Each vowel sound has its own characteristic pattern of
frequency
stripes, like barcodes once again.
Richard-Dawkins-Unweaving-the-Rainbow
In very different ways, the possibility that the universe is teeming with life, and the opposite possibility that we are totally alone, are equally exciting.
Either way, the urge to know more about the universe seems to me irresistible, and I cannot imagine that anybody of truly poetic sensibility could disagree.
I am ironically amused by how much of what we have discovered so far is a direct extrapolation of unweaving the rainbow.
And the poetic beauty of what that unweaving has now revealed, from the nature of the stars to the expansion of the universe, could not fail to catch the imagination of Keats; would be bound to send Coleridge into a frenzied reverie; would make Wordsworth's heart leap up as never before.
The great Indian astrophysicist Subrahmanyan Chandrasekhar said, in a lecture in 1975:
This 'shuddering before the beautiful', this incredible fact that a discovery motivated by a search after the beautiful in mathematics should find its exact replica in Nature, persuades me to say that beauty is that to which the human mind responds at its deepest and most profound.
How much more sincere that sounds than Keats's better-known expression of a superficially similar emotion:
'Beauty is truth, truth beauty,'- that is all Ye know on earth, and all ye need to know.
'Ode on a Grecian Urn' (1820)
Keats and Lamb should have raised their glass to poetry, and to mathematics, and to the poetry of mathematics. Wordsworth would have needed no encouragement. He (and Coleridge) had been inspired by the
Scottish poet James Thomson, and might have recalled Thomson's 'To the Memory of Sir Isaac Newton' (1727):
. . . Even Light itself, which every thing displays. Shone undiscovered, till his brighter mind Untwisted all the shining robe of day;
And, from the whitening undistinguished blaze. Collecting every ray into his kind,
To the charmed eye educed the gorgeous train Of parent colours.
First the flaming red
Sprung vivid forth; the tawny orange next; And next delicious yellow; by whose side
Fell the kind beams of all-refreshing green
Then the pure blue, that swells autumnal skies.
Ethereal played; and then, of sadder hue,
Emerged the deepened indigo, as when
The heavy-skirted evening droops with frost;
While the last gleamings of refracted light
Died in the fainting violet away. These, when the clouds distil the rosy shower,
Shine out distinct adown the watery how;
While o 'er our heads the dewy vision bends
Delightful, melting on the fields beneath.
Myriads of mingling dyes from these result,
And myriads still remain - infinite source
Of beauty, ever flushing, ever new.
Did ever poet image aught so fair,
Dreaming in whispering groves by the hoarse brook?
Or prophet, to whose rapture heaven descends?
Even now the setting sun and shifting clouds,
Seen, Greenwich, from thy lovely heights, declare
How just, how beauteous the refractive law.
4
BARCODES ON THE AIR
We shall find the Cube of the Rainbow, Of that, there is no doubt But the Arc of a Lover's conjecture Eludes the finding out.
EMILY DICKINSON (1894)
On the air, in contemporary English, means on the radio. But radio waves have nothing to do with air, they are better regarded as invisible
light waves with long wavelengths. Airwaves can sensibly mean only one thing and that is sound. This chapter is about sound and other slow waves, and how they, too, can be unwoven like a rainbow. Sound weaves travel about a million times more slowly than light (or radio) waves, not much faster than a Boeing 747 and slower than a Concorde. Unlike light and other electromagnetic radiation, which propagates best through a vacuum, sound waves travel only through a material medium such as air or water. They are waves of compression and rarefaction (thickening and thinning) of the medium. In air, this means waves of increasing and then decreasing local barometric pressure. Our ears are tiny barometers capable of tracking highspeed rhythmic changes of pressure. Insect ears work in another way entirely. In order to understand the difference, we need a small digression to examine what pressure really is.
We feel pressure on our skin, when we place our hand over the outlet of a bicycle pump, for example, as a kind of springy push. Actually, pressure is the summed bombardments of thousands of molecules of air, whizzing about in random directions (as opposed to a wind, where the molecules predominantly flow in one particular direction). If you hold your palm up to a high wind you feel the equivalent of pressure - bombardment of molecules. The molecules in a confined space, say, the interior of a well-pumped bicycle tyre, press outwards on the walls of the tyre with a force proportional to the number of molecules in the tyre and to the temperature. At any temperature higher than -275? C (the lowest possible temperature, corresponding to complete motionlessness of molecules), the molecules are in continuous random motion, bouncing off each other like billiard balls. They don't only bounce off each other, they bounce off the inside walls of the tyre - and the walls of the tyre 'feel' it as pressure. As an additional effect, the hotter the air, the faster the molecules rush about (that's what temperature means), so the pressure of a given volume of air goes up when you heat it. By the same token, the temperature of a given quantity of air goes up when you compress it, i. e. raise the pressure by reducing the volume.
Sound waves are waves of oscillating local pressure change. The total pressure in, say, a sealed room is determined by the number of molecules in the room and the temperature, and these numbers don't change in the short term. On average, every cubic centimetre in the room will have the same number of molecules as every other cubic centimetre, and therefore the same pressure. But this doesn't stop there being local variations in pressure. Cubic centimetre A may experience a momentary rise in pressure at the expense of cubic centimetre B, which has temporarily donated some molecules to it. The increased pressure in A will tend to push molecules back to B and redress the balance. On the much larger scale of geography, this is what winds are - flows of air from high-pressure areas to low-pressure areas. On a smaller scale sounds
can be understood in this way, but they are not winds because they oscillate backwards and forwards very fast.
If a tuning fork is struck in the middle of a room, the vibration disturbs the local molecules of air, causing them to bump into neighbouring molecules of air. The tuning fork vibrates back and forth at a particular frequency, causing ripples of disturbance to propagate outwards in all directions as a series of expanding shells. Each wavefront is a zone of increased pressure, with a zone of decreased pressure following in its wake. Then the next wavefront comes, after an interval determined by
the rate at which the tuning fork is vibrating. If you stick a tiny, very fast-acting barometer anywhere in the room, the barometer needle will swing up and down as each wavefront passes over it. The rate at which the barometer needle oscillates is the frequency of the sound. A fast- acting barometer is exactly what a vertebrate ear is. The eardrum moves in and out under the changing pressures that hit it. The eardrum is connected (via three tiny bones, the famous hammer, anvil and stirrup, sequestered in evolution from the bones of the reptilian jaw hinge) to a kind of inverse harp in miniature, called the cochlea. As in a harp, the 'strings' of the cochlea are arranged across a tapering frame. Strings at the small end of the frame vibrate in sympathy with high-pitched sounds, those at the big end vibrate in sympathy with low-pitched sounds. Nerves from along the cochlea are mapped in an orderly way in the brain, so the brain can tell whether a low-pitched or a high-pitched sound is vibrating the eardrum.
Insect ears, by contrast, are not little barometers, they are little weather- vanes. They actually measure the flow of molecules as a wind, albeit a queer kind of wind which travels only a very short distance before reversing its direction. The expanding wavefront which we detect as a change in pressure is also a wave of movement of molecules: movement into a local area as the pressure goes up, then movement back out of that area as the pressure goes down again. Whereas our barometer ears have a membrane stretched over a confined space, insect weather-vane ears have either a hair, or a membrane stretched over a chamber with a hole. In either case, it is literally blown back and forth by the rhythmic, backward and forward movements of the molecules.
Sensing the direction of a sound is therefore second nature for insects. Any fool with a weather-vane can distinguish a north wind from an east wind, and a single insect ear finds it easy to tell a north-south oscillation from an east-west oscillation. Directionality is built into insects' method of detecting sound. Barometers aren't like that. A rise in pressure is just a rise in pressure, and it doesn't matter from which direction the added molecules come. We vertebrates therefore, with our barometer ears, have to calculate the direction of sound by comparing the reports of the two
ears, rather as we calculate colour by comparing the reports of different classes of cones. The brain compares the loudness at the two ears and separately it compares the time of arrival of sounds (especially staccato sounds) at the two ears. Some kinds of sounds lend themselves to such comparisons less readily than others. Cricket song is cunningly pitched and timed so as to be hard for vertebrate ears to locate, but easy for female crickets, with their weather-vane ears, to home in upon. Some cricket chirps even create the illusion, at least to my vertebrate brain, that the (in fact stationary) cricket is leaping about like a jumping squib.
Sound waves form a spectrum of wavelengths, analogous to the rainbow. The sound rainbow is also subject to unweaving, which is why it is possible to make any sense of sounds at all. Just as our sensations of colour are the labels that the brain slaps on to light of different wavelengths, the equivalent internal labels that it uses for sounds are the different pitches. But there is a lot more to sound than simple pitch, and this is where unweaving really comes into its own.
A tuning fork or a glass harmonica (an instrument favoured by Mozart, made from fine glass bowls tuned by the depth of water they contain, sounded by a wetted finger drawn around the rim) emit a crystalline pure sound. Physicists call these sine waves. Sine waves are the simplest kind of waves, sort of theoretical ideal waves. The smooth curves that snake along a rope when you wiggle one end up and down are more or less sine waves, although of much lower frequency than sound waves, of course. Most sounds are not simple sine waves but are more jagged and complicated, as we shall see. For the moment we shall think of a tuning fork or glass harmonica, singing out its smooth, curvaceous waves of pressure change that race away from the source in concentrically expanding spheres. A barometer ear placed at one spot detects a smooth increase in pressure followed by a smooth decrease, rhythmically oscillating with no kinks or wiggles in the curve. With every doubling in frequency (or halving in wavelength, which is the same thing) we hear a jump of one octave. Very low frequencies, the deepest notes of the organ, shudder through our bodies and are hardly heard by our ears at all. Very high frequencies are inaudible to humans (especially older humans) but audible to bats and used by them, in the form of echoes, to find their way about. This is one of the most enthralling stories in all natural history, but I've devoted a whole chapter to it in The Blind Watchmaker so will resist the temptation to expand.
