Cat out of Bel

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.

Live and Let Dice

How many ways are there to die? The answer is actually five, if by “die” you mean “roll a die” and by “rolled die” you mean “Platonic polyhedron”. The Platonic polyhedra are the solid shapes in which each polygonal face and each vertex (meeting-point of the edges) are the same. There are surprisingly few. Search as long and as far as you like: you’ll find only five of them in this or any other universe. The standard cubic die is the most familiar: each of its six faces is square and each of its eight vertices is the meeting-point of three edges. The other four Platonic polyhedra are the tetrahedron, with four triangular faces and four vertices; the octahedron, with eight triangular faces and six vertices; the dodecahedron, with twelve pentagonal faces and twenty vertices; and the icosahedron, with twenty triangular faces and twelve vertices. Note the symmetries of face- and vertex-number: the dodecahedron can be created inside the icosahedron, and vice versa. Similarly, the cube, or hexahedron, can be created inside the octahedron, and vice versa. The tetrahedron is self-spawning and pairs itself. Plato wrote about these shapes in his Timaeus (c. 360 B.C.) and based a mathemystical cosmology on them, which is why they are called the Platonic polyhedra.

An animated gif of a tetrahedron

Tetrahedron


An animated gif of a hexahedron

Hexahedron

An animated gif of an octahedron

Octahedron


An animated gif of a dodecahedron

Dodecahedron

An animated gif of an icosahedron

Icosahedron

They make good dice because they have no preferred way to fall: each face has the same relationship with the other faces and the centre of gravity, so no face is likelier to land uppermost. Or downmost, in the case of the tetrahedron, which is why it is the basis of the caltrop. This is a spiked weapon, used for many centuries, that always lands with a sharp point pointing upwards, ready to wound the feet of men and horses or damage tyres and tracks. The other four Platonic polyhedra don’t have a particular role in warfare, as far as I know, but all five might have a role in jurisprudence and might raise an interesting question about probability. Suppose, in some strange Tycholatric, or fortune-worshipping, nation, that one face of each Platonic die represents death. A criminal convicted of a serious offence has to choose one of the five dice. The die is then rolled f times, or as many times as it has faces. If the death-face is rolled, the criminal is executed; if not, he is imprisoned for life.

The question is: Which die should he choose to minimize, or maximize, his chance of getting the death-face? Or doesn’t it matter? After all, for each die, the odds of rolling the death-face are 1/f and the die is rolled f times. Each face of the tetrahedron has a 1/4 chance of being chosen, but the tetrahedron is rolled only four times. For the icosahedron, it’s a much smaller 1/20 chance, but the die is rolled twenty times. Well, it does matter which die is chosen. To see which offers the best odds, you have to raise the odds of not getting the death-face to the power of f, like this:

3/4 x 3/4 x 3/4 x 3/4 = 3/4 ^4 = 27/256 = 0·316…

5/6 ^6 = 15,625 / 46,656 = 0·335…

7/8 ^8 = 5,764,801 / 16,777,216 = 0·344…

11/12 ^12 = 3,138,428,376,721 / 8,916,100,448,256 = 0·352…

19/20 ^20 = 37,589,973,457,545,958,193,355,601 / 104,857,600,000,000,000,000,000,000 = 0·358…

Those represent the odds of avoiding the death-face. Criminals who want to avoid execution should choose the icosahedron. For the odds of rolling the death-face, simply subtract the avoidance-odds from 1, like this:

1 – 3/4 ^4 = 0·684…

1 – 5/6 ^6 = 0·665…

1 – 7/8 ^8 = 0·656…

1 – 11/12 ^12 = 0·648…

1 – 19/20 ^20 = 0·642…

So criminals who prefer execution to life-imprisonment should choose the tetrahedron. If the Tycholatric nation offers freedom to every criminal who rolls the same face of the die f times, then the tetrahedron is also clearly best. The odds of rolling a single specified face f times are 1/f ^f:

