The Midwich Cuckoos by John Wyndham (1957)

‘I say, sir, this is a bit of a facer, isn’t it?’ said Alan
‘I’m afraid it is,’ Zellaby agreed.
(The Midwich Cuckoos, page 80)

John Wyndham’s husband-and-wife teams

The Midwich Cuckoos opens as if it’s going to be another husband-and-wife story, much like The Kraken Wakes. Having read the 15 short stories in Jizzle I can now see that Wyndham is, by inclination, a whimsical and humorous writer. He slips into a homely, drawing room style whenever he writes about his nice middle-class couples, in which the woman is invariably the stronger, more determined one and the slightly-henpecked, narrating husband wryly acknowledges her superior qualities. The entire attitude is epitomised in one of many similar exchanges from Kraken:

‘Mike, darling, just shut up; there’s a love,’ said my devoted wife.

Like Kraken (whose couple are named Mike and Phyllis), Midwich (couple named Richard and Janet) is littered with throwaway jests about this or that aspect of married life, along with sardonic jokes about his or her jobs, stereotyped social attitudes to marriage, pregnancy and so on, pregnancy being, of course, the central subject of the story.

A village story

That said, after the opening scenes, Midwich Cuckoos quite quickly opens up to cover a far larger canvas than just a husband and wife. Indeed Richard and Janet disappear from the text for long stretches, as it focuses more on the household who live at Kyle Manor, namely the thoughtful but long-winded old author, Gordon Zellaby, his (second) wife, Angela, their fragrantly pukkadaughter Ferrelyn, and her fiancé, dashing Second-Lieutenant Alan Hughes, currently serving in the army.

But it’s more than just these half dozen upper-middle-class types; the novel opens out to include a larger cast of characters and to become a kind of portrait of an English village in the mid-1950s. Thus there are quite large speaking parts for the vicar and his wife, the village doctor and his wife, the landlord of the village pub (The Scythe and Stone), the village baker, half a dozen labourer families, and various pretty village girls and their sweethearts, not forgetting the striking inclusion of a pair of village lesbians, Miss Latterly and Miss Lamb.

Cast list

One aspect of the large cast of characters is the sense the novel gives you of the gentle but persistent class divide between the (presumably privately) educated, upper-middle-class types (the Gayfords and the Zellabies), the middle-to-lower-middle class professionals who service them and the other authority figures (the vicar, doctor, police chief, fire chief) and ‘the rest’, the ruck of villagers and rustics, ranging from small shopkeepers (pub landlord, baker, grocer) and local farmers down to the manual labourers and their harassed wives, with a floating population of pretty young things who are no better than they should be. It’s sweet.

The Posh

  • Gordon Zellaby, who Janet jokingly refers to as ‘the sage of Midwich’ (p.101), working away on his latest book, facetiously referred to as the ‘Current Work, lives at spacious Kyle Manor with his second wife, Angela
  • their posh daughter Ferrelyn
  • her fiancé Lieutenant Alan Hughes
  • the initial narrator, writer Richard Gayford and his wife Janet
  • Mr Arthur Crim OBE, Director of the Research Station located in the Grange (p.52)
  • Tilly Foresham, jodhpurs and three dogs

It’s worth noting that the Zellabies employ a cook and maybe other domestic staff, as breakfast, luncheon, tiffin, dinner and late supper all appear as if by magic, prepared by unseen, unnamed hands.

The admin class

  • the Reverend Hubert Leebody, the vicar (p.91) and his wife, Dora Leebody (who has a breakdown and is sent away to a rest home)
  • Miss Polly Rushton, their pretty young niece
  • Dr Charley Willers and his wife, Milly (p.89)
  • Nurse Daniels

The lower-middle class

  • Miss Ogle, an elderly gossip who runs the village post office and telephone exchange
  • Mr Tapper, the retired gardener
  • Miss Latterly and Miss Lamb the village lesbians (pp.82)
  • Wilfred Williams, landlord of the Scythe and Stone
  • Harriman the baker

The working classes

  • Mr Brant the blacksmith and his wife
  • Alfred Wait
  • Harry Crankhart
  • Arthur Flagg labourer
  • Tom Dorry, rating in the Navy
  • Mr Histon

As we hear more about all these figures and are given little vignettes about them, the village comes to seem more like an Ealing Comedy than a disaster movie. There are quite a few bits of dialogue which come straight from the lips of pukka chaps in 1950s movies (‘I say, I’ll have to step on it. See you tomorrow, darling’) or which you can imagine being voiced by Joyce Grenfell in one of the original St Trinian’s movies (which appeared over exactly the same period as Wyndham’s classic novels):

  • The Belles of St Trinian’s (1954)
  • Blue Murder at St Trinian’s (1957)
  • The Pure Hell of St Trinian’s (1960)

There are two schools of thought about this aspect of Wyndham. One is the well-known Brian Aldiss criticism that his novels portray all-too ‘cosy catastrophes’ in which decent middle-class types respond with improbable decency and moral rectitude to global catastrophes, never going to pieces or being corrupted. There’s a lot of truth in this rather brusque putdown.

But there’s the equal and opposite interpretation, that the catastrophes he describes are made all the more realistic and scarey for not having technicolor special effects and not having characters go into psychotic states as per J.G. Ballard’s stories, but remaining stiff-upper-lip, pukka Brits in the face of complete social collapse (Triffids and Kraken in particular).

Having met so many public school types, now, I’m inclined to think most of them would survive a world apocalypse very well, and put their experience of the officer training corps, running big organisations, and huntin’, shootin’ and fishin’ to very effective use in post-apocalyptic scenarios.

Either way, The Midwich Cuckoos is obviously a science fiction yarn, but it’s maybe useful to flag up the way it is also a fascinating piece of 1950s social history.

Wyndham’s fateful nights

Of Wyndham’s four Big Novels, three start with ‘fateful nights’ when ‘the world changes forever!’

In Day of the Triffids, it’s the night of Tuesday 7 May when the whole world watches the spectacular meteor shower and, as a result, goes blind.

In The Kraken Wakes, it’s 11.15pm on the night of 15 July when Mike and Phyllis, on a honeymoon cruise, see the first fireballs fall into the sea.

And in The Midwich Cuckoos the novelist narrator and his wife are up in London celebrating him having signed a book contract with an American publisher, which means they’re not present in the nondescript, quiet little village of Midwich on the fateful night of 26 September!

(And, once you realise that The Chrysalids is set in the aftermath of a calamitous nuclear war, you realise it’s likely that that, too, took place on a specific day, maybe night, although, centuries later no-one has any way of knowing when.)

Brief plot summary

The Midwich Cuckkos is 220 pages long in the old Penguin classic edition I own, a comfy, sensible length for an adventure novel. The text is in 21 chapters divided into 2 parts, 15 in the long part one, five in the short part two.

The story is fairly well known, not least from the terrifying 1960 movie adaptation, Village of the Damned, so successful at the box office that it prompted a sequel.

 

 

During the ‘fateful night’ of 26 September all the occupants of the village of Midwich pass out. Everyone trying to enter a perfectly circular radius around the village also passes out, presumably due to what used to be called a ‘force field’. The authorities get wind of it and the village is sealed off. 24 hours later the mystery condition disappears and everything returns to normal. Except that, a few months later, all the women of childbearing age report that they are pregnant (which causes obvious difficulty among couples who have stopped having sex, or for single women).

Nine months later the pregnant women all give birth. Their babies are all perfectly healthy but, as they develop, have an eerie similarity of appearance, with platinum blonde hair and piercing golden eyes. The inhabitants knew something strange has happened, and realise the children aren’t natural. And as they grow it becomes clear that the Children can impose their wishes on their parents through some form of telepathy or mental control, which is eerie enough. But it’s only towards the end of the story that one of the leading figures, retired author Gordon Zellaby, comes to appreciate just how much of a threat they pose to all human life, and decides to take drastic action.

