Cat out of Bel

Thursday, 28th Mar, 2013 by Krilling for Company in Art, Biology, Science and tagged 19th century, 19th-century art, A. jubatus, Acinonyx jubatus, art, artist, Belgian art, Belgian artist, Belgian painter, Belgian symbolist, Belgium, big cats, biological, biology, cheetah, cheetah DNA, cheetah inbreeding, Des Caresses, F. pardus, Felis pardus, Fernand Khnopff, genetic bottleneck, great cats, heavy-jawed face, incest, incestuous themes, Khnopf, Knopf, Knopff, L'Art ou Des Caresses, leopard, Marguerite Khnopff, nineteenth century, nineteenth-century art, Oedipus and the Sphinx, On n'a que soi, One has only oneself, P. pardus, painter, painting, Panthera pardus, sister, spotted big cat, spotted cat, spotted felid, subconscious, symbolism, symbolist art, The Caress, the sphinx | Leave a comment

The Belgian symbolist Fernand Khnopff (1858-1921) is one of my favourite artists; Caresses (1896) is one of his most famous paintings. I like it a lot, though I find it more interesting than attractive. It’s a good example of Khnopff’s art in that the symbols are detached from clear meaning and float mysteriously in a world of their own. As Khnopff used to say: On n’a que soi – “One has only oneself.” But he was clearly inspired by the story of Oedipus and the Sphinx, which is thousands of years old. Indeed, an alternate title for the painting is The Sphinx.

Caresses by Fernand Khnopff (click for larger image)

Caresses (1896) by Fernand Khnopff (click for larger image)

Even older than the Oedipus story is another link to the incestuous themes constantly explored by Khnopff, who was obsessed with his sister Marguerite and portrayed her again and again in his art. That’s her heavy-jawed face rubbing against the heavy-jawed face of the oddly nippled man, but Khnopff has given her the body of a large spotted felid. Many people misidentify it as a leopard, Panthera pardus. It’s actually a stranger and rarer felid: a cheetah, Acinonyx jubatus, which occupies a genus of its own among the great cats. And A. jubatus, unlike P. pardus, is an incestuous animal par excellence:

Cheetahs are very inbred. They are so inbred that genetically they are almost identical. The current theory is that they became inbred when a “natural” disaster dropped their total world population down to less than seven individual cheetahs – probably about 10,000 years ago. They went through a “Genetic Bottleneck”, and their genetic diversity plummeted. They survived only through brother-to-sister or parent-to-child mating. (Cheetah Extinction)

It must have been a large disaster. Perhaps cheetahs barely survived the inferno of a strike by a giant meteor, which would make them a cat out of hell. In 1896, they became a cat out of Bel too when Khnopff unveiled Caresses. Back then, biologists could not analyse DNA and discover the ancient history of a species like that. So how did Khnopff know the cheetah would add extra symbolism to his painting? Presumably he didn’t, though he must have recognized the cheetah as unique in other ways. All the same, I like to think that perhaps he had extra-rational access to scientific knowledge from the future. As he dove into the subconscious, Khnopff used symbols like weights to drag himself and his art deeper and darker. So perhaps far down, in the mysterious black, where time and space lose their meaning, he encountered a current of telepathy bearing the news of the cheetah’s incestuous nature. And that’s why he chose to give his sphinx-sister a cheetah’s body.

Numbered Days

Monday, 18th Mar, 2013 by Krilling for Company in Art, History, Mathematics, Philosophy, Philosophy of mathematics, Poetry and tagged a girl he hardly knew, arrogance, Arthur Rimbaud, Évariste Galois, biographical, biography, Carl Gustav Jacobi, Deus ex Machina, died early, duel, early death, French literature, French poet, French poetry, Galois theory, infamous coquette, literature, math, mathematics, maths, Niels Henrik Abel, nineteenth century, poet, Poetry, rebel, rebellion, Rimbaud's poetry, Srinivasa Ramanujan, stormy adolescence, Verlaine | 2 Comments

Numbered Days: Literature, Mathematics and the Deus Ex Machina

Think French. Think genius. Think rebellious, tormented, iconoclastic. Finally, think dead tragically young in the nineteenth century… And if you’re thinking of anyone at all, I think you’ll be thinking of Rimbaud.

And you’d be right to do so. But only half-right. Because there were in fact two rebellious, tormented, iconoclastic French geniuses who died tragically young in the nineteenth century. One was called Arthur Rimbaud (1854-91) and the other Évariste Galois (1811-32). Rimbaud is still famous, Galois never has been. At least not to the general educated public, though on all objective criteria – but one – you might expect his fame to be greater. In every way – but one – Galois has the more powerful appeal.

