Dubliners by James Joyce (1914)

Dublin is such a small city: everyone knows everyone else’s business.
(The Boarding House)

Dubliners, that book of traps…
(Literary critics Hugh Kenner)

‘Dubliners’ is a collection of fifteen short stories by James Joyce, written between 1904 and 1907, and published as one volume, after various problems and delays, in 1914. The earlier ones are mostly pretty short and so have been described as vignettes, a vignette being ‘a brief evocative description, account or episode.’ The later ones are longer and more complex.

On the face of it the Dubliners stories present naturalistic depictions of Irish middle-class life in and around Dublin in the early twentieth century, although some readers, and subsequently a small army of academic scholars, have detected all manner of subtle symbolism and clever structuring in all of them.

  1. The Sisters (9 pages)
  2. An Encounter (9 pages)
  3. Araby (7 pages)
  4. Eveline (6 pages)
  5. After the Race (7 pages)
  6. Two Gallants (11 pages)
  7. The Boarding House (8 pages)
  8. A Little Cloud (14 pages)
  9. Counterparts (12 pages)
  10. Clay (8 pages)
  11. A Painful Case (10 pages)
  12. Ivy Day in the Committee Room (17 pages)
  13. A Mother (13 pages)
  14. Grace (22 pages)
  15. The Dead (41 pages)

1. The Sisters

A young boy is taken to see the lying-in of his dead priest.

A young boy who lives with his philistine uncle and aunt, reacts to the death of an old priest, the reverend James Flynn, who taught him much. From the start he is very alert to words, he lives through words which are as real as people:

Every night as I gazed up at the window I said softly to myself the word paralysis. It had always sounded strangely in my ears, like the word gnomon in the Euclid and the word simony in the Catechism. But now it sounded to me like the name of some maleficent and sinful being. It filled me with fear, and yet I longed to be nearer to it and to look upon its deadly work.

The title comes from the fact that the narrator is taken by his aunt to visit the two spinster sisters who looked after the dead man, Eliza and Nanny, to be shown the corpse in his coffin, then have a glass of sherry and a gossip.

2. An Encounter

Two schoolboys run into a flasher.

Another story about boyhood but told in a much more stilted and pompous style:

A spirit of unruliness diffused itself among us and, under its influence, differences of culture and constitution were waived. We banded ourselves together, some boldly, some in jest and some almost in fear: and of the number of these latter, the reluctant Indians who were afraid to seem studious or lacking in robustness, I was one.

Three boys bunk off school to go swanning round Dublin.

We pleased ourselves with the spectacle of Dublin’s commerce—the barges signalled from far away by their curls of woolly smoke, the brown fishing fleet beyond Ringsend, the big white sailing-vessel which was being discharged on the opposite quay.

Except one of them, tubby Joe Dillon, doesn’t show up. So the narrator and Mahony roam round town till they come to rest in a field. Here they approached by a furtive old pervert, ‘a queer old josser!’ He asks about their girlfriends, talking about girls in a strange obsessive way. He excuses himself and goes off to a corner of the field and, it is strongly implied, masturbates.

After a silence of a few minutes I heard Mahony exclaim: “I say! Look what he’s doing!”

Then he comes back to the boys and, when Mahony goes off chasing a cat, launches into a monologue about how such boys should be whipped, repeating the word and idea obsessively.

It’s an encounter with a ‘flasher’, a case of indecent exposure, for sure, and creepy. But the man is also a type of mental blockage and paralysis, unable to get beyond his maundering obsessively repetitive phrases about girls and whipping. Perversion as paralysis.

3. Araby

An adolescent boy tries to impress an older girl he has a crush on but fails.

Everything around Joyce becomes charged with meanings and symbolism. So the apparently simple opening sentence is both realistic and symbolic:

North Richmond Street, being blind, was a quiet street except at the hour when the Christian Brothers’ School set the boys free.

One way to start with Joyce is not the awe-ful weight of the intellectual frameworks and symbolism, but more simply responding to his lyricism.

When the short days of winter came dusk fell before we had well eaten our dinners. When we met in the street the houses had grown sombre. The space of sky above us was the colour of ever-changing violet and towards it the lamps of the street lifted their feeble lanterns. The cold air stung us and we played till our bodies glowed.

The narrator is a pubescent boy who is romantically obsessed with the sister of his schoolfriend Mangan, who lives in the house opposite. He takes her image in his heart everywhere, amid the hurly-burly of the Dublin streets and shops, giving rise to the famous sentence:

I bore my chalice safely through a throng of foes.

A bazaar comes to town. In an unclear passage, the narrator thinks Mangan’s sister says she wishes she could go but her convent are going on a retreat, so he promises to go and bring her back a present. All weeks he shirks schoolwork, burning to perform his quest for beautiful Mangan’s sister.

When Saturday comes he waits for his uncle (who’s gone out) to get home and give him a little pocket money to go to the bazaar but uncle, a bit drunk, doesn’t get home till past nine, and has to be reminded to give the boy some money.

He hastens to the train station to catch a train out to the bazaar and doesn’t make it till nearly ten, as it’s closing up, desolate and empty. He walks among different stalls, is asked whether he wants to buy anything by a bored shop assistant, reluctantly says no, and walks back through the now-empty bazaar, burning with humiliation.

Another story about frustration and paralysis and unfreedom.

4. Eveline

Young Evelyn is invited by her boyfriend to elope abroad and escape her closeted life, but at the last minute bottles out.

Eveline Hill is about to elope with a young fellow. She takes a last look round the family home, at the rooms she’s dusted once a week, at the estate of new houses which used to be fields where she played with her childhood friends, all grown up and moved away now. Reflecting on the weekly struggle to pool her own earnings at the department store where she is routinely demeaned, with whatever she can extract from her drunken bully of a father. She promised her dying mother to keep the home together as long as she could but the time has come. She’s been walking out with a young sailor named Frank, tall and handsome who’s back in Ireland on holiday from the merchant ships. Her father found out about the affair and tried to ban it. But now she’s written goodbye letters to him and to her surviving brother, Harry. When she remembers her mother’s final descent into madness, she is overcome with panic:

She stood up in a sudden impulse of terror. Escape! She must escape! Frank would save her. He would give her life, perhaps love, too. But she wanted to live. Why should she be unhappy? She had a right to happiness. Frank would take her in his arms, fold her in his arms. He would save her.

