The World as Worm

In “Hymn to Herm”, I wrote about a religion based on √2, or the square root of two, the number that, multiplied by itself, equals 2. In the religion, neophytes learn the mystery and majesty of this momentous number when they try to calculate its exact value. The calculation involves adding and subtracting fractions based on powers of two. The first step is this: 1 x 1 = 1. So that’s too small. Add 1/2^1 = ½ and re-multiply: 1½ x 1½ = 2¼. Too big. So subtract 1/2^2 = ¼, and re-multiply. 1¼ x 1¼ = 1+9/16. Too small. Add 1/8 and re-multiply. 1+3/8 x 1+3/8 = 1+57/64. Too small again. Add 1/16 and re-multiply. And so on.

In effect, what the neophytes are doing is calculate the digits of √2 in binary, or base two. When the multiplication is too small, put a 1; when it’s too big, put a 0. Like this:

1 x 1 = 1 < 2, so √2 ≈ 1·…
1½ x 1½ = 2¼ > 2, so √2 ≈ 1·0…
1¼ x 1¼ = 1+9/16 < 2, so √2 ≈ 1·01…
(1+3/8) x (1+3/8) = 1+57/64 < 2, so √2 ≈ 1·011…
(1+7/16) x (1+7/16) = 2+17/256 > 2, so √2 ≈ 1·0110…
(1+13/32) x (1+13/32) = 1+1001/1024 < 2, so √2 ≈ 1.01101…
(1+27/64) x (1+27/64) = 2+89/4096 > 2, so √2 ≈ 1.011010…
(1+53/128) x (1+53/128) = 1+16377/16384 < 2, so √2 ≈ 1·0110101…
(1+107/256) x (1+107/256) = 2+697/65536 > 2, so √2 ≈ 1·01101010…
(1+213/512) x (1+213/512) = 2+1337/262144 > 2, so √2 ≈ 1·011010100…
(1+425/1024) x (1+425/1024) = 2+2449/1048576 > 2, so √2 ≈ 1·0110101000…
(1+849/2048) x (1+849/2048) = 2+4001/4194304 > 2, so √2 ≈ 1·01101010000…
(1+1697/4096) x (1+1697/4096) = 2+4417/16777216 > 2, so √2 ≈ 1·011010100000…
(1+3393/8192) x (1+3393/8192) = 1+67103361/67108864 < 2, so √2 ≈ 1·0110101000001…

Mathematically naïve neophytes, seeing the process miss 2 by smaller and smaller amounts on either side, might imagine that eventually the exact root will appear and the calculations end. But they would be wrong. They could work a year or a million years: they would never calculate the exact square root of two. There is no ratio of whole numbers, a/b, such that a^2/b^2 = 2. In other words, √2 is an irrational number, or number that can’t be represented as a ratio of integers (please see appendix for the proof).

This discovery, made by Greek mathematicians more than two millennia ago, is both mind-boggling and world-shattering. In fact, it’s mind-boggling in part because it’s world-shattering. √2 shatters the world because the world is too small to contain it: in the words of the Cult of Infinite Hermaphrodites, “Were the sky all parchment, the seas all ink, and gulls all plucked for quills”, the square root of two could not be recorded in full. This is far more certain than tomorrow’s sunrise, because predicting tomorrow’s sunrise depends on fallible scientific reasoning from incomplete knowledge. Proving the irrationality of √2 depends on infallible mathematical reasoning.

At least, it’s as close to infallible as human beings can get. But that’s another part of what is mind-boggling about √2. A finite, feeble human being, with a speck of soon-decaying brain, can prove the existence of things larger than the universe. A few binary digits of √2 are shown above. Here are a few more:

