The two most powerful drugs in the world are DHMO and mathematics.
“One of mighty union-smashing Maggie’s few big mistakes – along with increasing comprehensive education, letting third-world immigration and enforced multiculturalism rip, leaving the NHS and BBC ‘safe in our hands’, smashing the fisheries, selling out the Northern Irish Protestants, increasing welfarism, ending academic freedom and trying to push through the Poll Tax – was to be unfriendly to German reunification.” — Chris Brand, gFactor.
“Homosexual men are nature’s Petri dishes.” — Greg Cochran, West Hunter.
It’s odd that probability theory is so counter-intuitive to human beings and so late-flowering in mathematics. Men have been gambling for thousands of years, but didn’t develop a good understanding of what happens when dice are rolled or coins are tossed until a few centuries ago. And an intuitive grasp of probability would have been useful long before gambling was invented. Our genes automatically equip us to speak, to walk and to throw, but they don’t equip us to understand by instinct why five-tails-in-a-row makes heads no more likely on the sixth coin-toss than it was on the first.
Dice and gambling tokens from ancient Rome
Or to understand why five-boys-in-a-row makes the birth of a girl next time no more likely than it was during the first pregnancy (at least in theory). Boy/girl, like heads/tails, is a binary choice, so binary numbers are useful for understanding the probabilities of birth or coin-tossing. Questions like these are often asked to test knowledge of elementary probability:
1. Suppose a family have two children and the elder is a boy. What is the probability that both are boys?
2. Suppose a family have two children and at least one is a boy. What is the probability that both are boys?
People sometimes assume that the two questions are equivalent, but binary makes it clear that they’re not. If 1 represents a boy, 0 represents a girl and digit-order represents birth-order, the first question covers these possibilities: 10, 11. So the chance of both children being boys is 1/2 or 50%. The second question covers these possibilities: 10, 01, 11. So the chance of both children being boys is 1/3 = 33·3%. But now examine this question:
3. Suppose a family have two children and only one is called John. What is the probability that both children are boys?
That might seem the equivalent of question 2, but it isn’t. The name “John” doesn’t just identify the child as a boy, it identifies him as a unique boy, distinct from any brother he happens to have. Binary isn’t sufficient any more. So, while boy = 1, John = 2. The possibilities are: 20, 21, 02, 12. The chance of both children being boys is then 1/2 = 50%.
The three questions above are very simple, but I don’t think Archimedes or Euclid ever addressed the mathematics behind them. Perhaps they would have made mistakes if they had. I hope I haven’t, more than two millennia later. Perhaps the difficulty of understanding probability relates to the fact that it involves movement and change. The Greeks developed a highly sophisticated mathematics of static geometry, but did not understand projectiles or falling objects. When mathematicians began understood those in Renaissance Italy, they also began to understand the behaviour of dice, coins and cards. Ideas were on the move then and this new mathematics was obviously related to the rise of science: Galileo (1564-1642) is an important figure in both fields. But the maths and science can be linked with apparently distinct phenomena like Protestantism and classical music. All of these things began to develop in a “band of genius” identified by the American researcher Charles Murray. It runs roughly from Italy through France and Germany to Scotland: from Galileo through Beethoven and Descartes to David Hume.
Map of Europe from Mercator’s Atlas Cosmographicae (1596)
But how far is geography also biology? Having children is a form of gambling: the dice of DNA, shaken in testicle- and ovary-cups, are rolled in a casino run by Mother Nature. Or rather, in a series of casinos where different rules apply: the genetic bets placed in Africa or Europe or Asia haven’t paid off in the same way. In other words, what wins in one place may lose in another. Different environments have favoured different sets of genes with different effects on both bodies and brains. All human beings have many things in common, but saying that we all belong to the same race, the human race, is like saying that we all speak the same language, the human language. It’s a ludicrous and anti-scientific idea, however widely it may be accepted (and enforced) in the modern West.
Languages have fuzzy boundaries. So do races. Languages have dialects and accents, and so, in a sense, do races. The genius that unites Galileo, Beethoven and Hume may have been a particular genetic dialect spoken, as it were, in a particular area of Europe. Or perhaps it’s better to see European genius as a series of overlapping dialects. Testing that idea will involve mathematics and probability theory, and the computers that crunch the data about flesh will run on binary. Apparently disparate things are united by mathematics, but maths unites everything partly because it is everything. Understanding the behaviour of dice in the sixteenth century leads to understanding the behaviour of DNA in the twenty-first.