1/4 x 1/4 x 1/4 x 1/4 = 1/4^4 = 1 / 256

1/6^6 = 1 / 46,656

1/8^8 = 1 / 16,777,216

1/12^12 = 1 / 8,916,100,448,256

1/20^20 = 1 / 104,857,600,000,000,000,000,000,000

But there are f faces on each polyhedron, so the odds of rolling any face f times are 1/f ^(f-1). On average, of every sixty-four (256/4) criminals who choose to roll the tetrahedron, one will roll the same face four times and be reprieved. If a hundred criminals face the death-penalty each year and all choose to roll the tetrahedron, one criminal will be reprieved roughly every eight months. But if all criminals choose to roll the icosahedron and they have been rolling since the Big Bang, just under fourteen billion years ago, it is very, very, very unlikely that any have yet been reprieved.

He Say, He Sigh, He Sow #7

“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).

Rep-Tile Reflections

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

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.

The rep-tile known as the fish

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.

Numbered Days

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

Pest Test

Health warning: I am not a mathematician. That said, here is a mathematical question:

Suppose there is a 99% accurate test for a medical condition – say a symptomless infection. You take the test and get a positive result. What are your chances of having the infection?

That obvious answer might seem to be 99%. But the obvious answer is wrong. The accuracy of the test is only half the information you need to answer the question. You also need to know how common the infection is. Say it occurs once in every hundred people. On average, then, if you test a hundred people, one of whom has the infection, you will get two positive results: one that is accurate and one that is inaccurate, i.e., a false positive. Under those circumstances, a positive result means that you have a ½, or 50%, chance of having the infection (see appendix for further discussion). Under some other circumstances, a positive result on an 80% or 90% accurate test would mean that you have a higher chance of having the infection. Here’s a graphic to illustrate this apparent paradox:

Graph illustrating confidence rates for medical tests of various accuracy

The x-axis represents infection rate per 10,000 of the population, the y-axis represents one’s chance of being infected, from 0%, for no chance, to 100%, for complete certainty. The coloured curves represent tests of different accuracy: 1% accurate, for the bottom curve, and 99% accurate, for the uppermost curve. The curves between the two represent tests of 10% to 90% accuracy. Note how the curves mirror each other: the 99% accurate test rises towards certainty very quickly, but takes a long time to finally get there. The 1% accurate test stays near complete uncertainty for a long time, then finally rises rapidly towards certainty. In other words, a positive result on a 99% accurate test is equivalent to a negative result on a 1% accurate test, and vice versa. Ditto for the 90% and 10% accurate tests, and so on. But a positive (or negative) result on a 50% accurate test is useless, because it never tells you anything new: your chance of being infected, given a positive result, is the same as the rate of infection in the population. And when exactly half the population is infected, your chance of being infected, given a positive result, is the same as the accuracy of the test, whether it’s 1%, 50%, or 99%.

Here is a table illustrating the same points:

Accuracy of test →


Infection rate ↓
1% 10% 20% 30% 40% 50% 60% 70% 80% 90% 99%
1/100 <1% 0.1% 0.3% 0.4% 0.7% 1% 1.5% 2.3% 3.9% 8.3% 50%
10/100 0.1% 1.2% 2.7% 4.5% 6.9% 10% 14.3% 20.6% 30.8% 50% 91.7%
20/100 0.3% 2.7% 5.9% 9.7% 14.3% 20% 27.3% 36.8% 50% 69.2% 96.1%
30/100 0.4% 4.5% 9.7% 15.5% 22.2% 30% 39.1% 50% 63.2% 79.4% 97.7%
40/100 0.7% 6.9% 14.3% 22.2% 30.8% 40% 50% 60.9% 72.7% 85.7% 98.5%
50/100 1% 10% 20% 30% 40% 50% 60% 70% 80% 90% 99%
60/100 1.5% 14.3% 27.3% 39.1% 50% 60% 69.2% 77.8% 85.7% 93.1% 99.3%
70/100 2.3% 20.6% 36.8% 50% 60.9% 70% 77.8% 84.5% 90.3% 95.5% 99.6%
80/100 3.9% 30.8% 50% 63.2% 72.7% 80% 85.7% 90.3% 94.1% 97.3% 99.7%
90/100 8.3% 50% 69.2% 79.4% 85.7% 90% 93.1% 95.5% 97.3% 98.8% 99.9%
99/100 50% 91.7% 96.1% 97.7% 98.5% 99% 99.3% 99.6% 99.7% 99.9% >99.9%
100/100 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100%