Continue reading Numbered Days…

Yew and Me

Thursday, 7th Mar, 2013 by Krilling for Company in A.E. Housman, Art, Biology, Book Reviews, Fibonacci Sequence, Fractals, Mathematics, Poetry and tagged A.E. Housman, Alan Mitchell, artist, aspen, aspens, Black Walnut, churches, churchyards, Common Walnut, Common Yew, conifer, conifers, David More, deciduous tree, deciduous trees, dendrophile, dendrophilia, Fibonacci Sequence, fractal structure, furniture, gunstocks, holy site, holy sites, Housman, illustration, illustrations, illustrator, Juglans nigra, Juglans regia, leaf, leaves, math, mathematics, maths, natural fractal, natural fractals, photosynthesis, pine-cone, pine-cones, poisonouns foliage, poisonous leaves, poisonous seeds, Populus tremula, sacred tree, sacred trees, symbol of immortality, symbols of immortality, Taxus baccata, The Pocket Guide to The Trees of Britain and Northern Europe, The Trees of Britain and Northern Europe, tree, tree-poem, tree-poems, tree-poetry, Trees, yew, yews | 3 Comments

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

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

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

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

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

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

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

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

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

More Poems, VIII.

Bones, Blinks, Books

Thursday, 7th Mar, 2013 by Krilling for Company in Art, Civilization, Philosophy and tagged allegorical, allegory, candle, Charity Hospital of Seville, coffin, death, extinguished candle, In a Blink, In an Eye-Blink, In Ictu Oculi, In the Blink of an Eye, Juan de Valdés Leal, mortality, Seville, skeleton, Spain, Spanish art, Spanish artist, symbol, symbolic, symbols, vanitas painting | Leave a comment

In Ictu Oculi (In the Blink of an Eye) by Juan de Valdés Leal (c. 1671).

Angst, Anguish, Abjection

Thursday, 7th Mar, 2013 by Krilling for Company in Album Art, Astronomy, Mathematics, Music, Music reviews and tagged A.W.D.I.M.T.B.F., a3, And What Does It Mean To Be Flesh?, And What Doth It Mean To Be Flesh?, AWDIMTBF, bat-twitter, bat-twitters, bee, bees, Breathing Vacuum, bumblebee, bumblebees, carnal question, Dredge-head, Dredge-heads, Dredgers, ear-worm, ear-worms, fleshtion, gig, gigs, griff, griffs, gruff riff, gruff riffs, industrial noise, infra-sonic, infra-sound, Invention of the Cross, Jerome Daziel, Kargokkult, Kargonauts, lead-singer Jerome Daziel, math, mathematics, maths, Nyctogigas, Ohrwürmer, Ohrwurm, plagiarism suit, pre-biotic, Pyramidion, resonance, resonances, Ruin-Dredger, Scylla / Charybdis, Seventh Sword, silence, star-clusters having tantrums, that A-fucker, Titanomachia, Triple-A, ultra-sonic, ultra-sound, unusual frequencies, unusual frequency, What Does It Mean To Be Flesh?, What Doth It Mean To Be Flesh?, Whilom, wolf-howl, wolves howling, Xoli-Hein | Leave a comment

It’s half tradition, half tic. At every Ruin-Dredger gig, the lead-singer Jerome Daziel asks the same simple question. Sometimes he shouts it and demands a reaction from the audience. Sometimes he whispers it and ignores what the audience does. Depending on the country, he’s asked it in French, Italian, Greek, Russian, Georgian, Mandarin, Thai, Samoan and Quechua. He’s also asked it in complete silence, having written it across his chest and on the palms of his hands in phosph-ink, invisible when the lights are on, glowing ghoulishly when they’re turned off. Occasionally he’s asked it backwards. In English, the question runs like this: “And What Doth It Mean To Be Flesh?”

But you could see the whole of a Ruin-Dredger gig as asking the same searching thing. The band specialize in unusual frequencies that hunt out – and hum out – the resonances of the human body: the lungs, the bones, the blood. And their music sets up strange resonances in the mind. It’s both mindless and masterful, at once tearful and tyrannous. Sometimes it sounds like mathematics trying to come to life, and sometimes like mathematics trying to commit suicide. There’s a lot of science in their music, and a lot of silence too. “Star-clusters having tantrums,” is how one early review ran. “With occasional episodes of narcolepsy.” That mixture of sound and silence is mutually reinforcing: the sounds are sterner, the silence is sharper. They began their career with the albums Xoli-Hein (1992) and Pyramidion (1996), where they forged a series of griffs, or “gruff riffs”, that were often Ohrwürmer, or “ear-worms”, as German calls tunes that stick in your head. Even if you don’t want them to. But I’m not sure “tune” has ever been the right word for the music Ruin-Dredger create. It’s part industrial noise, part wolf-howl, part bat-twitter, but mostly “folded, fused, fissured, fractured, fidgety phonaesthesia.” And if you want to sample it, this album from the turn of the century is a good place to start.

What to call the album is one of the first puzzles it will set you. The band’s website usually calls it “a³” or “a3”; in interviews, the band themselves refer to it as “Triple-A” or “that A-fucker”. The second name comes from a plagiarism suit by the astro-music veterans Kargokkult that put Ruin-Dredger’s career on hold for nearly a year, 2002-3, and allegedly threatened to bankrupt their record-company. In the end the case was thrown out of court and even today some conspiracy-minded Dredge-heads claim it was cooked up for publicity between the ’Dredgers and the Kargonauts. The case might never have got as far as it did without that lunar cover for Triple-A, where the corroded letters of the band’s name and the album’s name hang above a lifeless moon-scape. Only it isn’t our moon. And it isn’t necessarily lifeless. Ruin-Dredger have a bee in their bonnet about the pre-biotic – the conditions necessary for the appearance of life. That’s what the first track on Triple-A, “Invention of the Cross”, is about: the chemicals that gave rise to life. And it literally has bees on it: the band sampled bees and bumblebees in flight and gathering nectar. They then altered the pitch and speed of the buzzing and made it sound both unearthly and unsettling. I’ve known people demand the track be turned off or skipped when it’s played to them.