Tuning forks and glass harmonicas aside, pure sine waves are largely a mathematical abstraction. Real sounds are mostly more complicated mixtures, and they richly repay unweaving. Our brains unweave them effortlessly and to astonishing effect. It is only with much labour that our mathematical understanding of what is going on has caught up, clumsily
and incompletely, with what our ears have effortlessly unwoven - and our brains rewoven - from childhood on.
Suppose we sound one tuning fork with an oscillating frequency of 440 cycles per second, or 440 Hertz (Hz). We shall hear a pure tone, the A above middle C. What is the difference between this and a violin playing the same A, a clarinet playing the same A, an oboe, a flute? The answer is that each instrument includes admixtures of waves whose frequencies are various multiples of the fundamental frequency. Any instrument playing the A above middle C will deliver most of its sound energy at the fundamental frequency, 440 Hz, but superimposed will be traces of vibration at 880 Hz, 1520 Hz and so on. These are called harmonics, although the word can be confusing since 'harmonies' are chords of several notes that we hear as distinct. A 'single' trumpet note is actually a mixture of harmonics, the particular mixture being a kind of trumpet 'signature' that distinguishes it from, say, a violin playing the 'same' note (with different, violin signature harmonics). There are additional complications, which I shall ignore, around the onset of sounds, for example the lippy irruption of a trumpet blast or the zing as a violin bow hits the string.
These complications aside, there is a characteristic trumpet (or violin, or whatever it is) quality to the sustained part of a note. It is possible to demonstrate that the apparently single tone of a particular instrument is a rewoven construct of the brain, summing up sine waves. The demonstration works as follows. Having decided which sine waves are involved in, say, trumpet sound, select the appropriate 'tuning fork' pure tones and sound them one at a time. For a brief period you can hear the separate notes, as if they really were a chord of tuning forks. Then, quite eerily, they click into focus with each other, the 'tuning forks' disappear, and you hear only what Keats called the silver, snarling trumpets, sounding the pitch of the fundamental frequency. A different barcode combination of frequencies is needed to make the sound of a clarinet, and "again you can fleetingly distinguish them as separate 'tuning forks' before the brain homes in on the illusion of one 'woody' clarinet note. The violin has its own barcode signature, and so on.
Now, if you watch a tracing of the pressure wave when a violin is playing some note, what you see is a complicated wiggly line repeating itself at the fundamental frequency but with smaller wiggles of higher frequency superimposed. What has happened is that the different sine waves that constitute violin noise have summed up to make the complicated wiggly line. It is possible to program a computer to analyse any complicatedly repeating pattern of wiggles back into its component pure waves, the separate sine waves that you would have to sum up to make the complicated pattern. Presumably, when you listen to an instrument, you
are performing something equivalent to this calculation, the ear first unweaving the component sine waves, then the brain weaving them together again and giving them the appropriate label: 'trumpet, 'oboe' or whatever it is.
But our unconscious feats of unweaving and weaving are greater even than this. Think what is happening when you listen to a whole orchestra. Imagine that, superimposed on a hundred instruments, your neighbour in the concert is whispering learned music criticism in your ear, others are coughing and, lamentably, somebody behind you is rustling a chocolate wrapper. All these sounds, simultaneously, are vibrating your eardrum and they are summed into a single, very complicated wriggling wave of pressure change. We know it is one wave because a full orchestra, and all the noises off, can be rendered into a single wavy groove on a phonograph disc, or a single fluctuating trace of magnetic substance on
a tape. The entire set of vibrations sums up into a single wiggly line on the graph of air pressure against time, as recorded by your eardrum. Mirabile dictu, the brain manages to sort out the rustling from the whispering, the coughing from the door banging, the instruments of the orchestra from each other. Such a feat of unweaving and re-weaving, or analysis and synthesis, is almost beyond belief, but we all do it effortlessly and without thinking. Bats are even more impressive, analysing stuttering volleys of echoes to build up, in their brains,
detailed and fast-changing three-dimensional images of the world
through -which they fly, including the insects which they catch on the wing, and even sorting out their own echoes from those of other bats.
The mathematical technique of decomposing 'wiggling waveforms into sine waves which can then be summed again to make the original wiggly line is called Fourier analysis, after the nineteenth-century French mathematician Joseph Fourier. It works not just for sound waves (indeed, Fourier himself developed the technique for a quite different purpose) but for any process that varies periodically, and it doesn't have to be high- speed waves like sound, or ultra-high-speed waves like light. We can think of Fourier analysis as a mathematical technique which is convenient for unweaving 'rainbows' where the vibration that makes up the spectrum is slow compared with that of light.
To go to a very slow vibration indeed, I recently saw, on a road in the Kruger National Park in South Africa, a wiggly wet line which followed the course of the road and apparently traced out some kind of complicated repeat pattern. My host and expert guide told me that it was a trail of urine from a male elephant in musth. When a bull elephant enters this curious state (perhaps the elephantine equivalent of an Australian on 'walkabout') he dribbles out urine more or less continuously, apparently for scent-marking purposes. The side-to-side
waving of the urine trail on the road was presumably produced by the long penis acting as a pendulum (it would be a sine wave if the penis were a perfect, Newtonian pendulum, which it is not) interacting with the more complicated periodicity of the lumbering four-footed gait of the whole animal. I took photographs with the vague intention of later performing a Fourier analysis. I am sorry to say I have never got around to doing it. But in theory it could be done. A tracing of the photographed urine line could be laid over squared paper and its coordinates digitized for feeding into a computer. The computer could then perform a modern version of Fourier's calculations and extract the component sine waves. There are easier (though not necessarily safer) ways to measure the length of an elephant's penis, but it would have been fun to do, and Baron Fourier himself would surely have been delighted at such an unexpected use of his mathematics. There is no reason why a urine trail might not fossilize, as footprints and worm casts do, in which case we could in principle use Fourier analysis to measure the penis length of an extinct mastodon or woolly mammoth, from the indirect evidence of its urine trail in musth.
An elephant's penis swings at a frequency much slower than sound (although in the same ballpark as sound when you compare it with the ultra high frequencies of light). Nature offers us other periodic waveforms, of much lower frequency still, with wavelengths measured in years or even millions of years. Some of these have been subjected to the equivalent of Fourier analysis, including the cycles of animal populations. Since 1756, the Hudson's Bay Company kept records of the abundance
of pelts brought in by Canadian fur trappers. The distinguished Oxford ecologist Charles Elton (1900-1991), who was employed as a consultant by the company, realized that these records could provide a read-out of fluctuating populations of snow-shoe hares, lynxes and other mammals persecuted by the fur trade. The figures rise and fall in complicated mixtures of rhythms, which have been much analysed. Among the wavelengths that have been pulled out by these analyses is a prominent one of approximately four-year periodicity, and another of around 11 years. One hypothesis that has been suggested to account for the four- year rhythms is a time-lagged interaction between predators and prey (a glut of prey feeds a plague of predators, who then nearly wipe out the prey; this in turn starves the predators, then the consequent drop in predator population allows a new boom in the prey population, and so on). As for the longer rhythm of 11 years, perhaps the most intriguing suggestion connects it with sun spot activity, which is known to vary on an approximately 11-year cycle. How the sun spots affect animal populations is open to discussion. Perhaps they change the earth's weather, which affects abundance of plant food.
Wherever you find regular cycles of very long wavelengths, they are likely to have astronomical origins. They stem from the fact that celestial objects often rotate on their own axis, or follow repetitious orbits around other celestial objects. Twenty-four-hour rhythms of activity pervade almost all the fine details of living bodies on this planet. The ultimate reason is the rotation of the earth about its own axis, but animals of many species, including humans, when isolated from direct contact with day and night, continue to cycle on with a rhythm of approximately 24 hours, showing that they have internalized the rhythm and can free-run it even in the absence of the external pacemaker. The lunar rhythm of 28 days is another prominent component of the mix of waves in the bodily functions of many creatures, especially marine ones. The moon exerts its rhythmic influence via the succession of spring and neap tides. The earth's orbital rhythm of slightly more than 365 days contributes its slower pendulum to the Fourier sum, manifesting itself via breeding seasons, seasons of migration, patterns of moulting and growth of winter coats.
Perhaps the longest wavelength picked up by the unweaving of biological rhythms is a suggested 26-million-year cycle of mass extinctions. Fossil experts reckon that more than 99 per cent of the species that have ever lived have become extinct. Fortunately, the rate of extinction is, over the long term, roughly balanced by the rate at which new species are formed by the splitting of existing ones. But this doesn't mean they stay
constant in the shorter term. Far from it. Extinction rates fluctuate all over the place, and so do the rates at which new species come into existence. There are bad times when species disappear, and good times when they burgeon. Probably the worst of the bad times, the most devastating Armageddon, occurred at the end of the Permian era, about a quarter of a billion years ago. Around 90 per cent of all species became extinct in that terrible time, including on land many mammal-like reptiles. Earth's fauna eventually bounced back on to the denuded stage, but with a very different cast list: on land the dinosaurs stepped into the range of costumes left by dead mammal-like reptiles. The next largest mass extinction - and the most talked about - is the famous Cretaceous extinction of 65 million years ago, in which all the dinosaurs, and many other species with them both on land and in the sea, were wiped out, instantaneously as far as the fossil record can tell. In the Cretaceous event, perhaps 50 per cent of all species went extinct, not as many as in the Permian but nevertheless this was a fearful global tragedy. Once again, our planet's devastated fauna bounced back and here we are, we mammals, descended from a few fortunate relicts of the once rich mammal-like reptile fauna. Now we, together with the birds, fill gaps left by the dead dinosaurs. Until, presumably, the next great extinction.
There have been many episodes of mass extinction, not as bad as the Permian and Cretaceous events, but still noticeable in the chronicles of the rocks. Statistical paleontologists have gathered the numbers of fossil species over the ages and fed them into computers to perform Fourier analysis and extract such rhythms as they can find, as if listening for the flutter of preposterously deep organ notes. The dominant rhythm that has been claimed (albeit controversially) is a periodicity of about 26 million years. What could cause rhythms of extinction with such a formidably long wavelength? Probably only a celestial cycle.
