Performativizing Papyrocentricity #31

Papyrocentric Performativity Presents:

Nor Severn ShoreThe Poems of A.E. Housman, edited by Archie Burnett (Clarendon Press 1997) (posted @ Overlord of the Über-Feral)

Knight and ClayThe Riddle of the Labyrinth: The Quest to Crack an Ancient Code and the Uncovering of a Lost Civilisation, Margalit Fox (Profile Books 2013)

Goal God GuideThe Secret Footballer’s Guide to the Modern Game: Tips and Tactics from the Ultimate Insider, The Secret Footballer (Guardian Books 2014)

Or Read a Review at Random: RaRaR

No Plaice Like Olm

European Reptile and Amphibian Guide by Axel KwetEuropean Reptile and Amphibian Guide, Axel Kwet (New Holland 2009)

An attractive book about animals that are mostly attractive, sometimes strange, always interesting. It devotes photographs and descriptive text to all the reptiles and amphibians found in Europe, from tree-frogs to terrapins, from skinks to slow-worms. Some of the salamanders look like heraldic mascots, some of the lizards like enamel jewellery, and some of the toads like sumo wrestlers with exotic skin-diseases. When you leaf through the book, you’ve moving through several kinds of space: geographic and evolutionary, aesthetic and psychological. Europe is a big place and has a lot of reptilian and amphibian variety, including one species of turtle, the loggerhead, Caretta caretta, and one species of chameleon, the Mediterranean, Chamaeleo chamaeleon.

But every species, no matter how dissimilar in size and appearance, has a common ancestor: the tiny crested newt (Triturus cristatus) to the far north-west in Scotland and the two-and-a-half metre whip snake (Dolichophis caspius) to the far south-east in Greece; the sun-loving Hermann’s tortoise (Testudo hermanni), with its sturdy shell, and the pallid and worm-like olm (Proteus anguinus), which lives in “underground streams in limestone karst country along the coast from north-east Italy to Montenegro” (pg. 55). Long-limbed or limbless, sun-loving or sun-shunning, soft-skinned or scaly – they’re all variations on a common theme.

Sample page

Sample page from European Reptile and Amphibian Guide

And that’s where aesthetic and psychological space comes in, because different species and families evoke different impressions and emotions. Why do snakes look sinister and skinks look charming? But snakes are sinuous too and in a way it’s a shame that a photograph can capture their endlessly varying loops and curves as easily as it can capture the ridigity of a tortoise. At one time a book like this would have had paintings or drawings. Nowadays, it has photographs. The images are more realistic but less enchanted: the images are no longer mediated by the hand, eye and brain of an artist. But some enchantment remains: the glass lizard, Pseudopus apodus, peering from a holly bush on page 199 reminds me of Robert E. Howard’s “The God in the Bowl”, because there’s an alien intelligence in its gaze. Glass lizards are like snakes but can blink and retain “tiny, barely visible vestiges of the hind legs” (pg. 198).

Other snake-like reptiles retain vestiges of the fore-limbs too, like the Italian three-toed skink (Chalcides chalcides). The slow-worm, Anguis fragilis, has lost its limbs entirely, but doesn’t look sinister like a snake and can still blink. Elsewhere, some salamanders have lost not limbs but lungs: the Italian cave salamander, Speleomantes italicus, breathes through its skin and the lining of its mouth. So does Gené’s cave salamander, Speleomantes genei, which is found only on the island of Sardinia. It “emits an aromatic scent when touched” (pg. 54). Toads can emit toxins and snakes can inject venoms: movement in evolutionary space means movement in chemical space, because every alteration in an animal’s appearance and anatomy involves an alteration in the chemicals created by its body. But chemical space is two-fold: genotypic and phenotypic. The genes change and so the products of the genes change. The external appearance of every species is like a bookmark sticking out of the Book of Life, fixing its position in gene-space. You have to open that book to see the full recipe for the animal’s anatomy, physiology and behaviour, though not everything is specified by the genes.