The short text cuts to her standing with Frank amid the swirling quay by the huge ship set to sail across the sea to Buenos Aires and when it comes to it, she has a panic attack, clutches the railing, and cannot move.

5. After the Race

Swept up into a glamorous international set, a rich young man gambles away the money entrusted to him by his father.

Crowds are gathered to watch an international car race through the roads around Dublin, a place characterised by ‘poverty and inaction’. The story focuses on the four young men crewing one of the motor cars.

  1. Charles Ségouin, the owner of the car
  2. André Rivière, his cousin, a young electrician of Canadian birth – both about to start a motor establishment in Paris with Rivière
  3. Villona – a huge Hungarian devoted to his food
  4. Jimmy Doyle – a neatly groomed young man, with a soft, light brown moustache and rather innocent-looking grey eyes

After the race, the four young men go on a prolonged binge. It starts with dinner at Doyle’s house where they are indulged by Doyle senior, a wealthy businessman who made his money the hard way. It is emphasised that Doyle senior has been grooming his son to take over the family business, sent him to posh private (Catholic) school in England, then to Cambridge where an indulgent father picked up the tab for young Jimmy’s moderate debauchery. Doyle senior has encouraged Jimmy’s friendship with Ségouin and this has crystallised into an agreement that the Doyles will invest in Ségouin’s new car company in France.

They had already bumped into an English chum, Routh who they bring to dinner. Afterwards, out on the town, they bump into another pal in the street, a rich American named Farley and drunkenly row out to his yacht anchored in the bay. Here there is heavy duty drunken gambling and, the implication is, Doyle gambles away all the money which was meant to be his family’s investment in Ségouin’s business.

The unsung hero of the piece is the Hungarian Villona who is on the face of it a greedyguts only interested in food but turns out to be knowledgeable about English madrigals, of all subjects, and is wise enough to sit out the card game and play the piano. Wisdom.

6. Two Gallants

A parasite waits for a cocky ladykiller to inveigle money out of his latest squeeze.

Lenehan is a leech, a ravaged-looking hanger-on, a sporting vagrant armed with a vast stock of stories, limericks and riddles who inveigles himself into partying groups. One evening he’s walking along with Corley, a swaggering police inspector’s son, who’s telling him all about a tart he picked up and has been seeing regularly; that they catch a tram out to the fields to have sex (he’s vaguely worried about her getting pregnant) but as important as the sex is the free fags and cigars she brings to every rendezvous. Lenehan listens and applauds and is all oily servility.

They walk through Dublin towards Corley’s rendezvous with the woman, Corley all the way regaling Lenehan with stories of past conquests. They come to the place where the girl is waiting and Lenehan gets a good look at here, minutely described. She looks like a tarty pig. Corley and she stroll off leaving Lenehan to kill time, because for some reason he is anxious to meet up with Corley afterwards, he is counting on Corley to pull off some kind of scam.

He pops into a cheap eatery, has a plate of hot peas, a ginger beer and laments his lot. He’ll be 31 next birthday and has no job or career and is fed up of leeching off people. Incidentally, all the stories reveal or display Joyce’s detailed knowledge of Dublin’s street layout.

He paid twopence halfpenny to the slatternly girl and went out of the shop to begin his wandering again. He went into Capel Street and walked along towards the City Hall. Then he turned into Dame Street. At the corner of George’s Street he met two friends of his and stopped to converse with them… He left his friends at a quarter to ten and went up George’s Street. He turned to the left at the City Markets and walked on into Grafton Street.

The aim of the story is to build up to a comic anticlimax. All the way through the narrative, every detail of his behaviour and thoughts rams it into our minds that Lenehan is desperately anxious that Corley ‘brings it off’, succeeds, achieves his goal, gets a result. Lenehan marches up and down the corner where he’d agreed to meet his palm long before he’s due there, it starts to rain and he begins to think it’s ‘no go’ bit then he sees the couple approaching. He ducks out of sight, watches the girl go down into the area (the low area in front of Georgian terraced houses), then sees her come out of the main door and skip down the steps and confer with Corley before disappearing back inside.

The bathetic anticlimax is that all this cloak-and-dagger behaviour has all been simply to extract some money from the poor girl. This, the story tells us, is the pitiful amount of time and nervous energy a leech and parasite expends on earning even a fraction of money.

‘Can’t you tell us?’ he said. ‘Did you try her?’ Corley halted at the first lamp and stared grimly before him. Then with a grave gesture he extended a hand towards the light and, smiling, opened it slowly to the gaze of his disciple. A small gold coin shone in the palm.

Squalid and pathetic. Lenehan goes on to appear in several chapters of ‘Ulysses’.

7. The Boarding House

A young man is intimidating into marrying the landlady’s daughter, who he’s unwisely had sex with.

At last, when she judged it to be the right moment, Mrs Mooney intervened. She dealt with moral problems as a cleaver deals with meat:

The situation is simple: a youngish (35) boarder in a boarding house (Mr Doran) has got into a relationship with the pretty daughter and servant in a boarding house (Polly Mooney) and had sex with her i.e. ‘taken her virginity’. Her mother and landlady of the house, the big solid no-nonsense Mrs Mooney, has got wind of the affair, obtained a full confession from her daughter. This vignette first of all gives a lot of backstory about Mrs Mooney (how she had to flee her drunken husband, and what became of him), how she set up the boarding house and how it became a popular venue for young artistic and musical types – before moving on to describe the tense mood of both young Polly and Mr Doran as they wait for Mrs D to call the young man in for an interview in which she will demand that he ‘does the decent thing’ and marries Polly i.e. half an hour which will change both their lives forever.

8. A Little Cloud

A flashy man who’s made his name abroad returns to Dublin and upstages his quiet sensitive friend who stayed at home.

Eight years ago Ignatius Gallaher left Dublin to start a career in the Press in London. Now he’s back in Dublin for a flying visit and has invited one of his old friends, shy timid Thomas Malone Chandler, to meet up with him at the loud garish Corless’s bar. Chandler fancies himself as a passionate poet but he is in reality ‘a delicate and abstinent person’, a chaste and methodical clerk, who long ago earned the nickname ‘Little Chandler’, timid and hesitant.

Predictably, the London man is large and hearty, wearing a vivid orange tie, and proceeds to regale timid Chandler with racy tales of life not only in London, but Paris and Berlin. When Chandler suggests he’ll settle down sooner or later, once he finds the right girl, Gallaher boomingly laughs off the idea.