The next step will be to control the DNA-dice as they roll. China has already begun trying to do that using science first developed in the West. But the West itself is still in the thrall of crypto-religious ideas about equality and environment. These differences have biological causes: the way different races think about genetics, or persuade other races to think about genetics, is related to their genetics. You can’t escape genes any more than you can escape maths. But the latter is a ladder that allows us to see over the old genetic wall and glimpse the possibilities beyond it. The Chinese are trying to climb over the wall using super-computers; the West is still insisting that there’s nothing on the other side. Interesting times are ahead for both flesh and binary.
Appendix
1. Suppose a family have three children and the eldest is a girl. What is the probability that all three are girls?
2. Suppose a family have three children and at least one is a girl. What is the probability that all three are girls?
3. Suppose a family have three children and only one is called Joan. What is the probability that all three are girls?
The possibilities in the first case are: 000, 001, 010, 011. So the chance of three girls is 1/4 = 25%.
The possibilities in the second case are: 000, 001, 010, 011, 100, 101, 110. So the chance of three girls is 1/7 = 14·28%.
The possibilities in the third case are: 200, 201, 210, 211, 020, 021, 120, 121, 002, 012, 102, 112. So the chance of three girls is 3/12 = 1/4 = 25%.
“However, many of the methods neuroscientists use to alter gene expression are not used by parasites (e.g. X-ray mutagenesis).” — a funny line in an interesting article: “Parasites: evolution’s neurobiologists” (2012).
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 (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.
“I had, also, during many years followed a golden rule, namely, that whenever a published fact, a new observation or thought came across me, which was opposed to my general results, to make a memorandum of it without fail and at once; for I had found by experience that such facts and thoughts were far more apt to escape from the memory than favourable ones.” — The Autobiography of Charles Darwin (1958).
A rep-tile, or repeat-tile, is a two-dimensional shape that can be divided completely into copies of itself. A square, for example, can be divided into smaller squares: four or nine or sixteen, and so on. Rectangles are the same. Triangles can be divided into two copies or three or more, depending on their precise shape. Here are some rep-tiles, including various rep-triangles:
Various rep-tiles — click for larger image
Some are simple, some are complex. Some have special names: the sphinx and the fish are easy to spot. I like both of those, particularly the fish. It would make a good symbol for a religion: richly evocative of life, eternally sub-divisible of self: 1, 9, 81, 729, 6561, 59049, 531441… I also like the double-square, the double-triangle and the T-tile in the top row. But perhaps the most potent, to my mind, is the half-square in the bottom left-hand corner. A single stroke sub-divides it, yet its hypotenuse, or longer side, represents the mysterious and mind-expanding √2, a number that exists nowhere in the physical universe. But the half-square itself is mind-expanding. All rep-tiles are. If intelligent life exists elsewhere in the universe, perhaps other minds are contemplating the fish or the sphinx or the half-square and musing thus: “If intelligent life exists elsewhere in the universe, perhaps…”
Mathematics unites human minds across barriers of language, culture and politics. But perhaps it unites minds across barriers of biology too. Imagine a form of life based on silicon or gas, on unguessable combinations of matter and energy in unreachable, unobservable parts of the universe. If it’s intelligent life and has discovered mathematics, it may also have discovered rep-tiles. And it may be contemplating the possibility of other minds doing the same. And why confine these speculations to this universe and this reality? In parallel universes, in alternative realities, minds may be contemplating rep-tiles and speculating in the same way. If our universe ends in a Big Crunch and then explodes again in a Big Bang, intelligent life may rise again and discover rep-tiles again and speculate again on their implications. The wildest speculation of all would be to hypothesize a psycho-math-space, a mental realm beyond time and matter where, in mathemystic communion, suitably attuned and aware minds can sense each other’s presence and even communicate.
Credo in Piscem…
So meditate on the fish or the sphinx or the half-square. Do you feel the tendrils of an alien mind brush your own? Are you in communion with a stone-being from the far past, a fire-being from the far future, a hive-being from a parallel universe? Well, probably not. And even if you do feel those mental tendrils, how would you know they’re really there? No, I doubt that the psycho-math-space exists. But it might and science might prove its existence one day. Another possibility is that there is no other intelligent life, never has been, and never will be. We may be the only ones who will ever muse on rep-tiles and other aspects of mathematics. Somehow, though, rep-tiles themselves seem to say that this isn’t so. Particularly the fish. It mimics life and can spawn itself eternally. As I said, it would make a good symbol for a religion: a mathemysticism of trans-biological communion. Credo in Piscem, Unum et Infinitum et Æternum. “I believe in the Fish, One, Unending, Everlasting.” That might be the motto of the religion. If you want to join it, simply wish upon the fish and muse on other minds, around other stars, who may be doing the same.