Detailed plot summary

Chapter 1 No entry to Midwich

Sets the scene, describes Midwich in the county of ‘Winshire’ (p.34) as an average English village with a handful of the usual historical episodes, including the dissolution of the local monastery, Cromwell’s men stopping over en route to some battle, a notorious 18th century highwayman, and so on.

The initial narrator of the story, author Richard Gayford, has lived in the village for just over a year (p.11) with his wife Janet. They are out of the village, up in London celebrating him signing a contract with American publishers on ‘the fateful night’ of 26 September.

On returning they find the village sealed off by the Army. Being naughty, they drive away from the roadblock but then double back, park at the entrance to a field and try to cut across fields to their cottage. Janet is making her way across a field when she suddenly drops to the ground unconscious. Richard runs forward and similarly blacks out.

Chapter 2 All quiet in Midwich

Quick overview of the village and what all its characters were up to on ‘the fateful night’ i.e. bickering in the pub, listening to the radio, trying to get a new-fangled television set to work, on the phone to a friend in London, relaxing in front of a nice roaring fire.

Chapter 3 Midwich rests

Briefly describes how a succession of early morning visitors to the village disappear, are heard from no more, including the baker’s van, local bus, an ambulance sent to find out what’s going on, a fire engine which goes to investigate reports of smoke, and so on.

Chapter 4 Operation Midwich

The army gets involved. Lieutenant Hughes finds himself consulting with the chiefs of the local fire brigade and police who are establishing a cordon round the village. Alan has the bright idea of getting a soldier to drive off to find a pet shop and requisition a canary in a cage which they can tentatively push forward into the ‘zone’ to see if it collapses. Then another soldier paints a white line on the ground and another indicates the perimeter on a map.

Richard and Janet are dragged by soldiers using a long hook a few yards from where they’re lying prone to just outside the ‘zone’ and immediately wake up and feel fine. They are driven along to the pub in the next door village, which they find packed with journalists, radio and TV people, and Richard is delighted to be hailed by Bernard Westcott, a colleague of his from back in the army days, who, it becomes clear, is now something in Military Intelligence.

Military Intelligence? Yes, they’re here not only because it’s an anomalous event, but because of The Grange. The Grange?

The Grange Upon investigation, it turns out that Midwich is not quite such a boring, average, run-of-the-mill village as the narrator initially implied. It is also home to an old grange building which has had a modern extension added which contains laboratories, amounting to a Research Station, supervised by Mr Arthur Crim OBE, Director of the Research. What kind of research goes on there? Well, a little surprisingly, we never really find out. And the entire question is, I think, a red herring, thrown in to complexify the early part of the story and make readers wonder whether the mysterious event is some kind of attack on the grange by ‘the enemy’. But by half way through it’s become clear that it wasn’t and the existence of the Grange is more or less irrelevant to the story.

But not here at the start. There is an impressive gathering of military and civil administrator types – army, air force Group Captain, chief policeman, head fireman and so on – who have a summit conference about how to deal with it. An airplane flies over and takes photos of the village. That and the patient perimeter work with the canary establish that the ‘zone’ comprises a perfect circle two miles in diameter., and at the dead centre sits a large object, which has a metallic appearance and looks like a convex spoon (p.36).

The Russians As in The Kraken Wakes there is much speculation about whether the event is an attack by the Russians, by ‘the other side’, by ‘those Ivans’ (p.38). This turns out to be irrelevant to the plot but it is a fascinating indication of how heavily the Cold War rivalry, and the threat from the Soviet bloc, and the constant fear of what new trick they might pull, weighed on the imagination of the West, or of western writers, or of western writers of science fiction, or of John Wyndham anyway.

Chapter 5 Midwich reviviscit

And then suddenly everybody wakes up. The advantage of Wyndham’s realistic style is he gives a very vivid description of what it feels like to wake up after 2 days suspended animation, in an unnatural position on the sofa or the floor, how you are utterly numb, the pain when the feeling slowly starts to return to your limbs and extremities.

Chapter 6 Midwich settles down

Describes how everyone concerned comes to cope with it, this strange event, which comes to be called the Dayout (p.47). No fewer than 11 people perished, several when their houses caught fire, several from exposure from lying out in the open for two days and nights (there’s a list on page 47).

Bernard Westcott pays a couple more visits to the village, specifically to check up on the Grange but drops into the Gayford cottage for chats. They invite Bernard for dinner and he asks Richard and Janet if they’ll be informal eyes and ears i.e. spy on the village. Janet is at first sceptical, what’s the need? Bernard points out there may be lingering after-effects: after all X-rays, radiation and so on are invisible. There’s no sign of those in the village, they’ve tested, but who knows what other after-effects there may be…

Chapter 7 Coming events

About two months later, in late November, Ferrelyn, after much nervousness, summons up the courage to tell Angela Zellaby, over posh breakfast at the Manor, that she’s pregnant. Angela astonishes Ferrelyn that shs is, too. What worries Ferrelyn, though, is that it isn’t Alan’s. It isn’t anyone’s. She’s a virgin. How can she be pregnant and she bursts into tears.

Briefly, the narrative explains how, over the next few days, women come forward to confide to the vicar, Mr Leebody, or the village doctor, Willers, that they are pregnant – from the oldest to the youngest, all fertile women in the village are pregnant!

Chapter 8 Heads together

Dr Willers calls on Gordon Zellaby to break the news that every fertile woman in the village is pregnant. Zellaby, in his detached intellectual way, considers the options, giving them smart Greek names:

  • parthenogenesis
  • some form of artificial insemination
  • xenogenesis

It is suggestive that the fertile women who spent the Dayout unconscious in the village bus are not pregnant because the bus was, for the duration, in plain sight of people outside the zone. Maybe whatever was done to the women inside the zone was not to be observed.

The Thinker Several points: Zellaby fulfils something of the same role as Bocker performs in Kraken Wakes and, up to a point, Uncle  Axel, in The Chrysalids – he is a figure peripheral to the main action, who can comment and analyse it. Exactly as Bocker is the first to realise that the fireballs in Kraken might come from another planet and is the first to grasp the threat they pose, so Zellaby in Cuckoos is the first to articulate the theory that the pregnancies are the result of conscious and co-ordinated action, the first to establish the Children’s telepath, and the first to grasp what a serious threat they pose.

But the role of all three characters (Bocker, Alex, Zellaby) is not only to crystallise the reader’s suspicions and move the plot forward, but to express intellectual ideas prompted by the book’s events. Thus Bocker not only warns about what is happening to earth, but speculates about what kind of intelligence has arrived on earth and interesting ideas about whether two intelligent but very different species can ever share a planet. (No, is the short answer).

Similarly, the central theme of The Chrysalids is ‘What is normality and what is deviance?’ and Uncle Alex is the mouthpiece of the author’s interesting ideas on the subject. For example, when Alex made his long sea voyage he discovered lots of communities which were ‘deviant’ in one way or another but each one regarded themselves as normal and all the others as the mutations. On a different but related trajectory, it is Alex who shares the speculation that, maybe David’s family and community, by trying to keep plant, animal and human lineage ‘pure’ and how they were before the nuclear holocaust, maybe they are setting themselves against biological change, when, in fact, evolution and change is the one constant of Life. So that maybe David’s mutation (he is a telepath) is an inevitable next step in human evolution and his family are trying to prevent the inevitable.

And so it is retired author and easily distracted Gordon Zellaby, his mind wandering on strange elusive patterns, who fulfils the same role in Cuckoos not only crystallising the action (I mean drawing together scattered events, making sense of them, as he explains them to Richard or Alan) but going on to express ideas and implications arising from the book’s premise.

Chapter 9 Keep it dark

This is a very interesting chapter because of the way the subject matter is treated. The plot level it is straightforward. Gordon and the doctor decide they must hold an Emergency Meeting of all the village’s womenfolk to explain to them what they think they’ve discovered, to bring it into the open and to air it.