But skipping track one of Triple-A is a bit like jumping from the frying-pan into the fire, because track two, “Seventh Sword”, is even more unearthly and even more unsettling. Bat-twitters hurtle through the speakers, falling from the ultra-sonic to the infra-sonic, rising in reverse, twisting, turning inside-out, mating, mutating and miscegenating. Then, as though the band have taken mercy on your ears and your mind, everything slows and soothes for track three, “Titanomachia”, which is often preceded in concert by the aforementioned carnal question: “And what doth it mean to be flesh?” This track is one of the last outings for the griffs of their early career: a slow, synth-based triple chord underlain by a sample of waves washing on an unknown shore. Track four, “Breathing Vacuum”, has also been known to provoke a “Turn it off!”, because the mumbling beneath the music is both sinister and sorrowful. You feel as though you should understand the words or, worse, that you will in your dreams. The chimes in the track are sinister too: they sound like a deep-sea, or deep-space, monster tapping on its fangs before putting them to famished use.

Which sets things up nicely, or nastily, for track five, “Scylla / Charybdis”. This is named after a pair of sea-monsters faced by Odysseus on his journey home from Troy and has been described by the ’Dredgers as a “battle-song”. The waves on “Titanomachia” are back, but bigger, badder and in a mood to fight. Daziel’s electronically treated voice wolf-howls a series of unintelligible questions, answered by patches of silence and gong-like drum-rolls. Track six, “Nyctogigas”, starts softly, builds back to the volume and violence of “Scyl/Char”, then breaks apart to allow the bats and bees of “Whilom” to steer your imagination out and up into the freezing star-light on the outer fringes of the solar system, where comets, shorn by the cold and dark, wait to swing sun-ward and regain their blazing locks. I like to listen to “Whilom” in the dark, wearing a blindfold, but then that’s the best way to listen to all of Ruin-Dredger’s music. Listening like that conjures visions and commands the viscera. Not an easy album, nor an unrewarding one, Triple-A isn’t their finest hour, if fan-polls and sales are any guide, but it’s an excellent guide to where they had come from and where they were about to go. If it’s the alpha-and-omega of their career, perhaps that explains the title: the “a” is the alpha (α) and the “3” an omega (ω) tipped on its side. I see it, or hear it, as a bridge between the ’nineties and the ’noughties: they’d give up the griffs and big up the bats, from then on, but they’ve never stopped asking that simple, sinister/sorrowful question of themselves and their listeners: “And What Doth It Mean To Be Flesh?”

a³ / a3 / Triple-A (S.R.K., 2000)

1. Invention of the Cross (5:26)
2. Seventh Sword (3:33)
3. Titanomachia (7:18)
4. Breathing Vacuum (9:03)
5. Scylla / Charybdis (6:11)
6. Nyctogigas (4:20)
7. Whilom (13:37)

Three Is The Key

Saturday, 23rd Feb, 2013 by Krilling for Company in Art, Magic squares, Mathematics, Post-Weird, Prime numbers and tagged 142857, 222, 223, 3, 37, David Wells, magic square, magic squares, math, mathematics, maths, Penguin Dictionary of Curious and Interesting Numbers, prime numbers, prime reciprocal, prime reciprocal magic square, prime reciprocal magic squares, prime reciprocals, primes, reciprocal, reciprocals, recreational math, recreational mathematics, recreational maths, Roses of Heliogabalus, Sir Lawrence Alma-Tadema, two hundred and twenty-two | Leave a comment

If The Roses of Heliogabalus (1888) is any guide, Sir Lawrence Alma-Tadema (1836-1912) thought that 222 is a special number. But his painting doesn’t exhaust its secrets. To get to another curiosity of 222, start with 142857. As David Wells puts it in his Penguin Dictionary of Curious and Interesting Numbers (1986), 142857 is a “number beloved of all recreational mathematicians”. He then describes some of its properties, including this:

142857 x 1 = 142857
142857 x 2 = 285714
142857 x 3 = 428571
142857 x 4 = 571428
142857 x 5 = 714285
142857 x 6 = 857142

The multiples are cyclic permutations: the order of the six numbers doesn’t change, only their starting point. Because each row contains the same numbers, it sums to the same total: 1 + 4 + 2 + 8 + 5 + 7 = 27. And because each row begins with a different number, each column contains the same six numbers and also sums to 27, like this:

1 4 2 8 5 7
+ + + + + +
2 8 5 7 1 4
+ + + + + +
4 2 8 5 7 1
+ + + + + +
5 7 1 4 2 8
+ + + + + +
7 1 4 2 8 5
+ + + + + +
8 5 7 1 4 2

= = = = = =

2 2 2 2 2 2
7 7 7 7 7 7

If the diagonals of the square also summed to the same total, the multiples of 142857 would create a full magic square. But the diagonals don’t have the same total: the left-right diagonal sums to 31 and the right-left to 23 (note that 31 + 23 = 54 = 27 x 2).