1·
0110101000001001111001100110011111110011101111001100100100001000
1011001011111011000100110110011011101010100101010111110100111110
0011101011011110110000010111010100010010011101110101000010011001
1101101000101111010110010000101100000110011001110011001000101010
1001010111111001000001100000100001110101011100010100010110000111
0101000101100011111111001101111110111001000001111011011001110010 
0001111011101001010100001011110010000111001110001111011010010100 
1111000000001001000011100110110001111011111101000100111011010001 
1010010001000000010111010000111010000101010111100011111010011100 
1010011000001011001110001100000000100011011110000110011011110111 
1001010101100011011110010010001000101101000100001000101100010100 
1000110000010101011110001110010001011110111110001001110001100111 
1000110110101011010100010100011100010111011011111101001110111001 
1001011001010100110001101000011001100011111001111001000010011011 
1110101001011110001001000001111100000110110111001011000001011101 
1101010101001001010000010001001100100000100000011001010010010101 
0000001001110010100101010110110110110001111110100001110111111011 
1110100110100111010000000101100111010111100100100111110000011000 
1000010011001001101101010111100110101010010100010110110010100011 
0111000110011110011010000011011011011111000001000110110110001110 
0000001000001001101110000000001111111100011001000110101001011110 
0110011001010100101111010011111011110111101101000011110101111111 
1110110101000011011111000111111110010100010001000010011000001111 
1011110101000000110001001000001111101111010101010000001110000101 
1000001111111001011110111011110101000101111011111011100001100110 
0011000100000111000101000101110101011111111010111110011101100101 
1010010010011110100101001110110001111111010110010111000100000101 
1111101111111100001011100001111110100111011000111110111100000001 
1111001101011001100111001000001011110010111111100101000000001011 
1000010010001100111100001011110100100101001010101110000001000110 
1011111110011111000111101111011110010100011111010100011001110110 
1001101011111000110000010100101111001100011001111100011111000010 
1001000010111110011101101001001010011011000001010111100011000001 
0000101101011000010011111011010010000111110010010010010011110101 
1011011100011111100000101101110011010010100100000011011000001001 
1101111011101000100100010010100110000011110101001110101010101101 
0000111011101010001100100001111101110100100010011111010001101010 
0111111010010000001100001011111000100000111110110111011010010100 
1110111110110101100011001001100110000100110011011101011100001010 
0001110110101001000001000101110000111101000100110011101000000110 
1000010000100011110101101110001110000011000000111101100100000001 
1011101010011101101000110100011101100110100001000111100101101100 
0101110011010101100101110010110111000000111111110011010101000000 
1100001101000001001010010100001011010110010000000110000100000001 
1110111101101111110001101101111010010001000101001010001010110100 
1111001001001000110001101000100111000110000000001011101101000000 
1010100010110101011010110000010000011111110101011101111001101110 
0000110111010000110001100110110101001000001100011111111001111111 
1111111101010111010101111110010001110001000010011000000011001101 
1011110101011100001001101000010010000101110110100101111010010001 
1011001111100010111100100000010110110111001001110010010110111001 
0111000111010110000010100001111110001000100011110000100010100000 
1010011011100001000000001100110011101101110000101100111001011011 
1101100110001010111011100111000111100100001011100010011010001101 
0011011110100110000001110010111100100010000000100011010001100001 
0011111111111100001000100100010100110100001110011110101010010111 
1010100110011001101101101100100111100011110011100111000111111001 
0100110101100000100100101010110011100001001000001010101110001110 
0101010100001110000011010101010100010001011010001000011000110001 
0111011110001100111101100000001101010000110100000010111111101000 
0101111100101001111011001000101111100101110001110010101110000000 
0111101011110101011101110001101110000010010110110011000010100000 
1110011110000011011101101010100100011100000010001100011010100111 
1111000011111000111100110010001110110011011000101000000111010010 
0010010101101000100111000000101101011010100000100000010001111101 
1011100110001001111101100011101010001010011001001110100001010001 
1001101111000000110100001100000111100010001000101000000001001000 
0100110110010100111101001111100110111011001111010100101100110001 
1101010010001001110101110101001000110001101101011100011000110011 
1100010010000000110010010110101111100101010010011011111101011101 
1001011001100111100010110100110100101100010011011101101010000110 
0111101111011000111001001000000000101001111111101010100011001000 
0001011100110101011001111100001010111010001111010011110011101001 
1101111111100000101111010001101101001101110101110111000100010111 
1000000001010111101101101001010110110111111010101111000110110000 
0101110000100010110010001101010111111110111010111101000001110111 
1111111011001001011011011011100011110111011110001111110000011100 
0010101110111011110011100001101101001001111010111111010110101111 
0100010001100000100010000010100101011000101011011101000000011100 
1010011111110001101101101011110000001011011111101100000110111100 
0110111000001010011011101101101111000110011111111000010110110010 
0111010011100000100001100001101100111010000100110111010101110001 
1011000101100101010010011000011100111101001000010001110001101010 
1010111001101001110110000000000111100101011110010100010001011011 
1100011000001010001111100000101001001111110110001001011010001110 
1011011110010100101111011100011100000010110101101001010001011101 
1010100101001011000001001010010001000000110010101011110010010100 
0011100001111100001111010010011011111101000011110011101111101000 
1010111101100011000001011010010100111010000101110111001010001000 
1010110010100001001111111011010000000110110010011000001010010001 
0101110110000011101110100000110100110101010110001101100000011101 
1101000100010101100111101001011001000011111010101010001001111110 
1011011101110101011110100010000001010010100101110101101101101111 
0100101010001000100111100011110100001001001010111011000111000110 
1000010101001000000011011100001011101001100110010100011110110011 
0111001011011110110110100000010111100010000110010010111110010101 
1011000110111001001001100101000100101011010000000100110000110011
0001100000011101011...

The distribution of 1’s and 0’s seems effectively random, as though the God of Mathematics were endlessly tossing a coin, putting 1 for heads, 0 for tails. Yet √2 is the opposite of a random number. Change a single digit anywhere and it ceases to be √2. Every 1 and every 0 is rigidly determined by “unalterable law”. So are the position and magnitude of the digits of √2 in every other base. Here, for example, is √2 in base 4:

1·
112220021321212133303233030210020230233230103121232222111133
103320322313230011311010213131100212131220233112100230012121
303020222211133210012002013111...

Another word for base-4 is DNA: genes are in fact written in a base-4 code based on the chemicals guanine, adenine, thymine and cytosine, or G, A, T, C for short. If the digits of √2 are truly random, in the statistical sense, then all genomes, actual and potential, occur somewhere along its length: yours, mine, the Emperor Heliogabalus’s, Bilbo Baggins’, the sabre-toothed tiger’s, the dodo’s, and so on. But almost all the “DNA” of √2 in base-4 will be meaningless: although √2 is the opposite of random, it is effectively a typing chimpanzee. Or a typing worm – a type-worm. √2 is like an endless worm that types out its own segments on a typewriter with two keys (for binary numbers) or four keys (for quaternary numbers) or ten keys (for decimal numbers) and so on.