What’s interesting is the extreme care they take to make it a women’s event – to invite only the women, and to ensure that the actual presentation is made by Angela Zellaby. It is a meeting for women, organised by women, and led by a woman. After she has made the initial presentation of the facts, she is emotionally shattered but insists to Gordon and the Willers (waiting in a room off to one side) that the next bit is the most important – it is absolutely vital that the women be given the space and time to talk about it, to talk it through and cultivate a feeling of communal solidarity.

Before and after Zellaby is given speeches, in his conversations with the village doctor, about how strange it is to be a woman and know your body is designed for childbirth, at the best of times, about the uncanniness of being so obviously an animal with a basic animal function of producing offspring, and yet fully human at the same time. A duality which men simply can’t understand, never fully.

This is also the chapter, at the meeting, where Miss Latterly, one of the pair of village lesbians gets up to storm out, outraged at the idea that she – who has never had anything to do with men – could be pregnant, only to be forced to stay when her lesbian partner, Miss Lamb mutely remain, dramatising in a surprisingly sensitive and effective way a) that the latter is pregnant b) her shame c) her partner’s mortification. It’s a good example of the way Wyndham’s terribly British way of handling these things conveys subtle shades of emotion.

Chapter 10 Midwich comes to terms

The Emergency Meeting leads to several outcomes. One is secrecy. No-one will tell anyone outside about it, not even the neighbouring villages, because Angela Zellaby made quite clear how hellish life would become if the world’s press were alerted and came to observe and report on every development during the remainder of the pregnancies.

The other is mutual support. Angela had made it plain that it is happening to all the women, regardless of married status, and so went out of her way to defuse stigma and shame and get all the other women to agree. Instead she led in setting up a programme of social activities and support and we are told the Zellabies themselves help out with money for the less well-off and for single mums.

Religion. In Triffids there was a conference of the survivors of the Great Blinding, held in a lecture room in Senate House during which a Miss Durrell expressed the Christian view that the catastrophe was God punishment of an immoral world. Similarly, in this novel, Mrs Dora Leebody, the vicar’s wife has a sort of breakdown and takes to preaching at the village war memorial that all the pregnant women have been cursed by God. A few days later she is found in the market square of the neighbouring town, dressed in sackcloth and ashes, preaching about God’s punishment. She is quietly brought home, sedated and then sent off by her husband to a rest home

But rather like the concern with the Russians expressed early in the novel, this brings home to the reader how prominent a factor in British culture Christianity was in the 1950s, in a way it probably wouldn’t be in the multicultural 2020s UK.

This comes out even more clearly in the final chapters where Zellaby engages in extended debates with the vicar about the morality of dealing with the Children, as they grow ever-more threatening.

Chapter 11 Well played, Midwich

Nerves hold up well through the spring until, in May, some of the heavily pregnant women start to crack under the uncertainty of not knowing what they are carrying in their wombs. Resilient and intelligent Angela Zellaby is given a speech declaring that men can never understand what it is like to be a woman, and not to have the faintest idea of the nightmare strain the pregnant women of Midwich are under (p.87).

Funnily enough, the first to have her baby is the lesbian Miss Lamb, who stumbles on a milk bottle on her doorstep, takes a fall and goes into labour. Hours later, having delivered the baby, the village doctor returns to his anxious wife and declares the baby is perfect in all respects. Over the coming month all the other babies are delivered, physically perfect specimens, but with golden eyes and blonde hair. 61 in total, 31 males, 30 females.

Chapter 12 Harvest home

The vicar falls into a stroll with Zellaby and assures him all the women have now had their babies. He is uneasy. Can’t shake the feeling it’s some kind of test. Zellaby makes remarks repeating his sense that, as men, they are hors du combat, outside the zone and cannot hope to understand what the women are going through.

Walking on Zellaby observes Mrs Brinkman pushing a pram and is a little surprised when she abruptly stops, takes the baby out, sits on the war memorial, unbuttons her blouse and starts suckling it. She is embarrassed when Zellaby draws abreast and explains that the baby made her do it. Walking up to the lodge, there’s a beep and Ferrelyn is in a car behind him. She too, flushed and upset, and says the baby made her come. Aha.

Chapter 13 Midwich centrocline

A centrocline is: ‘An equidimensional basin characteristic of cratonic areas, in which the strata dip to a central low point.’

Over the coming weeks every single mum who’d moved away from Midwich (for example most of the women researchers from the Grange who had been on secondments and gone elsewhere for their pregnancies and births) find themselves compelled to return

The text quotes a report Dr Willers submits to his superiors, outlining the sequence of births, the compulsion all the mothers felt to return and other matters, above all emphasising that some kind of official study should be being made of the children’s births, weights, development and so on.

Bernard turns up, goes for a chat with Zellaby, then comes for dinner with Richard and Janet, repeating some of Zellaby’s speculations. Apparently, Zellaby wonders whether it was a mistake that Homo sapiens is so very different from all other animal species, if our culture would be improved if we had to deal with at least one other intelligent life form on the planet. (This is one of the ideas floated in the Kraken Wakes.)

Chapter 14 Matters arising

Precisely half way through the book, Alan pays a call (he is currently stationed by the army a long way away, in Scotland, and can only get leave to visit Midwich occasionally).

Gordon takes him for a chat out in the garden of the manor. In garden chairs on the fine lawn under the old cedar tree, Gordon expounds his theory that the women have borne alien children. Earlier generations would have recognised them as changelings (p.106) – ‘deformed or imbecilic offspring of fairies or elves substituted by them surreptitiously for a human infant’. We moderns, Zellaby says, might think of them as cuckoos (p.106), laid in another species’ nests, force the mothers to work themselves to death to feed them, then exterminate all the true fledgelings.

That’s why he’s asking Alan to persuade Ferrelyn to leave the baby in his care and depart Midwich, go with him to Scotland. Nobody knows what it means or what might happen, but Zellaby introduces the idea that, if you were going to attack a civilisation and had plenty of time to plan it, might it not be a good idea to introduce a fifth column to work against the host nation from within. Maybe that’s what the babies are.

Chapter 15 Matters to arise

Months pass. The Grange is emptied and all its staff leave, but leaving four babies behind, in a new nursery. Over the winter pneumonia carries off some of the parents and three of the babies, leaving 58.

A dessicated couple called the Freemans move into the cottage vacated by Crim, and turn out to be officials sent to monitor developments, but they do it in a very ham-fisted way and become known as the Noseys.

Early in the summer Gordon pays Richard and Janet a visit and asks them to come with him to witness an experiment. The Children (everyone refers to them with a capital C, now) are barely a year old but look like healthy 2-year-olds. Gordon drops in on a family with one, asks the mum’s permission, then presents the child with a cunning Japanese wooden box with a sweet inside. The child struggles for a while, then Gordon shows him how to unlock it, relocks it. Given it again, the child unlocks it easily, but that’s not the point. Gordon takes them to see several other children and they all unlock it easily. Once one knows, they all know. Gordon presents his interpretation: they may have different physical bodies, but what if the Children compose one mind! He has christened it collective-individualism’ (p.123)

With typical intellectual sprezzatura Gordon speculates that maybe Homo sapiens is stagnating, the race limited to individuals with just the one mind, all jostling. Maybe the next breakthrough in evolution would be to combine the powers of individual minds into a collective. Maybe they are the progenitors of a new race. That’s why, he says, looking vaguely out the window at a bumble bee hovering over the lavender, he keeps thinking the collective boys and the collective girls should be renamed – Adam and Eve.

On the last page of Part One, Richard gets a job in Canada, leaving at once, and Janet follows soon after. She expresses relief to be shot of Midwich and its weird atmosphere and God, so grateful they were out of the village on ‘the fateful night’ and so she never bore one of those monster children.