Octopus: The Ocean’s Intelligent Invertebrate: A Natural History, Jennifer A. Mather, Roland C. Anderson and James B. Wood (Timber Press, 2010)
Who knows humanity who only human knows? We understand ourselves better by looking at other animals, but most other animals are not as remarkable as the octopus. These eight-armed invertebrates are much more closely related to oysters, limpets and ship-worms than they are to fish, let alone to mammals, but they lead fully active lives and seem fully conscious creatures of strong and even unsettling intelligence. Octopuses are molluscs, or “soft ones” (the same Latin root is found in “mollify”), with no internal skeleton and no rigid structure. Unlike some of their relatives, however, they do have brains. And more than one brain apiece, in a sense, because their arms are semi-autonomous. They don’t really have bodies, though, which is why they belong to the class known as Cephalopoda, or “head-foots”. Squid and cuttlefish, which are also covered in this book, are in the same class but do have more definite bodies, because they swim in open water rather than, like octopuses, living on the sea-floor. Another difference between the groups is that octopuses don’t have tentacles. Their limbs are too adaptable for that:
Because the arms are lined with suckers along the underside, octopuses can grasp anything. And since the animal has no skeleton, it can flex its arms and move them in any direction. The arms aren’t tentacles: tentacles are used for prey capture in squid, and these arms, with their flexibility, are used for many different actions. (“Introduction: Meet the Octopus”, pg. 15)
Octopuses would be interesting even if we humans knew ourselves perfectly. But one of the interesting things is whether they could be us, given time and opportunity. That is, could they become a tool-making, culture-forming, language-using species like us? After all, unlike most animals, they don’t use their limbs simply for locomotion or aggression: octopuses can manipulate objects with reasonably good precision. I used to think that one obstacle to their use of tools was their inability to make fine discriminations between shapes, because I remembered reading in the Oxford Book of the Mind (2004) that they couldn’t tell cubes from spheres. The explanation there was that their arms are too flexible and can’t, like rigid human arms and fingers, be used as fixed references to judge a manipulated object against. But this book says otherwise:
[The British researcher J.M.] Wells found that common octopuses can learn by touch and can tell a smooth cylinder from a grooved one or a cube from a sphere. They had much more trouble, though, telling a cube with smoothed-off corners from a sphere… They couldn’t learn to distinguish a heavy cylinder from a lighter one with the same surface texture. (ch. 9, “Intelligence”, pg. 130)
The problem isn’t simply that their arms are too flexible: their arms are also too independent:
Maybe the common octopus could not use information about the amount of sucker bending to send to the brain and calculate what an object’s shape would be, or calculate how much the arm bent to figure out weight. Octopuses have a lot of local control of arm movement: there are chains of ganglia [nerve-centres] down the arm and even sucker ganglia to control their individual actions. If local information is processed as reflexes in these ganglia, most touch and position information might not go to the brain and then couldn’t used in associative learning. (Ibid., pg. 130-1)
Or in manipulating an object with high precision and accuracy. An octopus can use rocks to make the entrance to its den narrower and less accessible to predators, but that’s a long way from being able to build a den. It is a start, however, and if man and other apes left the scene, octopuses would be a candidate to occupy his vacant throne one day. But I would give better odds to squirrels and to corvids (crow-like birds) than to cephalopods. Living in the sea may be a big obstacle to developing full, language-using, world-manipulating intelligence. The brevity of that life in the sea is definitely an obstacle: one deep-sea species of octopus may live over ten years, which would be “the longest for any octopus” (ch. 1, “In the Egg”). In shallower, warmer water, the Giant Pacific Octopus, Enteroctopus dofleini, is senescent at three or four years; some other species are senescent at a year or less. Males die after fertilizing the females, females die after guarding their eggs to hatching. In such an active, enquiring animal, senescence is an odd and unsettling process. A male octopus will stop eating, lose weight and start behaving in unnatural ways:
Senescent male giant Pacific octopuses and red octopuses are found crawling out of the water onto the beach [which is] likely to lead to attacks by gulls, crows, foxes, river otters or other animals… Senescent males have even been found in river mouths, going upstream to their eventual death from the low salinity of the fresh water. (ch. 10, “Sex at Last”, pg. 148)