Pleuronectes platessa on the sea-floor

Pleuronectes platessa on the sea-floor

The force of gravity is one ingredient in an animal’s development, for example. So is sunlight or its absence. Or water, sand, warmth, cold. The descendants of that common ancestor occupy many ecological niches. And in fact one of those descendants wrote this book: humans and all other mammals share an ancestor with frogs, skinks and vipers. Before that, we were fish. So a plaice is a distant cousin of an olm, despite the huge difference in their appearance and habitat. One is flat, one is tubular. One lives in the sea, one lives in caves. But step by step, moving through genomic and topological space, you can turn a plaice into an olm. Or into anything else in this book. Just step back through time to the common ancestor, then take another evolutionary turning. One ancestor, many descendants. That ancestor was itself one descendant among many of something even earlier.
Olm in a Slovenian cave

Olm in a Slovenian cave

But there’s another important point: once variety appeared, it began to interact with itself. Evolutionary environment includes much more than the inanimate and inorganic. We mammals share more than an ancestor with reptiles and amphibians: we’ve also shared the earth. So we’re written into their genes and some of them are probably written into ours. Mammalian predators have influenced the evolution of skin-colour and psychology, making some animals camouflaged and cautious, others obtrusive and aggressive. But it works both ways: perhaps snakes seem sinister because we’re born with snake-sensitive instincts. If it’s got no limbs and it doesn’t blink, it might have a dangerous bite. That’s why the snake section of this book seems so different to the salamander section or the frog section. But all are interesting and all are important. This is a small book with some big themes.

Tattoo Your Ears

“The most merciful thing in the world,” said H.P. Lovecraft, “is the inability of the human mind to correlate all its contents.” Nowadays we can’t correlate all the contents of our hard-drives either. But occasionally bits come together. I’ve had two MP3s sitting on my hard-drive for months: “Drink or Die” by Erotic Support and “Hunter Gatherer” by Swords of Mars. I liked them both a lot, but until recently I didn’t realize that they were by two incarnations of the same Finnish band.

Cover of "Die by the..." Swords of Mars
They don’t sound very much alike, after all. But now that I’ve correlated them, they’ve inspired some thoughts on music and mutilation. “Drink or Die” is a dense, fuzzy, leather-lunged rumble-rocker that, like a good Mötley Crüe song, your ears can snort like cocaine. But, unlike Mötley Crüe, the auditory rush lasts the whole song, not just the first half. “Hunter Gatherer” is much more sombre. Erotic Support were “Helsinki beercore”; Swords of Mars are darker, doomier and dirgier. They’ve also got a better name – “Erotic Support” seems to have lost something in translation. Finnish is a long way from English: it’s in a different and unrelated language family, the Finno-Ugric, not the Indo-European. So it lines up with Hungarian and Estonian, not English, German and French. But Erotic Support’s lyrics are good English and “Drink or Die” is a clever title. They’d have been a more interesting band if they’d sung entirely in Finnish, but also less successful, because less accessible to the rest of the world.

Es war einmal eine Königstochter, die ging hinaus in den Wald und setzte sich an einen kühlen Brunnen. Sie hatte eine goldene Kugel, die war ihr liebstes Spielwerk, die warf sie in die Höhe und fing sie wieder in der Luft und hatte ihre Lust daran. Einmal war die Kugel gar hoch geflogen, sie hatte die Hand schon ausgestreckt und die Finger gekrümmt, um sie wieder zufangen, da schlug sie neben vorbei auf die Erde, rollte und rollte und geradezu in das Wasser hinein.

Some Indo-European

Mieleni minun tekevi, aivoni ajattelevi
lähteäni laulamahan, saa’ani sanelemahan,
sukuvirttä suoltamahan, lajivirttä laulamahan.
Sanat suussani sulavat, puhe’et putoelevat,
kielelleni kerkiävät, hampahilleni hajoovat.

Veli kulta, veikkoseni, kaunis kasvinkumppalini!
Lähe nyt kanssa laulamahan, saa kera sanelemahan
yhtehen yhyttyämme, kahta’alta käytyämme!
Harvoin yhtehen yhymme, saamme toinen toisihimme
näillä raukoilla rajoilla, poloisilla Pohjan mailla.