Part two

Chapter 16 Now we are nine

Eight years pass. Richard and Janet live in Canada now, but occasionally pop back to the old country. On one such trip, Richard bumps into Bernard, who is now a colonel. They go for a drink and the subject of Midwich comes up. Richard has almost forgotten about it, says how are things going, Bernard says he’s scheduled to pop down for a visit next day, would Richard like to come?

The reader thinks this might be the first of several episodic visits, but in fact it turns into one continuous visit which leads to the climax of the story.

On the drive down Bernard tells Richard the Grange has been converted into a special school for the Children. Zellaby was right, what one boy learns they all learn, what one girl learns, ditto. The Children have developed at twice normal speed and now look 17 or 18. The news blackout has continued to be a success, the neighbouring communities regarding Midwich as ‘touched’ by the event, and the inhabitants retarded. The word they use is ‘daytouched’ (p.133). They consider the entire community a kind of open asylum. Some of the mothers were reluctant to let their children attend the new school but one by one the Children went of their own accord, to be together.

Bernard is driving down for a post-mortem on a local young man, Jim Pawle. Richard attends. It is a tense affair, with a very bad mood among the villagers attending, although nothing out of the ordinary is done or said. Zellaby greets Richard as if they’d only said goodbye the day before, invites him and Bernard to the Manor, describes what happened. He was an eye-witness. The local boy was driving his car along a lane when he hit one of a group of four Children by mistake. Zellaby watched as the other three focused their mental force on making the unhappy driver get back into his car and set off at top speed towards a wall, hitting it head on and dying.

Others saw it too. It gave Zellaby a very bad shock. Now he shares his feelings with Bernard and Richard. What if it had been him or Angela or Ferrelyn driving? He tells them Dr Willers died a few years earlier, suicide, overdose of barbiturates (p.143). Richard is surprised, he didn’t seem the sort. Gordon agrees, and wonders now whether… Whether the Children made him do it? Richard completes the thought. My God. Now for the first time, Zellaby says he is scared, thinking he should send Angela away.

Angela appears from the house, comes onto the veranda, joins the conversation, and mentions the incident of the dog – which bit one of the Children and promptly ran in front of a tractor – and the bull – which attacked one of them and promptly ran through several fields and drowned itself in a mill pond. She is in no doubt the children cause the deaths of anyone or anything which harms them.

The mother of the driver of the car wanted to attend and denounce the Children, but her other son and husband prevented her. What good would it do? The entire village is now living in fear.

Bernard and Richard say their goodbyes and leave, driving very carefully. They come on a group of four Children and Bernard slows down to let Richard appreciate just how much they have grown. Their golden eyes make them look like semi-precious stones. Both are stunned when a gunshot goes off and one of the Children falls to the ground. Richard gets out, a Child turns to look at him and he feels a gust of confusion and weakness flood through him.

Then they are aware of a high moaning keening sound and realise it is the other Children, a way off, expressing the same pain the shot one is feeling. And then they hear whimpering and another shot fired and screaming. Pushing through the hedge they come across a young man who has blown his own head off and his girlfriend, Elsa, next to him, hysterical. It’s the brother of the young man whose inquest they attended. He was taking revenge on the Children by shooting one of them and now they’ve killed him, too.

Local labourers come running, lift up the girl, take her home, the ones Richard hears vowing revenge against ‘the murderin’ young bastards.’ Richard and Bernard motor back to the Manor where Gordon hears the full story over a fortifying drink. Hmm. This is how blood feuds begin…

Chapter 17 Midwich protests

Shaken, Bernard and Richard return to Kyle Manor where the Zellabies graciously offer to put them up and invite them for dinner. They have barely withdrawn to the living room (the cook and other invisible servants having, presumably, cleared away the meal things) than the vicar, Leebody, enters in a fret. He warns that the situation is escalating.

Leebody and Zellaby engage in quite a high-flown debate about the morality of the Childrens’ activities. Leebody says they have the appearance of humans but, if they are not human inside, in their souls, then the laws of the Bible and conventional morality do not apply. Zellaby gives his view which is that the laws devised by one species to regulate its societies do not apply to a completely different species.

This high-flown talk is interrupted by Mrs Brant, who makes her apologies to ‘is worship Mr Zellaby, and then physically drags Leebody to the door, saying the Midwich men had been gathered in the pub, working themselves up into a fury, and have now set off in a body to burn the Grange to the ground and murder all the children. Only Mr Leebody can stop them, and she drags him, fluttering and stammering off into the night.

Zellaby, Bernard and Richard are about to follow, but Angela slams the door shut and stands in front of it, absolutely implacable. She knows there is going to be trouble and absolutely forbids any of them to leave. And they meekly accept her orders.

Chapter 18 Interview with a child

The Chief Constable of Winshire looked in at Kyle Manor the next morning, just at the right time for a glass of Madeira and a biscuit.

That gives you a sense of the sedate, well-mannered, upper-middle-class milieu we are operating in. We quickly learn that the attempt to torch the Grange backfired disastrously, as the Children made the attackers attack each other with the result that three men and a woman are dead and many others injured. Angela was quite right to prevent her menfolk going along.

What quickly transpires is the chief constable knows nothing about the Children, their special history or ability, and Zellaby, Bernard and Richard struggle to convey it to him.

The mildly comic scene where the phlegmatic policeman becomes more and more frustrated is interspersed with vignettes from the village. Passengers attempting to enter the village bus find their feet unable to move. Polly Rushton seeking to drive back to London finds herself stopping at the village perimeter and turning back. In other words, the Children have set up a kind of psychic boundary which the villagers can’t escape.

The Chief Constable goes up to the Grange where the current administrator, Mr Torrance, arranges an interview with one of the Children. This boy announces in forthright tones that the Children did make the village men attack each other in self defence because they knew the men had come to burn down the Grange. Well, why not just turn them back? asks the policeman. Because they needed to make an example to warn off other would-be attackers.

The Chief Constable is so appalled at the boy’s arrogance and the casual way he mentions the murder of four civilians that he starts abusing him and goes to stand, when he suddenly freezes, choking, then falls to the floor gasping and whimpering, vomits and passes out. Bernard watches all this in terror. He and Torrance call some of the police officers and have the CC carried to a car and taken away, still unconscious, then Bernard returns to the Manor.

Richard tries to leave but finds himself unable to, unable to shift gear or push the accelerator and so reluctantly turns back. Looks like he’s trapped along with the others.

Chapter 19 Impasse

Bernard returns to the Manor, has a couple of strong whiskeys and recounts what he saw. Gordon and Angela, Bernard and Richard sit down to another fine luncheon prepared by cook (p.178), and their conversation includes some major revelations. These last 40 pages of the novel become very wordy. There is more and more theorising and less and less action – up until the abrupt climax, that is.

Now, at this meal, Zellaby and Bernard both agree that they think the children are the result of the intervention of non-terrestrial aliens (p.188). But Bernard now makes the revelation of the book: that during the three or so weeks surrounding the Dayout, radar detected an unusual number of unidentified flying objects and that Dayouts happened at other communities.

He knows about incidences in the Northern Territory of Australia where, for reasons unknown, all the children died on birth. In an Eskimo settlement in northern Canada where the community was so outraged at the incident that it exposed the babies at birth. One at a remote community in the Irkutsk region of Mongolia where the local men considered their women had slept with the devil and murdered not only babies but mothers. And another in Gizhinsk. This is the important one.

For here the children were allowed to grow by the Soviet authorities who, after initially suspecting a capitalist trick, decided the children’s powers may be of some advantage in the Cold War. However, the Soviets eventually concluded their Children were a threat not only to the local community but to the state itself and – here’s the point – struck the town with atomic weapons. The town of Gizhinsk no longer exists.

And the other guests are electrified to learn that this happened only the previous week, just before the Children murdered Pawle. They knew. Somehow they knew about the murder of their peers in Russia and, from that moment, have escalated their actions, retaliating for even mild slights with immediate disproportionate violence.

