The Wonderful Story of Henry Sugar and Six More by Roald Dahl (1977)

And what marvellous exciting fun it was!
(Lucky Break)

This 1977 collection of Roald Dahl short stories is, as one of his schoolboys might say, a bit of a swizz because, out of the seven texts in this collection only four of are actually short stories – the last two are autobiographical sketches about the war and ‘The Mildenhall Treasure’ is a factual article from way back in 1946, all three of which had been previously published elsewhere.

  1. The Boy Who Talked With Animals (story)
  2. The Hitch-Hiker (story)
  3. The Mildenhall Treasure (article)
  4. The Swan (story)
  5. The Wonderful Story of Henry Sugar (story)
  6. Lucky Break (memoir)
  7. A Piece of Cake (memoir)

They’re all children’s stories, even the war memoirs – not for small children, exactly; probably for younger teens. It’s indicative that the edition I read was published by Puffin, Penguin’s imprint for children. One of aspects of the children-y approach is the gleeful hyperbole found throughout the pieces:

  • As a matter of fact, he told himself he was now almost certainly able to make money faster than any other man in the entire world. (page 144)
  • ‘You will be the richest man on earth.’ (p.156)

Another minor verbal tic which indicates their target audience is the liberal use of Dahl’s favourite words, ‘marvellous’ and ‘fantastic’, both of which, of course, appear in the titles of two of his most popular children’s books.

And now, very quickly, there began to come to him the great and marvellous idea that was to change everything. (Henry Sugar, page 153)

The Boy Who Talked with Animals (23 pages)

A strange and eerie story told by a narrator who’s gone on holiday to Jamaica. The taxi driver taking him to the hotel spooks him with stories of weird voodoo stuff which still goes on in the mountains. Then when he arrives at the hotel it’s perfectly pleasant and yet it gives him a bad vibe. And then the maid tells him all about a guest, a Mr Wasserman who was taking a photo of the sunset from the beach when a huge coconut fell on his head and knocked him dead. Although all this is quite serious it has a comic-book simplicity about it.

Anyway, the main action kicks off when the narrator, idling sitting on his balcony one day, hears a great hubbub from a crown of guests assembling on the beach.

This is a first-person fiction piece of medium-length writing. The narrator, on advice from friends, decides to vacation in Jamaica. One night, a sea turtle, ancient and huge, is caught by a group of fishermen. Rich people want to buy it, while the manager of a nearby hotel wants to make turtle soup out of it, but both plans are foiled when a little boy appears and shames the crowd for their cruelty. His parents explain that he has a deep affinity for animals, and even talks to them. The boy’s father pays off the fisherfolk and hotel manager, and the turtle is set free. The next day, the boy is missing, and the fisherfolk reveal that they have seen the child riding on the back of the sea turtle into the distance.

A turtle has landed on a resort beach in Jamaica and everyone wants to kill it for the meat and its shell. A small boy David becomes hysterical and tries to save the turtle. His parents explain that he is very sensitive to animals and they volunteer to buy the turtle from the resort owner. While they are haggling over the price, David talks to the turtle and tells it to swim away. During the night the boy himself disappears and next day two local fishermen come back with a crazy story – they have seen David riding the turtle out in the middle of the ocean!

The Hitch-Hiker (15 pages)

That rare thing, a Roald Dahl story with a happy ending, no revenge or poisoning or murder in sight.

The narrator is driving up to London in his brand new BMW 3.3 Li when he spots a hitchhiker. As the man gets in the narrator observes his rat-like features and long white hands, his drab grey coat which makes him look even more rattish. They talk about the model of car the narrator’s driving and when the narrator boasts that its top speed is 129 mph, the hitch-hiker encourages him to put the manufacturer’s claims to the test. So the narrator puts his foot down, 80, 90, 100, 105, 110, 115 miles an hour. Just as they get into the 120s they both hear a police siren go off and realise a police motor cycle is after them.

The traffic cop is strict, unbending and sarcastic. He takes his time and is rude and officious to both of them before writing out a ticket and hinting that breaking the limit by such a whopping margin will definitely result in a big fine and maybe even a prison sentence. With that threat he motors off leaving the narrator to resume his journey at a sensible law abiding speed.