Female octopuses stop eating and lose weight, but can’t behave unnaturally like that, because they have eggs to guard. Evolution keeps them on duty, because females that abandoned their eggs would leave fewer offspring. Meanwhile, males can become what might be called demob-demented: once they’ve mated, their behaviour doesn’t affect their offspring. In the deep sea, longer-lived species follow the same pattern of maturing, mating and senescing, but aren’t so much living longer as living slower. These short, or slow, lives wouldn’t allow octopuses to learn in the way human beings do. The most important part of human learning is, of course, central to this book and this review: language. Cephalopods don’t have good hearing, but they do have excellent sight and the ability to change the colour and patterning of their skin. So Arthur C. Clarke (1917-2008) suggested in his short-story “The Shining Ones” (1962) that they could become autodermatographers, or “self-skin-writers”, speaking with their skin. The fine control necessary for language is already there:
Within the outer layers of octopus skin are many chromatophores – sacs that contain yellow, red or brown pigment within an elastic container. When a set of muscles pulls a chromatophore sac out to make it bigger, its color is allowed to show. When the muscles relax, the elastic cover shrinks the sac and the color seems to vanish. A nerve connects to each set of chromatophore muscles, so that nervous signals from the brain can cause an overall change in color in less than 100 milliseconds at any point in the body… When chromatophores are contracted, there is another color-producing layer beneath them. A layer of reflecting cells, white leucophores or green iridophores depending on the area of the body, produces color in a different way: Like a hummingbird’s feathers, which only reflect color at a specific angle, these cells have no pigment themselves but reflect all or some of the colors in the environment back to the observer… (ch. 6, “Appearances”, pg. 89)
“Observer” is the operative word: changes in skin-colour, -texture and -shape are a way to fool the eyes and brains of predators. The molluscan octopus can adopt many guises: it can look like rocks, sand or seaweed. But the champion changer is Thaumoctopus mimicus, which lives in shallow waters off Indonesia. Its generic name means “marvel-octopus” and its specific name means “mimicking”. And its modes of mimicry are indeed marvellous:
This octopus can flatten its body and move across the sand, using its jet for propulsion and trailing its arms, with the same undulating motion as a flounder or sole. It can swim above the mud with its striped arms outspread, looking like a venomous lionfish or jellyfish. It can narrow the width of its combined slender body and arms to look like a striped sea-snake. And it may be able to carry out other mimicries we have yet to see. Particularly impressive about the mimic octopus is that not only can it take on the appearance of another animal but it can also assume the behaviour of that animal. (ch. 7, “Not Getting Eaten”, pg. 109)
But octopuses also change their skin to fool the eyes and brains of prey. The “Passing Cloud” may sound like a martial arts technique, but it’s actually a molluscan hunting technique. And it’s produced entirely within the skin, as the authors of this book observed after videotaping octopuses “in an outdoor saltwater pond on Coconut Island”, Hawaii:
Back in the lab and replaying the video frame by frame, we found how complex the Passing Cloud display is. The Passing Cloud formed on the posterior mantle, flowed forward past the head and became more of a bar in shape, then condensed into a small blob below the head. The shape then enlarged and moved out onto the outstretched mantle, flowing off the anterior mantle and disappearing. (ch. 6, “Appearances”, pg. 93)
It’s apparently used to startle crabs that have frozen and are hard to see. When the crab moves in response to the Passing Cloud, the octopus can grab it and bite it to death with its “parrotlike beak”. They “also use venom from the posterior salivary gland that can paralyze prey and start digestion” (ch. 3, “Making a Living”, pg. 62). But a bite from an octopus can kill much bigger things than crabs:
Blue-ringed octopuses, the four species that are members of the genus Hapalochlaena, display stunning coloration. Like other spectacular forms of marine and terrestrial life, they have vivid color patterns as a warning signal. These small octopuses pose a serious threat to humans. They pack a potent venomous bite that makes them among the most dangerous creatures on Earth. Their venom, the neurotoxin tetrodotoxin (TTX) described by Scheumack et al in 1978, is among the few cephalopod venoms that can affect humans. A variety of marine and terrestrial animals produce TTX [including] poisonous arrow frogs [untrue, according to Wikipedia, which refers to “toads of the genus Atelopus” instead], newts, and salamanders… but the classic example, and what the compound is named after, is the tetraodon puffer fish. The puffers are what the Japanese delicacy fufu is made from. If the fish is prepared correctly, extremely small amounts of TTX cause only a tingling or numbing sensation. But if it is prepared incorrectly, the substance kills by blocking sodium channels on the surface of nerve membranes. A single milligram, 1/2500 of the weight of a penny, will kill an adult human… Even in the minuscule doses delivered by a blue-ringed octopus’s nearly unnoticeable bite, TTX can shut down the nervous system of a large person in just minutes; the risk of death is very high. (“Postscript: Keeping a Captive Octopus”, pg. 170)