After luncheon Bernard announces he is going back up to the Grange for a proper conversation with Torrance. He walks. However on the way he stops by two Children sitting on a bank. They are looking up. Bernard hears the drone of a jet plane passing high overhead. He sees five dots appear from it. For a moment I thought they were bombs and that’s how the book might end, but instead they are parachutes. The Children have made the five crew on the plane bail out, the plane will fly on till it crashes somewhere.

Bernard tells them that’s a very expensive plane, they could just have got to the pilots to turn back. The children calmly logically reply that that might have been put down to instrument failure. They must make their message plain.

‘Oh, you want to instil fear, do you? Why?’ inquired Bernard.
‘Only to make you leave us alone,’ said the boy. ‘It is a means; not an end.’ His golden eyes were turned towards Bernard, with a steady, earnest look. ‘Sooner or later, you will try to kill us. However we behave, you will want to wipe us out. Our position can be made stronger only if we take the initiative.’
The boy spoke quite calmly, but somehow the words pierced right through the front that Bernard had adopted. (p.196)

The Children explain in terms way beyond their years (and reminiscent of Zellaby who has, after all, been teaching them for years) that it is a clash of species. They explain that they know about the murder of the Children of Gizhinsk. And then they proceed to give a merciless analysis of the political and moral situation here in England. In Soviet Russia the individual exists to support the state and individuals can be arrested, imprisoned or liquidated if their existence or thoughts, words or actions threaten the state.

By contrast, here in the West, the State exists to support the wish for self-fulfilment and freedom of vast numbers of heterogenous individuals. No government could unilaterally wipe out a settlement like Midwich with all its innocent civilians. That’s why they’ve erected an invisible barrier and no-one can leave. The civilians are hostages. Any government which wipes Midwich out will never be re-elected. Meanwhile all kinds of mealy-mouthed do-gooders and experts on ethics will wring their hands about the Childrens’ rights. And they will use this time to get stronger.

Bernard becomes aware that he is sweating, panicking at hearing such cold-blooded sentiments coming out the mouth of a teenager. The Child moves beyond a shrewd analysis of the Realpolitik of the situation to a deeper, biological or Darwinian interpretation.

‘Neither you, nor we, have wishes that count in the matter – or should one say that we both have been given the same wish – to survive? We are all, you see, toys of the life-force. It made you numerically strong, but mentally undeveloped; it made us mentally strong, but physically weak: now it has set us at one another, to see what will happen. A cruel sport, perhaps, from both our points of view, but a very, very old one. Cruelty is as old as life itself. There is some improvement: humour and compassion are the most important of human inventions; but they are not very firmly established yet, though promising well.’ He paused, and smiled. ‘A real bit of Zellaby, that – our first teacher,’ he put in, and then went on. ‘But the life force is a great deal stronger than they are; and it won’t be denied its blood-sports.’ (p.200)

Chapter 20 Ultimatum

Meanwhile Zellaby takes Richard for a turn round his favourite Thinking Walk. Here he propounds at length his speculation that, we maybe describing the Children as aliens, but what if the human races are also alien interlopers? Impregnated into low-intelligence Neanderthals by the aliens, to create a step-change in evolution?

His evidence is the remarkable lack of fossil evidence for the evolution of Homo sapiens combined with the huge gap between us and any other living thing. What if we too were planted here by a Maker or a team of extra-terrestrial scientists carrying out experiments in evolution and the earth is their testbed? (p.205)

Bernard arrives back from his conversation with the two Children. They had concluded by presenting an ultimatum, hence the title of the chapter. More accurately, a demand. They want to be transported to somewhere where they will be safe. They will supervise all aspects of the transportation. They want Bernard to escalate it to his superiors and, ultimately to the Prime Minister.

Zellaby is not surprised. In the latest of his many speculations and formulations, he amuses himself by saying the they now face a ‘moral dilemma of some niceness’:

‘On the one hand, it is our duty to our race and culture to liquidate the Children, for it is clear that if we do not we shall, at best, be completely dominated by them, and their culture, whatever it may turn out to be, will extinguish ours. On the other hand, it is our culture that gives us scruples about the ruthless liquidation of unarmed minorities, not to mention the practical obstacles to such a solution.’ (p.208)

If you like moral dilemmas, this is the one at the core of the book. Do we have the right to ‘liquidate’ the apparently harmless, if we have good suspicions they will eventually come to pose a threat to us?

If absolute moral values can’t help us decide, then Zellaby invokes the classic Utilitarian argument for making decisions based on their practical outcomes.

‘In a quandary where every course is immoral, there still remains the ability to act for the greatest good of the greatest number. Ergo, the Children ought to be eliminated at the least possible cost, with the least possible delay. I am sorry to have to arrive at that conclusion. In nine years I have grown rather fond of them…’ (p.208)

And that is what he does. Bernard says his goodbyes and sets off to London to convey the Children’s ultimatum. Richard stays on at the Manor.

Chapter 21 Zellaby of Macedon

Next morning Gordon asks Angela to get a jar of bullseyes, the Children’s favourite sweet, from the shops in Trayne. He is preparing to give them one of his regular film shows, about the Aegean Islands. When Richard joins him on the veranda before luncheon, Zellaby calmly says life goes on, he’s happy to give the Children another film show and lecture, they enjoy it, he likes them despite everything. The key thing is they trust him.

Early that evening Richard helps load his projector gear into the car, a surprising number of surprisingly heavy boxes and then drives Gordon to the Grange, helps the Children unload and carry the equipment into the building. Richard asks to stay, since he is still recently enough returned to be fascinated by the Children but Gordon suavely asks him to go back to the Manor and be with Angela, her nerves are so high strung, poor thing. So Richard reluctantly drives off.

He has barely parked, entered the Manor, poured a drink and begun chatting to Angela who is expressing her fears about what the children will do next, when there is a flash, a colossal bang and then a shock wave hits the Manor and shatters all its windows. When Richard picks himself up and runs to the french windows he sees detritus all across the lawn, creepers ripped off the facade of the Manor, and flames rising from the Grange up on the hill.

Gordon had packed the projector boxes with explosive and has set it off, killing himself and all the children. From the endless stream of speculations and musings which dominate the final chapters, it appears there were real conclusions and a practical outcome endless. It was a war of species. The Children needed to be liquidated in order to preserve our species. And if moral speculation was no use, then utilitarian considerations provided a basis for action. Which he took, knowing that the Children’s trust was a unique quality which he alone of maybe the entire human race had. And so he abused it to murder them all. If it was murder (see the long discussion with the vicar about the morality of inter-species killing).

The Midwich Cuckoos is a gripping, thrilling read, which is strangely inflected between, on the one hand its jolly pukka, upper-middle-class, English characters and, on the other hand, the frequent and very thought-provoking debates about morality, the rights and wrong of eliminating a racial threat, the possibility that the entire human race is a galactic experiment, and other quietly mind-bending topics.


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Innumeracy by John Allen Paulos (1988)

Our innate desire for meaning and pattern can lead us astray… (p.81)

Giving due weight to the fortuitous nature of the world is, I think, a mark of maturity and balance. (p.133)

John Allen Paulos is an American professor of mathematics who won fame beyond his academic milieu with the publication of this short (134-page) but devastating book thirty years ago, the first of a series of books popularising mathematics in a range of spheres from playing the stock market to humour.

As Paulos explains in the introduction, the world is full of humanities graduates who blow a fuse if you misuse ‘infer’ and ‘imply’, or end a sentence with a dangling participle, but are quite happy to believe and repeat the most hair-raising errors in maths, statistics and probability.