But √2 doesn’t just encode the genomes of individual people, animals and plants: it encodes everything they do throughout their lives. In fact, it encodes the entire universe. And perhaps the universe is √2 or some number like it. Perhaps, in some sense, everything exists within the digits of an irrational number, or a sufficiently large rational number. If so, then √2 has become aware of itself through human beings: the World as Worm has bitten its own tail.

Appendix: Proof of the irrationality of √2

1. Suppose that there is some ratio, a/b, such that

2. a and b have no factors in common and

3. a^2/b^2 = 2.

4. It follows that a^2 = 2b^2.

5. Therefore a is even and there is some number, c, such that 2c = a.

6. Substituting c in #4, we derive (2c)^2 = 4c^2 = 2b^2.

7. Therefore 2c^2 = b^2 and b is also even.

8. But #7 contradicts #2 and the supposition that a and b have no factors in common.

9. Therefore, by reductio ad absurdum, there is no ratio, a/b, such that a^2/b^2 = 2. Q.E.D.

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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.

Roo’s Who

11 is a prime number, divisible by only itself and 1. If you add its digits, 1 + 1, you get 2. 11 + 2 = 13, another prime number. And 13 + (1 + 3) = 17, a third prime number. And there it ends, because 17 + (1 + 7) = 25 = 5 x 5. I call (11, 13, 17) kangaroo primes, because one jumps to another. In base 10, the record for numbers below 1,000,000 is this:

6 primes: 516493 + 28 = 516521 + 20 = 516541 + 22 = 516563 + 26 = 516589 + 34 = 516623.

In base 16, the record is this:

8 primes: 97397 = 17,C75[b=16] + 32 = 97429 = 17,C95[b=16] + 34 = 97463 = 17,CB7[b=16] + 38 = 97501 = 17,CDD[b=16] + 46 = 97547 = 17,D0B[b=16] + 32 = 97579 = 17,D2B[b=16] + 34 = 97613 = 17,D4D[b=16] + 38 = 97651 = 17,D73[b=16].

Another kind of kangaroo prime is found not by adding the sum of digits, but by adding their product, i.e., the result of multiplying the digits (except 0). 23 + (2 x 3) = 29. 29 + (2 x 9) = 47. But 47 + (4 x 7) = 75 = 3 x 5 x 5. So (23, 29, 47) are kangaroo primes too. In base 10, the record for numbers below 1,000,000 is this:

9 primes: 524219 + 720 = 524939 + 9720 = 534659 + 16200 = 550859 + 9000 = 559859 + 81000 = 640859 + 8640 = 649499 + 69984 = 719483 + 6048 = 725531.

But what about subtraction? For a reason I don’t understand, subtracting the digit-sum doesn’t seem to create any kangaroo-primes in base 10. But 11 in base 8 is 13 = 1 x 8^1 + 3 x 8^0 and 13[b=8] – (1 + 3) = 7. In base 2, this sequence appears:

1619 = 11,001,010,011[b=2] – 6 = 1613 = 11,001,001,101[b=2] – 6 = 1607 = 11,001,000,111[b=2] – 6 = 1601 = 11,001,000,001[b=2] – 4 = 1597.

However, subtracting the digit-product creates kangaroo-primes in base 10. For example, 23 – (2 x 3) = 17. The record below 1,000,000 is this (when 0 is found in the digits of a number, it is not included in the multiplication):

7 primes: 64037 – 504 = 63533 – 810 = 62723 – 504 = 62219 – 216 = 62003 – 36 = 61967 – 2268 = 59699.

Base 2 also provides examples of addition/subtraction pairs of kangaroo-primes, like this:

3 = 11[b=2] + 2 = 5 = 101[b=2] | 5 = 101[b=2] – 2 = 3

277 = 100,010,101[b=2] + 4 = 281 = 100,011,001[b=2] | 281 – 4 = 277

311 = 100,110,111[b=2] + 6 = 317 = 100,111,101[b=2] | 317 – 6 = 311

In base 10, addition/subtraction pairs are created by the digit-product, like this:

239 + 54 = 293 | 293 – 54 = 239
563 + 90 = 653 | 653 – 90 = 563
613 + 18 = 631 | 631 – 18 = 613
2791 + 126 = 2917 | 2917 – 126 = 2791
3259 + 270 = 3529 | 3529 – 270 = 3259
5233 + 90 = 5323 | 5323 – 90 = 5233
5297 + 630 = 5927 | 5927 – 630 = 5297
6113 + 18 = 6131 | 6131 – 18 = 6113
10613 + 18 = 10631 | 10631 – 18 = 10613
12791 + 126 = 12917 | 12917 – 126 = 12791

You could call these boxing primes, like boxing kangaroos. The two primes in the pair usually have the same digits in different arrangements, but there are also pairs like these:

24527 + 560 = 25087 | 25087 – 560 = 24527
25183 + 240 = 25423 | 25423 – 240 = 25183
50849 + 1440 = 52289 | 52289 – 1440 = 50849