Cut back to Little Chandler at home, at the end of the evening. He has irritated his prim wife, Annie, by forgetting to bring home some coffee. She’s loaded him with the sleeping baby and gone out. He looks at a photo of his wife and notes her pretty features, pretty but cold and prim. Compare with the lurid erotic fantasies conjured up by brassy Gallagher’s brave talk of rich Jewesses with dark oriental eyes, full of passion and voluptuous longing!

Dandling the baby he opens a book of Byron’s poetry and is transported. Why can’t he write poetry like that? The baby awakes, starts crying, refuses to be quieted and suddenly he feels trapped.

It was useless. He couldn’t read. He couldn’t do anything. The wailing of the child pierced the drum of his ear. It was useless, useless! He was a prisoner for life.

So he shouts ‘STOP’ at the baby which, after a moment of amazement, starts screaming even louder. And that’s when his wife walks back in, horrified and demanding to know what he’s done to the baby. Yes, he is trapped forever.

The story contains a line that may have been heartfelt for Joyce, who himself felt stifled by Dublin’s parochial and nationalist culture:

There was no doubt about it: if you wanted to succeed you had to go away. You could do nothing in Dublin.

Which is, of course, precisely what Joyce did, moving to Trieste in the 1900s, Zurich during the Great War and then onto Paris (1920 to 1940).

9. Counterparts

Angry frustrated man, humiliated at work and hard up, gets angry drunk and returns to take it out on his poor young son.

Farrington works as a clerk and copyist in the offices of Crosbie & Alleyne and hates it. He is:

tall and of great bulk. He had a hanging face, dark wine-coloured, with fair eyebrows and moustache: his eyes bulged forward slightly and the whites of them were dirty.

Farrington is a slacker and a drinker. Despite being warned he must finish off a long copying job before 5.30, he nips out to a nearby snug for a quick pint of porter. He is a little tipsy, stressed and discombobulated when the owner calls him out in front of the entire staff for not including two letters in an important tranche of documents he gave him. But he turns the moment into a crisis by choosing to answer back to the boss. The exchange is, in modern terms, hard to understand.

‘Tell me,’ [Mr Alleyne] added, glancing first for approval to the lady beside him, ‘do you take me for a fool? Do you think me an utter fool?’
The man glanced from the lady’s face to the little egg-shaped head and back again; and, almost before he was aware of it, his tongue had found a felicitous moment: ‘I don’t think, sir,’ he said, ‘that that’s a fair question to put to me.’
There was a pause in the very breathing of the clerks. Everyone was astounded.

Not the snappiest reparteee I’ve ever heard, but 5.30 comes and Farrington 1) pawns his watch and chain for six shillings, then 2) makes a beeline for his favourite pub, Davy Byrne’s, where he keeps a succession of arriving friends in awe with recounting of this devastating wit. His mates are: Nosey Flynn, O’Halloran and Paddy Leonard, and Higgins from the office who retells the story with great drama.

They pub crawl on to another bar called the Scotch House where they are introduced to Weathers, an acrobat in the Tivoli, and Farrington buys another round. When the Scotch House closes, they go round to Mulligan’s, to a parlour room at the back. Here Farrington spots a couple of dolled-up ladies and a man who come in and sit at a nearby table; he spends some time ogling one of the women and is irritated when they leave and she fails to turn round and give him an encouraging glance. He’s also irritated that he’s spent all his money on drinks for the others, who he now thinks of as spongers, instead of saving some to impress a lady.

The conversation turns to physique and Weathers shows off his strong arms. The others call on Farrington, the biggest there, to defend Irish national honour and so they stage an arm-wrestling contest. Weathers wins twice, which makes Farrington even angrier.

Drunk and angry, Farrington gets a cheap tram back to his house. It is a squalid household. His wife, Ada, is a little sharp-faced woman who bullies her husband when he is sober and is bullied by him when he is drunk. They have five children.

One of the small boys come down and tells him his mother’s gone to chapel. Farrington, boiling over with rage, takes it out on the harmless child, blaming him for letting the fire in the kitchen go out, taking his walking stick and mercilessly beating the poor child on his thighs.

I needed Wikipedia to explain to me that the story is titled ‘Counterparts’ for two reasons:

  1. For Joyce’s the term ‘counterparts’ could be expected to suggest (hand-written) duplicate copies of legal documents.
  2. At the story’s end, Farrington is seen as the ‘counterpart’ of Mr. Alleyne because just as his superior at his workplace humiliates him, so he, Farrington, abuses his child at home.

10. Clay

The timid life of a mousey spinster.

‘Maria is a very, very small person indeed but she had a very long nose and a very long chin.’ She is a small, middle-aged spinster, very popular at the laundry where she works, Dublin by Lamplight.

It’s Halloween which Irish Catholics celebrated with a party and traditional games. The story follows her helping with evening tea at the laundry, distributing slices of ‘barmbrack’ to all the ladies, then being toasted and cheered, she is so popular.

As soon as that tea is tidied away, she sets off by tram for the house of a man called Joe Donnelly who she nursed when he was a boy, along with his brother Alphy.

She goes to several shops on the way spending a lot of time worrying about which cake to buy to take with her eventually choosing a big slice of plumcake. On the tram to Joe’s she is made room for and shown great courtesy by a stout gentleman wearing a brown hard hat, with a square red face and a greyish moustache, a ‘colonel-looking gentleman’. The implication is he’s a bit tipsy and flirtatious.

She is welcomed with fanfare and affection at Joe’s house by him and his wife and children and plunges straight into tea and games. but when she goes to look for the plumcake can’t find it, asks the children if they’ve hidden or eaten it, and only finally realises the colonel looking gentleman must have stolen it off her.

Joe is keen to brush over this and so gets on with the main Halloween game which is being blindfolded and led to a table on which are a variety of objects. these include a Bible and a ring, and what you select predicts your future. Blindfolded, Maria puts her hands in something soft and squidgy, leading to silence and then a hurried taking of it away. Only later did I realise this is the clay of the story, clay brought in from the garden by the children and put into one of the saucers, clay which, in the symbolism of the game, stands for Death. Which is why there’s an embarrassed silence, then it’s quickly taken away and Maria told to have another go.