The aim of this book was:

  • to lay out examples of classic maths howlers and correct them
  • to teach readers to be more alert when maths, stats and data need to be used
  • and to provide basic rules in order to understand when innumerate journalists, politicians, tax advisors and other crooks are trying to pull the wool over your eyes, or are just plain wrong

There are five chapters:

  1. Examples and principles
  2. Probability and coincidence
  3. Pseudoscience
  4. Whence innumeracy
  5. Statistics, trade-offs and society

Many common themes emerge:

Don’t personalise, numeratise

One contention of this book is that innumerate people characteristically have a strong tendency to personalise – to be misled by their own experiences, or by the media’s focus on individuals and drama… (p.1)

Powers

The first chapter uses lots of staggering statistics to get the reader used to very big and very small numbers, and how to compute them.

1 million seconds is 11 and a half days. 1 billion seconds is 32 years.

He suggests you come up with personal examples of numbers for each power up to 12 or 13 i.e. meaningful embodiments of thousands, tens of thousands, hundreds of thousands and so on to help you remember and contextualise them in a hurry.

A snail moves at 0.005 miles an hour, Concorde at 2,000 miles per hour. Escape velocity from earth is about 7 miles per second, or 25,000 miles per hour. The mass of the Earth is 5.98 x 1024 kg

Early on he tells us to get used to the nomenclature of ‘powers’ – using 10 to the power 3 or 10³ instead of 1,000, or 10 to negative powers to express numbers below 1. (In fact, right at this early stage I found myself stumbling because one thousand means more to me that 10³ and a thousandth means more than more 10-3 but if you keep at it, it is a trick you can acquire quite quickly.)

The additive principle

He introduces us to basic ideas like the additive principle (aka the rule of sum), which states that if some choice can be made in M different ways and some subsequent choice can be made in N different ways, then there are M x N different ways these choices can be made in succession – which can be applied to combinations of multiple items of clothes, combinations of dishes on a menu, and so on.

Thus the number of results you get from rolling a die is 6. If you roll two dice, you can now get 6 x 6 = 36 possible numbers. Three numbers = 216. If you want to exclude the number you get on the first dice from the second one, the chances of rolling two different numbers on two dice is 6 x 5, of rolling different numbers on three dice is 6 x 5 x 4, and so on.

Thus: Baskin Robbins advertises 31 different flavours of ice cream. Say you want a triple scoop cone. If you’re happy to have any combination of flavours, including where any 2 or 3 flavours are the same – that’s 31 x 31 x 31 = 29,791. But if you ask how many combinations of flavours there are, without a repetition of the same flavour in any of the cones – that is 31 x 30 x 29 = 26,970 ways of combining.

Probability

I struggled with even the basics of probability. I understand a 1 in five chance of something happening, reasonably understand a 20% chance of something happening, but struggled when probability was expressed as a decimal number e.g. 0.2 as a way of writing a 20 percent or 1 in 5 chance.

With the result that he lost me on page 16 on or about the place where he explained the following example.

Apparently a noted 17th century gambler asked the famous mathematician Pascal which is more likely to occur: obtaining at least one 6 in four rolls of a single die, or obtaining at least one 12 in twenty four rolls of a pair of dice. Here’s the solution:

Since 5/6 is the probability of not rolling a 6 on a single roll of a die, (5/6)is the probability of not rolling a 6 in four rolls of the die. Subtracting this number from 1 gives us the probability that this latter event (no 6s) doesn’t occur; in other words, of there being at least one 6 rolled in four tries: 1 – (5/6)= .52. Likewise, the probability of rolling at least one 12 in twenty-four rolls of a pair of dice is seen to be 1 – (35/36)24 = .49.

a) He loses me in the second sentence which I’ve read half a dozen times and still don’t understand – it’s where he says the chances that this latter event doesn’t occur: something about the phrasing there, about the double negative, loses me completely, with the result that b) I have no idea whether .52 is more likely or less likely than .49.

He goes on to give another example: if 20% of drinks dispensed by a vending machine overflow their cups, what is the probability that exactly three of the next ten will overflow?

The probability that the first three drinks overflow and the next seven do not is (.2)x (.8)7. But there are many different ways for exactly three of the ten cups to overflow, each way having probability (.2)x (.8)7. It may be that only the last three cups overflow, or only the fourth, fifth and ninth cups, and so on. Thus, since there are altogether (10 x 9 x 8) / (3 x 2 x 1) = 120 ways for us to pick three out of the ten cups, the probability of some collection of exactly three cups overflowing is 120 x (.2)x (.8)7.

I didn’t understand the need for the (10 x 9 x 8) / (3 x 2 x 1) equation – I didn’t understand what it was doing, and so didn’t understand what it was measuring, and so didn’t understand the final equation. I didn’t really have a clue what was going on.

In fact, by page 20, he’d done such a good job of bamboozling me with examples like this that I sadly concluded that I must be innumerate.

More than that, I appear to have ‘maths anxiety’ because I began to feel physically unwell as I read that problem paragraph again and again and again and didn’t understand it. I began to feel a tightening of my chest and a choking sensation in my throat. Rereading it now is making it feel like someone is trying to strangle me.

Maybe people don’t like maths because being forced to confront something you don’t understand, but which everyone around you is saying is easy-peasy, makes you feel ill.

2. Probability and coincidence

Having more or less given up on trying to understand Paulos’s maths demonstrations in the first twenty pages, I can at least latch on to his verbal explanations of what he’s driving at, in sentences like these:

A tendency to drastically underestimate the frequency of coincidences is a prime characteristic of innumerates, who generally accord great significance to correspondences of all sorts while attributing too little significance to quite conclusive but less flashy statistical evidence. (p.22)

It would be very unlikely for unlikely events not to occur. (p.24)

There is a strong general tendency to filter out the bad and the failed and to focus on the good and the successful. (p.29)

Belief in the… significance of coincidences is a psychological remnant of our past. It constitutes a kind of psychological illusion to which innumerate people are particularly prone. (p.82)

Slot machines light up and make a racket when people win, there is unnoticed silence for all the failures. Big winners on the lottery are widely publicised, whereas every one of the tens of millions of failures is not.

One result is ‘Golden Age’ thinking when people denigrate today’s sports or arts or political figures, by comparison with one or two super-notable figures from the vast past, Churchill or Shakespeare or Michelangelo, obviously neglecting the fact that there were millions of also-rans and losers in their time as well as ours.

The Expected value of a quality is the average of its values weighted according to their probabilities. I understood these words but I didn’t understand any of the five examples he gave.

The likelihood of probability In many situations, improbability is to be expected. The probability of being dealt a particular hand of 13 cards in bridge is less than 1 in 600 billion. And yet it happens every time someone is dealt a hand in bridge. The improbable can happen. In fact it happens all the time.

The gambler’s fallacy The belief that, because a tossed coin has come up tails for a number of tosses in a row, it becomes steadily more likely that the next toss will be a head.

3. Pseudoscience

Paulos rips into Freudianism and Marxism for the way they can explain away any result counter to their ‘theories’. The patient gets better due to therapy: therapy works. The patient doesn’t get better during therapy, well the patient was resisting, projecting their neuroses on the therapist, any of hundreds of excuses.

But this is just warming up before he rips into a real bugbear of  his, the wrong-headedness of Parapsychology, the Paranormal, Predictive dreams, Astrology, UFOs, Pseudoscience and so on.

As with predictive dreams, winning the lottery or miracle cures, many of these practices continue to flourish because it’s the handful of successes which stand out and grab our attention and not the thousands of negatives.

Probability

As Paulos steams on with examples from tossing coins, rolling dice, playing roulette, or poker, or blackjack, I realise all of them are to do with probability or conditional probability, none of which I understand.

This is why I have never gambled on anything, and can’t play poker. When he explains precisely how accumulating probabilities can help you win at blackjack in a casino, I switch off. I’ve never been to a casino. I don’t play blackjack. I have no intention of ever playing blackjack.

When he says that probability theory began with gambling problems in the seventeenth century, I think, well since I don’t gamble at all, on anything, maybe that’s why so much of this book is gibberish to me.

Medical testing and screening

Apart from gambling the two most ‘real world’ areas where probability is important appear to be medicine and risk and safety assessment. Here’s an extended example he gives of how even doctors make mistakes in the odds.