Appendix

We’ve seen that we have to take false positives into account, but what about false negatives? Suppose that the rate of infection is 1 in 100 and the accuracy of the test is 99%. If the population is 10,000, then 100 people will have the disease and 9,900 will not. If the population is tested, on average 100 x 99% = 99 of the infected people will get an accurate positive result and 100 x 1% = 1 will get an inaccurate negative result, i.e., a false negative. Similarly, 9,900 x 1% = 99 of the non-infected people will get a false positive. So there will be 99 + 99 = 198 positive results, of which 99 are accurate. 99/198 = 1/2 = 50%.

Performativizing Papyrocentricity #8

Papyrocentric Performativity Presents:

Auto-BiommiIron Man: My Journey through Heaven and Hell with Black Sabbath, Tony Iommi, as told to T.J. Lammers (Simon & Schuster, 2011)

Halfway to ParalysedHalfway to Paradise: The Birth of British Rock, Alwyn W. Turner (V&A Publishing, 2008)


Or Read a Review at Random: RaRaR

Guise and Molls

Front cover of Octopus: The Ocean’s Intelligent Invertebrate: A Natural History, by Jennifer A. Mather et al
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.

Poetry and Putridity

Poetry and Putridity: Interrogating Issues of Narrativistic Necrocentricity in A.E. Housman and Clark Ashton Smith

Thanatic fanatic. Say it. Savour it, if you’re that way inclined. I certainly am: I am obsessed with words. The sound of them, the shape of them, their history, meaning and flavours. If I were a Guardianista, I’d say I was “passionate about” words. But it’s partly because I’m obsessed with words that I’m not a Guardianista. The Guardian and its readers use them badly. I like people who use them well: A.E. Housman and Clark Ashton Smith, for example. AEH (1859-1936) was an English classicist, CAS (1893-1961) a Californian jack-of-all-trades. But they were both masters of the English language.

They were also thanatic fanatics: obsessed with death. But in different ways. You could say that Housman was more death-as-dying, Smith more death-as-decaying. Not that Smith didn’t deal in dying too: he wrote powerfully and disturbingly about our departure from life, not just about what happens to us beyond it. But Housman didn’t dabble in decomposition and decay. In A Shropshire Lad (1896), the death is fresh, not foetid: necks break, throats are slit, athletes die young, men muse on drowning, fiancées arrive at church in coffins, not coaches. Sometimes the effect, and affect, are ludicrous. Sometimes they’re not. Sometimes it’s hard to decide:

On moonlit heath and lonesome bank
  The sheep beside me graze;
And yon the gallows used to clank
  Fast by the four cross ways.

A careless shepherd once would keep
  The flocks by moonlight there,*
And high amongst the glimmering sheep
  The dead man stood on air.

They hang us now in Shrewsbury jail:
  The whistles blow forlorn,
And trains all night groan on the rail
  To men that die at morn.

There sleeps in Shrewsbury jail to-night,
  Or wakes, as may betide,
A better lad, if things went right,
  Than most that sleep outside.

And naked to the hangman’s noose
  The morning clocks will ring
A neck God made for other use
  Than strangling in a string.

And sharp the link of life will snap,
  And dead on air will stand
Heels that held up as straight a chap
  As treads upon the land.

So here I’ll watch the night and wait
  To see the morning shine,
When he will hear the stroke of eight
  And not the stroke of nine;

And wish my friend as sound a sleep
  As lads’ I did not know,
That shepherded the moonlit sheep
  A hundred years ago.

*Hanging in chains was called keeping sheep by moonlight.

A Shropshire Lad, IX.