But where does 142857 come from? It’s actually the first six digits of the reciprocal of 7, i.e. 1/7 = 0·142857… Those six numbers repeat for ever, because 1/7 is a prime reciprocal with maximum period: when you calculate 1/7, all integers below 7 are represented in the remainders. The square of multiples above is simply another way of representing this:

1/7 = 0·142857…
2/7 = 0·285714…
3/7 = 0·428571…
4/7 = 0·571428…
5/7 = 0·714285…
6/7 = 0·857142…
7/7 = 0·999999…

The prime reciprocals 1/17 and 1/19 also have maximum period, so the squares created by their multiples have the same property: each row and each column sums to the same total, 72 and 81, respectively. But the 1/19 square has an additional property: both diagonals sum to 81, so it is fully magic:

01/19 = 0·0 5 2 6 3 1 5 7 8 9 4 7 3 6 8 4 2 1…
02/19 = 0·1 0 5 2 6 3 1 5 7 8 9 4 7 3 6 8 4 2…
03/19 = 0·1 5 7 8 9 4 7 3 6 8 4 2 1 0 5 2 6 3…
04/19 = 0·2 1 0 5 2 6 3 1 5 7 8 9 4 7 3 6 8 4…
05/19 = 0·2 6 3 1 5 7 8 9 4 7 3 6 8 4 2 1 0 5…
06/19 = 0·3 1 5 7 8 9 4 7 3 6 8 4 2 1 0 5 2 6…
07/19 = 0·3 6 8 4 2 1 0 5 2 6 3 1 5 7 8 9 4 7…
08/19 = 0·4 2 1 0 5 2 6 3 1 5 7 8 9 4 7 3 6 8…
09/19 = 0·4 7 3 6 8 4 2 1 0 5 2 6 3 1 5 7 8 9…
10/19 = 0·5 2 6 3 1 5 7 8 9 4 7 3 6 8 4 2 1 0…
11/19 = 0·5 7 8 9 4 7 3 6 8 4 2 1 0 5 2 6 3 1…
12/19 = 0·6 3 1 5 7 8 9 4 7 3 6 8 4 2 1 0 5 2…
13/19 = 0·6 8 4 2 1 0 5 2 6 3 1 5 7 8 9 4 7 3…
14/19 = 0·7 3 6 8 4 2 1 0 5 2 6 3 1 5 7 8 9 4…
15/19 = 0·7 8 9 4 7 3 6 8 4 2 1 0 5 2 6 3 1 5…
16/19 = 0·8 4 2 1 0 5 2 6 3 1 5 7 8 9 4 7 3 6…
17/19 = 0·8 9 4 7 3 6 8 4 2 1 0 5 2 6 3 1 5 7…
18/19 = 0·9 4 7 3 6 8 4 2 1 0 5 2 6 3 1 5 7 8…

First line = 0 + 5 + 2 + 6 + 3 + 1 + 5 + 7 + 8 + 9 + 4 + 7 + 3 + 6 + 8 + 4 + 2 + 1 = 81

Left-right diagonal = 0 + 0 + 7 + 5 + 5 + 9 + 0 + 3 + 0 + 4 + 2 + 8 + 7 + 5 + 6 + 7 + 5 + 8 = 81

Right-left diagonal = 9 + 9 + 2 + 4 + 4 + 0 + 9 + 6 + 9 + 5 + 7 + 1 + 2 + 4 + 3 + 2 + 4 + 1 = 81

In base 10, this doesn’t happen again until the 1/383 square, whose magic total is 1719 (= 383-1 x 10-1 / 2). But recreational maths isn’t restricted to base 10 and lots more magic squares are created by lots more primes in lots more bases. The prime 223 in base 3 is one of them. Here the first line is

1/223 = 1/22021₃ = 0·

0000100210210102121211101202221112202
2110211112001012200122102202002122220
2110110201020210001211000222011010010
2222122012012120101011121020001110020
0112011110221210022100120020220100002
0112112021202012221011222000211212212…

The digits sum to 222, so 222 is the magic total for all rows and columns of the 1/223 square. It is also the total for both diagonals, so the square is fully magic. I doubt that Alma-Tadema knew this, because he lived before computers made calculations like that fast and easy. But he was probably a Freemason and, if so, would have been pleased to learn that 222 had a link with squares.

Vigor Mortis

Monday, 18th Feb, 2013 by Krilling for Company in Album Art, Biology, History, Music, Our Lady of the Gutter, Post-Weird and tagged band, Best of Black Sabbath, Black Sabbath, compilation album, crustacean, crustaceans, Daphnia, dessication, fresh water, fresh-water biology, fresh-water microbiology, heavy metal, Heysham, Lancashire, Morecambe Bay, ostracod, ostracods, Our Lady of the Gutter, parthenogenesis, parthenogenetic, plankton, rock-grave, rock-graves, seed-shrimp, seed-shrimps, St Patrick’s Chapel, stagnant water, swarm, virgin birth, water-flea, water-fleas, waterflea, waterfleas, winter eggs | Leave a comment

