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

Alex’s Adventures In Numberland by Alex Bellos (2010)

Alexander Bellos (born in 1969) is a British writer and broadcaster. He is the author of books about Brazil and mathematics, as well as having a column in The Guardian newspaper. After adventures in Brazil (see his Wikipedia page) he returned to England in 2007 and wrote this, his first book. It spent four months in the Sunday Times bestseller list and led on to five more popular maths books.

It’s a hugely enjoyable read for three reasons:

  1. Bellos immediately establishes a candid, open, good bloke persona, sharing stories from his early job as a reporter on the Brighton Argus, telling some colourful anecdotes about his time in Brazil and then being surprisingly open about the way that, when he moved back to Britain, he had no idea what to do. The tone of the book is immediately modern, accessible and friendly.
  2. However this doesn’t mean he is verbose. The opposite. The book is packed with fascinating information. Every single paragraph, almost every sentence contains a fact or insight which makes you sit up and marvel. It is stufffed with good things.
  3. Lastly, although its central theme is mathematics, it approaches this through a wealth of information from the humanities. There is as much history and psychology and anthropology and cultural studies and philosophy as there is actual maths, and these are all subjects which the average humanities graduate can immediately relate to and assimilate.

Chapter Zero – A Head for Numbers

Alex meets Pierre Pica, a linguist who’s studied the Munduruku people of the Amazon and discovered they have little or no sense of numbers. They only have names for numbers up to five. Also, they cluster numbers together logarithmically i.e. the higher the number, the closer together they clustered them. Same thing is done by kindergarten children who only slowly learn that numbers are evenly spaced, in a linear way.

This may be because small children and the Munduruku don’t count so much as estimate using the ratios between numbers.

It may also be because above a certain number (five) Stone Age man needed to make quick estimates along the lines of, Are there more wild animals / members of the other gang, than us?

Another possibility is that distance appears to us to be logarithmic due to perspective: the first fifty yards we see in close detail, the next fifty yards not so detailed, beyond 100 yards looking smaller, and so on.

It appears that we have to be actively taught when young to overcome our logarithmic instincts, and to apply the rule that each successive whole number is an equal distance from its predecessor and successor i.e. the rational numbers lies along a straight line at regular intervals.

More proof that the logarithmic approach is the deep, hard-wired one is the way most of us revert to its perspective when considering big numbers. As John Allen Paulos laments, people make no end of fuss about discrepancies between 2 or 3 or 4 – but are often merrily oblivious to the difference between a million or a billion, let alone a trillion. For most of us these numbers are just ‘big’.

He goes on to describe experiments done on chimpanzees, monkeys and lions which appear to show that animals have the ability to estimate numbers. And then onto experiments with small babies which appear to show that as soon as they can focus on the outside world, babies can detect changes in number of objects.

And it appears that we also have a further number skill, that guesstimating things – the journey takes 30 or 40 minutes, there were twenty or thirty people at the party, you get a hundred, maybe hundred and fifty peas in a sack. When it comes to these figures almost all of us give rough estimates.

To summarise:

  • we are sensitive to small numbers, acutely so of 1, 2, 3, 4, less so of 5, 6, 7, 8, 9
  • left to our own devices we think logarithmically about larger numbers i.e lose the sense of distinction between them, clump them together
  • we have a good ability to guesstimate medium size numbers – 30, 40, 100

But it was only with the invention of notation, a way of writing numbers down, that we were able to create the linear system of counting (where every number is 1 larger than its predecessor, laid out in a straight line, at regular intervals).

And that this cultural invention enabled human beings to transcend our vague guesstimating abilities, and laid the basis for the systematic manipulation of the world which followed

Chapter One – The Counter Culture

The probable origins of counting lie in stock taking in the early agricultural revolution some 8,000 years ago.

We nowadays count using a number base 10 i.e. the decimal system. But other bases have their virtues, especially base 12. It has more factors i.e. is easier to divide: 12 can be divided neatly by 2, 3, 4 and 6. A quarter of 10 is 2.5 but of 12 is 3. A third of 10 is 3.333 but of 12 is 4. Striking that a version of the duodecimal system (pounds, shillings and pence) hung on in Britain till we finally went metric in the 1970s. There is even a Duodecimal Society of America which still actively campaigns for the superiority of a base 12 counting scheme.