Evidence is accumulating that the Cretaceous catastrophe was caused when a large asteroid or comet, the size of a mountain and travelling at tens of thousands of miles per hour, scored a direct hit on our planet, probably somewhere around what we now call the Yucatan peninsula in the gulf of Mexico. Asteroids hurtle round the sun in a belt which lies inside the orbit of Jupiter. There are plenty of asteroids out there - small ones are hitting us all the time - and a few of them are large enough to cause cataclysmic extinctions if they were to hit us. The comets have larger, eccentric orbits around the sun, mostly well outside what we conventionally think of as the solar system, but occasionally coming inside it, as Halley's comet does every 76 years and the Hale Bopp comet every 4,000 years or so. Perhaps the Permian event was caused by an even larger comet strike than the Cretaceous one. Perhaps the suggested 2 6-million-year cycle of mass extinctions is caused by a rhythmic boost in the rate of comet strikes.
But why should comets become more likely to hit us every million years? Here we launch ourselves into deep speculation. It has been suggested that the sun has a sister star, and the two orbit each other with a periodicity of about 26 million years. This hypothetical binary partner, which has never been seen but which has nevertheless been given the dramatic name Nemesis, passes, once per orbital rotation, through the so-called Oort Cloud, the belt of perhaps a trillion comets which orbits the sun beyond the planets. If there was a Nemesis that passed close to, or through, the Oort Cloud, it is plausible that it would disturb the comets, and this might increase the likelihood of one of them hitting earth. If this all happened - and the chain of reasoning is admittedly tenuous - it could account for the 26-million-year periodicity of mass extinctions that some people think the fossil record shows. It is a pleasing thought that mathematical unweaving of the noisy spectrum of animal extinctions might be the only means we have of detecting an otherwise unknown star.
Starting with the ultra high frequencies of light and other electromagnetic waves, we passed, via the intermediate frequencies of sound and the swinging elephant's penis, to ultra low frequencies and
the alleged 26-million-year wavelength of mass extinctions. Let's return to sound, and in particular that crowning feat of the human brain, the weaving and unweaving of speech sounds. The vocal 'cords' are really a pair of membranes which vibrate together in the breathing passage like a pair of woodwind reeds. Consonants are produced as more or less explosive interruptions of the air flow, caused by closure and contact of the lips, teeth, tongue and back of throat. Vowels vary in the same kind of way as trumpets differ from oboes. We make different vowel sounds rather as a trumpeter moves a mute in and out, to shift the preponderant sine waves summing into the composite sound. Different vowels have different combinations of harmonics above the fundamental frequency. The fundamental frequency itself, of course, is lower for men than for women and children, yet male vowels sound similar to the corresponding female vowels because of the pattern of harmonics.
Each vowel sound has its own characteristic pattern of frequency stripes, like barcodes once again. In the study of speech, the barcode stripes are called 'formants'.
Any one language, or dialect within a language, has a finite list of vowel sounds, and each of those vowel sounds has its own formant barcode. Other languages, and different accents within languages, have different vowel sounds which are made by holding the mouth and tongue in intermediate positions, again as a trumpeter disposes the mute in the
bell of the instrument. Theoretically there is a continuous spectrum of vowel sounds. Any one language employs a useful selection, a discontinuous repertoire picked out from the continuous spectrum of available vowels. Different languages pick out different points along the spectrum. The vowel in the French tu and the German uber, which doesn't occur in (my version of) English, is approximately intermediate between oo and ee. It doesn't too much matter which landmark points along the spectrum of available vowels a language picks on, so long as they are spaced far enough apart to avoid ambiguity within that language.
The story for consonants is more complicated, but there is a similar range of consonant barcodes, with actual languages employing a limited subset from those available. Some languages employ sounds which are far off the spectrum of the majority of languages, for example the clicks of some southern African tongues. As with vowels, different languages parcel up the available repertoire differently. Several of the languages of the Indian subcontinent have a dental sound which is intermediate between the English 'd' and 't'. The French hard 'c' as in comme is intermediate between the English hard 'c' and hard 'g' (and the 'o' is intermediate between the English vowels in cod and cud). The tongue, lips and voice can be modulated to produce an almost infinite variety of consonants and vowels. When the barcodes are patterned in time to form
phonemes, syllables, words and sentences, the range of ideas that can be communicated is unlimited.
Stranger yet, the things that can be communicated include images, ideas, feelings, love and exultation - the kind of thing that Keats does so sublimely.
My heart aches, and a drowsy numbness pains My sense, as though of hemlock I had drunk, Or emptied some dull opiate to the drains One minute past, and Lethe-wards had sunk: Tis not through envy of thy happy lot, But being too happy in thy happiness - That thou, light- winged Dryad of the trees, In some melodious plot Of beechen green, and shadows numberless, Singest of summer in full-throated ease.
'Ode to a Nightingale' (1820)
Read the words aloud and the images tumble into your brain, as if you really were drugged by a nightingale's song in a leafy summer beechwood. At one level it is all done by a pattern of air pressure waves, a pattern whose richness is first unwoven into sine waves in the ear and then rewoven together in the brain to reconstruct images and emotions. Stranger yet, the pattern can be broken down mathematically into a stream of numbers, and it retains its power to transport and haunt the imagination. When a laser disc (CD) is made, say, of the Saint Matthew Passion, the rising and falling pressure wave, with all its wiggles and kinks, is sampled at frequent intervals and translated into digital data. The digits could, in principle, be printed as dull, black and white zeroes and ones on reams of paper. Yet the numbers retain the power, if transduced back into pressure waves, to move a listener to tears.
Keats may not have intended it literally, but the idea of nightingale song working as a drug is not totally far-fetched. Consider what it is doing in nature, and what natural selection has shaped it to do. Male nightingales need to influence the behaviour of female nightingales, and of other males. Some ornithologists have thought of song as conveying information: 'I am a male of the species Luscinia megarhynchos, in breeding condition, with a territory, hormonally primed to mate and build a nest. ' Yes, the song does contain that information, in the sense that a female who acts on the assumption that it is true could benefit thereby. But another way to look at it has always seemed to me more vivid. The song is not informing the female but manipulating her. It is not so much changing what the female knows as directly changing the internal physiological state of her brain. It is acting like a drug.
There is experimental evidence from measuring the hormone levels of female doves and canaries, as well as their behaviour, that the sexual
state of females is directly influenced by the vocalizations of males, the effects being integrated over a period of days. The sounds from a male canary flood through the female's ears into her brain where they have an effect that is indistinguishable from one that an experimenter can procure with a hypodermic syringe. The male's 'drug' enters the female through the portals of her ears rather than through a hypodermic, but this difference does not seem particularly telling.
The idea that birdsong is an auditory drug gains plausibility when you look at how it develops during the individual's lifetime. Typically, a young male songbird teaches himself to sing by practising: matching up fragments of trial song against a 'template' in his brain, a pre- programmed notion of what the song of his species 'ought' to sound like. In some species, such as the American song sparrow, the template is built in, programmed by the genes. In other species, such as the white crowned sparrow or the European chaffinch, it is derived from a 'recording' of another male's song, made early in the young male's life from listening to an adult. Wherever the template comes from, the young male teaches himself how to sing in such a way as to match it.
That, at least, is one way to talk about what happens when a young bird perfects his song. But think of it another way. The song is ultimately designed to have a strong effect on the nervous system of another member of the species, either a prospective mate or a possible territorial rival who needs to be warned off. But the young bird himself is a member of his own species. His brain is a typical brain from that species. A sound that is effective in arousing his own emotions is likely to be as effective in arousing a female of the same species. Instead of speaking of the young male trying to shape his practice song to 'match' a built-in 'template', we could think of him as practising on himself as a typical member of his species, trying out fragments of song to see whether they excite his own passions, that is, experimenting with his own drugs on himself. And, to complete the circuit, perhaps it is not too surprising that nightingale song should have acted like a drug on the nervous system of John Keats. He was not a nightingale, but he was a vertebrate, and most drugs that work on humans have a comparable effect upon other vertebrates. Man- made drugs are the products of comparatively crude trial and error testing by chemists in the laboratory Natural selection has had thousands of generations in which to fine-tune its drug technology.
Should we feel indignant on Keats's behalf at such a comparison? I do not believe that Keats himself would have done so - Coleridge even less. The 'Ode to a Nightingale' accepts the implication of the drug analogy, makes it wonderfully real. It is not demeaning to human emotion that we try to analyse and explain it, any more than, to a balanced judge, the rainbow is diminished when a prism unweaves it.
In this chapter and the previous one, I have used the barcode as a symbol of precise analysis, in all its beauty. Mixed light is sorted into its rainbow of component colours and everybody sees beauty. That is a first analysis. Closer detail reveals fine lines and a new elegance, the elegance of detection, of the bringing of order and understanding. Fraunhofer barcodes speak to us of the exact elemental nature of distant stars. A precisely measured pattern of stripes is a coded message from across the parsecs. There is grace in the sheer economy of unweaving intimate details about a star which, one had thought, could be found only through the costly undertaking of a journey lasting 3,000 human lifetimes. On another scale, we find a similar story when we look at the formant stripes in speech, the harmonic barcodes of music. There is elegance, too, in the barcodes of dendrochronology: the stripes across ancient Sequoia wood which tell us precisely in which year BC the tree was seeded, and what the weather was like in every one of the intervening years (for weather conditions are what give tree rings their characteristic widths). Like Fraunhofer's lines transmitted across space, tree rings transmit messages to us across time, and again there is a supple economy. It is the power - the fact that we can learn so much by precise analysis of what seems so little information - that gives these unweavings their beauty. The same is true, perhaps even more dramatically, of sound waves in speech and music - barcodes on the air.
Recently we have been hearing much about another kind of barcode - DNA 'fingerprints', barcodes in the blood. DNA barcodes expose and reconstruct details of human affairs that one might have supposed forever inaccessible even to legendarily great detectives. The main practical use of barcodes in the blood so far is in courts of law, and it is to them - and the benefits that a scientific attitude may bring to them - that we turn in the next chapter.
5
BARCODES AT THE BAR
And he said, Woe unto you also, ye lawyers! for ye lade men with burdens grievous to be borne, and ye yourselves touch not the burdens with one of your fingers. . . . Woe unto you, lawyers', for ye have taken away the key of knowledge: ye entered not in yourselves, and them that were entering in ye hindered.