The narrator frets over the doom awaiting him and so the hitchhiker sets about cheering him up. He challenges the narrator to guess his true profession. As a clue he starts to reveal various items from the narrator’s person starting off, improbably enough, with his belt, before going on to reveal the narrator’s wallet, watch and even shoelace.

Gobsmacked, the narrator calls the hitchhiker a pickpocket but the latter is a bit miffed and insists on being called a ‘fingersmith’ – just as a goldsmith has mastered gold, so he has mastered the adept use of his long and silky fingers, which he refers to as his ‘fantastic fingers’.

After his initial amazement at his friend’s abilities the narrator relapses back into gloom at the prospect of being charged, fined and maybe even imprisoned for his moment of madness. At which point, in a dazzling conclusion to the story, the hitchhiker reveals that he has stolen both of the police officer’s notebooks, which contain the cop’s copies of the tickets he gave them and the details of their offence.

Delighted, the narrator pulls over and he and the hitchhiker gleefully make a little bonfire of the policeman’s notebooks. A rare example of a Dahl story with a joyful ending.

The Mildenhall Treasure (1946: 27 pages)

Not a short story at all, but a factual article.

A modern preface explains that Dahl was unmarried and living with his mother when he read about the discovery of the Mildenhall treasure. He motored over to interview the hero of the story, Gordon Butcher, a humble ploughman, and this 27-page text is a kind of dramatisation of events.

Put simply, in January 1942 the owner of some farmland in Suffolk contracted one Sydney Ford to plough his fields for him and Ford sub-contracted the job to Gordon Butcher. Butcher was ploughing away when his plough struck something. When he investigated he found the edge of a big metal disc. Not sure what to do he went to see Ford who accompanied him back to the field and the pair dug out over thirty pieces of obviously man-made metal objects. As they did it snow began to fall and eventually the hole was covered in snow and Butcher’s extremities had gone numb with cold so he was happy enough when Ford told him to go home to his wife and a roaring fire and forgot all about it.

Meanwhile Ford took the treasure home in a sack and, over the following weeks and months, used domestic metal cleaner to clean off the tarnish and reveals the objects for what they were, the most impressive hoard of buried Roman treasure ever found in Britain.

Now all this took place during wartime, and from Ford’s house he could hear Allied bombers taking off to pound German cities and many of the norms and conventions of civilian life had been suspended. On the face of it, according to law, Butcher and Ford should have reported the find; it would have been claimed in its entirety by His Majesty’s government but Butcher, as the first finder, would have been eligible for the full market value of the trove, which Dahl gives as over half a million pounds.

But neither man reported it, in breach of English law. The digging in the increasingly heavy snowfall is the first significant or dramatic scene. The next one comes when Dahl describes the mounting excitement of Ford as he uses ordinary domestic cleaner to slowly work off the centuries of grime and reveal the sparkling silver underneath.

The third one comes when Ford has an unexpected visitor, Dr Hugh Alderson Fawcett, a keen and expert archaeologist who used, before the war, to visit Ford once a year to assess whatever finds Ford had made for, as the text explains, old arrowheads and minor historical debris often crop up in the fields of Suffolk which were, in the Dark Ages, the most inhabited part of Britain.

Anyway, by some oversight Ford kept most of the treasure under lock and key but had left out two beautiful silver spoons, which each had the name of a Roman child on them and so were probably Roman Christening spoons. The most dramatic moment in the story comes when Ford welcomes Fawcett into his living room but then realises the spoons are on the mantlepiece, in full sight. He tries to distract the doctor’s attention but eventually Fawcett sees them, asks what they are, and, upon examining them, almost has a heart attack as he realises their cultural importance and immense value.

Ford reluctantly confesses to when he found them and even more reluctantly admits there are more. When he unlocks his cupboard and shows the hoard to Fawcett the latter nearly expires with excitement.