Bellos describes a bewildering variety of other counting systems and bases. In 1716 King Charles XII of Sweden asked Emmanuel Swedenborg to devise a new counting system with a base of 64. The Arara in the Amazon count in pairs, the Renaissance author Luca Paccioli was just one of hundreds who have devised finger-based systems of counting – indeed, the widespread use of base 10 probably stems from the fact that we have ten fingers and toes.

He describes a complicated Chinese system where every part of the hand and fingers has a value which allows you to count up to nearly a billion – on one hand!

The Yupno system which attributes a different value for parts of the body up to its highest number, 33, represented by the penis.

Diagram showing numbers attributed to parts of the body by the Yupno tribe

Diagram showing numbers attributed to parts of the body by the Yupno tribe

There’s another point to make about his whole approach which comes out if we compare him with the popular maths books by John Allen Paulos which I’ve just read.

Paulos clearly sees the need to leaven his explanations of comparative probability and Arrow’s Theorem and so on with lighter material and so his strategy is to chuck into his text things which interest him: corny jokes, anecdotes about baseball, casual random digressions which occur to him in mid-flow. But al his examples clearly 1. emanate from Paulos’s own interests and hobby horses (especially baseball) and 2. they are tacked onto the subjects being discussed.

Bellos, also, has grasped that the general reader needs to be spoonfed maths via generous helpings of other, more easily digestible material. But Bellos’s choice of material arises naturally from the topic under discussion. The humour emerges naturally and easily from the subject matter instead of being tacked on in the form of bad jokes.

You feel yourself in the hands of a master storyteller who has all sorts of wonderful things to explain to you.

In fourth millennium BC, an early counting system was created by pressing a reed into soft clay. By 2700 BC the Sumerians were using cuneiform. And they had number symbols for 1, 10, 60 and 3,600 – a mix of decimal and sexagesimal systems.

Why the Sumerians grouped their numbers in 60s has been described as one of the greatest unresolved mysteries in the history of arithmetic. (p.58)

Measuring in 60s was inherited by the Babylonians, the Egyptians and the Greeks and is why we still measure hours in 60 minutes and the divisions of a circle by 360 degrees.

I didn’t know that after the French Revolution, when the National Convention introduced the decimal system of weights and measures, it also tried to decimalise time, introducing a new system whereby every day would be divided into ten hours, each of a hundred minutes, each divided into 100 seconds. Thus there were a very neat 10 x 100 x 100 = 100,000 seconds in a day. But it failed. An hour of 60 minutes turns out to be a deeply useful division of time, intuitively measurable, and a reasonable amount of time to spend on tasks. The reform was quietly dropped after six months, although revolutionary decimal clocks still exist.

Studies consistently show that Chinese children find it easier to count than European children. This may be because of our system of notation, or the structure of number names. Instead of eleven or twelve, Chinese, Japanese and Koreans say the equivalent of ten one, ten two. 21 and 22 become two ten one and two ten two. It has been shown that this makes it a lot simpler and more intuitive to do basic addition and subtraction.

Bellos goes on to describe the various systems of abacuses which have developed in different cultures, before explaining the phenomenal popularity of abacus counting, abacus clubs, and abacus championships in Japan which helps kids develop the ability to perform anzan, using the mental image of an abacus to help its practitioners to sums at phenomenal speed.

Chapter Two – Behold!

The mystical sense of the deep meaning of numbers, from Pythagoras with his vegetarian religious cult of numbers in 4th century BC Athens to Jerome Carter who advises leading rap stars about the numerological significance of their names.

Euclid and the elegant and pure way he deduced mathematical theorems from a handful of basic axioms.

A description of the basic Platonic shapes leads into the nature of tessalating tiles, and the Arab pioneering of abstract design. The complex designs of the Sierpinski carpet and the Menger sponge. And then the complex and sophisticated world of origami, which has its traditionalists, its pioneers and surprising applications to various fields of advanced science, introducing us to the American guru of modern origami, Robert Lang, and the Japanese rebel, Kazuo Haga, father of Haga’s Theorem.