Some Finno-Ugric

All the same, being inaccessible sometimes helps a band’s appeal to the rest of the world: the mystique of black metal is much stronger in bands that use only Norwegian or one of the other Scandinavian languages. Erotic Support haven’t joined that rebellion against Coca-Colonization and tried to create an indigenous genre. They’re happy to reproduce more or less American music using the more or less American invention known as the electric guitar. But amplified music would have appeared in Europe even if North America had been colonized by the Chinese, so I wonder what rock would sound like if it had evolved in Europe instead. It wouldn’t be called rock, of course, but what other differences would it have? Would it be more sophisticated, for example? I think it would. The success of American exports depends in part on their strong and simple flavours. “Drink or Die” has those flavours: it’s about volume, rhythm and power. It’s full of a certain “drug-addled, crab-infested, tinnitus-nagged spirit” — the “urge to submerge in the raw bedrock viscerality of rock”, as some metaphor-mixing, über-emphasizing idiot once put it (I think it was me).

Cover of "II" by Erotic Support

Erotic Support are “beercore”, remember. Beer marks the brain with hangovers, just as tattoos mark the skin with ink. And just as loud music marks the ears with tinnitus. There are various kinds of self-mutilation in rock and that self-mutilation can have unhealthy motives. It can be an expression of boredom, angst, anomie and self-hatred. Unsurprisingly, Finland has the nineteenth highest suicide rate in the world. Beer, tattoos and tinnitus are part of the louder, dirtier and loutier end of rock: unlike Radiohead or Coldplay, Erotic Support sound like a band with tattoos who are used to hangovers. “Drink or Die” is a joke about exactly that. But what if rock had evolved in a wine-drinking culture? Would it be less of a sado-masochistic ritual, more a refined rite? Maybe not: the god of wine is Dionysos and he was Ho Bromios, the Thunderer. His brother Pan induces panic with loud noises. But black metal looks towards northern paganism: it’s music for pine forests, cold seas and beer-drinkers, not olive groves, warm seas and oenopotes.

Erotic Support don’t create soundscapes for Finland the way black metal creates soundscapes for Norway, but they do create beer-drinkers’ music, so they do express Finnishness to that extent. Swords of Mars, being darker, doomier and dirgier, are moving nearer an indigenous Finnish rock, or an indigenous Scandinavian rock, at least. This may be related to the fact that genes express themselves more strongly as an individual ages: for example, the correlation between the intelligence of parents and their children is strongest when the children are adults. Erotic Support create faster, more aggressive music than Swords of Mars, so it isn’t surprising that they’re the younger version of the same band. In biology, the genotype creates the phenotype: DNA codes for bodies and behaviour. Music is part of what Richard Dawkins calls the “extended phenotype”, like the nest of a bird or the termite-fishing-rods of a chimpanzee. A bird’s wings are created directly by its genes; a bird’s nest is created indirectly by its genes, viâ the brain. So a bird’s wings are part of the phenotype and a bird’s nest part of the extended phenotype.

Both are under the influence of the genes and both are expressions of biology. Music (like bird-song) is an expression of biology too, as is the difference between the music of Erotic Support and Swords of Mars. As brains age, the behaviour they create changes. Swords of Mars are older and not attracted to reckless self-mutilation as Erotic Support were: it’s not music to precede hangovers and induce tinnitus any more. Sword of Mars aren’t trying to tattoo your ears but to educate your mind.

Stories and Stars

A story is stranger than a star. Stronger too. What do I mean? I mean that the story has more secrets than a star and holds its secrets more tightly. A full scientific description of a star is easier than a full scientific description of a story. Stars are much more primitive, much closer to the fundamentals of the universe. They’re huge and impressive, but they’re relatively simple things: giant spheres of flaming gas. Mathematically speaking, they’re more compressible: you have to put fewer numbers into fewer formulae to model their behaviour. A universe with just stars in it isn’t very complex, as you would expect from the evolution of our own universe. There were stars in it long before there were stories.

A universe with stories in it, by contrast, is definitely complex. This is because stories depend on language and language is the scientific mother-lode, the most difficult and important problem of all. Or rather, the human brain is. The human brain understands a lot about stars, despite their distance, but relatively little about itself, despite brains being right on the spot. Consciousness is a tough nut to crack, for example. Perhaps it’s uncrackable. Language looks easier, but linguistics is still more like stamp-collecting than science. We can describe the structure of language in detail – use labels like “pluperfect subjunctive”, “synecdoche”, “bilabial fricative” and so on – but we don’t know how that structure is instantiated in the brain or where language came from. How did it evolve? How is it coded in the human genome? How does meaning get into and out of sounds and shapes, into and out of speech and writing? These are big, important and very interesting questions, but we’ve barely begun to answer them.

