, are delicate and fold their wings at rest; the Anisoptera, or dragonflies, are robust and always hold their wings at right angles to their bodies. Both come in a huge variety of colours, pure and mixed, as their common names prove: damselflies include the Azure, the Goblet-Marked, the Orange White-legged, the Scarce Blue-Tailed and the Scarce Emerald; dragonflies include the Green and Mosaic Darners, the Banded, Red-Veined, Scarlet, Violet-marked and Yellow-winged Darters, the Orange-spotted Emerald, and the Four-spotted Skimmer. There’s also Somatochlora metallica, the Brilliant Emerald dragonfly, which looks as though it’s made of bright green metal or enamel.
These rich colours, with the complex venation of their wings, have made the Odonata a popular subject for artists and jewellers: for example, the art nouveau master René Lalique (1860-1945) made dragonfly mascots for cars. Unfortunately, the book doesn’t cover the Odonata in art: it’s a scientific text, a microcosm of the macrocosm of biology. Biology depends on accurate description and classification, so odonatology has a rich vocabulary: antehumeral stripes, arculus, carina, clypeus, diapause, discoidal cell, gynomorph, medial supplemental vein, pronotum, pseudopterostigma, siccation, and so on. Even the segments of the abdomen are numbered, from S1, just below the wings, to S9 and S10 at the tip of the tail, where the females have their almost clockwork genitalia. Males have theirs beneath S2, so mating in the Odonata is a complicated, almost tantric, business, as some of the photographs prove. Nomenclature in the Odonata is a complicated, almost incantatory business: Calopteryx splendens, virgo, xanthostoma; Enallagma cyathigerum; Pyrrhosoma nymphula; Anax parthenope, imperator; Ophiogomphus cecilia; Onychogomphus forcipatus; Libellula quadrimaculata; Sympetrum depressiusculum; Zygonyx torridus.
That nomenclature, and that sex-life, are two of the ways that the Odonata are CASean creatures; that is, their complexity, strangeness, and beauty remind me of the work of “the Emperor of Dreams”, the Californian writer Clark Ashton Smith (1893-1961). The obsessive, minutely detailed nature of the book is CASean too, and some of its subjects might literally be emperors in dreams: the common name of the Anax genus is the Emperors. One of these Emperors answered a CASean question I had as I leafed through the book: distribution tides washed back and forth across the little map of Europe that accompanied each specific description, submerging here Britain and Ireland, there France and Spain, here Germany and Scandinavia, there Greece and Turkey, and sometimes all of them at once.
But the strange, isolated island of Iceland, though included on every map, always seemed redundant, like a wall-flower at the Odonatan dance. “Was it a dragon- and damselfly desert?” I wondered. Then I came across Anax epihippiger, or the Vagrant Emperor: “A. epihippiger is the only dragonfly ever recorded on Iceland.” From the magnificent to the minute, from damselflies in the burning deserts of Morocco to dragonflies amid the frosty volcanoes of Iceland, it’s all here in a book that truly does deserve to represent European civilization in the twenty-first century. But doesn’t, alas.
The Majikalph Script
Majikalph was created by Simon Whitechapel in 2012 to combine his interests in artificial alphabets and recreational mathematics. It is based on the patterns created when lines are drawn between numbers of various 4×4 magic squares. In a magic square, every row, column, and diagonal of numbers adds to the same total. In the 4×4 magic square below, the most interesting patterns are created when each number is connected to the number 2 or 4 places higher than it (e.g. 2 goes to 4 or 6; 13 goes to 15 or 1).
Majikalph is used for writing English and is written from right to left. There is no distinction between upper and lower case. No character of the script is invented: each is based on one or another of the 880 possible 4×4 magic squares (for further information, please see MagicSquares.net).
The sample text is an extract from Tennyson’s The Princess (1847):
Oh, hark, oh, hear! how thin and clear,
And thinner, clearer, farther going!
Oh, sweet and far from cliff and scar
The horns of Elfland faintly blowing!
Blow, let us hear the purple glens replying:
Blow, bugle; answer, echoes, dying, dying, dying.
Alfred, Lord Tennyson (1809-1892).