That poem mingles beauty and bathos as it contemplates death. Other poems have more or less of one or the other, but for Housman death is metaphor and metaphysics, not morbidity and mephitis. He uses it as a symbol of loss and despair and those are his real concerns. There is no literal death here:

’Tis time, I think, by Wenlock town
  The golden broom should blow;
The hawthorn sprinkled up and down
  Should charge the land with snow.

Spring will not wait the loiterer’s time
  Who keeps so long away;
So others wear the broom and climb
  The hedgerows heaped with may.

Oh tarnish late on Wenlock Edge,
  Gold that I never see;
Lie long, high snowdrifts in the hedge
  That will not shower on me.

A Shropshire Lad, XXXIX.

That is an example of multum in parvo: “much in little”. Using simple words and simple metre, Housman creates great beauty and can conjure overwhelming emotion. He was one of the greatest classicists in history, an expert in the rich and complex literature of the ancient world, a profound scholar of Latin and Greek. But his poetry is remarkable for its lack of classical vocabulary. There is no Latin or Greek in the poem above and only two words of French. Clark Ashton Smith was quite different:

“Look well,” said the necromancer, “on the empire that was yours, but shall be yours no longer.” Then, with arms outstretched toward the sunset, he called aloud the twelve names that were perdition to utter, and after them the tremendous invocation: Gna padambis devompra thungis furidor avoragomon.

Instantly, it seemed that great ebon clouds of thunder beetled against the sun. Lining the horizon, the clouds took the form of colossal monsters with heads and members somewhat resembling those of stallions. Rearing terribly, they trod down the sun like an extinguished ember; and racing as if in some hippodrome of Titans, they rose higher and vaster, coming towards Ummaos. Deep, calamitous rumblings preceded them, and the earth shook visibly, till Zotulla saw that these were not immaterial clouds, but actual living forms that had come forth to tread the world in macrocosmic vastness. Throwing their shadows for many leagues before them, the coursers charged as if devil-ridden into Xylac, and their feet descended like falling mountain crags upon far oases and towns of the outer wastes.

Like a many-turreted storm they came, and it seemed that the world shrank gulfward, tilting beneath the weight. Still as a man enchanted into marble, Zotulla stood and beheld the ruining that was wrought on his empire. And closer drew the gigantic stallions, racing with inconceivable speed, and louder was the thundering of their footfalls, that now began to blot the green fields and fruited orchards lying for many miles to the west of Ummaos. And the shadow of the stallions climbed like an evil gloom of eclipse, till it covered Ummaos; and looking up, the emperor saw their eyes halfway between earth and zenith, like baleful suns that glare down from soaring cumuli.

“The Dark Eidolon” (1935).

Smith’s logomania could not be satisfied beyond the bounds of English, in Latin, Greek and French: he stepped outside history altogether and created his own languages to weave word-spells with. If you didn’t know CAS or AEH or their writing, who would seem more like the world-famous classicist? Based on what I have quoted so far, it would perhaps be Smith. But that is part of what is astonishing about his writing: he wasn’t merely a Beethoven of prose, creating gigantic melodies with rich and rolling words, he was a poorly educated Beethoven. Here is another contrast with his fellow thanatic fanatic. Housman was not poorly educated and was given a chance Smith never had: to attend and adorn one of the world’s greatest universities. The chance was dropped. Housman attended, but he didn’t adorn:

After showing himself, as an undergraduate [at Oxford], to be a brilliant – even arrogantly brilliant – student of Latin and Greek, apparently set for a lifetime of scholarship, he produced a performance in his final examination that astonished all who knew him. He handed in a series of blank, or nearly blank, papers and was failed outright. Retrieving the situation as best he could, he completed the requirements for a pass degree, got through the Civil Service examination, and secured a post at the Patent Office. (The Collected Poems of A.E. Housman, Wordsworth, 2005, Michael Irwin’s Introduction, pg. 8)