Distribution of dental fricatives and the O blood-group in Europe (from David Crystal's )

Distribution of dental fricatives and the O blood-group in Europe (from David Crystal’s Cambridge Encyclopedia of Language)

But certain things seem clear already. Language-genes must differ in important ways between different groups, influencing their linguistic skills and their preferences in phonetics and grammar. For example, there are some interesting correlations between blood-groups and use of dental fricatives in Europe. The invention of writing has exerted evolutionary pressures in Europe and Asia in ways it hasn’t in Africa, Australasia and the Americas. Glossogenetics, or the study of language and genes, will find important differences between races and within them, running parallel with differences in psychology and physiology. Language is a human universal, but that doesn’t mean one set of identical genes underlies the linguistic behaviour of all human groups. Skin, bones and blood are human universals too, but they differ between groups for genetic reasons.

Understanding the evolution and effects of these genetic differences is ultimately a mathematical exercise, and understanding language will be too. So will understanding the brain. For one thing, the brain must, at bottom, be a maths-engine or math-engine: a mechanism receiving, processing and sending information according to rules. But that’s a bit like saying fish are wet. Fish can’t escape water and human beings can’t escape mathematics. Nothing can: to exist is to stand in relation to other entities, to influence and be influenced by them, and mathematics is about that inter-play of entities. Or rather, that inter-play is Mathematics, with a big “M”, and nothing escapes it. Human beings have invented a way of modelling that fundamental micro- and macroscopic inter-play, which is mathematics with a small “m”. When they use this model, human beings can make mistakes. But when they do go wrong, they can do so in ways detectable to other human beings using the same model:

In 1853 William Shanks published his calculations of π to 707 decimal places. He used the same formula as [John] Machin and calculated in the process several logarithms to 137 decimal places, and the exact value of 2^721. A Victorian commentator asserted: “These tremendous stretches of calculation… prove more than the capacity of this or that computer for labor and accuracy; they show that there is in the community an increase in skill and courage…”

Augustus de Morgan thought he saw something else in Shanks’s labours. The digit 7 appeared suspiciously less often than the other digits, only 44 times against an average expected frequency of 61 for each digit. De Morgan calculated that the odds against such a low frequency were 45 to 1. De Morgan, or rather William Shanks, was wrong. In 1945, using a desk calculator, Ferguson found that Shanks had made an error; his calculation was wrong from place 528 onwards. Shanks, fortunately, was long dead. (The Penguin Dictionary of Curious and Interesting Numbers, 1986, David Wells, entry for π, pg. 51)

Unlike theology or politics, mathematics is not merely self-correcting, but multiply so: there are different routes to the same truths and different ways of testing a result. Science too is self-correcting and can test its results by different means, partly because science is a mathematical activity and partly because it is studying a mathematical artifact: the gigantic structure of space, matter and energy known as the Universe. Some scientists and philosophers have puzzled over what the physicist Eugene Wigner (1902-95) called “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”. In his essay on the topic, Wigner tried to make two points:

The first point is that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it. Second, it is just this uncanny usefulness of mathematical concepts that raises the question of the uniqueness of our physical theories. (Op. cit., in Communications in Pure and Applied Mathematics, vol. 13, No. I, February 1960)

I disagree with Wigner: it is not mysterious or uncanny and there is a rational explanation for it. The “effectiveness” of small-m maths for scientists is just as reasonable as the effectiveness of fins for fish or of wings for birds. The sea is water and the sky is air. The universe contains both sea and sky: and the universe is maths. Fins and wings are mechanisms that allow fish and birds to operate effectively in their water- and air-filled environments. Maths is a mechanism that allows scientists to operate effectively in their maths-filled environment. Scientists have, in a sense, evolved towards using maths just as fish and birds have evolved towards using fins and wings. Men have always used language to model the universe, but language is not “unreasonably effective” for understanding the universe. It isn’t effective at all.