The Isle of the Torturer

Front cover of The Doors of Perception by Aldous HuxleyAldous Huxley (1894-1963), the author of Brave New World (1932) and After Many A Summer (1939), is a bad but interesting writer. One of his bad but interesting books is The Doors of Perception (1954), in which he discusses mescalin and mysticism. I like this comment a lot:

In a world where education is predominantly verbal, highly educated people find it all but impossible to pay serious attention to anything but words and notions. There is always money for, there are always doctorates in, the learned foolery of research into what, for scholars, is the all-important question: Who influenced whom to say what when? (Op. cit., pg. 61 of the 1985 Panther paperback)

It’s an insightful and entertaining point. There are analogous questions in biology: what genes influence what and where do they come from? But biologists can answer questions like that much more precisely, because genes are physical entities, susceptible to precise chemical analysis. They can be easily mathematized, turned into statistics, tested for correlations and other patterns. We can’t yet do that to “words and notions” and get the same precise answers. That’s why it’s sometimes easier to answer questions about human prehistory over hundreds of millennia than about human history over decades. For example, we now know that ancient human beings migrating from Africa picked up genes from Neanderthals and a lesser-known group called the Denisovans, while those human beings that stayed behind in Africa picked up genes from other archaic hominids.

But we don’t know whether the Californian author Clark Ashton Smith (1894-1961) influenced the British author Ian Fleming (1908-64). At least, I don’t know, because I think I am the first person to raise the possibility. After all, they aren’t obvious literary associates: Smith wrote highly ornate fantasy set on a quasi-mediaeval far future earth; Fleming wrote vice-and-violence spy-thrillers set in contemporary Europe, America and Japan. And in the Caribbean, which is why the question of CAS’s influence occurred to me. Fleming was the creator of James Bond and one of his Bond adventures, published in 1958, is called Dr. No. It is named after its anti-hero, a Chinese-German megalomaniac called Doctor Julius No who lives on the mountainous island of Crab Key near Jamaica. He is conducting research into the human capacity for suffering:

“Silence!” Doctor No’s voice was the crack of a whip. “Enough of this foolery. Of course it will hurt. I am interested in pain. I am also interested in finding out how much the human body can endure. From time to time I make experiments on those of my people who have to be punished. And on trespassers like yourselves. You have both put me to a great deal of trouble. In exchange I intend to put you to a great deal of pain. I shall record the length of your endurance. The facts will be noted. One day my findings will be given to the world. Your deaths will have served the purposes of science.” (Op. cit., ch. XVI, “Horizons of Agony”)

Front cover of Dr No (Pan paperback)

He is talking to James Bond and Bond’s companion, the beautiful blonde Honeychile Rider. Bond will have to run an “obstacle race, an assault course against death”, which is designed to be unbeatable. Meanwhile, Honeychile will be “pegged out” on the mountain-side as part of another experiment. With sadistic relish, Doctor No reveals what will happen to her:

“This island is called Crab Key. It is called by that name because it is infested with crabs, land crabs — what they call in Jamaica ‘black crabs’. You know them. They weigh about a pound each and they are as big as saucers. At this time of year they come up in thousands from their holes near the shore and climb up towards the mountain. … The crabs devour what they find in their path. … And tonight, in the middle of their path, they are going to find the naked body of a woman pegged out — a banquet spread for them — and they will feel the warm body with their feeding pincers, and one will make the first incision with his fighting claws and then… and then…”

And then Honeychile faints. But, like all the best super-villains, Doctor No mixes sensibility with his sadism. This is what Bond and Honeychile first see when they step from a lift into the heart of Doctor No’s underground lair:

It was a high-ceilinged room about sixty feet long, lined on three sides with books to the ceiling. At first glance, the fourth wall seemed to be made of solid blue-black glass. … Bond’s eye caught a swirl of movement in the dark glass. He walked across the room. A silvery spray of small fish with a bigger fish in pursuit fled across the dark blue. … What was this? An aquarium? Bond looked upwards. A yard below the ceiling, small waves were lapping at the glass. Above the waves was a strip of greyer blue-black, dotted with sparks of light. The outlines of Orion were the clue. This was not an aquarium. This was the sea itself and the night sky. The whole of one side of the room was made of armoured glass. They were under the sea, looking straight into its heart, twenty feet down.

Front cover of Dr No (Pan paperback)

Bond and the girl stood transfixed. As they watched, there was the glimpse of two great goggling orbs. A golden sheen of head and deep flank showed for an instant and was gone. A big grouper? A silver swarm of anchovies stopped and hovered and sped away. The twenty-foot tendrils of a Portuguese man-o’-war drifted slowly across the window, glinting violet as they caught the light. Up above there was the dark mass of its underbelly and the outline of its inflated bladder, steering with the breeze.