Housman would end his life, laden with honours, as a Professor of Latin at Cambridge, but that isn’t surprising. The fiasco at Oxford certainly was. Why did it happen? A nervous breakdown or failure to work, perhaps, because of his unrequited love for a fellow student: Moses Jackson, who was healthy, heterosexual, and had no time for classical scholarship. In later life, travelling to cities like Paris and Venice, Housman would indulge much more than his gastronomic and aesthetic appetites. But he seems to have believed that sex without love is like food without flavour. And he never ceased loving Jackson. When he completed volume one of his magnum opus, a definitive edition of the Roman poet Manilius (fl. 1st century A.D.), he dedicated it to Jackson in Latin, dubbing him harum litterarum contemptor, “a scorner of these writings”. That was in 1903, when Jackson was married and living in India. Jackson would later move to Canada, where he died of anaemia in 1923. His death was anticipated by this cri du cœur from Housman:

The half-moon westers low, my love,
  And the wind brings up the rain;
And wide apart lie we, my love,
  And seas between the twain.

I know not if it rains, my love,
  In the land where you do lie;
And oh, so sound you sleep, my love,
  You know no more than I.

Last Poems (1922), XXVI.

But cri du cœur is not the mot juste: it is a very simple poem with only a single foreign word. That is, if “apart” can be called foreign, after centuries on the tongues and lips of English-speakers. Almost everything else has been there millennia and that is part of Housman’s word-magic. His poems are really about depth, not distance. One of the most famous says, in the same simple vocabulary, that far away is close at hand:

On Wenlock Edge the wood’s in trouble;
  His forest fleece the Wrekin heaves;
The gale, it plies the saplings double,
  And thick on Severn snow the leaves.

’Twould blow like this through holt and hanger
  When Uricon the city stood:
’Tis the old wind in the old anger,
  But then it threshed another wood.

Then, ’twas before my time, the Roman
  At yonder heaving hill would stare:
The blood that warms an English yeoman,
  The thoughts that hurt him, they were there.

There, like the wind through woods in riot,
  Through him the gale of life blew high;
The tree of man was never quiet:
  Then ’twas the Roman, now ’tis I.

The gale, it plies the saplings double,
  It blows so hard, ’twill soon be gone:
To-day the Roman and his trouble
  Are ashes under Uricon.

A Shropshire Lad, XXXI.

Death for Housman, as it was for Swinburne, is “a sleep”: when the body is ashes, the brain is troubled no more. Death does not necessarily sleep in Clark Ashton Smith:

Natanasna (chanting):

Muntbauut, maspratha butu, [Mumbavut, lewd and evil spirit,]
Varvas runu, vha rancutu. [Wheresoever thou roamest, hear me.]
Incubus, my cousin, come,
Drawn from out the night you haunt,
From the hollow mist and murk
Where discarnate larvae lurk,
By the word of masterdom.
Hell will keep its covenant,
You shall have the long-lost thing
That you howl and hunger for.
Borne on sable, sightless wing,
Leave the void that you abhor,
Enter in this new-made grave,
You that would a body have:
Clothed with the dead man’s flesh,
Rising through the riven earth
In a jubilant rebirth,
Wend your ancient ways afresh,
By the mantra laid on you
Do the deed I bid you do.
Vora votha Thasaidona [By (or through) Thasaidon’s power]
Sorgha nagrakronitlhona. [Arise from the death-time-dominion.]

(After a pause)

Vachat pantari vora nagraban [The spell (or mantra) is finished by the necromancer.]

Kalguth: Za, mozadrim: vachama vongh razan. [Yes, master: the vongh (corpse animated by a demon) will do the rest. (These words are from Umlengha, an ancient language of Zothique, used by scholars and wizards.)]

(The turf heaves and divides, and the incubus-driven Lich of Galeor rises from the grave. The grime of interment is on its face, hands, and clothing. It shambles forward and presses close to the outer circle, in a menacing attitude. Natanasna raises the staff, and Kalguth the arthame, used to control rebellious sprits. The Lich shrinks back.)

The Lich (in a thick, unhuman voice): You have summoned me,
And I must minister
To your desire.