She moved her hand about here and there in the air and descended on one of the saucers. She felt a soft wet substance with her fingers and was surprised that nobody spoke or took off her bandage. There was a pause for a few seconds; and then a great deal of scuffling and whispering. Somebody said something about the garden, and at last Mrs Donnelly said something very cross to one of the next-door girls and told her to throw it out at once: that was no play. Maria understood that it was wrong that time and so she had to do it over again: and this time she got the prayer-book.

The prayer-book symbolising a life of spiritual vocation (service at a convent, suggests Joe’s wife). After more games for the children and wine for the adults, Maria is asked to sing. Mrs Donnelly plays the piano while Maria sings ‘I Dreamt I Dwelt in Marble Halls’ from the opera The Bohemian Girl by Michael Balfe.

The narrative tells us that she by ‘mistake’ sang the first verse twice. Characters in Joyce might make mistakes but Joyce never does. In a story fraught with symbolism this omission, too, is symbolic, because in the second verse of the song the singer imagines being beset with lovely suitors, thoughts and imagery inappropriate to the confirmed spinster status of little old Maria.

In an ironic conclusion, Joe is so moved by her singing that he can’t find a corkscrew and has to ask his wife where it is. Much earlier Maria had said she loved Joe except when he drank, for then he became a different person.

Only she hoped that Joe wouldn’t come in drunk. He was so different when he took any drink.

Very subtly it’s implying that some men can only cope with emotion by drinking, thus channeling emotion into the familiar channels of inebriation. Given the horrible violence drunken frustration triggers in Farrington in the previous story, this casts a small shadow over the narrative (as did the tipsy colonel-type nicking her cake).

Not only is Maria, like so many of the characters, trapped in her condition, but she is hemmed round by these threats and risks, mostly from men.

11. A Painful Case

An emotionally constipated would-be intellectual starts an affair with a married woman but as soon as she becomes really engaged, backs off, with tragic consequences.

A portrait of a middle-aged man painfully isolated life, even from his own life, who begins a platonic affair with a married woman but, when she starts to have feelings for him, hurriedly breaks it off.

Mr Duffy is a middle-aged bank cashier of extraordinarily rigid lifestyle, every aspect of his life meticulous and ordered so as to incur as little social contact as possible. One night at a concert he meets a Mrs Emily Sinico, a middle-aged married woman. They strike up a conversation, arrange to meet again, and again.

These meetings are perfectly chaste and mostly an opportunity for Mr Duffy to sound off about his abstruse intellectual concerns. He feels uneasy about the surreptitious nature of the meetings and so asks to be invited to the family home, where me meets the husband, Mr Sinico, who mistakenly thinks his regular visits are by way of wooing their daughter. And so their friendship continues with Duffy sounding off and impressing her with his many intellectual interests.

Little by little he entangled his thoughts with hers. He lent her books, provided her with ideas, shared his intellectual life with her. She listened to all.

In a scene which shows what a gulf there is between Joyce’s Edwardian times and our own, in the areas of sex and relationships, one night at a meeting, Mrs Sinico displays unusual levels of ‘excitement’ and then impulsively takes Duffy’s hand and presses it to her cheek.

This shocks our man in two ways, that he realises the lady hasn’t been listening to his lectures in the high-falutin’ way he intended but also that she’s getting sticky and he risks being sucked into human contact and emotion. So he arranges one last meeting, they walk round the park for three hours as he painfully extricates himself from the relationship. When she shows signs of getting emotional he jumps on the nearest tram and legs it.

As in a fairy story, four years pass and Mr Duffy has reverted to his utterly inflexible, chilly lifestyle when one evening he sees an item in his evening paper. Joyce quotes at length a fictional newspaper report about Mrs Sinico who was knocked over by a train while crossing the line at a station. The train wasn’t going very fast and obliquely from witnesses at the coroner’s enquiry it emerges that in the last few years she had changed character and taken to drink.

The title of the newspaper article is ‘A Painful Case’ which gives the story its title.

Duffy is at first disgusted by the report, dismissive of Mrs Sinico and thinking it weakness that led to her drinking. He is agitated enough to go out for a walk and drops into the local pub for a drink but as he reflects on their time together more, and then leaves the pub to walk into the park up a hill and looking out over Dublin, he slowly, guiltily, starts to think maybe it was his rejection of her which led to her drinking and, ultimately, her death.

He spots young people lying by the wall of the park, no doubt engaged in amorous activities and suddenly realises how lonely he is. ‘He gnawed the rectitude of his life; he felt that he had been outcast from life’s feast’.

Unrelentingly sad aren’t they, these stories.

12. Ivy Day in the Committee Room

Rambling portrait of ten or so Dublin characters involved in a local election campaign.

The stories get steadily longer. This one is a sort of portmanteau piece, introducing us to quite a number of Dublin characters, men involved in the half-hearted politics of a local election, being:

  • Old Jack – the caretaker, ‘an old man’s face, very bony and hairy. The moist blue eyes blinked at the fire and the moist mouth fell open at times, munching once or twice mechanically when it closed’
  • Mr O’Connor – ‘a grey-haired young man, whose face was disfigured by many blotches and pimples’
  • Mr Richard J. Tierney – the Nationalist candidate
  • Mr Hynes – ‘a tall, slender young man with a light brown moustache’
  • Mr Henchy – ‘a bustling little man with a snuffling nose and very cold ears’
  • Father Keon – pops in, in search of someone, then pops lout again
  • Crofton – ‘a very fat man whose blue serge clothes seemed to be in danger of falling from his sloping figure. He had a big face which resembled a young ox’s face in expression, staring blue eyes and a grizzled moustache’
  • Lyons – ‘much younger and frailer, had a thin, clean-shaven face. He wore a very high double collar and a wide-brimmed bowler hat’

One by one they enter like actors onto a set, coming through the door to the outside where it’s a wet cold October day, and into the hall where there’s a fire, stoked by Old Jack the caretaker. For me, the overall impression of the thing is the slack amateurism of all involved but chances are it’s an accurate description of political canvassing in Dublin circa 1908 because, apparently, Joyce’s own father did just such canvassing. The Wikipedia summary is thus:

In a committee room, Matthew O’Connor, a canvasser for Richard Tierney, a candidate in an upcoming municipal election, discusses child-rearing with Old Jack, who tries to keep a fire going. Joe Hynes, another canvasser, arrives and needles O’Connor on whether he’s been paid for his work yet. He proceeds to defend rival candidate Colgan’s working-class background and maintains that Tierney, although a Nationalist, will likely present a welcome address at the upcoming visit of King Edward VII to which, as the spokesman for the working class, he objects. This sparks a debate about whether they, Dubliners, the Irish, should welcome the King or not.