Chapter Three – Something About Nothing

A bombardment of information about the counting systems of ancient Hindus, Buddhists, about number symbols in Sanskrit, Hebrew, Greek and Latin. How the concept of zero was slowly evolved in India and moved to the Muslim world with the result that the symbols we use nowadays are known as the Arabic numerals.

A digression into ‘a set of arithmetical tricks known as Vedic Mathematics ‘ devised by a young Indian swami at the start of the twentieth century, Bharati Krishna Tirthaji, based on a series of 16 aphorisms which he found in the ancient holy texts known as the Vedas.

Shankaracharya is a commonly used title of heads of monasteries called mathas in the Advaita Vedanta tradition. Tirthaji was the Shankaracharya of the monastery at Puri. Bellos goes to visit the current Shankaracharya who explains the closeness, in fact the identity, of mathematics and Hindu spirituality.

Chapter Four – Life of Pi

An entire chapter about pi which turns out not only to be a fundamental aspect of calculating radiuses and diameters and volumes of circles and cubes, but also to have a long history of mathematicians vying with each other to work out its value to as many decimal places as possible (we currently know the value of pi to 2.7 trillion decimal places) and the surprising history of people who have set records reciting the value if pi.

Thus, in 2006, retired Japanese engineer Akira Haraguchi set a world record for reciting the value of pi to the first 100,000 decimal places from memory! It took 16 hours with five minute beaks every two hours to eat rice balls and drink some water.

There are several types or classes of numbers:

  • natural numbers – 1, 2, 3, 4, 5, 6, 7…
  • integers – all the natural numbers, but including the negative ones as well – …-3, -2, -1, 0, 1, 2, 3…
  • fractions
  • which are also called rational numbers
  • numbers which cannot be written as fractions are called irrational numbers
  • transcendent numbers – ‘a transcendental number is an irrational number that cannot be described by an equation with a finite number of terms’

The qualities of the heptagonal 50p coin and the related qualities of the Reuleux triangle.

Chapter Five – The x-factor

The origin of algebra (in Arab mathematicians).

Bellos makes the big historical point that for the Greeks (Pythagoras, Plato, Euclid) maths was geometric. They thought of maths as being about shapes – circles, triangles, squares and so on. These shapes had hidden properties which maths revealed, thus giving – the Pythagoreans thought – insight into the secret deeper values of the world.

It is only with the introduction of algebra in the 17th century (Bellos attributes its widespread adoption to Descartes’s Method in the 1640s) that it is possible to fly free of shapes into whole new worlds of abstract numbers and formulae.

Logarithms turn the difficult operation of multiplication into the simpler operation of addition. If X x Y = Z, then log X + log Y = log Z. They were invented by a Scottish laird John Napier, and publicised in a huge book of logarithmic tables published in 1614. Englishman Henry Briggs established logarithms to base 10 in 1628. In 1620 Englishman Edmund Gunter marked logarithms on a ruler. Later in the 1620s Englishman William Oughtred placed two logarithmic rulers next to each other to create the slide rule.

Three hundred years of dominance by the slide rule was brought to a screeching halt by the launch of the first pocket calculator in 1972.

Quadratic equations are equations with an x and an x², e.g. 3x² + 2x – 4 = 0. ‘Quadratics have become so crucial to the understanding of the world, that it is no exaggeration to say that they underpin modern science’ (p.200).

Chapter Six – Playtime

Number games. The origin of Sudoku, which is Japanese for ‘the number must appear only once’. There are some 5 billion ways for numbers to be arranged in a table of nine cells so that the sum of any row or column is the same.

There have, apparently, only been four international puzzle crazes with a mathematical slant – the tangram, the Fifteen puzzle, Rubik’s cube and Sudoku – and Bellos describes the origin and nature and solutions to all four. More than 300 million cubes have seen sold since Ernö Rubik came up with the idea in 1974. Bellos gives us the latest records set in the hyper-competitive sport of speedcubing: the current record of restoring a copletely scrambled cube to order (i.e. all the faces of one colour) is 7.08 seconds, a record held by Erik Akkersdijk, a 19-year-old Dutch student.