Bond walked along the wall, fascinated by the idea of living with this slow, endlessly changing moving picture. A big tulip shell was progressing slowly up the window from the floor level, a frisk of demoiselles and angel fish and a ruby-red moonlight snapper were nudging and rubbing themselves against a corner of the glass and a sea centipede quested along, nibbling at the minute algae that must grow every day on the outside of the window. (Op. cit., ch. XIV, “Come Into My Parlour”)

Yes, the sea-window is a fascinating idea, but where does the idea come from? Here is another literary character, King Fulbra, in the underground domain of another sadist:

After descending many stairs, they came to a ponderous door of bronze; and the door was unlocked by one of the guards, and Fulbra was compelled to enter; and the door clanged dolorously behind him. The chamber into which he had been thrust was walled on three sides with the dark stone of the island, and was walled on the fourth with heavy, unbreakable glass. Beyond the glass he saw the blue-green, glimmering waters of the undersea, lit by the hanging cressets of the chamber; and in the waters were great devil-fish whose tentacles writhed along the wall; and huge pythonomorphs with fabulous golden coils receding in the gloom; and the floating corpses of men that stared in upon him with eyeballs from which the lids had been excised.

That is from Clark Ashton Smith’s short story “The Isle of the Torturers” (1933), which was originally published in the pulp magazine Weird Tales. Like the evil King Ildrac of Smith’s story, Doctor No lives on an island, tortures people and has a glass wall set onto the undersea. But that is not all they have in common. Here is Fleming’s description of Doctor No:

He stood looking at them benignly, with a thin smile on his lips. … (Bond was to get used to that thin smile) … Bond’s first impression was of thinness and erectness and height. Doctor No was at least six inches taller than Bond, but the straight immovable poise of his body made him seem still taller. The head also was elongated and tapered from a round, completely bald skull down to a sharp chin so that the impression was of a reversed raindrop — or rather oildrop, for the skin was of a deep almost translucent yellow.

It was impossible to tell Doctor No’s age: as far as Bond could see, there were no lines on the face. It was odd to see a forehead as smooth as the top of the polished skull. Even the cavernous indrawn cheeks below the prominent cheekbones looked as smooth as fine ivory. There was something Dali-esque about the eyebrows, which were fine and black, and sharply upswept as if they had been painted on as makeup for a conjurer. Below them, slanting jet black eyes stared out of the skull. They were without eyelashes. (ch. XIV, “Come Into My Parlour”)

When King Fulbra is shipwrecked on Uccastrog, the Isle of the Torturers, this is his first sight of its inhabitants:

The people drew near, thronging about the barge and the galley. They wore fantastic turbans of blood-red, and were clad in closely fitting robes of vulturine black. Their faces and hands were yellow as saffron; their small and slaty eyes were set obliquely beneath lashless lids; and their thin lips, which smiled eternally, were crooked as the blades of scimitars. (“The Isle of the Torturers”)

Fulbra surrenders to them with misgivings and is taken to the throne-room of his fellow king, where his misgivings grow:

Soon he came into the presence of Ildrac, who sat on a lofty brazen chair in a vast hall of the palace. Ildrac was taller by half a head than any of his followers; and his features were like a mask of evil wrought from some pale, gilded metal; and he was clad in vestments of a strange hue, like sea-purple brightened with fresh-flowing blood. About him were many guardsmen, armed with terrible scythe-like weapons; and the sullen, slant-eyed girls of the palace, in skirts of vermilion and breast-cups of lazuli, went to and fro among huge basaltic columns. About the hall stood numerous engineries of wood and stone and metal such as Fulbra had never beheld, and having a formidable aspect with their heavy chains, their beds of iron teeth and their cords and pulleys of fish-skin. (Op. cit.)

Master of the Crabs from Weird TalesThe similarities between Doctor No and “The Isle of the Torturers” are obvious. But how likely is it that Fleming had read Smith’s story and then incorporated elements of it into his novel, consciously or unconsciously? Smith wrote of a tall, slant-eyed, yellow-skinned king who ruled an island and oversaw ingenious tortures. Fleming wrote of a tall, slant-eyed, yellow-skinned scientist who ruled an island and oversaw ingenious tortures. The scientist also used crabs as weapons, like the wizard Sarcand in Smith’s story “The Master of the Crabs” (1948):

So saying, he raised his hand and described a peculiar sign with the index finger, on which the ring flashed like a circling orb. The double column of crabs suspended their crawling for a moment. Then, moved as if by a single impulse, they began to scuttle toward us, while others appeared from the cavern’s entrance and from its inner recesses to swell their rapidly growing numbers. They surged upon us with a speed beyond belief, assailing our ankles and shins with their knife-sharp pincers as if animated by demons. I stooped over, striking and thrusting with my arthame; but the few that I crushed in this manner were replaced by scores; while others, catching the hem of my cloak, began to climb it from behind and weigh it down. Thus encumbered, I lost my footing on the slippery ground and fell backward amid the scuttling multitude. (“The Master of the Crabs”)

And that doesn’t exhaust the parallels between Smith’s stories and Fleming’s novel. Here is more of Doctor No’s appearance:

The bizarre, gliding figure looked like a giant venomous worm wrapped in grey tin-foil, and Bond would not have been surprised to see the rest of it trailing slimily along the carpet behind. (ch. XIV, “Come Into My Parlour”)

This is from Smith’s story “The Coming of the White Worm” (1941):

At sight of this entity, the pulses of Evagh were stilled for an instant by terror; and, following quickly upon the terror, his gorge rose within him through excess of loathing. In all the world there was naught that could be likened for its foulness to Rlim Shaikorth. Something he had of the semblance of a fat white worm; but his bulk was beyond that of the sea-elephant. His half-coiled tail was thick as the middle folds of his body; and his front reared upward from the dais in the form of a white round disk, and upon it were imprinted vaguely the lineaments of a visage belonging neither to beast of the earth nor ocean-creature. (“The Coming of the White Worm”)