When Hynes points out that it is Ivy Day (October 6), a date appointed to commemorate the Irish Nationalist leader Charles Stewart Parnell, a nostalgic silence fills the room. Another canvasser, John Henchy, enters and criticises Tierney for not having paid him yet. When Hynes leaves, Henchy voices a suspicion that the man is a spy for Colgan.

A priest, Father Keogh, makes a brief appearance, asking after a Mr Fanning and, when told Fanning’s at a certain pub, exits, triggering gossip about the priest, some wondering whether he’s even a priest at all.

A ‘boy’, in fact 16, enters to deliver a crate of stout from the nearby pub, the Black Eagle. He’s asked to pop out and fetch a corkscrew for the bottles, upon his return old Jack opens three of them and, reluctantly, one for the delivery boy, who finishes his off and exits with the corkscrew.

Henchy badmouths another canvasser, Crofton, just before Crofton himself enters with Bantam Lyons. Crofton had worked for the Conservative candidate until the party withdrew and gave their support to Tierney. Henchy offers Crofton and Lyons a drink but they realise they have no corkscrew to open the bottles. So Henchy shows them a trick, he places the bottles on the hob of the fire and, once they’ve warmed up enough, the corks pop out by themselves. This struck me as dangerous – what if the bottles crack before the corks pop out – and disgusting – drinking fire-warmed beer? Yuk.

The talk of politics drifts to Charles Stewart Parnell, who has his defenders and detractors in the room. Hynes returns and is encouraged to read his sentimental poem dedicated to Parnell. The poem is in simple ballad form and criticises those who betrayed Parnell, including the Catholic Church, and places Parnell among the ancient heroes of Ireland. All applaud the performance and seem to forget their differences for the moment.

Commentary

Apart from the air of amateurishness and laziness, the other thing that comes over, and which is odd for a story about canvassing for an election, is the lack of politics. Nobody really discusses political policies except objecting to a possible visit to Dublin by King Edward; some object they shouldn’t truckle to a German king (Edward’s father was the German Prince Albert); others say he’s a good fellow coming on a well-intentioned visit to meet and talk to his subjects, so they shouldn’t reject or heckle him before they’ve even met him, it will only confirm negative English stereotypes of the Irish.

In other words, the only thing close to a policy they discuss is their response to the English monarchy, on which they’re largely split. And the only thing that gives them all a temporary unity is sentimental nostalgia for the disgraced nationalist leader, Charles Stewart Parnell.

But tipsy nostalgia is not a political platform. The lack of debate, the lack of readiness or preparation, the lack of discussion of any policies at all, is interesting background to the confusion and disagreement which afflicted all parties when radical political change was triggered by the Easter Uprising 6 or so years later.

13. A Mother

Pushy mother embarrasses her young singer daughter at a public recital.

The mother in question is Mrs Kearney. With characteristic thoroughness, Joyce gives us her backstory, how she was an educated, romantic, accomplished young lady named Miss Devlin, who intimidated man of her acquaintance and so ended up marrying the solid, reliable , who was very accomplished at a young age but found that the young men of her class were intimidated by her, which prompted her to marry the working class Mr Kearney, who was a bootmaker on Ormond Quay, ‘out of spite’.

So she becomes a mum and raises her girls with his educational and cultural standards. When the Irish Revival comes along in the 1890s she gets her girls educated in Gaelic and folklore. Her daughter Kathleen becomes an accomplished enough pianist to be offered gigs as an accompanist at concerts.

And that’s where the narrative proper commences: A Mr Holohan, assistant secretary of the Eire Abu Society, is organising a series of four concerts and approaches Mrs K to ask if Katherine could be the pianist. Mrs K agrees and sets the price at 8 guineas, and this is the core of the story because the concerts turn out to be very badly planned and publicised. Although Mrs K lends a lot of shrewd help to the creation of the posters, the night of the first concert is very poorly attended.

The second one has a larger audience but Mrs Kearney is bothered by both the behaviour of the audience and the casual attitude of the society’s secretary, Mr. Fitzpatrick, ‘a little man, with a white vacant face. She noticed that he wore his soft brown hat carelessly on the side of his head and that his accent was flat.’

The third concert is cancelled and Mrs Kearney now becomes concerned that her daughter will not be paid the full contracted price but is unable to get a straight answer on the matter from Holohan or Fitzpatrick. She brings her husband to the final concert, anticipating a confrontation.

She respected her husband in the same way as she respected the General Post Office, as something large, secure and fixed…

and confrontation there is. In readiness for this final night, we get a full list of the performers, being:

  • The bass, Mr Duggan, was a slender young man with a scattered black moustache. He was the son of a hall porter in an office in the city and, as a boy, he had sung prolonged bass notes in the resounding hall. From this humble state he had raised himself until he had become a first-rate artiste.
  • Mr Bell, the second tenor, was a fair-haired little man who competed every year for prizes at the Feis Ceoil. On his fourth trial he had been awarded a bronze medal. He was extremely nervous and extremely jealous of other tenors and he covered his nervous jealousy with an ebullient friendliness.
  • Miss Healy, the contralto.
  • Madam Glynn, the soprano, wearing a faded blue dress which was stretched upon a meagre body.

In addition there are some gentlemen from the press:

  • the man from the Freeman – a grey-haired man, with a plausible voice and careful manners. He held an extinguished cigar in his hand and the aroma of cigar smoke floated near him – due to miss the concert in order to attend a lecture by an American priest
  • Mr O’Madden Burke who will write the notice

So you can see that there’s a narrative of sorts, but that arguably the point of the story is the range of characters, the sense of the variety of Dublin society.

Anyway the crisis of the story is that as the theatre fills up and then audience start to get restless, Mrs Kearney absolutely refuses to let her daughter go on until she is paid the contracted 4 guineas. At last, after a lot of feverish whispering and haggling, Haloran manages to return from the mysterious ‘committee’ he’s always talking about, with four pounds (a guinea is a pound and a shilling so he’s four shillings short).