In the Christian religion, the resurrection follows the virgin birth. In the rock-graves at Heysham, the virgin birth follows the resurrection. Or rather: the virgin-births follow the resurrections. There are many of both. The rock-graves at Heysham* are carved in solid rock near the remains of St Patrick’s chapel, an ancient ruin overlooking Morecambe Bay on the coast of Lancashire in England. You may have seen them before, because they appear on the cover of a compilation album by the heavy-metal band Black Sabbath, where they’re filled with ice and look suitably dark and sinister. But the graves are sometimes full of life and activity. In spring, as the rainwater filling them begins to warm, there are resurrections – dozens of them. Tiny crustaceans (a group of animals that includes crabs, shrimps and woodlice) hatch from eggs that have over-wintered in the sediment on the floors of the graves. Some of the crustaceans are called water-fleas, others are called seed-shrimps. Water-fleas, whose scientific name is Daphnia, hop through the water with jerks of their antennae, sieving it for fresh-water plankton. Seed-shrimps, or ostracods, are enclosed in tiny double-sided shells through which their legs protrude. They trundle over the stone sides of the graves, scraping off algae and catching even smaller and simpler animals like rotifers and protozoa.

The rock graves at Heysham (c. 11th century A.D.)

Rock graves at Heysham, Lancs. (c. 1000s)

Water-fleas are famous for parthenogenesis, or their ability to produce offspring without sex. Those that hatch first in spring are female and give birth without mating with any males. A single water-flea in a jar of stagnant water soon becomes a swarm. It’s only later in the year that males are born and the water-fleas mate to produce winter eggs, which sink to the floor of the graves and lie there through the cold weather. The eggs of water-fleas and ostracods can also survive desiccation, or drying-up, and can be blown on the wind to new sites. That is probably how these crustaceans arrived in the rock-graves, which they must have occupied for centuries, through the coldest winters and the hottest summers, dying and being reborn again and again. When a human being or large animal dies, chemical changes in the body make the muscles rigid and wood-like. The scientific term for this is rigor mortis, or the “stiffness of death”. Rigor mortis wears off in time and the body begins to rot. The rock-graves at Heysham are an example of vigor mortis, or the “vigour of death”. Medieval human beings created the graves to bury their dead, but the bodies that were once there have been lost to history. The water-fleas and the seed-shrimps remain, tiny, overlooked and fascinating.

A seed-shrimp

A water-flea

*Heysham is pronounced HEE-shum and is an old coastal village near the city of Lancaster, after which Lancashire is named.

Roses Are Golden

Thursday, 14th Feb, 2013 by Krilling for Company in Art, Civilization, History, φ, Mathematics and tagged Aelius Lampridius, Alma-Tadema, ancient Rome, Anglo-Dutch, classical history, Elagabalus, golden ratio, golden section, Heliogabalus, Historia Augusta, φ, Liverpool, math, mathematics, mathematics in art, maths, oil-painting, painting, phi, Roman emperor, Roman history, Sir Laurence Alma-Tadema, Sir Lawrence Alma-Tadema, The Roses of Heliogabalus, Victorian art, Victorian artist, Victorian painting, Vita Heliogabali, Walker Art Gallery | Leave a comment

Sir Lawrence Alma-Tadema’s painting The Roses of Heliogabalus (1888) is based on an apocryphal episode in the sybaritic life of the Roman Emperor Elagabalus (204-222 A.D.), who is said to have suffocated guests with flowers at one of his feasts. The painting is in a private collection, but I saw it for real in an Alma-Tadema exhibition at the Walker Art Gallery in Liverpool sometime during the late 1990s. I wasn’t disappointed: it was a memorable meeting with a painting I’d been interested in for years. Roses is impressively large and impressively skilful. Close-up, the brush-strokes are obvious, obtrusive and hard to interpret as people and objects. It isn’t till you step back, far beyond the distance at which Alma-Tadema was painting, that the almost photographic realism becomes apparent. But you get more of the many details at close range, like the Latin inscription on a bowl below and slightly to the right of that scowling water-mask. Alas, I forgot to take a note of what the inscription was, though perhaps the memory is still locked away somewhere in my subconscious.

The Roses of Heliogabalus (1888)

Whatever it is, I feel sure it is significant, because Roses is rich with meaning. That’s a large part of why I’m interested in it. Yes, I like it a lot as art, but the women would have to be more attractive for it to be higher in the list of my favourite paintings. As it is, I think there are only four reasonably good-looking people in it: the man with the beard on the right; the flautist striding past the marble pillar on the left; the red-headed girl with a crown of white flowers; and Heliogabalus himself, crowned in roses and clutching a handful of grapes beside the overweight man who’s wearing a wreath and sardonically saluting one of the rose-pelted guests in the foreground. When I first wrote about Roses in a pub-zine whose name escapes me, I misidentified the overweight man as Heliogabalus himself, even though I noted that he seemed many years old than Heliogabalus, toppled as a teen tyrant, should have been. It was a bad mistake, but one that, with less knowledge and more excuse, many people must make when they look at Roses, because the overweight man and his sardonic salute are a natural focus for the eye. Once your eye has settled on and noted him, you naturally follow the direction of his gaze down to the man in the foreground, who’s gazing right back.