It is effective, however, in manipulating and controlling other human beings, which explains its importance in politics and theology. In politics, language is used to manipulate; in science, language is used to explain. That is why mathematics is so important in science and so carefully avoided in politics. And in certain academic disciplines. But the paradox is that physics is much more intellectually demanding than, say, literary theory because the raw stuff of physics is actually much simpler than literature. To understand the paradox, imagine that two kinds of boulder are strewn on a plain. One kind is huge and made of black granite. The other kind is relatively small and made of chalk. Two tribes of academic live on the plain, one devoted to studying the black granite boulders, the other devoted to studying the chalk boulders.

The granite academics, being unable to lift or cut into their boulders, will have no need of physical strength or tool-making ability. Instead, they will justify their existence by sitting on their boulders and telling stories about them or describing their bumps and contours in minute detail. The chalk academics, by contrast, will be lifting and cutting into their boulders and will know far more about them. So the chalk academics will need physical strength and tool-making ability. In other words, physics, being inherently simpler than literature, is within the grasp of a sufficiently powerful human intellect in a way literature is not. Appreciating literature depends on intuition rather than intellect. And so strong intellects are able to lift and cut into the problems of physics as they aren’t able to lift and cut into the problems of literature, because the problems of literature depend on consciousness and on the hugely complex mechanisms of language, society and psychology.

Intuition is extremely powerful, but isn’t under conscious control like intellect and isn’t transparent to consciousness in the same way. In the fullest sense, it includes the senses, but who can control his own vision and hearing or understand how they turn the raw stuff of the sense-organs into the magic tapestry of conscious experience? Flickering nerve impulses create a world of sight, sound, scent, taste and touch and human beings are able to turn that world into the symbols of language, then extract it again from the symbols. This linguifaction is a far more complex process than the ignifaction that drives a star. At present it’s beyond the grasp of our intellects, so the people who study it don’t need and don’t build intellectual muscle in the way that physicists do.

Or one could say that literature is at a higher level of physics. In theory, it is ultimately and entirely reducible to physics, but the mathematics governing its emergence from physics are complex and not well-understood. It’s like the difference between a caterpillar and a butterfly. They are two aspects of one creature, but it’s difficult to understand how one becomes the other, as a caterpillar dissolves into chemical soup inside a chrysalis and turns into something entirely different in appearance and behaviour. Modelling the behaviour of a caterpillar is simpler than modelling the behaviour of a butterfly. A caterpillar’s brain has less to cope with than a butterfly’s. Caterpillars crawl and butterflies fly. Caterpillars eat and butterflies mate. And so on.

Stars can be compared to caterpillars, stories to butterflies. It’s easier to explain stars than to explain stories. And one of the things we don’t understand about stories is how we understand stories.

2:1 Now when Jesus was born in Bethlehem of Judaea in the days of Herod the king, behold, there came wise men from the east to Jerusalem, 2:2 Saying, Where is he that is born King of the Jews? for we have seen his star in the east, and are come to worship him. 2:3 When Herod the king had heard these things, he was troubled, and all Jerusalem with him. 2:4 And when he had gathered all the chief priests and scribes of the people together, he demanded of them where Christ should be born. 2:5 And they said unto him, In Bethlehem of Judaea: for thus it is written by the prophet, 2:6 And thou Bethlehem, in the land of Juda, art not the least among the princes of Juda: for out of thee shall come a Governor, that shall rule my people Israel. 2:7 Then Herod, when he had privily called the wise men, enquired of them diligently what time the star appeared. 2:8 And he sent them to Bethlehem, and said, Go and search diligently for the young child; and when ye have found him, bring me word again, that I may come and worship him also. 2:9 When they had heard the king, they departed; and, lo, the star, which they saw in the east, went before them, till it came and stood over where the young child was. 2:10 When they saw the star, they rejoiced with exceeding great joy. 2:11 And when they were come into the house, they saw the young child with Mary his mother, and fell down, and worshipped him: and when they had opened their treasures, they presented unto him gifts; gold, and frankincense and myrrh. – From The Gospel According to Saint Matthew.

Ave Aves!

Front cover of Collins Bird Guide by Lars SvenssonCollins Bird Guide: The Most Complete Guide to the Birds of Britain and Europe (second edition), text and maps by Lars Svensson, illustrations and captions by Killian Mullarney and Dan Zetterström, with a significant contribution by Peter J. Grant, translated by David Christie and Lars Svensson (HarperCollins, 2009)

A literate musician can read a score and hear a symphony in his head. I wonder whether the mega-minds of the future will be able to do something similar with genomes: read a DNA recipe and see the animal or plant cooked from it. The mega-minds will need to know about the oven, that is, the womb, egg or seed, but then musicians need to know about instruments, not just notes. The code can’t exist in isolation: it needs a world to be realized in and a musician’s mind can mimic that world.