Assume there is a test for cancer which is 98% accurate i.e. if someone has cancer, the test will be positive 98 percent of the time, and if one doesn’t have it, the test will be negative 98 percent of the time. Assume further that .5 percent – one out of two hundred people – actually have cancer. Now imagine that you’ve taken the test and that your doctor sombrely informs you that you have tested positive. How depressed should you be? The surprising answer is that you should be cautiously optimistic. To find out why, let’s look at the conditional probability of your having cancer, given that you’ve tested positive.

Imagine that 10,000 tests for cancer are administered. Of these, how many are positive? On the average, 50 of these 10,000 people (.5 percent of 10,000) will have cancer, and, so, since 98 percent of them will test positive, we will have 49 positive tests. Of the 9,950 cancerless people, 2 percent of them will test positive, for a total of 199 positive tests (.02 x 9,950 = 199). Thus, of the total of 248 positive tests (199 + 49 = 248), most (199) are false positives, and so the conditional probability of having cancer given that one tests positive is only 49/248, or about 20 percent! (p.64)

I struggled to understand this explanation. I read it four or five times, controlling my sense of panic and did, eventually, I think, follow the argumen.

However, worse in a way, when I think I did finally understand it, I realised I just didn’t care. It’s not just that the examples he gives are hard to follow. It’s that they’re hard to care about.

Whereas his descriptions of human psychology and cognitive errors in human thinking are crystal clear and easy to assimilate:

If we have no direct evidence of theoretical support for a story, we find that detail and vividness vary inversely with likelihood; the more vivid details there are to a story, the less likely the story is to be true. (p.84)

4. Whence innumeracy?

It came as a vast relief when Paulos stopped trying to explain probability and switched to a long chapter puzzling over why innumeracy is so widespread in society, which kicks off by criticising the poor level of teaching of maths in school and university.

This was like the kind of hand-wringing newspaper article you can read any day of the week in a newspaper or online, and so felt reassuringly familiar and easy to assimilate. I stopped feeling so panic-stricken.

This puzzling over the disappointing level of innumeracy goes on for quite a while. Eventually it ends with a digression about what appears to be a pet idea of his: the notion of introducing a safety index for activities and illnesses.

Paulos’s suggestion is that his safety index would be on a logarithmic scale, like the Richter Scale – so straightaway he has to explain what a logarithm is: The logarithm for 100 is 2 because 100 is 102, the logarithm for 1,000 is 3 because 1,000 is 103. I’m with him so far, as he goes on to explain that the logarithm of 700 i.e. between 2 (100) and 3 (1,000) is 2.8. Since 1 in 5,300 Americans die in a car crash each year, the safety index for driving would be 3.7, the logarithm of 5,300. And so on with numerous more examples, whose relative risks or dangers he reduces to figures like 4.3 and 7.1.

I did understand his aim and the maths of this. I just thought it was bonkers:

1. What is the point of introducing a universal index which you would have to explain every time anyone wanted to use it? Either it is designed to be usable by the widest possible number of citizens; or it is a neat exercise on maths to please other mathematicians and statisticians.

2. And here’s the bigger objection – What Paulos, like most of the university-educated, white, liberal intellectuals I read in papers, magazines and books, fails to take into account is that a large proportion of the population is thick.

Up to a fifth of the adult population of the UK is functionally innumerate, that means they don’t know what a ‘25% off’ sign means on a shop window. For me an actual social catastrophe being brought about by this attitude is the introduction of Universal Credit by the Conservative government which, from top to bottom, is designed by middle-class, highly educated people who’ve all got internet accounts and countless apps on their smartphones, and who have shown a breath-taking ignorance about what life is like for the poor, sick, disabled, illiterate and innumerate people who are precisely the people the system is targeted at.

Same with Paulos’s scheme. Smoking is one of the most dangerous and stupid things which any human can do. Packs of cigarettes have for years, now, carried pictures of disgusting cancerous growths and the words SMOKING KILLS. And yet despite this, about a fifth of adults, getting on for 10 million people, still smoke. 🙂

Do you really think that introducing a system using ornate logarithms will get people to make rational assessments of the risks of common activities and habits?

Paulos then goes on to complicate the idea by suggesting that, since the media is always more interested in danger than safety, maybe it would be more effective, instead of creating a safety index, to create a danger index.

You would do this by

  1. working out the risk of an activity (i.e. number of deaths or accidents per person doing the activity)
  2. converting that into a logarithmic value (just to make sure than nobody understands it) and then
  3. subtracting the logarithmic value of the safety index from 10, in order to create a danger index

He goes on to say that driving a car and smoking would have ‘danger indices’ of 3.7 and 2.9, respectively. The trouble was that by this point I had completely ceased to understand what he’s saying. I felt like I’ve stepped off the edge of a tall building into thin air. I began to have that familiar choking sensation, as if someone was squeezing my chest. Maths anxiety.

Under this system being kidnapped would have a safety index of 6.7. Playing Russian roulette once a year would have a safety index of 0.8.

It is symptomatic of the uselessness of the whole idea that Paulos has to remind you what the values mean (‘Remember that the bigger the number, the smaller the risk.’ Really? You expect people to run with this idea?)

Having completed the danger index idea, Paulos returns to his extended lament on why people don’t like maths. He gives a long list of reasons why he thinks people are so innumerate a condition which is, for him, a puzzling mystery.

For me this lament is a classic example of what you could call intellectual out-of-touchness. He is genuinely puzzled why so many of his fellow citizens are innumerate, can’t calculate simple odds and fall for all sorts of paranormal, astrology, snake-oil blether.

He proposes typically academic, university-level explanations for this phenomenon – such as that people find maths too cold and analytical and worry that it prevents them thinking about the big philosophical questions in life. He worries that maths has an image problem.

In other words, he fails to consider the much more obvious explanation that maths, probability and numeracy in general might be a combination of fanciful, irrelevant and deeply, deeply boring.

I use the word ‘fanciful’ deliberately. When he writes that the probability of drawing two aces in succession from a pack of cards is not (4/52 x 4/52) but (4/52 x 3/51) I do actually understand the distinction he’s making (having drawn one ace there are only 3 left and only 52 cards left) – I just couldn’t care less. I really couldn’t care less.

Or take this paragraph:

Several years ago Pete Rose set a National League record by hitting safely in forty-four consecutive games. If we assume for the sake of simplicity that he batted .300 (30 percent of the time he got a hit, 70 percent of the time he didn’t) and that he came to bat four times a game, the chances of his not getting a hit in any given game were, assuming independence, (.7)4 – .24… [at this point Paulos has to explain what ‘independence’ means in a baseball context: I couldn’t care less]… So the probability he would get at least one hit in any game was 1-.24 = .76. Thus, the chances of him getting a hit in any given sequence of forty-four consecutive games were (.76)44 = .0000057, a tiny probability indeed. (p.44)

I did, in fact, understand the maths and the working out in this example. I just don’t care about the problem or the result.

For me this is a – maybe the – major flaw of this book. This is that in the blurbs on the front and back, in the introduction and all the way through the text, Paulos goes on and on about how we as a society need to be mathematically numerate because maths (and particularly probability) impinges on so many areas of our life.

But when he tries to show this – when he gets the opportunity to show us what all these areas of our lives actually are – he completely fails.

Almost all of the examples in the book are not taken from everyday life, they are remote and abstruse problems of gambling or sports statistics.

  • which is more likely: obtaining at least one 6 in four rolls of a single die, or obtaining at least one 12 in twenty four rolls of a pair of dice?
  • if 20% of drinks dispensed by a vending machine overflow their cups, what is the probability that exactly three of the next ten will overflow?
  • Assume there is a test for cancer which is 98% accurate i.e. if someone has cancer, the test will be positive 98 percent of the time, and if one doesn’t have it, the test will be negative 98 percent of the time. Assume further that .5 percent – one out of two hundred people – actually have cancer. Now imagine that you’ve taken the test and that your doctor sombrely informs you that you have tested positive. How depressed should you be?
  • What are the odds on Pete Rose getting a hit in a sequence of forty-four games?