Luke 11
On the face of it, the law may seem about as far as you can get from poetry or the wonder of science. Perhaps there is poetic beauty in the abstract ideas of justice or fairness, but I doubt if many lawyers are moved by it. In any case, that is not what this chapter is about. I shall be looking at an example of the role of science in the law: at a different aspect of science and its importance in society; a sense in which scientific understanding may become a valuable part of good citizenship. In courts of law, juries are increasingly asked to understand evidence which the lawyers themselves may not fully comprehend. Evidence from the unweaving of DNA - what we shall come to see as barcodes in the blood - is the outstanding example, and it is the main subject of this chapter. But it is not just facts about DNA that scientists can contribute. More importantly, it is the underlying theory of probability and statistics; it is scientific ways of making inferences that need to be brought to bear. Such matters stretch beyond the narrow subject of DNA evidence.
I am told on good authority that defence lawyers in the United States sometimes object to jury candidates on the grounds that they have had a scientific education. What can this mean? I would not question the right of defence lawyers to disallow the selection of particular jurors. A juror may be prejudiced against the race or class to which the defendant belongs. It is obviously undesirable that a raving homophobe should try a case of anti-homosexual violence. It is for this kind of reason that defence lawyers in some countries are allowed to cross-examine potential jurors and strike them off the list. In the USA lawyers can be completely blatant about their criteria for jury selection. A colleague tells me of a time when he was up for selection to a jury, on an injury litigation case. The lawyer asked, 'Would anyone here have a problem awarding a substantial amount of money to my client, perhaps in the millions? '
A lawyer can also disqualify a juror without giving reasons. Although this may be just, the only time I have seen it happen it misfired. I was a member of a panel of 24 individuals from which juries of 12 were to be selected. I had already participated in two juries with members of this panel, and I knew their individual foibles. One particular man was cast- iron prosecution fodder; he would take the same hard line almost regardless of the particular case. The defence lawyer waved him through like a breeze. The next one up, a large middle-aged woman, was the opposite: a guaranteed softie, a pure gift to the defence. But her appearance perhaps suggested the opposite, and it was against her that the defence lawyer chose to exercise his right of veto. I have never forgotten the look of wounded hurt on her face as, with a cutting movement of the hand, learned counsel struck her - whom he little knew could have been his secret weapon - out of the jury box.
But, to repeat the astonishing fact, lawyers in the United States have been known to use the following reason for striking down potential jurors: the prospective juror is well educated in science, or has some knowledge of genetics or probability theory. What is the problem? Are geneticists known to harbour deep-seated prejudices against certain sections of society? Are mathematicians especially likely to be of the "flog 'em . . . string 'em up . . . it's the only language they understand . . . law and
order' persuasion? Of course not. Nobody has ever claimed such a thing.
The lawyers' objections are more ignobly based. There is a new kind of evidence increasingly coming into the criminal courts: evidence from
DNA fingerprinting, and it is extremely powerful. If your client is innocent, DNA' evidence may well provide a knock-down convincing way to establish his innocence. Conversely, if he is guilty, DNA evidence has a good chance of establishing his guilt in cases where no other evidence can. DNA evidence is quite hard to understand at the best of times.
There are controversial aspects of it which are even harder. In these circumstances, you would think that an honest lawyer who wishes to see justice done would welcome jurors capable of grasping the arguments. Wouldn't it be an obviously good thing to have at least one or two people in the jury room who can redress the ignorance of their baffled colleagues? What kind of a lawyer is it who prefers a jury incapable of following the case that either attorney is making?
The answer is a lawyer who is more interested in winning than in seeing justice done. A lawyer, in other words. And it seems to be a fact that advocates, of both prosecution and defence, frequently disallow individual jurors specifically because they are educated in science.
Courts of law have always needed to establish individual identity. Was the individual seen hurrying from the scene Richard Dawkins? Is the hat dropped at the scene of the crime his hat? Are those his fingerprints on the weapon? A yes answer to one of these questions does not by itself prove his guilt, but it is certainly an important factor to be taken into account. Most of us, including most jurors and lawyers, have an intuitive sense that there is something specially reliable about eye-witness evidence. In this we are almost certainly wrong, but the error is a pardonable one. It may even be built into us by millennia of evolutionary history in which eye-witness evidence really was the most reliable. If I see a man in a red woolly hat climbing a drainpipe, you will have a hard time persuading me later that he was actually wearing a blue beret. Our intuitive biases are such that eye-witness evidence trumps all other categories. Yet numerous studies have shown that eye-witnesses, however convinced they may be, however sincere and well-meaning, frequently mis-remember even conspicuous details such as the colour of clothing and the number of assailants present.
When individual identification is important, for instance when a woman who has been raped is called upon to identify her attacker, courts perform a rudimentary statistical test known as the identity parade or line-up. The woman is led past a line of men, one of whom the police suspect on other grounds. The others have been pulled in off the streets or are out-of-work actors, or police officers dressed in plain clothes. If the woman picks out one of these stooges, her identification evidence is discounted. But if she picks out the man the police already suspect, her evidence is taken seriously.
Rightly so. Especially if the number of people in the identity parade is large. We are all statisticians enough to see why this is. The prior suspicion of the police must be open to doubt - otherwise there would be no point in seeking the woman's evidence at all. What impresses us is agreement between the woman's identification and the independent evidence offered by the police. If the identity parade contains only two men, the witness would have a 50 per cent chance of picking the man already suspected by the police, even if she chose at random - or if she were mistaken. Since the police might also be mistaken, this represents an unacceptably high risk of injustice. But if there are 20 men in the line, the woman has only a 1 in 20 chance of choosing, by guesswork or error, the man the police already suspect. The coincidence of her identification and the police's prior suspicion probably really means something. What
is going on here is the assessment of coincidence, or the odds that something might happen by chance alone. The probability of meaningless coincidence is even less if the identity parade has 100 men, because a 1 in 100 chance of error is noticeably less than a 1 in 20 chance of error. The longer the line-up, the more secure the eventual conviction.
We also have an intuitive sense that the men chosen for the line-up must not look too obviously different from the suspect. If the woman originally told the police to look for a man with a beard, and the police have now arrested a bearded suspect, it is clearly unjust to stand him in a line with 19 clean-shaven men. He might as well be standing by himself. Even if the woman has said nothing about the appearance of her attacker, if the police have arrested a punk in a leather jacket it would be wrong to stand him in a line of suited accountants with furled umbrellas. In multiracial countries such considerations have added importance. Everyone understands that a black suspect should not be placed in an otherwise all-white line-up, or vice versa.
When we think about how we identify somebody, the face first leaps to mind. We are particularly good at distinguishing faces. As we shall see in another connection, we even seem to have evolved a special part of the brain set aside for the purpose, and certain kinds of brain damage
disable our face-recognition faculty while leaving the rest of vision intact. In any case, faces are good for recognition because they are so variable. With the well-known exception of identical twins, you seldom meet two people whose faces are confusable. It is not totally unknown, however, and an actor can be made up to look very like somebody else. Dictators often employ doubles to perform for them when they are too busy, or to draw the fire of assassins. It has been suggested that one reason charismatic leaders so often sport moustaches (Hitler, Stalin, Franco, Saddam Hussein, Oswald Mosley) is to make it easier for doubles to impersonate them. Mussolini's shaven head perhaps served the same purpose.
Apart from identical twins, ordinary close relatives are sometimes sufficiently alike to fool people who don't know them well. (Unfortunately the story that Doctor Spooner, when Warden of my college, once stopped an undergraduate and said, 'I never can remember is it you or your brother was killed in the war? ' is probably not true, like most alleged Spoonerisms. ) The resemblance of brothers and sisters, of fathers and sons, of grandparents and grandchildren, serves to remind us of the huge pool of facial variety in the general population of non-relatives.
But faces are only a special case. We are riddled with idiosyncrasies which, with sufficient training, can be used to identify individuals. I had
a school friend who claimed (and my spot checks confirmed it) that he could recognize any member of the 80-strong residence in which we lived purely by listening to their footsteps. I had another friend from Switzerland who claimed that when she walked into a room she could tell, by smell, which members of her circle of acquaintances had recently left the room. It is not that her colleagues didn't wash, just that she was unusually sensitive. That this is in principle possible is confirmed by the fact that police dogs can distinguish between any two human beings by smell alone, with the exception, yet again, of identical twins. As far as I know, the police haven't adopted the following technique, but I bet you could train bloodhounds to track down a kidnapped child after giving them a sample sniff of his brother. A way might even be found to use a jury of bloodhounds to decide paternity cases.
Voices are as idiosyncratic as faces, and various research teams are working on computer voice recognition systems for authenticating identity. It would be a great boon if, in the future, we could dispense with front door keys and rely on a voice-operated computer to obey our personal Open Sesame command. Handwriting is sufficiently individual for the written signature to be used as a guarantee of identity on bank cheques and important legal documents. Signatures are actually not particularly secure because they are too easily forged, but it is still impressive how recognizable handwriting can be. A promising newcomer
to the list of individual 'signatures' is the iris of the eye. At least one bank is experimenting with automated iris-scanning machines as a way of verifying identity. The customer stands in front of a camera which photographs the eye, digitizes the image into what a newspaper described as 'a 256 byte: human barcode'. But none of these methods of verifying human identity even comes close to the potential of DNA fingerprinting, properly applied.
It is not surprising that police dogs can smell the difference between any two humans except identical twins. Our sweat contains a complicated cocktail of proteins, and the precise details of all proteins are minutely specified by the coded DNA instructions that are our genes. Unlike handwriting and faces, which vary continuously and grade smoothly into one another, genes are digital codes, much like those used in computers. Again with the exception of identical twins, we differ genetically from all other people in discrete, discontinuous ways: an exact number of ways that you could even count if you had the patience. The DNA in each one of my cells (give or take a tiny minority of mistakes, and not including red blood cells which have lost all their DNA, or reproductive cells which contain a random half of my genes) is identical to the DNA in all my other cells. It differs from the DNA in every one of your cells, not in some vague, impressionistic way but at a precise number of locations dotted along the billions of DNA letters that we both have.