I can’t claim that it’s probable that Fleming had read Smith or even a strong possibility that he did so, but the shared elements are suggestive. The fact that Doctor No and King Ildrac are both tall could easily, on its own, be a coincidence: size is an obvious and widely used marker of importance and dominance. But each additional similarity reduces the possibility that Fleming was inventing Doctor No ex nihilo. He was certainly familiar with American popular culture and the cheap publications in which Smith’s work appeared. Here are descriptions from two more Bond novels:

There were two or three all-night diners to choose from and they [Bond and a girl called Solitaire] pushed through the door that announced “Good Eats” in the brightest neon. It was the usual sleazy food-machine — two tired waitresses behind a zinc counter loaded with cigarettes and candy and paper-backs and comics. (Live and Let Die, 1954, Chapter XII, “The Everglades”)

At 12.30 they [Bond and his companion Felix Leiter] stopped for lunch at The Chicken in the Basket, a log-built Frontier-style road-house with standard equipment — a tall counter covered with the best-known proprietary brands of chocolates and candies, cigarettes, cigars, magazines and paperbacks, a juke box blazing with chromium and coloured lights that looked like something out of science fiction … (Diamonds Are For Ever, 1956, Chapter 10, “Studillac to Saratoga”)

Smith’s themes – death, pain and suffering – would certainly have appealed to Fleming, who practised sado-masochism with his wife Ann and returned again and again to those themes in his Bond books. This is from You Only Live Twice (1964):

“That is so. You are indeed a genius, lieber Ernst. You have already established this place as a shrine to death for evermore. People read about such fantasies in the works of Poe, Lautréamont, de Sade, but no one has ever created such a fantasy in real life. It is as if one of the great fairy tales has come to life. A sort of Disneyland of Death. But of course,” she hastened to add, “on an altogether grander, more poetic scale.” (Op. cit., Part 2, ch. 17, “Something Evil Comes This Way”)

So it seems that Fleming had read and appreciated Poe and Lautréamont. If he had come across Smith’s work during his trips to America, I suggest that he would not have dismissed it. And it may indeed have influenced his novel Dr. No. Perhaps literary forensics will be able to confirm or reject the hypothesis in future by analysing patterns in Smith’s and Fleming’s work.

At present, the influence of the obscure Californian Smith on the world-famous Briton Fleming remains just that: a hypothesis. But I think there is a stronger case for another influence, this time flowing in the opposite direction: from world-famous Briton to obscure Californian. I quoted above from “The Master of the Crabs”. Here is some more:

Even as we veered landward through the crystalline calm, there was a sudden seething and riffling about us, as if some monster had risen beneath. The boat began to shoot with plummet-like speed toward the cliffs, the sea foaming and streaming all around as though some kraken were dragging us to its caverned lair. Borne like a leaf on a cataract, we toiled vainly with straining oars against the ineluctable current.

Heaving higher momentarily, the cliffs seemed to shear the heavens above us, unscalable, without ledge or foothold. Then, in the sheer wall, appeared the low, broad arch of a cavern-mouth that we had not discerned heretofore, toward which the boat was drawn with dreadful swiftness.

“It is the entrance!” cried the Master. “But some wizard tide has flooded it.”

We shipped our useless oars and crouched down behind the thwarts as we neared the opening: for it seemed that the lowness of the arch would afford bare passage to our high-built prow. There was no time to unstep the mast, which broke instantly like a reed as we raced on without slackening into blind torrential darkness. (“The Master of the Crabs”)

NKing Solomon's Mines by H. Rider Haggardext comes the encounter with giant crabs quoted previously. So Smith’s short story describes a boat drawn by an irresistible current beneath a low entrance to an encounter with giant crabs. Now try H. Rider Haggard’s Allan Quatermain (1887), a sequel to King Solomon’s Mines (1885). Haggard’s adventurers are hunting wildfowl on a lake when they are caught in a strong current:

We realized our danger now and rowed, or rather paddled, furiously in our attempt to get out of the vortex. In vain; in another second we were flying straight for the arch like an arrow, and I thought that we were lost. Luckily I retained sufficient presence of mind to shout out, instantly setting the example by throwing myself into the bottom of the canoe, “Down on your faces — down!” and the others had the sense to take the hint. In another instant there was a grinding noise, and the boat was pushed down till the water began to trickle over the sides, and I thought that we were gone. But no, suddenly the grinding ceased, and we could again feel the canoe flying along [on an underground river]. … (Allan Quatermain, Chapter IX, “Into the Unknown”)