At this point young Kathleen intervenes and insists on going onstage with the performers despite her mother’s wishes, and the first half of the concert is a triumph

The first part closed with a stirring patriotic recitation delivered by a young lady who arranged amateur theatricals. It was deservedly applauded; and, when it was ended, the men went out for the interval, content.

In the climax tempers get out of control and when Holohan tells her the committee will pay the remained the following Tuesday, Mrs Kearney says that’s not good enough and refuses to allow her daughter to go back onstage. At which all the performers, Holohan, Fitzpatrick et al roundly condemn her. Timid Miss Healy agrees to play one or two accompaniments, and when the performers troop back onstage for part two and the first act commences, Mrs Kearney forces her husband and daughter out the side entrance and into a cab in a blazing fury.

14. Grace

Four kind-hearted men try to talk their friend into reforming his alcoholic ways, employing comically ignorant Catholic theology along the way.

The story opens with two men helping to his feet a man who’s passed out drunk in the downstairs toilet of a pub. Carried upstairs, and a policeman called, he’s identified by a pal of his, a Mr Power, who identifies him as Mr Tom Kernan and promises the copper to get him home to his wife, which he does, in a cab. They carry him up to bed then Power is embarrassed before the hapless wife, used to Kernan’s drunkenness and who has nothing to offer him by way of hospitality. As if to make amends for this, Power tells her that he and Kernan’s other buddies will help Kernan turn over a new leaf.

And that’s what they do. Powers organises a plan with two other buddies, M’Coy and Cunningham, to get Kernan along to a Catholic retreat with them. The long central part of the ‘story’ consists of an extended dialogue between these four guys, as the three in on the plan chip in with various suggestions and pledged until Kernan is shamed into agreeing to join them. His wife tries hard to conceal her delight at the prospect of her husband stopping being such a pitiful drunk.

Cut to the third scene, which sees all four chaps in the Jesuit church in Gardiner Street and the arrival of the priest, Father Purdon, in the pulpit to deliver a sermon. Far from the high-falutin’ theology of redemption you might have expected, the priest’s approach is surprisingly mundane and worldly:

He came [Father Purdon said] to speak to businessmen and he would speak to them in a businesslike way. If he might use the metaphor, he said, he was their spiritual accountant; and he wished each and every one of his hearers to open his books, the books of his spiritual life, and see if they tallied accurately with conscience.

Commentary

1. Characters As so often, in one sense the most interesting part of the narrative is the backstory of the central characters. These are stated clearly and bluntly, as in a presentation: I mean they aren’t conveyed with subtle and scattered hints, but all plonked down in one interest bio.

Mr Kernan was a commercial traveller of the old school which believed in the dignity of its calling. He had never been seen in the city without a silk hat of some decency and a pair of gaiters. By grace of these two articles of clothing, he said, a man could always pass muster. He carried on the tradition of his Napoleon, the great Blackwhite, whose memory he evoked at times by legend and mimicry. Modern business methods had spared him only so far as to allow him a little office in Crowe Street on the window blind of which was written the name of his firm with the address—London, E.C. On the mantelpiece of this little office a little leaden battalion of canisters was drawn up and on the table before the window stood four or five china bowls which were usually half full of a black liquid. From these bowls Mr Kernan tasted tea. He took a mouthful, drew it up, saturated his palate with it and then spat it forth into the grate. Then he paused to judge.

Mr Power, a much younger man, was employed in the Royal Irish Constabulary Office in Dublin Castle. The arc of his social rise intersected the arc of his friend’s decline, but Mr Kernan’s decline was mitigated by the fact that certain of those friends who had known him at his highest point of success still esteemed him as a character. Mr Power was one of these friends. His inexplicable debts were a byword in his circle; he was a debonair young man.

Mrs Kernan… was an active, practical woman of middle age. Not long before she had celebrated her silver wedding and renewed her intimacy with her husband by waltzing with him to Mr Power’s accompaniment. In her days of courtship Mr Kernan had seemed to her a not ungallant figure: and she still hurried to the chapel door whenever a wedding was reported and, seeing the bridal pair, recalled with vivid pleasure how she had passed out of the Star of the Sea Church in Sandymount, leaning on the arm of a jovial well-fed man, who was dressed smartly in a frock-coat and lavender trousers and carried a silk hat gracefully balanced upon his other arm. After three weeks she had found a wife’s life irksome and, later on, when she was beginning to find it unbearable, she had become a mother. The part of mother presented to her no insuperable difficulties and for twenty-five years she had kept house shrewdly for her husband. Her two eldest sons were launched. One was in a draper’s shop in Glasgow and the other was clerk to a tea-merchant in Belfast. They were good sons, wrote regularly and sometimes sent home money. The other children were still at school.

See how much time and detail, precision and effect, Joyce spends on each character. They are highly defined and positioned. As many people have pointed out, in ‘Dubliners’ Joyce feels like he’s taken nineteenth century naturalism as far as it can go. Nobody could write more careful detailed descriptions of his characters. Which is why, having reached the end of the line, he burst through the boundaries of the genre into something post-naturalist, experimenting with free indirect speech in ‘A Portrait of the Artist as a Young Man’, and then bursting the bounds of what a novel even is, in ‘Ulysses’.

2. Catholic dogma A good deal of the long central section consists of the three would-be conspirators struggling with various aspects of the Catholic faith, from the mottos of various popes to the role of the Jesuits, the difference between Catholics and Protestants, and so on.

Why is it called ‘Grace’? Is it a sympathetic view that the grace of spiritual rebirth stems from pretty much as low as one could go, a man falling down dead drunk in an underground toilet? Or is Joyce mocking religion, suggesting that there is no grace, here or anywhere? That fits the spirit of irony and satire which informs the entire collection.

15. The Dead

Beautiful extended description of a traditional Christmas party which ends with a sensitive husband suddenly made aware of the tragic death of his beautiful wife’s first love.

The Dead is routinely described as one of the greatest short stories in the English language. It is noted for its tenderness, and lyrical acceptance of lost love, death and bereavement. The main character is Gabriel Conroy who takes his beautiful wife Gretta to the annual Christmas party thrown by his lovely aunts, Miss Kate and Miss Julia Morkan, ‘in the dark gaunt house on Usher’s Island’. The narrative describes the preparations, the arrival of the guests, numerous conversations, dancing and singing, the big Christmas dinner at which Gabriel carves the roast goose, and then makes a movingly gracious speech of thanks to the old aunts, and then the slow winding down towards thank yous and farewells.