A visit to the annual Gathering for Gardner, honouring Martin Gardner, one of the greatest popularisers of mathematical games and puzzles who Bellos visits. The origin of the ambigram, and the computer game Tetris.

Chapter Seven – Secrets of Succession

The joy of sequences. Prime numbers.

The fundamental theorem of arithmetic – In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 either is a prime number itself or can be represented as the product of prime numbers.

The Goldbach conjecture – one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states that, Every even integer greater than 2 can be expressed as the sum of two primes. The conjecture has been shown to hold for all integers less than 4 × 1018, but remains unproven despite considerable effort.

Neil Sloane’s idea of persistence – The number of steps it takes to get to a single digit by multiplying all the digits of the preceding number to obtain a second number, then multiplying all the digits of that number to get a third number, and so on until you get down to a single digit. 88 has a persistence of three.

88 → 8 x 8 = 64 → 6 x 4 = 24 → 2 x 4 = 8

John Horton Conway’s idea of the powertrain – For any number abcd its powertrain goes to abcd, in the case of numbers with an odd number of digits the final one has no power, abcde’s powertrain is abcde.

The Recamán sequence Subtract if you can, unless a) it would result in a negative number or b) the number is already in the sequence. The result is:

0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11….

Gijswijt’s sequence a self-describing sequence where each term counts the maximum number of repeated blocks of numbers in the sequence immediately preceding that term.

1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 2, 3, 2, 1, …

Perfect number A perfect number is any number that is equal to the sum of its factors. Thus 6 – its factors (the numbers which divided into it) are 1, 2 and 3. Which also add up to (are the sum of) 6. The next perfect number is 28 because its factors – 1, 2, 4, 7, 14 – add up to 28. And so on.

Amicable numbers A number is amicable if the sum of the factors of the first number equals the second number, and if the sum of the factors of the second number equals the first. The factors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110. Added together these make 284. The factors of 284 are 1, 2, 4, 71 and 142. Added together they make 220!

Sociable numbers In 1918 Paul Poulet invented the term sociable numbers. ‘The members of aliquot cycles of length greater than 2 are often called sociable numbers. The smallest two such cycles have length 5 and 28’

Mersenne’s prime A prime number which can be written in the form 2n – 1 a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer n. The exponents n which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, … and the resulting Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, …

These and every other sequence ever created by humankind are documented on The On-Line Encyclopedia of Integer Sequences (OEIS), also cited simply as Sloane’s. This is an online database of integer sequences, created and maintained by Neil Sloane while a researcher at AT&T Labs.

Chapter Eight – Gold Finger

The golden section a number found by dividing a line into two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part.

Phi The number is often symbolized using phi, after the 21st letter of the Greek alphabet. In an equation form:

a/b = (a+b)/a = 1.6180339887498948420 …

As with pi (the ratio of the circumference of a circle to its diameter), the digits go on and on, theoretically into infinity. Phi is usually rounded off to 1.618.

The Fibonnaci sequence Each number in the sequence is the sum of the two numbers that precede it. So the sequence goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on. The mathematical equation describing it is Xn+2= Xn+1 + Xn.

as the basis of seeds in flowerheads, arrangement of leaves round a stem, design of nautilus shell and much more.

Chapter Nine – Chance Is A Fine Thing

A chapter about probability and gambling.

Impossibility has a value 0, certainty a value 1, everything else is in between. Probabilities can be expressed as fractions e.g. 1/6 chance of rolling a 6 on a die, or as percentages, 16.6%, or as decimals, 0.16…

The probability is something not happening is 1 minus the probability of that thing happening.

Probability was defined and given mathematical form in 17th century. One contribution was the questions the Chevalier de Méré asked the mathematical prodigy Blaise Pascal. Pascal corresponded with his friend, Pierre de Fermat, and they worked out the bases of probability theory.