It is almost impossible to exaggerate the importance of the digital revolution in molecular genetics. Before Watson and Crick's epochal announcement in 1953 of the structure of DNA, it was still possible to agree with the concluding words of Charles Singer's authoritative A Short History of Biology, published in 1931:
.
The great Indian astrophysicist Subrahmanyan Chandrasekhar said, in a lecture in 1975:
This 'shuddering before the beautiful', this incredible fact that a discovery motivated by a search after the beautiful in mathematics should find its exact replica in Nature, persuades me to say that beauty is that to which the human mind responds at its deepest and most profound.
How much more sincere that sounds than Keats's better-known expression of a superficially similar emotion:
'Beauty is truth, truth beauty,'- that is all Ye know on earth, and all ye need to know.
'Ode on a Grecian Urn' (1820)
Keats and Lamb should have raised their glass to poetry, and to mathematics, and to the poetry of mathematics. Wordsworth would have needed no encouragement. He (and Coleridge) had been inspired by the
Scottish poet James Thomson, and might have recalled Thomson's 'To the Memory of Sir Isaac Newton' (1727):
. . . Even Light itself, which every thing displays. Shone undiscovered, till his brighter mind Untwisted all the shining robe of day;
And, from the whitening undistinguished blaze. Collecting every ray into his kind,
To the charmed eye educed the gorgeous train Of parent colours.
First the flaming red
Sprung vivid forth; the tawny orange next; And next delicious yellow; by whose side
Fell the kind beams of all-refreshing green
Then the pure blue, that swells autumnal skies.
Ethereal played; and then, of sadder hue,
Emerged the deepened indigo, as when
The heavy-skirted evening droops with frost;
While the last gleamings of refracted light
Died in the fainting violet away. These, when the clouds distil the rosy shower,
Shine out distinct adown the watery how;
While o 'er our heads the dewy vision bends
Delightful, melting on the fields beneath.
Myriads of mingling dyes from these result,
And myriads still remain - infinite source
Of beauty, ever flushing, ever new.
Did ever poet image aught so fair,
Dreaming in whispering groves by the hoarse brook?
Or prophet, to whose rapture heaven descends?
Even now the setting sun and shifting clouds,
Seen, Greenwich, from thy lovely heights, declare
How just, how beauteous the refractive law.
4
BARCODES ON THE AIR
We shall find the Cube of the Rainbow, Of that, there is no doubt But the Arc of a Lover's conjecture Eludes the finding out.
EMILY DICKINSON (1894)
On the air, in contemporary English, means on the radio. But radio waves have nothing to do with air, they are better regarded as invisible
light waves with long wavelengths. Airwaves can sensibly mean only one thing and that is sound. This chapter is about sound and other slow waves, and how they, too, can be unwoven like a rainbow. Sound weaves travel about a million times more slowly than light (or radio) waves, not much faster than a Boeing 747 and slower than a Concorde. Unlike light and other electromagnetic radiation, which propagates best through a vacuum, sound waves travel only through a material medium such as air or water. They are waves of compression and rarefaction (thickening and thinning) of the medium. In air, this means waves of increasing and then decreasing local barometric pressure. Our ears are tiny barometers capable of tracking highspeed rhythmic changes of pressure. Insect ears work in another way entirely. In order to understand the difference, we need a small digression to examine what pressure really is.
We feel pressure on our skin, when we place our hand over the outlet of a bicycle pump, for example, as a kind of springy push. Actually, pressure is the summed bombardments of thousands of molecules of air, whizzing about in random directions (as opposed to a wind, where the molecules predominantly flow in one particular direction). If you hold your palm up to a high wind you feel the equivalent of pressure - bombardment of molecules. The molecules in a confined space, say, the interior of a well-pumped bicycle tyre, press outwards on the walls of the tyre with a force proportional to the number of molecules in the tyre and to the temperature. At any temperature higher than -275? C (the lowest possible temperature, corresponding to complete motionlessness of molecules), the molecules are in continuous random motion, bouncing off each other like billiard balls. They don't only bounce off each other, they bounce off the inside walls of the tyre - and the walls of the tyre 'feel' it as pressure. As an additional effect, the hotter the air, the faster the molecules rush about (that's what temperature means), so the pressure of a given volume of air goes up when you heat it. By the same token, the temperature of a given quantity of air goes up when you compress it, i. e. raise the pressure by reducing the volume.
Sound waves are waves of oscillating local pressure change. The total pressure in, say, a sealed room is determined by the number of molecules in the room and the temperature, and these numbers don't change in the short term. On average, every cubic centimetre in the room will have the same number of molecules as every other cubic centimetre, and therefore the same pressure. But this doesn't stop there being local variations in pressure. Cubic centimetre A may experience a momentary rise in pressure at the expense of cubic centimetre B, which has temporarily donated some molecules to it. The increased pressure in A will tend to push molecules back to B and redress the balance. On the much larger scale of geography, this is what winds are - flows of air from high-pressure areas to low-pressure areas. On a smaller scale sounds
can be understood in this way, but they are not winds because they oscillate backwards and forwards very fast.
If a tuning fork is struck in the middle of a room, the vibration disturbs the local molecules of air, causing them to bump into neighbouring molecules of air. The tuning fork vibrates back and forth at a particular frequency, causing ripples of disturbance to propagate outwards in all directions as a series of expanding shells. Each wavefront is a zone of increased pressure, with a zone of decreased pressure following in its wake. Then the next wavefront comes, after an interval determined by
the rate at which the tuning fork is vibrating. If you stick a tiny, very fast-acting barometer anywhere in the room, the barometer needle will swing up and down as each wavefront passes over it. The rate at which the barometer needle oscillates is the frequency of the sound. A fast- acting barometer is exactly what a vertebrate ear is. The eardrum moves in and out under the changing pressures that hit it. The eardrum is connected (via three tiny bones, the famous hammer, anvil and stirrup, sequestered in evolution from the bones of the reptilian jaw hinge) to a kind of inverse harp in miniature, called the cochlea. As in a harp, the 'strings' of the cochlea are arranged across a tapering frame. Strings at the small end of the frame vibrate in sympathy with high-pitched sounds, those at the big end vibrate in sympathy with low-pitched sounds. Nerves from along the cochlea are mapped in an orderly way in the brain, so the brain can tell whether a low-pitched or a high-pitched sound is vibrating the eardrum.
Insect ears, by contrast, are not little barometers, they are little weather- vanes. They actually measure the flow of molecules as a wind, albeit a queer kind of wind which travels only a very short distance before reversing its direction. The expanding wavefront which we detect as a change in pressure is also a wave of movement of molecules: movement into a local area as the pressure goes up, then movement back out of that area as the pressure goes down again. Whereas our barometer ears have a membrane stretched over a confined space, insect weather-vane ears have either a hair, or a membrane stretched over a chamber with a hole. In either case, it is literally blown back and forth by the rhythmic, backward and forward movements of the molecules.
Sensing the direction of a sound is therefore second nature for insects. Any fool with a weather-vane can distinguish a north wind from an east wind, and a single insect ear finds it easy to tell a north-south oscillation from an east-west oscillation. Directionality is built into insects' method of detecting sound. Barometers aren't like that. A rise in pressure is just a rise in pressure, and it doesn't matter from which direction the added molecules come. We vertebrates therefore, with our barometer ears, have to calculate the direction of sound by comparing the reports of the two
ears, rather as we calculate colour by comparing the reports of different classes of cones. The brain compares the loudness at the two ears and separately it compares the time of arrival of sounds (especially staccato sounds) at the two ears. Some kinds of sounds lend themselves to such comparisons less readily than others. Cricket song is cunningly pitched and timed so as to be hard for vertebrate ears to locate, but easy for female crickets, with their weather-vane ears, to home in upon. Some cricket chirps even create the illusion, at least to my vertebrate brain, that the (in fact stationary) cricket is leaping about like a jumping squib.
Sound waves form a spectrum of wavelengths, analogous to the rainbow. The sound rainbow is also subject to unweaving, which is why it is possible to make any sense of sounds at all. Just as our sensations of colour are the labels that the brain slaps on to light of different wavelengths, the equivalent internal labels that it uses for sounds are the different pitches. But there is a lot more to sound than simple pitch, and this is where unweaving really comes into its own.
A tuning fork or a glass harmonica (an instrument favoured by Mozart, made from fine glass bowls tuned by the depth of water they contain, sounded by a wetted finger drawn around the rim) emit a crystalline pure sound. Physicists call these sine waves. Sine waves are the simplest kind of waves, sort of theoretical ideal waves. The smooth curves that snake along a rope when you wiggle one end up and down are more or less sine waves, although of much lower frequency than sound waves, of course. Most sounds are not simple sine waves but are more jagged and complicated, as we shall see. For the moment we shall think of a tuning fork or glass harmonica, singing out its smooth, curvaceous waves of pressure change that race away from the source in concentrically expanding spheres. A barometer ear placed at one spot detects a smooth increase in pressure followed by a smooth decrease, rhythmically oscillating with no kinks or wiggles in the curve. With every doubling in frequency (or halving in wavelength, which is the same thing) we hear a jump of one octave. Very low frequencies, the deepest notes of the organ, shudder through our bodies and are hardly heard by our ears at all. Very high frequencies are inaudible to humans (especially older humans) but audible to bats and used by them, in the form of echoes, to find their way about. This is one of the most enthralling stories in all natural history, but I've devoted a whole chapter to it in The Blind Watchmaker so will resist the temptation to expand.
Tuning forks and glass harmonicas aside, pure sine waves are largely a mathematical abstraction. Real sounds are mostly more complicated mixtures, and they richly repay unweaving. Our brains unweave them effortlessly and to astonishing effect. It is only with much labour that our mathematical understanding of what is going on has caught up, clumsily
and incompletely, with what our ears have effortlessly unwoven - and our brains rewoven - from childhood on.