By the river’s edge was a little shore formed of round fragments of rock washed into this shape by the constant action of water, and giving the place the appearance of being strewn with thousands of fossil cannon balls. … And here … we determined to land, in order to rest ourselves a little after all that we had gone through … It was a dreadful place, but it would give an hour’s respite from the terrors of the river, and also allow of our repacking and arranging the canoe. Accordingly we selected what looked like a favourable spot, and with some little difficulty managed to beach the canoe and scramble out on to the round, inhospitable pebbles. … The gloom was so intense that we could scarcely see the way to cut our food and convey it to our mouths. Still we got on pretty well, till I happened to look behind me — my attention being attracted by a noise of something crawling over the stones, and perceived sitting upon a rock in my immediate rear a huge species of black freshwater crab, only it was five times the size of any crab I ever saw. This hideous and loathsome-looking animal had projecting eyes that seemed to glare at one, very long and flexible antennae or feelers, and gigantic claws. Nor was I especially favoured with its company. From every quarter dozens of these horrid brutes were creeping up, drawn, I suppose, by the smell of the food, from between the round stones and out of holes in the precipice. (Allan Quatermain, Chapter X, “The Rose of Fire”)

The similarities between Allan Quatermain and “The Master of the Crabs” seem stronger and clearer than those between “The Isle of the Torturers” and Dr. No. Haggard is widely read even today, in the twenty-first century, and was hugely popular in Smith’s lifetime. It is very difficult to believe that Smith was not familiar with most or all of his work. But if he borrowed ideas from Allan Quatermain, he transformed what he borrowed and produced a better and subtler story. He was, in fact, a much better writer than his probable influence H. Rider Haggard and his putative influencee Ian Fleming. That is part of why he achieved little of their success: he wrote too well, transcending his genre but not the ghetto of his genre.

That’s my opinion, at least, but I can’t prove it, any more than I prove that Smith influenced Fleming or Haggard influenced Smith. Nevertheless, I would argue that the quality of a literary work is a mathematical phenomenon, dependant for its power on the way it manipulates the implicit mathematics of the language faculty in a reader’s brain. Given this, I think that it will some day be possible to analyse two texts mathematically and give objective reasons for preferring one to another. If that happens, I think Smith will be shown to be a literary equivalent of Mozart or Bach, far above the entertaining but crude pop or rock’n’roll of Haggard and Fleming.

It’s already apparent that the patterns of literature are akin to the patterns of music: like poetry, prose has rhythms, melodies, motifs and so on. Words are equivalent to notes, or rather to chords. A word has both a sound and a meaning, or layers of meaning. On the page or screen it has a shape too, but how important word-shapes are in good writing is a difficult question. Shape may be most important in onomastics, or naming systems. Compare two names: Katherine-with-a-K and Catherine-with-a-C. The letter C is more attractive than the letter K and I think the second spelling of the name is more attractive too. So would Smith’s Isle of Torture “Uccastrog”, with a double-c, be more effective as “Ukkastrog”, with a double-k? Or does the guttural sound clash effectively with the elegant double-c?

Gullivers Travels by Jonathan Swift

I think the latter and I think “Uccastrog” is an example of Smith’s onomastic skill. But the name has echoes of Gulliver’s Travels (1726), which describes the “great prophet Lustrog” (pt. 1, ch. IV) and the islands Luggnagg and Glubbdubdrib (pt. III). Smith certainly read Gulliver’s Travels and certainly shared Swift’s sardonic and satirical tastes. But how much did Swift shape those tastes, rather than merely chime with them? As we saw at the beginning, Aldous Huxley playfully reduced literary scholarship to a game of “Who influenced whom to say what when?” But it’s also a case of “What influenced whom to be influenced by whom?” Did Swift shape Smith, or merely chime with what was already there? If Clark Ashton Smith and his Isle of Torture did not influence Ian Fleming and Dr. No, how we do explain the shared elements? The shared personality of Smith and Fleming? Their shared genetics? Their shared reading of yet another text of which I am not aware? The questions can unwind for ever. But as we wait for science to answer them, the texts and their dark pleasures remain.

Keeping It Gweel

Gweel & Other Alterities, Simon Whitechapel (Ideophasis Press, 2011)

This review is a useless waste of time. I can tell you very little about Gweel. It’s a book, if that helps. It’s made of paper. It has pages. Lots of little words on the pages.

What I can’t do is classify Gweel into a genre, not because none of them fit, but because the concept of a genre doesn’t seem to apply to Gweel. It stands alone, without classification. Calling Gweel “experimental” or “avant garde” would be like stamping a barcode on a moon rock.

It may have been written for an audience of one: author Simon Whitechapel. If we make the very reasonable assumption that he owns a copy of his own book, he may have attained 100% market saturation. However, there could be a valuable peripheral market: people who want to read a book that is very different from anything they’ve read before.

It is a collection of short pieces of writing, similar in tone but not in form, exploring “dread, death, and doom.” “Kopfwurmkundalini” and “Beating the Meat” resemble horror stories, and manage to be frightening yet strangely fantastic. The first one is about a man – paralysed in a motorbike accident, able to communicate only by eye-blinks – and his induction into a strange new reality. It contains a rather thrilling story-within-a-story called “MS Found in a Steel Bottle”, about two men journeying to the bottom of the ocean in a bathysphere. “Kopfwurmkundalini”’s final pages are written in a made-up language, but the author has encluded a glossary so that you can finish the story.