Expected value is what you can expect to get out of a bet. Bellos takes us on a tour of the usual suspects – rolling dice, tossing coins, and roulette (invented in France).

Payback percentage if you bet £10 at craps, you can expect – over time – to receive an average of about £9.86 back. In other words craps has a payback percentage of 98.6 percent. European roulette has a payback percentage of 97.3 percent. American roulette, 94.7 percent. On other words, gambling is a fancy way of giving your money away. A miserly slot machine has a payback percentage of 85%. The National Lottery has a payback percentage of 50%.

The law of large numbers The more you play a game of chance, the more likely the results will approach the statistical probability. Toss a coin three times, you might get three heads. Toss a coin a thousand times, the chances are you will get very close the statistical probability of 50% heads.

The law of very large numbers With a large enough sample, outrageous coincidences become likely.

The gambler’s fallacy The mistaken belief that, if something happens more frequently than normal during a given period, it will happen less frequently in the future (or vice versa). In other words, that a random process becomes less random, and more predictable, the more it is repeated.

The birthday paradox The probability that, in a set of n randomly chosen people, some pair of them will have the same birthday. By the pigeonhole principle, the probability reaches 100% when the number of people reaches 367 (since there are only 366 possible birthdays, including February 29). However, 99.9% probability is reached with just 70 people, and 50% probability with 23 people. (These conclusions are based on the assumption that each day of the year (excluding February 29) is equally probable for a birthday.) In other words you only need a group of 23 people to have an evens chance that two of them share a birthday.

The drunkard’s walk

The difficulty of attaining true randomness and the human addiction to finding meaning in anything.

The distinction between playing strategy (best strategy to win a game) and betting strategy (best strategy to maximise your winnings), not always the same.

Chapter Ten – Situation Normal

Carl Friedrich Gauss, the bell curve, normal distribution aka Gaussian distribution. Normal or Gaurrian distribution results in a bell curve. Bellos describes the invention and refinement of the bell curve (he explains that ‘the long tail’ results from a mathematician who envisioned a thin bell curve as looking like two kangaroos facing each other with their long tails heading off in opposite directions). And why

Regression to the mean – if the outcome of an event is determined at least in part by random factors, then an extreme event will probably be followed by one that is less extreme. And recent devastating analyses which show how startlingly random sports achievements are, from leading baseball hitters to Simon Kuper and Stefan Szymanski’s analysis of the form of the England soccer team.

Chapter Eleven – The End of the Line

Two breakthroughs which paved the way for modern i.e. 20th century, maths: the invention of non-Euclidean geometry, specifically the concept of hyperbolic geometry. To picture this draw a triangle on a Pringle. it is recognisably a triangle but all its angles do not add up to 180°, therefore it defies, escapes, eludes all the rule of Euclidean geometry, which were designed for flat 2D surfaces.

Bellos introduces us to Daina Taimina, a maths prof at Cornell University, who invented a way of crocheting hyperbolic surfaces. The result looks curly, like curly kale or the surface of coral.

Anyway, the breakaway from flat 2-D Euclidean space led to theories about curved geometry, either convex like a sphere, or hyperbolic like the pringle. It was this notion of curved space, which paved the way for Einstein’s breakthrough ideas in the early 20th century.

The second big breakthrough was Georg Cantor’s discovery that you can have many different types of infinity. Until Cantor the mathematical tradition from the ancient Greeks to Galileo and Newton had fought shy of infinity which threatened to disrupt so many formulae.

Cantor’s breakthrough was to stop thinking about numbers, and instead think of sets. This is demonstrated through the paradoxes of Hilbert’s Hotel. You need to buckle your safety belt to understand it.

Thoughts

This is easily the best book about maths I’ve ever read. It gives you a panoramic history of the subject which starts with innumerate cavemen and takes us to the edge of Einstein’s great discoveries. But Bellos adds to it all kinds of levels and abilities.

He is engaging and candid and funny. He is fantastically authoritative, taking us gently into forests of daunting mathematical theory without placing a foot wrong. He’s a great explainer. He knows a good story when he sees one, and how to tell it engagingly. And in every chapter there is a ‘human angle’ as he describes his own personal meetings and interviews with many of the (living) key players in the world of contemporary maths, games and puzzles.