It’s interesting to see how often toxicity has evolved among animals. Puffer-fish and blue-ringed octopuses may get their toxin from bacteria or algae, while poison-arrow frogs get the even more potent batrachotoxin from eating beetles, as do certain species of bird on New Guinea. Accordingly, toxicity is found in animals with no legs, two legs, four legs, six legs, eight legs and ten legs (if squid have a poisonous bite too). Evolution has found similar solutions to similar problems in unrelated groups, because evolution is a way of exploring space: that of possibility. And it is all, in one way or another, chemical possibility. Blue-ringed octopuses have found a chemical solution to hunting and evading predators. Other cephalopods have found a chemical solution to staying afloat:
Another substance used to keep plankton buoyant is ammonia, again lighter than water. Ammonia is primarily used by the large squid species, including the giant squid (Architeuthis dux), in their tissues, although the glass squid (Cranchia scabra) concentrates ammonia inside a special organ. The ammonia in the tissues of these squid makes the living or dead animal smell pungent. Dead or dying squid on the ocean’s surface smell particularly foul. The ammonia in these giant squid also makes them inedible – there will be no giant squid calamari. (ch. 2, “Drifting and Settling”)
Other deep-sea solutions from chemical possibility-space include bioluminescence. This is used by a cephalopod that was little-known until it was used as a metaphor for the greedy behaviour of Goldman-Sachs and other bankers:
…although they do not have an ink-sac, vampire squid have a bioluminescent mucus that they can jet out, presumably at the approach of a potential predator, likely distracting it in the same way as a black ink jet for a shallow-water octopus or squid. Second, they have a pair of light organs at the base of the fins with a moveable flap that can be used as a shutter. These could act as a searchlight, turning a beam of light onto a potential prey species that tactile sensing from the [tentacle-like] filaments has picked up. And third, they have a huge number of tiny photophores all over the body and arms. These could work two ways: they might give a general dim lighting as a visual counter-shading. With even a little light from above, a dark animal would stand out in silhouette from below. With low-level light giving just enough illumination, it could blend in. And the second function of these lights has been seen by ROV [remotely operated underwater vehicle] viewers: a disturbed vampire squid threw its arms back over its body and flashed the lights on the arms, which should startle any creature. (ch. 11, “The Rest of the Group”, pg. 161)
I was surprised to learn that vampire squid can be prey, but in fact their scientific name – Vampyroteuthis infernalis – is almost as big as they are: “for those imagining that vampire squid are monsters of the deep, they are tiny – only up to 5 in. (13 cm) long” (ibid., pg. 162). Even less-studied, even deeper-living, and even longer-named is Vulcanoctopus hydrothermalis, the “specialized deep-sea vent octopus”, which is “found, as its name suggests, near deep-sea hydrothermal vents way down at 6000 ft. (2000 m)” (“Introduction: Meet the Octopus”, pg. 15). Life around hydrothermal vents, or mini-volcanoes on the ocean floor, is actually independent of the sun, because the food-pyramid there is based on bacteria that live on the enriched water flowing from the vents. So an asteroid strike or mega-volcano that clouded the skies and stopped photosynthesis wouldn’t directly affect that underwater economy. But vents sometimes go extinct and Vulcanoctopus hydrothermalis must lead a precarious existence.
I’d like to know more about the species, but it’s one interesting octopus among many. This book is an excellent introduction to this eight-limbed group and cousins like the ten-limbed squid and the sometimes ninety-limbed nautiluses. It will guide you through all aspects of their lives and behaviour, from chromatophores, detachable arms and jet propulsion to siphuncles, glue-glands and the hectocotylus, the “modified mating arm” of male cephalopods that was once thought to be a parasitic worm. That mystery has been solved, but lots more remain. Octopus: The Ocean’s Intelligent Invertebrate should appeal to any thalassophile who shares the enthusiasm of H.P. Lovecraft or Arthur C. Clarke for a group that has evolved high intelligence without ever leaving the ocean.
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.
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)
Overlord In Terms of Core Issues Around Maximal Engagement with Key Notions of the Über-Feral 