Are these the kinds of problems you are going to encounter today? Or tomorrow? Or ever?

No. The longer the book went on, the more I realised just how little a role maths plays in my everyday life. In fact more or less the only role maths plays in my life is looking at the prices in supermarkets, where I am attracted to goods which have a temporary reduction on them. But I do that because they’re labels are coloured red, not because I calculate the savings. Being aware of the time, so I know when to do household chores or be somewhere punctually. Those are the only times I used numbers today.

5. Statistics, trade-offs and society

This feeling that the abstruseness of the examples utterly contradicts the bold claims that reading the book will help us with everyday experiences was confirmed in the final chapter, which begins with the following example.

Imagine four dice, A, B, C and D, strangely numbered as follows: A has 4 on four faces and 0 on two faces; B has 3s on all six faces; C has four faces with 2 and two faces with 6; and D has 5 on three faces and 1 on three faces…

I struggled to the end of this sentence and just thought: ‘No, no more, I don’t have to make myself feel sick and unhappy any more’ – and skipped the couple of pages detailing the fascinating and unexpected results you can get from rolling such a collection of dice.

This chapter goes on to a passage about the Prisoner’s Dilemma, a well-known problem in logic, which I have read about and instantly forgotten scores of times over the years.

Paulos gives us three or four variations on the idea, including:

  • Imagine you are locked up in prison by a philanthropist with 20 other people.

Or:

  • Imagine you are locked in a dungeon by a sadist with 20 other people.

Or:

  • Imagine you are one of two drug traffickers making a quick transaction on a street corner and forced to make a quick decision.

Or:

  • Imagine you are locked in a prison cell, and another prisoner is locked in an identical cell down the corridor.

Well, I’m not any of these things, I’m never likely to be, and I am not really interested in these fanciful speculations.

Moreover, I am well into middle age, have travelled round the world, had all sorts of jobs in companies small, large and enormous – and I am not aware of having ever been in any situation which remotely resembled any variation of the Prisoner’s Dilemma I’ve ever heard of.

In other words, to me, it is another one of the endless pile of games and puzzles which logicians and mathematicians love to spend all day playing but which have absolutely no impact whatsoever on any aspect of my life.

Pretty much all of his examples conclusively prove how remote mathematical problems and probabilistic calculation is from the everyday lives you and I lead. When he asks:

How many people would there have to be in a group in order for the probability to be half that at least two people in it have the same birthday? (p.23)

Imagine a factory which produces small batteries for toys, and assume the factory is run by a sadistic engineer… (p.117)

It dawns on me that my problem might not be that I’m innumerate, so much as I’m just uninterested in trivial or frivolous mental exercises.

Someone offers you a choice of two envelopes and tells you one has twice as much money in it as the other. (p.127)

Flip a coin continuously until a tail appears for the first time. If this doesn’t happen until the twentieth (or later) flip, you win $1 billion. If the first tail occurs before the twentieth flip, you pay $100. Would you play? (p.128)

No. I’d go and read an interesting book.

Thoughts

If Innumeracy: Mathematical Illiteracy and Its Consequences is meant to make its readers more numerate, it failed with me.

This is for a number of reasons:

  1. crucially – because he doesn’t explain maths very well; or, the way he explained probability had lost me by about page 16 – in other words, if this is meant to be a primer for innumerate people it’s a fail
  2. because the longer it goes on, the more convinced I became that I rarely use maths, arithmetic and probability in my day today life: whole days go by when I don’t do a single sum, and so lost all motivation to submit myself to the brain-hurting ordeal of trying to understand his examples

3. Also because the structure and presentation of the book is a mess. The book meanders through a fog of jokes, anecdotes and maths trivia, baseball stories and gossip about American politicians – before suddenly unleashing a fundamental aspect of probability theory on the unwary reader.

I’d have preferred the book to have had a clear, didactic structure, with an introduction and chapter headings explaining just what he was going to do, an explanation, say, of how he was going to take us through some basic concepts of probability one step at a time.

And then for the concepts to have been laid out very clearly and explained very clearly, from a number of angles, giving a variety of different examples until he and we were absolutely confident we’d got it – before we moved on to the next level of complexity.

The book is nothing like this. Instead it sacrifices any attempt at logical sequencing or clarity for anecdotes about Elvis Presley or UFOs, for digressions about Biblical numerology, the silliness of astrology, the long and bewildering digression about introducing a safety index for activities (summarised above), or prolonged analyses of baseball or basketball statistics. Oh, and a steady drizzle of terrible jokes.

Which two sports have face-offs?
Ice hockey and leper boxing.

Half way through the book, Paulos tells us that he struggles to write long texts (‘I have a difficult time writing at extended length about anything’, p.88), and I think it really shows.

It certainly explains why:

  • the blizzard of problems in coin tossing and dice rolling stopped without any warning, as he switched tone copletely, giving us first a long chapter about all the crazy irrational beliefs people hold, and then another chapter listing all the reasons why society is innumerate
  • the last ten pages of the book give up the attempt of trying to be a coherent narrative and disintegrate into a bunch of miscellaneous odds and ends he couldn’t find a place for in the main body of the text

Also, I found that the book was not about numeracy in the broadest sense, but mostly about probability. Again and again he reverted to examples of tossing coins and rolling dice. One enduring effect of reading this book is going to be that, the next time I read a description of someone tossing a coin or rolling a die, I’m just going to skip right over the passage, knowing that if I read it I’ll either be bored to death (if I understand it) or have an unpleasant panic attack (if I don’t).

In fact in the coda at the end of the book Paulos explicitly says it has mostly been about probability – God, I wish he’d explained that at the beginning.

Right at the very, very end he briefly lists key aspects of probability theory which he claims to have explained in the book – but he hasn’t, some of them are only briefly referred to with no explanation at all, including: statistical tests and confidence intervals, cause and correlation, conditional probability, independence, the multiplication principle, the notion of expected value and of probability distribution.

These are now names I have at least read about, but they are all concepts I am nowhere near understanding, and light years away from being able to use in practical life.

Innumeracy – or illogicality?

Also there was an odd disconnect between the broadly psychological and philosophical prose explanations of what makes people so irrational, and the incredibly narrow scope of the coin-tossing, baseball-scoring examples.

What I’m driving at is that, in the long central chapter on Pseudoscience, when he stopped to explain what makes people so credulous, so gullible, he didn’t really use any mathematical examples to disprove Freudianism or astrology or so on: he had to appeal to broad principles of psychology, such as:

  • people are drawn to notable exceptions, instead of considering the entire field of entities i.e.
  • people filter out the bad and the failed and focus on the good and the successful
  • people seize hold of the first available explanation, instead of considering every single possible permutation
  • people humanise and personalise events (‘bloody weather, bloody buses’)
  • people over-value coincidences

My point is that there is a fundamental conceptual confusion in the book which is revealed in the long chapter about pseudoscience which is that his complaint is not, deep down, right at bottom, that people are innumerate; it is that people are hopelessly irrational and illogical.

Now this subject – the fundamental ways in which people are irrational and illogical – is dealt with much better, at much greater length, in a much more thorough, structured and comprehensible way in Stuart Sutherland’s great book, Irrationality, which I’ll be reviewing and summarising later this week.

Innumeracy amounts to random scratches on the surface of the vast iceberg which is the deep human inability to think logically.

Conclusion

In summary, for me at any rate, this was not a good book – badly structured, meandering in direction, unable to explain even basic concepts but packed with digressions, hobby horses and cul-de-sacs, unsure of its real purpose, stopping for a long rant against pseudosciences and an even longer lament on why maths is taught so badly  – it’s a weird curate’s egg of a text.

Its one positive effect was to make me want to track down and read a good book about probability.


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