In a way the most interesting moment comes when Dahl, showing the insight of a storyteller, admits that the most interesting part of the tale, all the dramatic bits, are over. Now it’s just the bureaucracy and administration. The hoard is reported to the police and packed off to the British Museum. In July 1946 a hearing is held under the jurisdiction of a coroner but it’s a jury which decides to award both Ford and Butcher £1,000, a lot of money but nowhere near the half million Butcher might have got if Ford had told him to report the find immediately.

You can read up-to-date information about the treasure on the Mildenhall Treasure Wikipedia page, including a reference to what Wikipedia calls Dahl’s ‘partly fictional account’.

The Swan (25 pages)

His lazy truck driver Dad buys thick, loutish Ernie, a .22 rifle for his 15th birthday. He and his mate Raymond go straight out on this fine May morning and start taking potshots at songbirds, stringing their bodies up from a stick Ernie carries over his shoulder. Then they come across school swot, weedy bespectacled 13-year-old Peter Watson.

At which point commences the main body of the story in which these two thugs really seriously bully Peter. First of all they march him to the nearby train line where they truss him hand and foot and then tie him to the sleepers. It is genuinely tense as Peter lies there trying to work out how low a train’s undercarriage is, and systematically moving his head and feet back and forth to try and dig deeper into the gravel. Dahl gives a tremendously vivid description of the express train suddenly appearing like a rocket, and roaring over Peter’s head till he feels like he’s been swallowed by a screaming giant.

But he survives, dazed and in shock. The bullies have watched from the nearby verge and now stroll down and untie Peter but keep his hands trussed. They push him ahead of them as they set off for the lake. Here they spot a duck and, despite Peter’s heartfelt please, shoot it. At which Ernie has the bright idea of treating Peter as their retriever, forcing him to wade into the water and bring back the corpse of the duck.

Next they spot a swan, a beautiful swan sitting regally atop a nest in the reeds. Peter begs them, tells them it’s illegal, tells them that swans are the most protected birds in the country, they’ll be arrested etc, but these guys are idiots as well as hooligans and Ernie raises his gun and shoots the swan dead. Then they threaten to kick and beat Peter unless he wades into the reeds and fetches the body.

It’s at this stage that things start to take a turn for the macabre or gruesome or possibly surreal. Peter loses all restraint and accuses Ernie of being a sadist and a brute at which point Ernie has another of his brainwaves and asks if Peter would like to see the swan come back to life, flying happily over the lake?

Peter asks what the devil he’s talking about, but then Ernie asks Ray for his pocket knife and sets about sawing off one of the swan’s wings. He then cuts six sections from the ball of string he always carries in his jacket and then…tells Peter to stretch out his arm. While Peter says he’s mental, Ernie proceeds to tie the swan’s wing tightly to Peter’s arm. Then he cuts off the other wing and ties it to Peter’s other arm. Now Peter has two swan’s arms attached to his arms.

So far so weird, but now the story moves towards a line or threshold, for Ernie now insists that Peter climbs a weeping willow growing by the lakeside, climbs right to the top and then ‘flies’. Peter seizes the opportunity of escaping from the bullies and makes the best of struggling up through a willow tree while encumbered with two whopping great swan wings, but eventually reaches the highest branch capable of bearing his weight, some 50 feet above the ground.

If he thought he could escape the bullies he was mistaken for they have stepped back to have clear sight of him, and Ernie proceeds to shout at him, telling him to fly. What madness, Peter thinks and doesn’t budge. At which point Ernie tells him he must fly or he will shoot. Peter doesn’t budge. Then Ernie says he’ll count to ten. He gets to ten and fires, deliberately shooting wide, in order to scare Peter who still doesn’t budge. Then, getting cross, Ernie shoots him in the thigh.

Now, at this pivotal moment, Dahl interjects a bit of editorialising. he tells us that there are two kinds of people, people who crumble and collapse under stress, pressure and danger or the smaller number of people who abruptly flourish and triumph. This, we take it, is experience garnered during his service in the war. But it also serves to paper over the crack, the red line, where the narrative crosses over from weird but plausible into wholly new realm of magical realism.