Those two/three stories make up about half of Gweel’s length. The remainder mostly consists of shorter work that seems to be more about creating an atmosphere or evoking an emotion. “Night Shift” is about a prison for planets (Venus, we learn, is serving a 10^3.2 year sentence for sex-trafficking), and a theme of prisons and planets runs through a fair few of the other stories here, although usually in a less surreal context. “Acariasis” is a vignette about a convict who sees a dust-mite crawling on his cell wall, and imagines it’s a grain of sand from Mars. The image is vivid and the piece has a powerful effect. “Primessence” is The Shawshank Redemption on peyote (and math). A prisoner believes that because his cell is a prime number, he will soon be snatched from it by some mathematical daemon (the story ends with the prisoner’s fate unknown). “The Whisper” is a ghost story of sorts, short and achingly sad.

No doubt my impression of Gweel differs from the one the author intended. But maybe his intention was that I have that different impression than him. Maybe Gweel reveals different secrets to each reader.

I can’t analyse it much, but Gweel struck me as an experience like Fellini’s Amarcord… lots of little story-threads, none of them terribly meaningful on their own. Experienced together, however, those threads will weave themselves into a tapestry in the hall of your mind, a tapestry that’s entirely unique… and your own.

Original review


Jesús say: I… S….. R… U… B… B… I… S…. H…. B… O… O… K…. | W… H… A…. N… K… C…. H… A… P… L…. E…. I… S…. H… I… J… O…. D… E…. P… U…. T… A…..

Previously pre-posted:

It’s The Gweel Thing…

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.

He Say, He Sigh, He Sow #14

39: This appears to be the first uninteresting number, which of course makes it an especially interesting number, because it is the smallest number to have the property of being uninteresting. It is therefore also the first number to be simultaneously interesting and uninteresting.” — David Wells, The Penguin Dictionary of Curious and Interesting Numbers (1986), entry for “39”, pg. 120

Flesh and Fear

Understanding Owls by Jemima Parry-JonesUnderstanding Owls: Biology, Management, Breeding, Training, Jemima Parry-Jones (David & Charles, 1998)

We come into the world ready for the world. And in more ways than one. We aren’t just born with sense-organs and a brain designed to use them: we’re born with instinctive likes and dislikes. That’s where phobias come from. The common ones, about heights or contamination or potentially dangerous animals, are based on things that we’ve been facing and surviving for millions of years. Or failing to survive, because we didn’t pay them sufficient attention or respect. Those who did pay sufficient attention and respect were those who had more offspring and passed down the relevant, phobogenic genes.

How precisely those genes encode fear is an interesting question. Are spiders and snakes written into our brains in some sense? Monkeys are instinctively afraid of snakes, for example, and though that fear has to be triggered by example, it is obviously there to be triggered. A mother-monkey apparently reacting with fear to a flower will not induce a fear of flowers in her offspring. But if she reacts with fear to a snake, she will induce a fear of snakes. Monkeys also have special warning-calls for birds of prey. Human beings have been too big for too long to be easily afraid of birds, but we were small enough once to be their prey and genetic memories may linger. That might help explain our fascination with birds of prey. But I don’t think owls are written into our brains the way spiders and snakes probably are.

They do trigger other instincts, however: their uncanny stare, their nocturnal lives, their loud calls and the silence of their flight all help explain why they’re psychologically special to human beings and part of myth and legend around the world. This book is a practical introduction to keeping owls as pets, not general guide, but it has lots of owls in it, so it has lots of uncanny and unblinking eyes too. And a lot of beauty: owls don’t often have elegant shapes, but they often have beautiful feathers. They’re also intelligent birds and can be trained to the hand rather like eagles and falcons. Unlike eagles and falcons, however, they generally hunt small ground-animals and at night, so “Hunting with Owls” is unrewarding and Jemima Parry-Jones gives it only two pages, one of which is mostly taken up by a photo of an eagle owl (Bubo sp.). But it’s an interesting addition to a short but interesting book, with lots of attractive pictures and practical advice.

He Say, He Sigh, He Sow #13

“In the early thirties Trotsky also spoke of ‘Bonapartism’ in the Stalinist regime. In 1935, however, he observed that in the French Revolution Thermidor had come first and Napoleon afterwards; the order should be the same in Russia, and, as there was already a Bonaparte, Thermidor must have come and gone.” — Leszek Kołakowski in Main Currents of Marxism: Vol. III, The Breakdown (1978).

Hit and Smith

Front cover of Songs that Saved Your Life by Simon GoddardSongs that Saved Your Life: The Art of The Smiths 1982-87, Simon Goddard (Titan Books 2013)

I enjoyed Simon Goddard’s Mozipedia – The Encyclopedia of Morrissey and The Smiths a lot. And learnt a lot from it too. But I haven’t bothered finishing Simon Goddard’s Songs that Saved Your Life: The Art of The Smiths 1982-87 (an updated edition of The Smiths: Songs That Saved Your Life, 2002). There’s too much rock-writer rhetoric, too many mixed metaphors, too few pictures. None, in fact, apart from the band-photo on the front cover and the tickets on the back. Part of the problem is that The Smiths were only Act One in Mozza’s career. Johnny Marr played guitar well and wrote some beautiful tunes. But Morrissey was the interesting, eclectic and original one in The Smiths: the Mogpie didn’t need Marr a quarter as much as Marr needed the Mogpie. That’s part of why Mozipedia is better. Use this book as a supplement, because it’s got a lot of disc-o-detail and the appendices are good, covering The Smiths on record, in concert and on TV and radio. Goddard doesn’t have room to get rock-o-rhetorical there.