Suppose we sound one tuning fork with an oscillating frequency of 440 cycles per second, or 440 Hertz (Hz). We shall hear a pure tone, the A above middle C. What is the difference between this and a violin playing the same A, a clarinet playing the same A, an oboe, a flute? The answer is that each instrument includes admixtures of waves whose frequencies are various multiples of the fundamental frequency. Any instrument playing the A above middle C will deliver most of its sound energy at the fundamental frequency, 440 Hz, but superimposed will be traces of vibration at 880 Hz, 1520 Hz and so on. These are called harmonics, although the word can be confusing since 'harmonies' are chords of several notes that we hear as distinct. A 'single' trumpet note is actually a mixture of harmonics, the particular mixture being a kind of trumpet 'signature' that distinguishes it from, say, a violin playing the 'same' note (with different, violin signature harmonics). There are additional complications, which I shall ignore, around the onset of sounds, for example the lippy irruption of a trumpet blast or the zing as a violin bow hits the string.
These complications aside, there is a characteristic trumpet (or violin, or whatever it is) quality to the sustained part of a note. It is possible to demonstrate that the apparently single tone of a particular instrument is a rewoven construct of the brain, summing up sine waves. The demonstration works as follows. Having decided which sine waves are involved in, say, trumpet sound, select the appropriate 'tuning fork' pure tones and sound them one at a time. For a brief period you can hear the separate notes, as if they really were a chord of tuning forks. Then, quite eerily, they click into focus with each other, the 'tuning forks' disappear, and you hear only what Keats called the silver, snarling trumpets, sounding the pitch of the fundamental frequency. A different barcode combination of frequencies is needed to make the sound of a clarinet, and "again you can fleetingly distinguish them as separate 'tuning forks' before the brain homes in on the illusion of one 'woody' clarinet note. The violin has its own barcode signature, and so on.
Now, if you watch a tracing of the pressure wave when a violin is playing some note, what you see is a complicated wiggly line repeating itself at the fundamental frequency but with smaller wiggles of higher frequency superimposed. What has happened is that the different sine waves that constitute violin noise have summed up to make the complicated wiggly line. It is possible to program a computer to analyse any complicatedly repeating pattern of wiggles back into its component pure waves, the separate sine waves that you would have to sum up to make the complicated pattern. Presumably, when you listen to an instrument, you
are performing something equivalent to this calculation, the ear first unweaving the component sine waves, then the brain weaving them together again and giving them the appropriate label: 'trumpet, 'oboe' or whatever it is.
But our unconscious feats of unweaving and weaving are greater even than this. Think what is happening when you listen to a whole orchestra. Imagine that, superimposed on a hundred instruments, your neighbour in the concert is whispering learned music criticism in your ear, others are coughing and, lamentably, somebody behind you is rustling a chocolate wrapper. All these sounds, simultaneously, are vibrating your eardrum and they are summed into a single, very complicated wriggling wave of pressure change. We know it is one wave because a full orchestra, and all the noises off, can be rendered into a single wavy groove on a phonograph disc, or a single fluctuating trace of magnetic substance on
a tape. The entire set of vibrations sums up into a single wiggly line on the graph of air pressure against time, as recorded by your eardrum. Mirabile dictu, the brain manages to sort out the rustling from the whispering, the coughing from the door banging, the instruments of the orchestra from each other. Such a feat of unweaving and re-weaving, or analysis and synthesis, is almost beyond belief, but we all do it effortlessly and without thinking. Bats are even more impressive, analysing stuttering volleys of echoes to build up, in their brains,
detailed and fast-changing three-dimensional images of the world
through -which they fly, including the insects which they catch on the wing, and even sorting out their own echoes from those of other bats.
The mathematical technique of decomposing 'wiggling waveforms into sine waves which can then be summed again to make the original wiggly line is called Fourier analysis, after the nineteenth-century French mathematician Joseph Fourier. It works not just for sound waves (indeed, Fourier himself developed the technique for a quite different purpose) but for any process that varies periodically, and it doesn't have to be high- speed waves like sound, or ultra-high-speed waves like light. We can think of Fourier analysis as a mathematical technique which is convenient for unweaving 'rainbows' where the vibration that makes up the spectrum is slow compared with that of light.
To go to a very slow vibration indeed, I recently saw, on a road in the Kruger National Park in South Africa, a wiggly wet line which followed the course of the road and apparently traced out some kind of complicated repeat pattern. My host and expert guide told me that it was a trail of urine from a male elephant in musth. When a bull elephant enters this curious state (perhaps the elephantine equivalent of an Australian on 'walkabout') he dribbles out urine more or less continuously, apparently for scent-marking purposes. The side-to-side
waving of the urine trail on the road was presumably produced by the long penis acting as a pendulum (it would be a sine wave if the penis were a perfect, Newtonian pendulum, which it is not) interacting with the more complicated periodicity of the lumbering four-footed gait of the whole animal. I took photographs with the vague intention of later performing a Fourier analysis. I am sorry to say I have never got around to doing it. But in theory it could be done. A tracing of the photographed urine line could be laid over squared paper and its coordinates digitized for feeding into a computer. The computer could then perform a modern version of Fourier's calculations and extract the component sine waves. There are easier (though not necessarily safer) ways to measure the length of an elephant's penis, but it would have been fun to do, and Baron Fourier himself would surely have been delighted at such an unexpected use of his mathematics. There is no reason why a urine trail might not fossilize, as footprints and worm casts do, in which case we could in principle use Fourier analysis to measure the penis length of an extinct mastodon or woolly mammoth, from the indirect evidence of its urine trail in musth.
An elephant's penis swings at a frequency much slower than sound (although in the same ballpark as sound when you compare it with the ultra high frequencies of light). Nature offers us other periodic waveforms, of much lower frequency still, with wavelengths measured in years or even millions of years. Some of these have been subjected to the equivalent of Fourier analysis, including the cycles of animal populations. Since 1756, the Hudson's Bay Company kept records of the abundance
of pelts brought in by Canadian fur trappers. The distinguished Oxford ecologist Charles Elton (1900-1991), who was employed as a consultant by the company, realized that these records could provide a read-out of fluctuating populations of snow-shoe hares, lynxes and other mammals persecuted by the fur trade. The figures rise and fall in complicated mixtures of rhythms, which have been much analysed. Among the wavelengths that have been pulled out by these analyses is a prominent one of approximately four-year periodicity, and another of around 11 years. One hypothesis that has been suggested to account for the four- year rhythms is a time-lagged interaction between predators and prey (a glut of prey feeds a plague of predators, who then nearly wipe out the prey; this in turn starves the predators, then the consequent drop in predator population allows a new boom in the prey population, and so on). As for the longer rhythm of 11 years, perhaps the most intriguing suggestion connects it with sun spot activity, which is known to vary on an approximately 11-year cycle. How the sun spots affect animal populations is open to discussion. Perhaps they change the earth's weather, which affects abundance of plant food.
Wherever you find regular cycles of very long wavelengths, they are likely to have astronomical origins. They stem from the fact that celestial objects often rotate on their own axis, or follow repetitious orbits around other celestial objects. Twenty-four-hour rhythms of activity pervade almost all the fine details of living bodies on this planet. The ultimate reason is the rotation of the earth about its own axis, but animals of many species, including humans, when isolated from direct contact with day and night, continue to cycle on with a rhythm of approximately 24 hours, showing that they have internalized the rhythm and can free-run it even in the absence of the external pacemaker. The lunar rhythm of 28 days is another prominent component of the mix of waves in the bodily functions of many creatures, especially marine ones. The moon exerts its rhythmic influence via the succession of spring and neap tides. The earth's orbital rhythm of slightly more than 365 days contributes its slower pendulum to the Fourier sum, manifesting itself via breeding seasons, seasons of migration, patterns of moulting and growth of winter coats.
Perhaps the longest wavelength picked up by the unweaving of biological rhythms is a suggested 26-million-year cycle of mass extinctions. Fossil experts reckon that more than 99 per cent of the species that have ever lived have become extinct. Fortunately, the rate of extinction is, over the long term, roughly balanced by the rate at which new species are formed by the splitting of existing ones. But this doesn't mean they stay
constant in the shorter term. Far from it. Extinction rates fluctuate all over the place, and so do the rates at which new species come into existence. There are bad times when species disappear, and good times when they burgeon. Probably the worst of the bad times, the most devastating Armageddon, occurred at the end of the Permian era, about a quarter of a billion years ago. Around 90 per cent of all species became extinct in that terrible time, including on land many mammal-like reptiles. Earth's fauna eventually bounced back on to the denuded stage, but with a very different cast list: on land the dinosaurs stepped into the range of costumes left by dead mammal-like reptiles. The next largest mass extinction - and the most talked about - is the famous Cretaceous extinction of 65 million years ago, in which all the dinosaurs, and many other species with them both on land and in the sea, were wiped out, instantaneously as far as the fossil record can tell. In the Cretaceous event, perhaps 50 per cent of all species went extinct, not as many as in the Permian but nevertheless this was a fearful global tragedy. Once again, our planet's devastated fauna bounced back and here we are, we mammals, descended from a few fortunate relicts of the once rich mammal-like reptile fauna. Now we, together with the birds, fill gaps left by the dead dinosaurs. Until, presumably, the next great extinction.
There have been many episodes of mass extinction, not as bad as the Permian and Cretaceous events, but still noticeable in the chronicles of the rocks. Statistical paleontologists have gathered the numbers of fossil species over the ages and fed them into computers to perform Fourier analysis and extract such rhythms as they can find, as if listening for the flutter of preposterously deep organ notes. The dominant rhythm that has been claimed (albeit controversially) is a periodicity of about 26 million years. What could cause rhythms of extinction with such a formidably long wavelength? Probably only a celestial cycle.
Evidence is accumulating that the Cretaceous catastrophe was caused when a large asteroid or comet, the size of a mountain and travelling at tens of thousands of miles per hour, scored a direct hit on our planet, probably somewhere around what we now call the Yucatan peninsula in the gulf of Mexico. Asteroids hurtle round the sun in a belt which lies inside the orbit of Jupiter. There are plenty of asteroids out there - small ones are hitting us all the time - and a few of them are large enough to cause cataclysmic extinctions if they were to hit us. The comets have larger, eccentric orbits around the sun, mostly well outside what we conventionally think of as the solar system, but occasionally coming inside it, as Halley's comet does every 76 years and the Hale Bopp comet every 4,000 years or so. Perhaps the Permian event was caused by an even larger comet strike than the Cretaceous one. Perhaps the suggested 2 6-million-year cycle of mass extinctions is caused by a rhythmic boost in the rate of comet strikes.