A comparison between Alma-Tadema's portrayal of Heliogabalus and a bust of Heliogabalus from the Musei Capitolini in Rome

Something Like the Sun

And by following that gaze, you’ve performed a little ratio-ritual, just as Alma-Tadema intended you to do. Yes, Roses is full of meaning and much of that meaning is mathematical. I think the angle of the gaze is one of many references in Roses to the golden ratio, or φ (phi), a number that is supposed to have special aesthetic importance and has certainly been used by many artists and musicians to guide their work. A rectangle with sides in the proportions 8:13, for example, approximates the golden ratio pretty closely, but φ itself is impossible to represent physically, because it’s an irrational number with infinitely many decimal digits, like π or √2, the square root of two. π represents the ratio of a circle’s circumference to its diameter and √2 the ratio of a square’s diagonal to its side, but no earthly circle and no earthly square can ever capture these numbers with infinite precision. Similarly, no earthly rectangle can capture φ, but the rectangle of Roses is a good attempt, because it measures 52″ x 84 ¹/₈". That extra eighth of an inch was my first clue to the painting’s mathematical meaningfulness. And sure enough, 52/84·125 = 416/673 = 0·61812…, which is a good approximation to φ’s never-ending 0·6180339887498948482045868343656…*

That deliberate choice of dimensions for the canvas led me to look for more instances of φ in the painting, though one of the most important and obvious might be called a meta-presence. The Roses of Heliogabalus is dated 1888, or 1666 years after the death of Heliogabalus in 222 AD. A radius at 222º divides a circle in the golden ratio, because 222/360 = 0·616… It’s very hard to believe Alma-Tadema didn’t intend this reference and I also think there’s something significant in 1888 itself, which equals 2 x 2 x 2 x 2 x 2 x 59 = 2⁵ x 59. Recall that 416 is the expanded short side of Roses. This equals 2⁵ x 13, while 673, the expanded long side, is the first prime number after 666. As one of the most technically skilled painters who ever lived, Alma-Tadema was certainly an exceptional implicit mathematician. But he clearly had explicit mathematical knowledge too and this painting is a phi-pie cooked by a master matho-chef. In short, when Roses is read, Roses turns out to be golden.

*φ is more usually represented as 1·6180339887498948482045868343656…, but it has the pecularity that ¹/_φ = φ-1, so the decimal digits don’t change and 0·6180339887498948482045868343656… is also legitimate.

Appendix I

I’ve looked at more of Alma-Tadema’s paintings to see if their dimensions approximate φ, √2, √3 or π, or their reciprocals. These were the results (ε = error, i.e. the difference between the constant and the ratio of the dimensions).

The Roman Wine Tasters (1861), 50" x 69 ²/₃": 150/209 = 0·717… ≈ ¹/_√2 (ε=0·02)
A Roman Scribe (1865), 21 ¹/₂" x 15 ¹/₂": 43/31 = 1·387… ≈ √2 (ε=0·027)
A Picture Gallery (1866), 16 ¹/₈" x 23": 129/184 = 0·701… ≈ ¹/_√2 (ε=0·012)
A Roman Dance (1866), 16 ¹/₈" x 22 ¹/₈": 43/59 = 0·728… ≈ ¹/_√2 (ε=0·042)
In the Peristyle (1866), 23" x 16": 23/16 = 1·437… ≈ √2 (ε=0·023)
Proclaiming Emperor Claudius (1867), 18 ¹/₂" x 26 ¹/₃": 111/158 = 0·702… ≈ ¹/_√2 (ε=0·009)
Phidias and the Frieze of the Parthenon Athens (1868), 29 ²/₃" x 42 ¹/₃": 89/127 = 0·7… ≈ ¹/_√2 (ε=0·012)
The Education of Children of Clovis (1868), 50" x 69 ²/₃": 150/209 = 0·717… ≈ ¹/_√2 (ε=0·02)
An Egyptian Juggler (1870), 31" x 19 ¹/₄": 124/77 = 1·61… ≈ φ (ε=0·007)
A Roman Art Lover (1870), 29" x 40": 29/40 = 0·725… ≈ ¹/_√2 (ε=0·034)
Good Friends (1873), 4 ¹/₂" x 7 ¹/₄": 18/29 = 0·62… ≈ φ (ε=0·006)
Pleading (1876), 8 ¹/₂" x 12 ³/₈": 68/99 = 0·686… ≈ ¹/_√2 (ε=0·041)
An Oleander (1882), 36 ¹/₂" x 25 ¹/₂": 73/51 = 1·431… ≈ √2 (ε=0·017)
Dolce Far Niente (1882), 9 ¹/₄" x 6 ¹/₂": 37/26 = 1·423… ≈ √2 (ε=0·008)
Anthony and Cleopatra (1884), 25 ³/₄" x 36 ¹/₃": 309/436 = 0·708… ≈ ¹/_√2 (ε=0·003)
Rose of All Roses (1885), 15 ¹/₄" x 9 ¹/₄": 61/37 = 1·648… ≈ φ (ε=0·03)
The Roses of Heliogabalus (1888), 52" x 84 ¹/₈": 416/673 = 0·618… ≈ φ (ε<0.001)
The Kiss (1891), 18" x 24 ³/₄": 8/11 = 0·727… ≈ ¹/_√2 (ε=0·039)
Unconscious Rivals (1893), 17 ³/₄" x 24 ³/₄": 71/99 = 0·717… ≈ ¹/_√2 (ε=0·019)
A Coign of Vantage (1895), 25 ¹/₄" x 17 ¹/₂": 101/70 = 1·442… ≈ √2 (ε=0·028)
A Difference of Opinion (1896), 15" x 9": 5/3 = 1·666… ≈ φ (ε=0·048)
Whispering Noon (1896), 22" x 15 ¹/₂": 44/31 = 1·419… ≈ √2 (ε=0·005)
Her Eyes Are With Her Thoughts And Her Thoughts Are Far Away (1897), 9" x 15": 3/5 = 0·6… ≈ φ (ε=0·048)
The Baths of Caracalla (1899), 60" x 37 ¹/₂": 8/5 = 1·6… ≈ φ (ε=0·018)
The Year’s at the Spring, All’s Right with the World (1902), 13 ¹/₂" x 9 ¹/₂": 27/19 = 1·421… ≈ √2 (ε=0·006)
Ask Me No More (1906), 31 ¹/₂" x 45 ¹/₂": 9/13 = 0·692… ≈ ¹/_√2 (ε=0·03)