Cast

As usual, Joyce pays scrupulous attention to each of his characters’ backstories and appearance.

  • Gabriel Conroy – ‘plump’, ‘a stout tallish young man. The high colour of his cheeks pushed upwards even to his forehead where it scattered itself in a few formless patches of pale red; and on his hairless face there scintillated restlessly the polished lenses and the bright gilt rims of the glasses which screened his delicate and restless eyes. His glossy black hair was parted in the middle and brushed in a long curve behind his ears where it curled slightly beneath the groove left by his hat’ — Gabriel is ‘son of their dead elder sister, Ellen, who had married T. J. Conroy of the Port and Docks’ — he is a college teacher and book reviewer
  • Gretta Conroy – Gabriel’s wife
  • Kate Morkan and Julia Morkan – Gabriel and Mary Jane’s aunts – ‘two small plainly dressed old women. Aunt Julia was an inch or so the taller. Her hair, drawn low over the tops of her ears, was grey; and grey also, with darker shadows, was her large flaccid face. Though she was stout in build and stood erect her slow eyes and parted lips gave her the appearance of a woman who did not know where she was or where she was going. Aunt Kate was more vivacious. Her face, healthier than her sister’s, was all puckers and creases, like a shrivelled red apple, and her hair, braided in the same old-fashioned way, had not lost its ripe nut colour.’
  • Mary Jane Morkan – niece of Kate and Julia, teaches music, ‘Many of her pupils belonged to the better-class families on the Kingstown and Dalkey line’
  • Lily – the caretaker’s daughter, ‘a slim, growing girl, pale in complexion and with hay-coloured hair’
  • Freddy Malins – an alcoholic and friend of the family – ‘a young man of about forty, was of Gabriel’s size and build, with very round shoulders. His face was fleshy and pallid, touched with colour only at the thick hanging lobes of his ears and at the wide wings of his nose. He had coarse features, a blunt nose, a convex and receding brow, tumid and protruded lips. His heavy-lidded eyes and the disorder of his scanty hair made him look sleepy’
  • Mrs Malins – Freddy Malins’ mother, ‘a stout feeble old woman with white hair. Her voice had a catch in it like her son’s and she stuttered slightly’, lives with her married daughter in Glasgow and comes to Dublin on a visit once a year
  • Molly Ivors – a long-time acquaintance of the family – ‘a frank-mannered talkative young lady, with a freckled face and prominent brown eyes. She did not wear a low-cut bodice and the large brooch which was fixed in the front of her collar bore on it an Irish device and motto’
  • Mr Browne – only Protestant guest at the party, ‘A tall wizen-faced man, with a stiff grizzled moustache and swarthy skin’
  • Bartell D’Arcy – a tenor, ‘a dark-complexioned young man with a smart moustache’
  • Other guests: Miss Furlong, Miss Daly and Miss Power, Mr Bergin and Mr Kerrigan

Incidents include:

– Upon arrival Gabriel tries to joke with his aunts’ maid, Lily, which doesn’t work out.

– He goes upstairs to join the rest of the guests, where he worries about the speech he has to give, worrying about too highfalutin’ reference to the poetry of Robert Browning, still, in the 1890s, considered difficult.

– When Freddy Malins arrives drunk, as the aunts had feared, Aunt Kate asks Gabriel to make sure he doesn’t cause trouble.

– As the party gathers pace, Gabriel is twitted by Miss Ivors, an Irish nationalist, because she has figured out that he is the GC who writes book reviews in the Unionist newspaper The Daily Express. She teases him by calling him a ‘West Briton’, repeatedly. Gabriel tries to reply but can’t come up with a convincing argument.

– Miss Ivor tells Gabriel she and some friends are organising a reading week in the West of Ireland. He says he can’t go but when he then tells his wife, she is excited at the thought of revisiting her childhood home of Galway.

– Dinner begins, with Gabriel seated at the head of the table. He boisterously carves and hands round the plates while the guests discuss music and theology. Once the eating is over, Gabriel rises to his feet again and makes his speech, courteously referring to Aunt Kate, Aunt Julia and Mary Jane as the Three Graces. The speech ends with a toast and the guests sing ‘For they are jolly gay fellows’.

– The party winds down and the guests leave one by one. Having got his coat Gabriel goes to the foot of the stairs and from the dark well looks up to see his wife lost in thought at the top of the stairs, listening to a song coming from the living room. She is listening to the famous tenor Bartell D’Arcy singing ‘The Lass of Aughrim’.

– They walk part of the way back to their hotel, then get a cab. Gabriel has rarely seen his wife looking so beautiful and suddenly he is overcome with lust. He can’t wait till they are back in the hotel room alone together. There is what I suppose for the time was fairly graphic description of his desire, specifically the fact that he needs her to want it too:

If she would only turn to him or come to him of her own accord! To take her as she was would be brutal. No, he must see some ardour in her eyes first.

– BUT once they are alone in their hotel room, Gabriel’s lust reaches a peak and then is utterly dashed. Gretta sits on their bed but not in the heat of desire at all; instead she is crying. She tearfully admits that the song she was listening to reminded her of her first true love, reminds her of a young boy, just 17, named Michael Furey who had courted her in her youth in Galway. He, too, used to sing ‘The Lass of Aughrim’ for her.

– The boy fell ill as she was leaving for the big city, but insisted on getting out of his sick bed to come to her house and stand under her window in the winter rain just to see her. He returned to bed even sicker and died soon after.

– Gretta is overcome with grief and cries herself to exhaustion and then to sleep leaving Gabriel dismayed that there was something of such importance in his wife’s life that he never knew about. Now alone in the bedroom he reflects that we will all die, Aunt Julia, Aunt Kate, all of them – and finds this strangely comforting. He can almost feel the presence of the dead:

His soul had approached that region where dwell the vast hosts of the dead. He was conscious of, but could not apprehend, their wayward and flickering existence. His own identity was fading out into a grey impalpable world: the solid world itself which these dead had one time reared and lived in was dissolving and dwindling.

And in the story’s famous last lines the narrative picks up on him looking out the window at the snow falling, to describe how it is falling all across Ireland.