But why should comets become more likely to hit us every million years? Here we launch ourselves into deep speculation. It has been suggested that the sun has a sister star, and the two orbit each other with a periodicity of about 26 million years. This hypothetical binary partner, which has never been seen but which has nevertheless been given the dramatic name Nemesis, passes, once per orbital rotation, through the so-called Oort Cloud, the belt of perhaps a trillion comets which orbits the sun beyond the planets. If there was a Nemesis that passed close to, or through, the Oort Cloud, it is plausible that it would disturb the comets, and this might increase the likelihood of one of them hitting earth. If this all happened - and the chain of reasoning is admittedly tenuous - it could account for the 26-million-year periodicity of mass extinctions that some people think the fossil record shows. It is a pleasing thought that mathematical unweaving of the noisy spectrum of animal extinctions might be the only means we have of detecting an otherwise unknown star.
Starting with the ultra high frequencies of light and other electromagnetic waves, we passed, via the intermediate frequencies of sound and the swinging elephant's penis, to ultra low frequencies and
the alleged 26-million-year wavelength of mass extinctions. Let's return to sound, and in particular that crowning feat of the human brain, the weaving and unweaving of speech sounds. The vocal 'cords' are really a pair of membranes which vibrate together in the breathing passage like a pair of woodwind reeds. Consonants are produced as more or less explosive interruptions of the air flow, caused by closure and contact of the lips, teeth, tongue and back of throat. Vowels vary in the same kind of way as trumpets differ from oboes. We make different vowel sounds rather as a trumpeter moves a mute in and out, to shift the preponderant sine waves summing into the composite sound. Different vowels have different combinations of harmonics above the fundamental frequency. The fundamental frequency itself, of course, is lower for men than for women and children, yet male vowels sound similar to the corresponding female vowels because of the pattern of harmonics.
Each vowel sound has its own characteristic pattern of frequency stripes, like barcodes once again. In the study of speech, the barcode stripes are called 'formants'.
Any one language, or dialect within a language, has a finite list of vowel sounds, and each of those vowel sounds has its own formant barcode. Other languages, and different accents within languages, have different vowel sounds which are made by holding the mouth and tongue in intermediate positions, again as a trumpeter disposes the mute in the
bell of the instrument. Theoretically there is a continuous spectrum of vowel sounds. Any one language employs a useful selection, a discontinuous repertoire picked out from the continuous spectrum of available vowels. Different languages pick out different points along the spectrum. The vowel in the French tu and the German uber, which doesn't occur in (my version of) English, is approximately intermediate between oo and ee. It doesn't too much matter which landmark points along the spectrum of available vowels a language picks on, so long as they are spaced far enough apart to avoid ambiguity within that language.
The story for consonants is more complicated, but there is a similar range of consonant barcodes, with actual languages employing a limited subset from those available. Some languages employ sounds which are far off the spectrum of the majority of languages, for example the clicks of some southern African tongues. As with vowels, different languages parcel up the available repertoire differently. Several of the languages of the Indian subcontinent have a dental sound which is intermediate between the English 'd' and 't'. The French hard 'c' as in comme is intermediate between the English hard 'c' and hard 'g' (and the 'o' is intermediate between the English vowels in cod and cud). The tongue, lips and voice can be modulated to produce an almost infinite variety of consonants and vowels. When the barcodes are patterned in time to form
phonemes, syllables, words and sentences, the range of ideas that can be communicated is unlimited.
Stranger yet, the things that can be communicated include images, ideas, feelings, love and exultation - the kind of thing that Keats does so sublimely.
My heart aches, and a drowsy numbness pains My sense, as though of hemlock I had drunk, Or emptied some dull opiate to the drains One minute past, and Lethe-wards had sunk: Tis not through envy of thy happy lot, But being too happy in thy happiness - That thou, light- winged Dryad of the trees, In some melodious plot Of beechen green, and shadows numberless, Singest of summer in full-throated ease.
'Ode to a Nightingale' (1820)
Read the words aloud and the images tumble into your brain, as if you really were drugged by a nightingale's song in a leafy summer beechwood. At one level it is all done by a pattern of air pressure waves, a pattern whose richness is first unwoven into sine waves in the ear and then rewoven together in the brain to reconstruct images and emotions. Stranger yet, the pattern can be broken down mathematically into a stream of numbers, and it retains its power to transport and haunt the imagination. When a laser disc (CD) is made, say, of the Saint Matthew Passion, the rising and falling pressure wave, with all its wiggles and kinks, is sampled at frequent intervals and translated into digital data. The digits could, in principle, be printed as dull, black and white zeroes and ones on reams of paper. Yet the numbers retain the power, if transduced back into pressure waves, to move a listener to tears.
Keats may not have intended it literally, but the idea of nightingale song working as a drug is not totally far-fetched. Consider what it is doing in nature, and what natural selection has shaped it to do. Male nightingales need to influence the behaviour of female nightingales, and of other males. Some ornithologists have thought of song as conveying information: 'I am a male of the species Luscinia megarhynchos, in breeding condition, with a territory, hormonally primed to mate and build a nest. ' Yes, the song does contain that information, in the sense that a female who acts on the assumption that it is true could benefit thereby. But another way to look at it has always seemed to me more vivid. The song is not informing the female but manipulating her. It is not so much changing what the female knows as directly changing the internal physiological state of her brain. It is acting like a drug.
There is experimental evidence from measuring the hormone levels of female doves and canaries, as well as their behaviour, that the sexual
state of females is directly influenced by the vocalizations of males, the effects being integrated over a period of days. The sounds from a male canary flood through the female's ears into her brain where they have an effect that is indistinguishable from one that an experimenter can procure with a hypodermic syringe. The male's 'drug' enters the female through the portals of her ears rather than through a hypodermic, but this difference does not seem particularly telling.
The idea that birdsong is an auditory drug gains plausibility when you look at how it develops during the individual's lifetime. Typically, a young male songbird teaches himself to sing by practising: matching up fragments of trial song against a 'template' in his brain, a pre- programmed notion of what the song of his species 'ought' to sound like. In some species, such as the American song sparrow, the template is built in, programmed by the genes. In other species, such as the white crowned sparrow or the European chaffinch, it is derived from a 'recording' of another male's song, made early in the young male's life from listening to an adult. Wherever the template comes from, the young male teaches himself how to sing in such a way as to match it.
That, at least, is one way to talk about what happens when a young bird perfects his song. But think of it another way. The song is ultimately designed to have a strong effect on the nervous system of another member of the species, either a prospective mate or a possible territorial rival who needs to be warned off. But the young bird himself is a member of his own species. His brain is a typical brain from that species. A sound that is effective in arousing his own emotions is likely to be as effective in arousing a female of the same species. Instead of speaking of the young male trying to shape his practice song to 'match' a built-in 'template', we could think of him as practising on himself as a typical member of his species, trying out fragments of song to see whether they excite his own passions, that is, experimenting with his own drugs on himself. And, to complete the circuit, perhaps it is not too surprising that nightingale song should have acted like a drug on the nervous system of John Keats. He was not a nightingale, but he was a vertebrate, and most drugs that work on humans have a comparable effect upon other vertebrates. Man- made drugs are the products of comparatively crude trial and error testing by chemists in the laboratory Natural selection has had thousands of generations in which to fine-tune its drug technology.
Should we feel indignant on Keats's behalf at such a comparison? I do not believe that Keats himself would have done so - Coleridge even less. The 'Ode to a Nightingale' accepts the implication of the drug analogy, makes it wonderfully real. It is not demeaning to human emotion that we try to analyse and explain it, any more than, to a balanced judge, the rainbow is diminished when a prism unweaves it.
In this chapter and the previous one, I have used the barcode as a symbol of precise analysis, in all its beauty. Mixed light is sorted into its rainbow of component colours and everybody sees beauty. That is a first analysis. Closer detail reveals fine lines and a new elegance, the elegance of detection, of the bringing of order and understanding. Fraunhofer barcodes speak to us of the exact elemental nature of distant stars. A precisely measured pattern of stripes is a coded message from across the parsecs. There is grace in the sheer economy of unweaving intimate details about a star which, one had thought, could be found only through the costly undertaking of a journey lasting 3,000 human lifetimes. On another scale, we find a similar story when we look at the formant stripes in speech, the harmonic barcodes of music. There is elegance, too, in the barcodes of dendrochronology: the stripes across ancient Sequoia wood which tell us precisely in which year BC the tree was seeded, and what the weather was like in every one of the intervening years (for weather conditions are what give tree rings their characteristic widths). Like Fraunhofer's lines transmitted across space, tree rings transmit messages to us across time, and again there is a supple economy. It is the power - the fact that we can learn so much by precise analysis of what seems so little information - that gives these unweavings their beauty. The same is true, perhaps even more dramatically, of sound waves in speech and music - barcodes on the air.
Recently we have been hearing much about another kind of barcode - DNA 'fingerprints', barcodes in the blood. DNA barcodes expose and reconstruct details of human affairs that one might have supposed forever inaccessible even to legendarily great detectives. The main practical use of barcodes in the blood so far is in courts of law, and it is to them - and the benefits that a scientific attitude may bring to them - that we turn in the next chapter.
5
BARCODES AT THE BAR
And he said, Woe unto you also, ye lawyers! for ye lade men with burdens grievous to be borne, and ye yourselves touch not the burdens with one of your fingers. . . . Woe unto you, lawyers', for ye have taken away the key of knowledge: ye entered not in yourselves, and them that were entering in ye hindered.