But mega-minds aren’t here yet for genetics, so we have to use books like this to see the product of DNA-recipes. Collins Bird Guide is effectively a genetic cook-book or genomic score, but we don’t see the naked genes, just the dish or symphony cooked or played from them. Lars Svensson describes thousands of birds of all shapes, sizes, colours, diets and habitats, from the huge golden eagle, Aquila chrysaetos, which can carry off a lamb, to the tiny goldcrest, Regulus regulus, which isn’t much bigger than a bumblebee. But these two, like all other birds, have a common ancestor: when you see a bird sitting in a tree, it is also, metaphorically speaking, sitting in a genetic tree whose twigs, branches and boughs spring from a single trunk. One DNA-recipe has turned into many under the influence of natural and sexual selection.

Birds, which often come in very distinct male and female forms, offer lots of good examples of sexual selection. One of the most spectacular examples isn’t native to the region covered by the book, but it has been introduced here. And so there are pleasant surprises in store for some European ornithophiles. I once came across a wild-living golden pheasant, Chrysolophus pictus, early one morning in a park in northern England. I thought for a moment that I was hallucinating: the bird has a crest of spun gold, a scarlet breast and belly, and an orange/black “nuchal cape”, or neck-feathers, that “can be raised like a fan when displaying” (“Partridges & Pheasants”, pg. 59). It also has yellow legs, blue wings and a long, attractively patterned tail. “Unmistakable!” notes the book.

That’s true of the ♂, at least. The ♀, whose eyes and brain are responsible for the spectacular appearance of the ♂, is undistinguished and similar to the ♀ of Lady Amherst’s pheasant, Chrysolophus amherstiae, whose ♂ is again “Unmistakable!”, thanks to the sexual selection of its ♀. These closely related species are native to eastern Asia and “occasionally hybridize” in Britain (pg. 59). In other words, their common ancestor was fairly recent and their DNA recipes can still work together. But these hybridizations may also be a function of small populations and restricted habitat in Britain. “Function” is the operative word: birds, like all other forms of life, are mechanisms with inputs, throughputs and outputs. For a pheasant, some of the input is sense-data. The throughput is the processing of sense-data in the brain. The output is behaviour: for example, mating with a less-than-ideal partner under the restricted conditions of Britain.

All this can be modelled mathematically, but in the widest and deepest sense it already is mathematical: the human invention of mathematics, with a small “m”, is a symbolic representation of Mathematics with a big “M”. Mathematical symbols represent entities and operations and are manipulated according to logical rules. This mimics the inter-play of entities in the real world, which are subject to the rules of logic implicit in physics and chemistry. Human mathematics is fallible, albeit self-correcting. The mathematics underlying reality realizes the pipe-dreams of the papacy and is infallible, in the sense that it never disobeys the rules by which it is governed.

But this infallible mathematics can fail the entities for whom it operates: birds can die young and fail to reproduce or have fewer offspring than their competitors. But this is the fuel of a larger mechanism: evolution, which is a mathematical process. Genes mutate and vary in frequency under the influence of natural and sexual selection, inter alia. Birds offer more good examples of the effects, because they have wings, beaks and feet. These are mathematical mechanisms, shaped by and for the physics of a particular environment: wings have input from the air and provide the output of flight. Or the output of swimming: some wings are adapted for movement underwater, as in the cormorants, or Phalacrocoracidae, whose beaks are adapted for seizing fish and feet for paddling.

Sample page from Collins Bird Guide by Lars Svensson

You can look through this book and survey the varying geometry of wings, beaks and feet, from gliding gulls to hovering warblers, from seed-cracking finches to flesh-tearing owls, from tiny-toed swifts to wading egrets. The tool-kit of the common ancestor has become many tool-kits and evolution has been morally neutral as it has worked its multiplicative magic. The feet of the odd and endearing wallcreeper, Tichodroma muraria, are adapted to clinging onto vertical rock; the feet of eagles and owls are adapted to puncturing nerve-filled flesh. And presumably each species enjoys using its adaptation. A distinct psychology will accompany each distinct wing, beak and foot, because no organ can change in isolation: it is evolving within the environment of the body, influencing and influenced by other organs, in particular the brain.