Like the Ian Stewart book but on a vastly bigger scale, Bellos makes you feel what it is like to be a mathematician, not just interested in nature’s patterns (the basis of Stewart’s book, Nature’s Numbers) but in the beauty of mathematical theories and discoveries for their own sakes. (This comes over very strongly in chapter seven with its description of some of the weirdest and wackiest number sequences dreamed up by the human mind.) I’ve often read scientists describing the beauty of mathematical theories, but Bellos’s book really helps you develop a feel for this kind of beauty.

For me, I think three broad conclusions emerged:

1. Most mathematicians are in it for the fun. Setting yourself, and solving, mathematical puzzles is obviously extremely rewarding. Maths includes the vast territory of puzzles and games, such as the Sudoku and so on he describes in chapter six. Obviously it has all sorts of real-world application in physics, engineering and so on, but Bellos’s book really brings over that a true understanding of maths begins in puzzles, games and patterns, and often remains there for a lifetime. Like everything else maths is no highly professionalised the property of tenured professors in universities; and yet even to this day – as throughout its history – contributions can be made by enthusiastic amateurs.

2. As he points out repeatedly, many insights which started out as the hobby horses of obsessives, or arcane breakthroughs on the borders of our understanding, and which have been airily dismissed by the professionals, often end up being useful, having applications no-one dreamed of. Either they help unravel aspects of the physical universe undreamed of when they were discovered, or have been useful to human artificers. Thus the development of random number sequences seemed utterly pointless in the 19th century, but now underlies much internet security.

On a profounder note, Bellos expresses the eerie, mystical sense many mathematicians have that it seems so strange, so pregnant with meaning, that so many of these arcane numbers end up explaining aspects of the world their inventors knew nothing of. Ian Stewart has an admirably pragmatic explanation for this: he speculates that nature uses everything it can find in order to build efficient life forms. Or, to be less teleological, over the past 3 and a half billion years, every combination of useful patterns has been tried out. Given this length of time, and the incalculable variety of life forms which have evolved on this planet, it would be strange if every number system conceivable by one of those life forms – humankind – had not been tried out at one time or another.

3. My third conclusion is that, despite John Allen Paulos’s and Bellos’s insistence, I do not live in a world ever-more bombarded by maths. I don’t gamble on anything, and I don’t follow sports – the two biggest popular areas where maths is important – and the third is the twin areas of surveys and opinion polls (55% of Americans believe in alien abductions etc etc) and the daily blizzard of reports (for example, I see in today’s paper that the ‘Number of primary school children at referral units soars’).

I register their existence but they don’t impact on me for the simple reason that I don’t believe any of them. In 1992 every opinion poll said John Major would lose the general election, but he won with a thumping majority. Since then I haven’t believed any poll about anything. For example almost all the opinion polls predicted a win for Remain in the Brexit vote. Why does any sane person believe opinion polls?

And ‘new and shocking’ reports come out at the rate of a dozen a day and, on closer examination, lots of them turn out to be recycled information, or much much more mundane releases of data sets from which journalists are paid to draw the most shocking and extreme conclusions. Some may be of fleeting interest but once you really grasp that the people reporting them to you are paid to exaggerate and horrify, you soon learn to ignore them.

If you reject or ignore these areas – sport, gambling and the news (made up of rehashed opinion polls, surveys and reports) – then unless you’re in a profession which actively requires the sophisticated manipulation of figures, I’d speculate that most of the rest of us barely come into contact with numbers from one day to the next.

I think that’s the answer to Paulos and Bellos when they are in their ‘why aren’t more people mathematically numerate?’ mode. It’s because maths is difficult, and counter-intuitive, and hard to understand and follow, it is a lot of work, it does make your head ache. Even trying to solve a simple binomial equation hurt my brain.

But I think the biggest reason that ‘we’ are so innumerate is simply that – beautiful, elegant, satisfying and thought-provoking though maths may be to the professionals – maths is more or less irrelevant to most of our day to day lives, most of the time.


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