For, transformed by rage and frustration, Peter spreads his swan’s wings and…flies! The bullet in his leg knocked both his feet from under him but instead of plummeting to earth he sees a great white light shining over the lake, beckoning him on, and spreads the great swan wings and goes soaring up into the sky.

The narrative cuts to the eye witnesses in the village who see a boy with swan wings flying overhead and then cuts to Peter’s mother, doing the washing up in the kitchen sink when she sees something big and white and feathered land in her garden and rushes out to find her beloved little boy, to cut him free from the wings and start to tend the wound in his leg.

The transcendence of this, the tying on of wings and a boy’s transformation into a bird, remind me of the several J.G. Ballard short stories which depict men obsessed with flying like birds, in particular the powerful 1966 story Storm-bird, Storm-dreamer.

The Wonderful Story of Henry Sugar (71 pages)

By far the longest of Dahl’s short stories, this tale is more accurately described as a novella, whose length justifies the compilation and naming of the book around it. Having just finished it I can see that it could possibly have been a book in its own right, padded out with illustrations to book length. Instead the publishers padded it out to book length by adding a couple of other stories and some already-published war memoirs.

It’s an odd production, firstly in that it contains lengthy stories nested within each other, as you’ll see. We start with an extended introduction to the character of Henry Sugar who is painted as a thoroughly despicable person. He has inherited great wealth, is lazy and idle and spends most of his time, like many of his class, gambling on anything that moves.

Sugar goes to stay with a posh lord (Sir William Wyndham at his house near Guildford) and when his friends set up a game of canasta he draws the short straw and is the odd man out, so he wanders disconsolately into the library and mooches around till he finds an old exercise book in which is written the second story, the story-within-a-story.

For the exercise book turns out to be an account written by a British doctor in India in 1934. It is titled ‘A Report on an Interview with Imhrat Khan, The Man Who Could See Without Eyes, by Dr John Cartwright, Bombay, India, December 1934’.

This is a long, detailed account in its own right. This Cartwright is sitting with others in the Doctors Rest Room in Bombay Hospital when an Indian comes in. He calmly explains that he can see without using his eyes. After their initial mockery the doctors test him by putting a temporary sealant on his eyes, covering them with bread dough, then cotton wool, then bandaging them thoroughly. But, to their astonishment, the man heads out into the corridor, avoids other people, manages the stairs just fine, walks out the building, gets onto a bicycle and cycles out into the roaring traffic all without the use of his eyes.

It turns out that this fellow makes his living as part of a travelling circus where he’s one among many gifted performers such as a prodigious juggler, a snake charmer and a sword swallower. Dr Cartwright finds this out when he goes to see the circus that evening (at the Royal Palace Hall, Acacia Street). He then goes backstage to Khan’s dressing room and asks if he can interview him about his amazing powers. He will write up the account and try to get it published in something like the British Medical Journal. Khan agrees so Cartwright takes him to a restaurant and over curry Khan tells him his story.

So this is the third account, a story-within-a-story-within-a-story, which switches to a first-person narrative. Khan explains that he had a lifelong fascination with magic. When he was 13 a conjurer came to his school. He was so entranced that he followed him to Lahore where he became his assistant. but is disillusioned when he discovers it is all trickery and not real magic. He learns about the yogi, holy men who develop special skills. While looking for one he joins a travelling theatre company to make a living. Then he learns that the greatest yogi in India is Mr Banerjee, so he sets off to find him. He tracks him down to the jungle outside Rishikesh where he hides and witnesses the great man praying and levitating. When he steps forward to introduce himself Banerjee is furious at being spied on and chases Khan away. But the boy returns day after day and his persistence wears Banerjee down. Eventually he agrees to talk, says he never takes disciples, but recommends a colleague, Mr Hardwar.

Hardwar takes him on and thus begins a series of challenging physical and mental exercises, for three years. Eventually he needs to earn a living and rejoins a travelling show where he performs conjuring tricks. In Dacca he comes across a crowd watching a man walk on fiery coals and, when volunteers are requested, he goes forward and walks on burning coals himself.