But changes in the brain aren’t easily visible. If they were, some parts of evolution would be much less controversial: racial differences in human intelligence, for example. But races differ in other ways: in their attitudes to animals, for example. One generalization is that northern Europeans like listening to songbirds and southern Europeans like shooting them. So it’s not surprising that this book was originally published in Swedish as Fågelguiden, Europas och Medelhavsområdets fåglar i fält (1999). It would also be interesting to see the statistics of ornithological publishing in Europe. Those statistics will reflect genetic differences in the white European race, and so will readers’ reactions to the book.

My interest is partly aesthetic and mathematical, for example, and I quail at the thought of learning the differences between what bird-watchers call “little brown jobs”: the various kinds of warbler are hard enough to tell apart in pictures, let alone in the wild. But things can get even worse at night: Lars Svensson notes of Savi’s warbler, Locustella luscinioides, that “A possible confusion risk at distance and at night in S and C Europe is the mole-cricket” (“Warblers”, pg. 318). Birdsong and bird-cries are another aspect of ornitho-mathematics, but it’s hard to represent them in print: “kru-kih karra-kru-kih chivi trü chivi chih” (clamorous reed warbler, Acrocephalus stentoreus, pg. 322), “glipp-glipp-glipp” (common crossbill, Loxia curvirostra, pg. 386), “trrsh, trre-trre-trre-rrerrerre” (sand martin, Riparia riparia, pg. 258), “pyük…popopo…” (pygmy owl, Glaucidium passerinum, pg. 226), “brrreep, bip bip bip” (red phalarope, Phalaropus fulicarius, pg. 162), and so on.

In an electronic manual of ornithology, you’d be able to hear the songs, rather than imagine them, but electronic manuals, by offering more, in some ways offer less. Because the book has so many species to cover, it can’t describe any species in detail. So there are occasional fleeting comments like this:

Asian Desert Warbler, Sylvia nana V*** [= rare vagrant in northern Europe]… has the peculiar habit of sometimes “tailing” the Desert Wheatear [Oenanthe deserti] (“Warblers”, pg. 310-1)

The accompanying illustration shows a desert warbler standing under a small bush and peering out at a nearby wheatear. It’s anthropomorphic and anthropocentric to be amused by the behaviour, but ornithology is a human invention and humans don’t have to be purely scientific. I get a boy-racer thrill from another “V***” bird, the white-throated needletail, Hirundapus caudacutus:

Big, with heavy compact body, neckless, stub-tailed (shape somewhere between fat cigar and “flying barrel”). Flight impressively fast, the bird seems to draw easily away from other swifts (though these are still fast flyers!). (“Vagrants”, pg. 415)

That I would like to see. In the meantime, I have this book and the multiplex mutational mathematics it captures in pictures and words.

Neuclid on the Block

How many blows does it take to demolish a wall with a hammer? It depends on the wall and the hammer, of course. If the wall is reality and the hammer is mathematics, you can do it in three blows, like this:

α’. Σημεῖόν ἐστιν, οὗ μέρος οὐθέν.
β’. Γραμμὴ δὲ μῆκος ἀπλατές.
γ’. Γραμμῆς δὲ πέρατα σημεῖα.

1. A point is that of which there is no part.
2. A line is a length without breadth.
3. The extremities of a line are points.

That is the astonishing, world-shattering opening in one of the strangest – and sanest – books ever written. It’s twenty-three centuries old, was written by an Alexandrian mathematician called Euclid (fl. 300 B.C.), and has been pored over by everyone from Abraham Lincoln to Bertrand Russell by way of Edna St. Vincent Millay. Its title is highly appropriate: Στοιχεῖα, or Elements. Physical reality is composed of chemical elements; mathematical reality is composed of logical elements. The second reality is much bigger – infinitely bigger, in fact. In his Elements, Euclid slipped the bonds of time, space and matter by demolishing the walls of reality with a mathematical hammer and escaping into a world of pure abstraction.

• Continue reading Neuclid on the Block

Flesh and Binary

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 from ancient Rome

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)

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.


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%.