Natanasna: Heed closely these instructions:
By alleys palled and posterns long disused,
Well-hidden from the moon and from men’s eyes,
You shall find ingress to the palace. There,
Through stairways only known to mummied kings
And halls forgotten save by ghosts, you must
Seek out the chamber of the queen Somelis,
And woo her lover-wise till that be done
Which incubi and lovers burn to do.

That is from Smith’s The Dead Will Cuckold You (1951), “A Drama in Six Scenes”. It is also a drama with a sex-scene, by implication, at least. The re-animated corpse follows its instructions, seeks out the palace and enters the “chamber of the queen Somelis”, who addresses it thus as her husband, King Smaragd, beats on the locked door:

Poor Galeor, the grave has left you cold:
I’ll warm you in my bed and in my arms
For those short moments ere the falling sword
Shatter the fragile bolts of mystery
And open what’s beyond. (Op. cit., Scene IV)

I read the play daunted by its erudition, delighted by its epeolatry, and disturbed by its emetic extremity. Some of Smith’s work is about something other than death. This play is about nothing but death. Compare it with Smith’s short-story “The Isle of Torturers” (1933), which contains both poetry and putridity. It’s part richness, part retching. There is poetry like this:

Creaming with a winy foam, full of strange murmurous voices and vague tales of exotic things, the halcyon sea was about the voyagers now beneath the high-lifting summer sun. But the sea’s enchanted voices and its long languorous, immeasurable cradling could not soothe the sorrow of Fulbra; and in his heart a despair abided, black as the gem that was set in the red ring of Vemdeez.

Howbeit, he held the great helm of the ebon barge, and steered as straightly as he could by the sun toward Cyntrom. The amber sail was taut with the favoring wind; and the barge sped onward all that day, cleaving the amaranth waters with its dark prow that reared in the carven form of an ebony goddess. And when the night came with familiar austral stars, Fulbra was able to correct such errors as he had made in reckoning the course.

“The Isle of Torturers” (1933).

There is also putridity like this:

Anon the drowned and dripping corpses went away; and Fulbra was stripped by the Torturers and was laid supine on the palace floor, with iron rings that bound him closely to the flags at knee and wrist, at elbow and ankle. Then they brought in the disinterred body of a woman, nearly eaten, in which a myriad maggots swarmed on the uncovered bones and tatters of dark corruption; and this body they placed on the right hand of Fulbra. And also they fetched the carrion of a black goat that was newly touched with beginning decay; and they laid it down beside him on the left hand. Then, across Fulbra, from right to left, the hungry maggots crawled in a long and undulant wave…

In The Dead Will Cuckold You, the poetry never escapes the putridity. After reading it, you will understand why L. Sprague de Camp remarked this of Smith: “Nobody since Poe has so loved a well-rotted corpse” (Literary Swordsmen and Sorcerers: the Makers of Heroic Fantasy, Arkham House 1976, pg. 206). Nor has anyone since Poe so loved an ingenious torture: in Scene V of the play, King Smaragd threatens his guards with a “douche” of “boiling camel-stale”. There’s humour in Smith’s morbidity, but I think that he dwelt too long on unhealthy themes. It shows both in his stories and in his popularity: the Weird Tales Big Three, H.P. Lovecraft (1890-1937), Robert E. Howard (1906-36), and Clark Ashton Smith, are rather like the three stars in the belt of Orion. Lovecraft and Howard are bright Alnilam and Mintaka, Smith is dimmer Alnitak. His luxuriant lexicon explains part of this, but his necrocentric narratives must repel people too.

Housman wrote about death more delicately and distantly. His work doesn’t so much narrativize the necrotic as thematicize the thanatic. It talks about dying, not decaying, and it doesn’t relish the repellent as Smith’s work often did. This helps explain why Housman is a bigger name in English literature than Smith, though I don’t think he was a greater writer. Housman is a minor poet with a major name. I think he deserves it for the beauty and simplicity of his verse. He’s a word-magician who can conjure tears. Smith is a word-magician who can conjure titans. He did more with English and deserves some of Housman’s fame. With his poetry, he might have won it; with his putridity, he lost his chance.

Yew and Me

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.