He has heard tell that the ultimate test of a yogi’s powers is to see without using your eyes and so sets his heart on achieving this skill. (p.123). Slowly he realises that our senses have two aspects, the outer obvious one, and the inner version of that sense. He cultivates his inner sense of sight and the narrative form allows Dahl to convince us that Khan slowly slowly acquires the ability to see objects with his eyes closed.

By 1933 when he is 28 he can read a book with his eyes closed. He explains to Cartwright that the seeing is now done by any part of his body and demonstrates it by placing himself behind a door except for his hand which he sticks round the door. Then he proceeds to read the first book Cartwright takes off the shelf with his hand. Cartwright is staggered.

It is now late and time for Khan to go to bed. Cartwright thanks him and drives him home, then goes back to his own place but can’t sleep. Surely this is one of the greatest discoveries ever made! If this skill can be taught then the blind could be made to see and the deaf to hear! Cartwright gets a clean notebook and writes down every detail of what Khan has told him.

Next morning Cartwright tells all to a fellow doctor and they agree to go to the performance that evening and afterwards take Khan away from the tacky world of travelling performers and set him up somewhere safe where scientists can study him.

But when they get to the Royal Palace Hall something is wrong, there is no crowd and someone has written ‘Performance cancelled’ across the poster. When Cartwright asks he is told that ‘The man who can see without eyes’ died peacefully in his sleep. At one point in his long narration, Khan had made a point of telling him that a good yogi is sworn to secrecy and is punished for divulging his secrets. Well, this is the handy narrative contrivance Dahl has used to eliminate his wonder-worker. He told his secrets, he died.

Cartwright is devastated, finishes writing up his account with this sad coda, signs it and…40 or so years later, this is the old exercise book which Henry Sugar has just randomly picked up and read in the library of Sir William Wyndham!

Sugar has read it alright but the only thing he took from it was one throwaway remark by Khan that he could read the value of playing cards from behind because he could see through playing cards. As an inveterate gambler Sugar is dazzled by the possibilities of this power. He steals the notebook and sets about copying the exercises detailed in it. Months pass and he thinks he’s beginning to acquire the ability to empty his mind and visualise.

At the end of one year of hard training to focus and visualise Sugar tests himself and discovers that he can see through the back of a playing card to see its value, although it takes about four minutes to do so. A month later he can do it in 90 seconds, six months later he’s got it down to 20 seconds. But thereafter it gets harder, and it takes another eight months before he gets it down to 10 seconds. By now he has developed phenomenal powers of concentration but getting his reading time down to his target of four seconds takes another whole year, making three years and three months in total.

Then commences the real core of the story. In a sense all the preliminary matter about the Indian yogi is so much guff; conceivably it could have been a scientific inventor coming up with the discovery or any other kind of pretext or excuse which gets the protagonist to this point, namely, Being able to see the value of concealed cards at a casino.

For on the evening of the day when he finally visualises a card in 4 seconds, Henry puts on a dinner jacket and catches a cab to one of the most exclusive casinos in London, Lord’s House. Here he discovers he can predict which number is going to come up at roulette, bets £100 and wins at odds of 36 to 1. (I was surprised at this because all the effort of the preceding narrative has been about seeing what’s there with his eyes shut whereas this, his first trick in a casino, is entirely about predicting the future, which is a completely different ability altogether.)

What makes these children’s stories, but very effective children’s stories, is their vivid exaggeration. Everyone and everything is always the best in the world:

[The cashier] had arithmetic in his fingers. But he had more than that. He had arithmetic, trigonometry and calculus and algebra and Euclidean geometry in every nerve of his body. He was a human calculating-machine with a hundred thousand electric wires in his brain. (p.145)

Also the simplicity of the thoughts, and of the layout which emphasises that simplicity. The following should be a paragraph but isn’t, it is laid out like this because it is catering to children:

And what of the future?
What was the next move going to be?
He could make a million in a month.
He could make more if he wanted to.
There was no limit to what he could make.

Anyway, the surprising thing is that Henry is not thrilled by his staggering winnings. A few years earlier such a win would have knocked his socks off and he would have gone somewhere and splashed the cash on champagne and partying. Not now. To his surprise Henry feels gloomy. He is realising the great truth, that ‘nothing is any fun if you can get as much of it as you want’ (p.148).