Appendix II

The Roses of Heliogabalus is based on this section from Aelius Lampridius’ pseudonymous and largely apocryphal Vita Heliogabali, or Life of Heliogabalus, in the Historia Augusta (late fourth century):

XXI. 1 Canes iecineribus anserum pavit. Habuit leones et leopardos exarmatos in deliciis, quos edoctos per mansuetarios subito ad secundam et tertiam mensam iubebat accumbere ignorantibus cunctis, quod exarmati essent, ad pavorem ridiculum excitandum. 2 Misit et uvas Apamenas in praesepia equis suis et psittacis atque fasianis leones pavit et alia animalia. 3 Exhibuit et sumina apruna per dies decem tricena cottidie cum suis vulvis, pisum cum aureis, lentem cum cerauniis, fabam cum electris, orizam cum albis exhibens. 4 Albas praeterea in vicem piperis piscibus et tuberibus conspersit. 5 Oppressit in tricliniis versatilibus parasitos suos violis et floribus, sic ut animam aliqui efflaverint, cum erepere ad summum non possent. 6 Condito piscinas et solia temperavit et rosato atque absentato…

Historia Augusta: Vita Heliogabali

XXI. 1 He fed his dogs on goose-livers. He had pet lions and leopards, which had been rendered harmless and trained by tamers, and these he would suddenly order during the dessert and the after-dessert to get on the couches, thereby causing laughter and panic, for none knew that they were harmless. 2 He sent grapes from Apamea to his stables for the horses, and he fed parrots and pheasants to his lions and other beasts. 3 For ten days in a row, moreover, he served wild sows’ udders with the matrices, at a rate of thirty a day, serving, besides, peas with gold-pieces, lentils with onyx, beans with amber, and rice with pearls; 4 and he also sprinkled pearls on fish and used truffles instead of pepper. 5 In a banqueting-room with a reversible ceiling he once buried his parasites in violets and other flowers, so that some were actually smothered to death, being unable to crawl out to the top. 6 He flavoured his swimming-pools and bath-tubs with essence of spices or of roses or wormwood…

Augustan History: Life of Heliogabalus

Mental Marine Music

Friday, 8th Feb, 2013 by Krilling for Company in Album Art, Music, Music reviews, The Sea and tagged A Grey Mist, drowned sound, electronic music, Exeter, Exeter band, Exeter experimental music, Exeter group, Exeter-based, experimental music, Gullsegg, Joseph Corvin, Magna Mater Marina, marine music, music, Seaside Excursion Guide, Silica, Slow Exploding Gulls, Swim with Elegant Gods, underwater sound, underwater sounds, Wassernyxe, wind noises, wind sounds, Yr Wylan Ddu | Leave a comment

“Thalassa! Thalassa!” The chant that began the first song on the first side of the first S.E.G. album is still inspiring the group twenty-six years and eighteen albums later. Few fans will need reminding that it is ancient Greek for “The Sea! The Sea!”, as shouted in ecstasy by a mercenary army after a long and dangerous retreat across Asia Minor in 401 BC. Ecstasy is not so much an inspiration to the group as an aspiration. They try to use melody, rhythm and “drowned sound” to take their listeners out of the everyday and into the otherwhere, to sink them “full fathom five” in music as rich and mysterious as the sea. The S.E.G. story begins in 1987, when Joseph Corvin, the ever-present Kapitän und Kappellmeister, as he jokingly calls himself, was living in an old house in the ancient Celto-Roman town of Exeter on the southern English coast. When the sea-wind blew, his living quarters became lowing quarters: “an eerie wailing used to sound from the roof and there were all sorts of weird sound effects in the bathroom, because of air moving in the overflow pipe and the walls. I liked what I heard and I thought I could do something with it, musically speaking.”