Luke 11
On the face of it, the law may seem about as far as you can get from poetry or the wonder of science. Perhaps there is poetic beauty in the abstract ideas of justice or fairness, but I doubt if many lawyers are moved by it. In any case, that is not what this chapter is about. I shall be looking at an example of the role of science in the law: at a different aspect of science and its importance in society; a sense in which scientific understanding may become a valuable part of good citizenship. In courts of law, juries are increasingly asked to understand evidence which the lawyers themselves may not fully comprehend. Evidence from the unweaving of DNA - what we shall come to see as barcodes in the blood - is the outstanding example, and it is the main subject of this chapter. But it is not just facts about DNA that scientists can contribute. More importantly, it is the underlying theory of probability and statistics; it is scientific ways of making inferences that need to be brought to bear. Such matters stretch beyond the narrow subject of DNA evidence.
I am told on good authority that defence lawyers in the United States sometimes object to jury candidates on the grounds that they have had a scientific education. What can this mean? I would not question the right of defence lawyers to disallow the selection of particular jurors. A juror may be prejudiced against the race or class to which the defendant belongs. It is obviously undesirable that a raving homophobe should try a case of anti-homosexual violence. It is for this kind of reason that defence lawyers in some countries are allowed to cross-examine potential jurors and strike them off the list. In the USA lawyers can be completely blatant about their criteria for jury selection. A colleague tells me of a time when he was up for selection to a jury, on an injury litigation case. The lawyer asked, 'Would anyone here have a problem awarding a substantial amount of money to my client, perhaps in the millions? '
A lawyer can also disqualify a juror without giving reasons. Although this may be just, the only time I have seen it happen it misfired. I was a member of a panel of 24 individuals from which juries of 12 were to be selected. I had already participated in two juries with members of this panel, and I knew their individual foibles. One particular man was cast- iron prosecution fodder; he would take the same hard line almost regardless of the particular case. The defence lawyer waved him through like a breeze. The next one up, a large middle-aged woman, was the opposite: a guaranteed softie, a pure gift to the defence. But her appearance perhaps suggested the opposite, and it was against her that the defence lawyer chose to exercise his right of veto. I have never forgotten the look of wounded hurt on her face as, with a cutting movement of the hand, learned counsel struck her - whom he little knew could have been his secret weapon - out of the jury box.
But, to repeat the astonishing fact, lawyers in the United States have been known to use the following reason for striking down potential jurors: the prospective juror is well educated in science, or has some knowledge of genetics or probability theory. What is the problem? Are geneticists known to harbour deep-seated prejudices against certain sections of society? Are mathematicians especially likely to be of the "flog 'em . . . string 'em up . . . it's the only language they understand . . . law and
order' persuasion? Of course not. Nobody has ever claimed such a thing.
The lawyers' objections are more ignobly based. There is a new kind of evidence increasingly coming into the criminal courts: evidence from
DNA fingerprinting, and it is extremely powerful. If your client is innocent, DNA' evidence may well provide a knock-down convincing way to establish his innocence. Conversely, if he is guilty, DNA evidence has a good chance of establishing his guilt in cases where no other evidence can. DNA evidence is quite hard to understand at the best of times.
There are controversial aspects of it which are even harder. In these circumstances, you would think that an honest lawyer who wishes to see justice done would welcome jurors capable of grasping the arguments. Wouldn't it be an obviously good thing to have at least one or two people in the jury room who can redress the ignorance of their baffled colleagues? What kind of a lawyer is it who prefers a jury incapable of following the case that either attorney is making?
The answer is a lawyer who is more interested in winning than in seeing justice done. A lawyer, in other words. And it seems to be a fact that advocates, of both prosecution and defence, frequently disallow individual jurors specifically because they are educated in science.
Courts of law have always needed to establish individual identity. Was the individual seen hurrying from the scene Richard Dawkins? Is the hat dropped at the scene of the crime his hat? Are those his fingerprints on the weapon? A yes answer to one of these questions does not by itself prove his guilt, but it is certainly an important factor to be taken into account. Most of us, including most jurors and lawyers, have an intuitive sense that there is something specially reliable about eye-witness evidence. In this we are almost certainly wrong, but the error is a pardonable one. It may even be built into us by millennia of evolutionary history in which eye-witness evidence really was the most reliable. If I see a man in a red woolly hat climbing a drainpipe, you will have a hard time persuading me later that he was actually wearing a blue beret. Our intuitive biases are such that eye-witness evidence trumps all other categories. Yet numerous studies have shown that eye-witnesses, however convinced they may be, however sincere and well-meaning, frequently mis-remember even conspicuous details such as the colour of clothing and the number of assailants present.
When individual identification is important, for instance when a woman who has been raped is called upon to identify her attacker, courts perform a rudimentary statistical test known as the identity parade or line-up. The woman is led past a line of men, one of whom the police suspect on other grounds. The others have been pulled in off the streets or are out-of-work actors, or police officers dressed in plain clothes. If the woman picks out one of these stooges, her identification evidence is discounted. But if she picks out the man the police already suspect, her evidence is taken seriously.
Rightly so. Especially if the number of people in the identity parade is large. We are all statisticians enough to see why this is. The prior suspicion of the police must be open to doubt - otherwise there would be no point in seeking the woman's evidence at all. What impresses us is agreement between the woman's identification and the independent evidence offered by the police. If the identity parade contains only two men, the witness would have a 50 per cent chance of picking the man already suspected by the police, even if she chose at random - or if she were mistaken. Since the police might also be mistaken, this represents an unacceptably high risk of injustice. But if there are 20 men in the line, the woman has only a 1 in 20 chance of choosing, by guesswork or error, the man the police already suspect. The coincidence of her identification and the police's prior suspicion probably really means something. What
is going on here is the assessment of coincidence, or the odds that something might happen by chance alone. The probability of meaningless coincidence is even less if the identity parade has 100 men, because a 1 in 100 chance of error is noticeably less than a 1 in 20 chance of error. The longer the line-up, the more secure the eventual conviction.
We also have an intuitive sense that the men chosen for the line-up must not look too obviously different from the suspect. If the woman originally told the police to look for a man with a beard, and the police have now arrested a bearded suspect, it is clearly unjust to stand him in a line with 19 clean-shaven men. He might as well be standing by himself. Even if the woman has said nothing about the appearance of her attacker, if the police have arrested a punk in a leather jacket it would be wrong to stand him in a line of suited accountants with furled umbrellas. In multiracial countries such considerations have added importance. Everyone understands that a black suspect should not be placed in an otherwise all-white line-up, or vice versa.
When we think about how we identify somebody, the face first leaps to mind. We are particularly good at distinguishing faces. As we shall see in another connection, we even seem to have evolved a special part of the brain set aside for the purpose, and certain kinds of brain damage
disable our face-recognition faculty while leaving the rest of vision intact. In any case, faces are good for recognition because they are so variable. With the well-known exception of identical twins, you seldom meet two people whose faces are confusable. It is not totally unknown, however, and an actor can be made up to look very like somebody else. Dictators often employ doubles to perform for them when they are too busy, or to draw the fire of assassins. It has been suggested that one reason charismatic leaders so often sport moustaches (Hitler, Stalin, Franco, Saddam Hussein, Oswald Mosley) is to make it easier for doubles to impersonate them. Mussolini's shaven head perhaps served the same purpose.
Apart from identical twins, ordinary close relatives are sometimes sufficiently alike to fool people who don't know them well. (Unfortunately the story that Doctor Spooner, when Warden of my college, once stopped an undergraduate and said, 'I never can remember is it you or your brother was killed in the war? ' is probably not true, like most alleged Spoonerisms. ) The resemblance of brothers and sisters, of fathers and sons, of grandparents and grandchildren, serves to remind us of the huge pool of facial variety in the general population of non-relatives.
But faces are only a special case. We are riddled with idiosyncrasies which, with sufficient training, can be used to identify individuals. I had
a school friend who claimed (and my spot checks confirmed it) that he could recognize any member of the 80-strong residence in which we lived purely by listening to their footsteps. I had another friend from Switzerland who claimed that when she walked into a room she could tell, by smell, which members of her circle of acquaintances had recently left the room. It is not that her colleagues didn't wash, just that she was unusually sensitive. That this is in principle possible is confirmed by the fact that police dogs can distinguish between any two human beings by smell alone, with the exception, yet again, of identical twins. As far as I know, the police haven't adopted the following technique, but I bet you could train bloodhounds to track down a kidnapped child after giving them a sample sniff of his brother. A way might even be found to use a jury of bloodhounds to decide paternity cases.
Voices are as idiosyncratic as faces, and various research teams are working on computer voice recognition systems for authenticating identity. It would be a great boon if, in the future, we could dispense with front door keys and rely on a voice-operated computer to obey our personal Open Sesame command. Handwriting is sufficiently individual for the written signature to be used as a guarantee of identity on bank cheques and important legal documents. Signatures are actually not particularly secure because they are too easily forged, but it is still impressive how recognizable handwriting can be. A promising newcomer
to the list of individual 'signatures' is the iris of the eye. At least one bank is experimenting with automated iris-scanning machines as a way of verifying identity. The customer stands in front of a camera which photographs the eye, digitizes the image into what a newspaper described as 'a 256 byte: human barcode'. But none of these methods of verifying human identity even comes close to the potential of DNA fingerprinting, properly applied.
It is not surprising that police dogs can smell the difference between any two humans except identical twins. Our sweat contains a complicated cocktail of proteins, and the precise details of all proteins are minutely specified by the coded DNA instructions that are our genes. Unlike handwriting and faces, which vary continuously and grade smoothly into one another, genes are digital codes, much like those used in computers. Again with the exception of identical twins, we differ genetically from all other people in discrete, discontinuous ways: an exact number of ways that you could even count if you had the patience. The DNA in each one of my cells (give or take a tiny minority of mistakes, and not including red blood cells which have lost all their DNA, or reproductive cells which contain a random half of my genes) is identical to the DNA in all my other cells. It differs from the DNA in every one of your cells, not in some vague, impressionistic way but at a precise number of locations dotted along the billions of DNA letters that we both have.
It is almost impossible to exaggerate the importance of the digital revolution in molecular genetics. Before Watson and Crick's epochal announcement in 1953 of the structure of DNA, it was still possible to agree with the concluding words of Charles Singer's authoritative A Short History of Biology, published in 1931:
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