Bored and a bit depressed Henry stands at the window of his Mayfair flat and, out of boredom, lets one of the £20 notes of his winnings be taken away by the breeze. An old man picks it up. He lets another go and a young couple get it. A crowd begins to form under his window. Eventually Henry throws his entire winnings of thousands of pounds into the street which, predictably, causes a small riot and blocks the traffic.

A few minutes later a very angry policeman knocks on his apartment door and tells him not to be such a blithering idiot. Where did he get the money from etc and Henry gives details of the casino, but what strikes home is the copper says if you want to chuck money away, why not give it to somewhere useful like an orphanage.

This gives Henry a brainwave. After thinking it through a bit he decides he will devote his life to charity. he will move from city to city, fleecing the casinos for huge sums before moving on to the next. And he will use all the money he makes to set up orphanages in each country.

He’ll need someone to handle the money side so he goes to see his accountant, a cautious man named John Winston. Winston doesn’t believe him so Henry a) tells him the values of cards laid face down on his table b) wins a fortune in matchsticks from a little game of blackjack they have in his office c) takes him to a casino that evening (not the Lord’s House) where he wins £17,500.

Winston agrees to be his partner but points out that the kind of revenue he’s suggesting will all be taken by the taxman. He suggests they set up the business in Switzerland so Henry gives him the £17,500 to organise the move, set up a new office, move his wife and children out there.

A year later Henry has sent the company they’ve set up £8 million and John has used it to set up orphanages. Over the next seven years he wins £50 million. Eventually, as in all good stories, things go wrong and trigger the climax. Henry is foolish enough to win $100,000 at three Las Vegas casinos owned by the same mob. Next morning the bellhop arrives to tell him some dodgy men are waiting in the foyer. The bellhop explains that, for a price, he’ll let Henry use his uniform to get away. But he must tie the bellhop up to make it look kosher. This he does, tucks a grand under the carpet as payment, and makes his escape dressed as a bellhop.

He catches a plane to Los Angeles because the use of a disguise has given him an idea. He goes to see the best makeup artist in Hollywood, Max Engelman. He explains his special powers and asks if he wants to earn $100,000 a year. Max joins him and together they travel the casinos of the world appearing at each one in disguise. The story has now become a full-on children’s story, revelling in the sheer pleasure of dressing up in ever-more preposterous identities, using faked passports and id cards.

Eventually the story ends when Henry Sugar dies. The narrator tots up the figures. Henry died aged 63. He had visited 371 major casinos in 21 different countries or islands. During that period he made £144 million which was used to set up 21 well-run orphanages around the world, one in each country he visited.

In the last few pages Dahl gives a children’s style version of how he came to write the book, namely John Winston rang him up, invited him to come and meet him and Max, showed him Cartwright’s notebook, and commissioned him to write a full account. Which is what he’s just done. No matter how absurd and fantastical the story, it is treated with Dahl’s trademark clear, frank limpidity.

Lucky Break

This is a non-fictional account of how Dahl became a writer, condensing material from his two autobiographical books, ‘Boy and ‘Going Solo’. It highlights key events from his childhood, school days and early manhood up to the publication of his first story.

A Piece of Cake (1946)

From Wikipedia:

An autobiographical account of Dahl’s time as a fighter pilot in the Second World War. It describes how Dahl was injured and eventually forced to leave the Mediterranean arena. The original version of the story was written for C. S. Forester so that he could get the gist of Dahl’s story and rewrite it in his own words. Forester was so impressed by the story (Dahl at the time did not believe himself a capable writer) that he sent it without modification to his agent, who had it published (as ‘Shot Down Over Libya’) in The Saturday Evening Post, thereby initiating Dahl’s writing career. It appeared in Dahl’s first short story collection ‘Over to You’, published in 1946.


Credit

The Wonderful Story of Henry Sugar and Six More by Roald Dahl was published by Jonathan Cape in 1977. References are to the 2001 Puffin paperback edition.

Related links

Roald Dahl reviews

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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