Corvin recorded some of the wind-sounds, mixed them with gull-cries and underwater engine-noise, added vocals and electronically treated flute and drums, and put out the results on a cassette-only album called Magna Mater Marina (Latin for Great Marine Mother), under the odd but memorable moniker of Slow Exploding Gulls. The name was inspired by Corvin’s love of the surrealists Salvador Dalí and Max Ernst, but it would dog him and his cohorts for years to come, partly because it pigeon-holed the group as “Kraut-rock” and partly because it suggested cruelty to animals, which was not appreciated by some of his potential audience. Both assumptions were completely wrong: Corvin says, first, that, as a fan, he was then much more into The Cure, The Smiths and Siouxsie and the Banshees than anything electronic or experimental, and, second, that far from advocating cruelty to gulls, he was celebrating them:

Not for one moment was I suggesting any harm to anything with wings or feathers. Gulls are my favourite birds, highly potent symbols of freedom, grace and the life-force. The title was meant to be metaphorical, not literal, and it was partly a reference to the explosion of joy that sudden sight of a flying gull can waken in your heart. There’s something very Nietzschean about them and yeah, I will admit to a Friedrich-fixation in the 1980s, though the Kraut-rock label was an albatross around our necks, no pun intended, for most of the ’90s. It came mainly from a review in the N.M.E. [New Musical Express, one of Britain’s big “pop-papers”] claiming to detect similarities between us and Einstürzende Neubaten, which means “Collapsing New Buildings”. Well, I can’t say there wasn’t a subliminal influence, name-wise, but I’d heard very little by any of the German groups at the time and when I did hear more, I didn’t detect many similarities between their music and ours. We were and always will be inspired by sea-sounds, everything you can hear under and over the water of the British coast. The next label they tried to stick on us was “goth”, on the ground that we made gloomy music and always dressed in black. We didn’t: it was dark blue, it wasn’t all the time and there’s nothing gloomy about our music, if it’s listened to right. (Interview on the fan-site GullSegg, November, 2003)

Corvin’s protests were to no avail: S.E.G.’s next album, A Grey Mist (1989), was reviewed under titles like “Submarine Electro-Goths” and “Solipsistic Entrail-Gazing”. Again he says the press had got hold of the wrong end of the stick: “The title of the album comes from ‘Sea-Fever’, a very beautiful poem by John Masefield, and far from attempting to be gloomy or depressing, it was all about the joy of the sea, the cold in the early morning and the bite of the wind, ‘the white clouds flying’ and mist as a symbol of mystery and possibility, not as anything glum and gothic.” Happily, S.E.G. would outlive that early hostility and journalists’ insistence on labelling, rather than listening to, the music they created, but a lasting effect of both has been the playful name-switching they’ve indulged in since their early days. They’ve released albums under at least eight different names and performed gigs under all those and more, but every name has been based on the acronym S.E.G. and had a maritime theme. 1994’s Mew Upsilon Sigma, for example, came out under the name Swim with Elegant Gods, and 2003’s re-mixed Yr Wylan Ddu (Welsh for The Black Gull) under the name Seaside Excursion Guide. They’ve also recorded songs with titles like “Sunken Etruscan Gold”, “Sailing to Ecstatic Gnosis”, “Submersed in the Eternal Gulf” and “She’s an Exeter Girl” (a reference to Cathleen Orne, Joseph’s then girlfriend, now wife, who is indeed an Exeter girl).

This S.E.G. motif means that hardcore fans, of whom they’ve garnered and retained a flighty fair few down the decades, are generally referred to as SEGheads, while their biggest – and best – fan-site is GullSegg, where you can find the earliest and most accurate news on the group’s activities, plus detailed and reasonably objective reviews of every piece of music they’ve ever recorded. So can S.E.G. be described as Shadowy Exeter Goths? No, Soaring Elemental Gods is much closer the mark and I join many mental-marine-music fans in wishing them well in their ambition of recording music in every major sea-side town of the British Isles. Wexford on the eastern coast of Ireland is next, according to GullSegg, and Wassernyxe, album #19 (and German/Greek for “Mermaid-Night”), should be released before the end of the year. It’s unlikely it will sail new seas, or sound new depths, but after twenty-six years of mer-music-making who could expect it to? Yes, never mind the rowlocks! S.E.G.’s Saline Esoterica Gangs on – and gongs on – every time someone plays a classic album like Mew or Thalas/Socratic, their 1996 split-EP with their own whale-song side-project Schatten über Exeter Gruppe (German for “Shadow over Exeter Group”).

Elsewhere other-posted:

• More Musings on Music

Previously pre-posted (please peruse):

• Stoch’! (In the Name of Dove)

Proviously post-posted (please peruse):

• The Sound of Silex

’Dith and the Maiden

Thursday, 31st Jan, 2013 by Krilling for Company in Art, Meredith Frampton, Post-Weird and tagged A Game of Patience, British art, British artist, English art, English artist, Ferens Art Gallery, Hull, Humberside, Kingston-on-Hull, Margaret Austin-Jones, Meredith Frampton, model, portrait, portrait-painter, portrait-painting, symbolism, symbolist, symbolist art, symbolist artist, symbolist painter, symbolist painting, Yorkshire | Leave a comment

A Game of Patience (1937) by Meredith Frampton (1894-1984), from the Ferens Art Gallery in Kingston-on-Hull, Yorkshire.

Overlord In Terms of Core Issues Around Maximal Engagement with Key Notions of the Über-Feral

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