A few light taps upon the pane made him turn to the window. It had begun to snow again. He watched sleepily the flakes, silver and dark, falling obliquely against the lamplight. The time had come for him to set out on his journey westward. Yes, the newspapers were right: snow was general all over Ireland. It was falling on every part of the dark central plain, on the treeless hills, falling softly upon the Bog of Allen and, farther westward, softly falling into the dark mutinous Shannon waves. It was falling, too, upon every part of the lonely churchyard on the hill where Michael Furey lay buried. It lay thickly drifted on the crooked crosses and headstones, on the spears of the little gate, on the barren thorns. His soul swooned slowly as he heard the snow falling faintly through the universe and faintly falling, like the descent of their last end, upon all the living and the dead.

There should not, by these closing lines, be a dry eye in the house.

When I first read this as a boy, I wished my Christmases were like this, festive and convivial with lots of singing, and I wished I would grow up as soulful and sensitive as Gabriel…

Swayed by their beauty, for years I remembered the story for the haunting beauty of its closing lines. I had completely forgotten that the key passages beforehand give a surprisingly frank expression of Gabriel’s desire, nay lust. He becomes really inflamed with lust and desperately wants to ‘take’ his wife as soon as they get back to the hotel. Everyone remembers the poetic ending. Not so many people comments on the way it is also a story about the inappropriateness of male desire; a description of how male desire flares up but then is crushed, mortified and embarrassed by superior female sensitivity.

Commentary

Human life

The stories offer a loosely chronological overview of the different stages of human life, starting with:

  • boyhood (in The Sisters, An Encounter, Araby)
  • young adulthood (After the Race, Two Gallants, The Boarding House)
  • maturity (Counterparts, Clay, A Painful Case, A Mother)
  • old age and mortality (The Dead)
  • with slyly comic digressions into contemporary politics (Ivy Day in the Committee Room) and the arts (A Mother)
  • before the grand meditation on mortality (The Dead)

Sociology

The light music of whisky falling into glasses made an agreeable interlude.

Fiction doesn’t have to be sociological i.e. comment on the social issues of its time (see Kafka or Borges) but realist fiction tends to do so because a realistic depiction tends to take time to fill in details of character or aspects of events, which themselves tend to reflect contemporary practice. The three themes which stick out for me are drunkenness, Irish nationalism and the broader one of paralysis and trapment.

1. Drunkenness is shown in numerous aspects:

  • the youthful exuberant party drunkenness of young Jimmy Doyle who gambles away his inheritance
  • the hardened middle-aged drunkenness of the angry failure Farrington, who takes out an evening of humiliations by beating his poor son
  • the pathetic fall-down-drunk inebriation of Tom Kernan
  • the sad, pitiful drunkenness of Mrs Sinico after Mr Duffy dumps her

In a number of other stories, nobody gets drunk but drink plays a role. Thus:

  • it’s notable how the bottles of beer are a necessary emollient which take the edge off the political frictions in ‘Ivy Day in the Committee Room’
  • Joe’s occasional drunkenness is a threat lurking at the edge of ‘Clay’
  • the scenes in which Little Chandler is compared with big brassy Ignatius Gallaher are set in a noisy bar where Gallaher not only knows his drinks but gets the bartender’s attention in a second whereas Chandler struggles to be seen etc

2. Paralysis Not much need be said because I’ve pointed out in individual stories where their guiding theme or mood is one of entrapment and paralysis. Almost all the characters are trapped in their behaviour patterns; when offered escape like Evelyn, they are too scared to take it. And entrapment becomes a way of life, for timid characters like Little Chandler or Maria; or underpins the alcoholic rage of a bully like Farrington.

Irish nationalism is well represented in the tales, notably in the character of Miss Ivors in ‘The Dead’ but the issues surrounding nationalism are most fully dramatised in ‘Ivy Day in the Committee Room’ – but in neither does the debate or argument get much beyond abuse – there doesn’t appear to be any plan or policy for how independence would be achieved, what steps are required, for example lobbying the Liberal government which was in power for most of the Edwardian period, and lobbying them for what, precisely?

In this way, the presentation of Irish nationalism – no doubt a massive issue in Joyce’s day and which flavours and sometimes becomes a dominant issue in all his writings – feels, ultimately, like a sub-set of the paralysis and stagnation which is the book’s central theme.

Lyricism

The volume concludes with the tremendous lyric vision at the end of ‘The Dead’ but this lyrical eloquence appears at key moments throughout all the stories. It is often very beautiful writing, worth savouring in its own right. It’s a large question for debate whether this lyricism can be said to underpin Joyce’s entire worldview, and how it is contained or subsumed in the more complex styles of his later works.


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The Book of Universes by John D. Barrow (2011)

This book is twice as long and half as good as Barrow’s earlier primer, The Origin of the Universe.

In that short book Barrow focused on the key ideas of modern cosmology – introducing them to us in ascending order of complexity, and as simply as possible. He managed to make mind-boggling ideas and demanding physics very accessible.

This book – although it presumably has the merit of being more up to date (published in 2011 as against 1994) – is an expansion of the earlier one, an attempt to be much more comprehensive, but which, in the process, tends to make the whole subject more confusing.

The basic premise of both books is that, since Einstein’s theory of relativity was developed in the 1910s, cosmologists and astronomers and astrophysicists have:

  1. shown that the mathematical formulae in which Einstein’s theories are described need not be restricted to the universe as it has traditionally been conceived; in fact they can apply just as effectively to a wide variety of theoretical universes – and the professionals have, for the past hundred years, developed a bewildering array of possible universes to test Einstein’s insights to the limit
  2. made a series of discoveries about our actual universe, the most important of which is that a) it is expanding b) it probably originated in a big bang about 14 billion years ago, and c) in the first few milliseconds after the bang it probably underwent a period of super-accelerated expansion known as the ‘inflation’ which may, or may not, have introduced all kinds of irregularities into ‘our’ universe, and may even have created a multitude of other universes, of which ours is just one

If you combine a hundred years of theorising with a hundred years of observations, you come up with thousands of theories and models.

In The Origin of the Universe Barrow stuck to the core story, explaining just as much of each theory as is necessary to help the reader – if not understand – then at least grasp their significance. I can write the paragraphs above because of the clarity with which The Origin of the Universe explained it.

In The Book of Universes, on the other hand, Barrow’s aim is much more comprehensive and digressive. He is setting out to list and describe every single model and theory of the universe which has been created in the past century.

He introduces the description of each model with a thumbnail sketch of its inventor. This ought to help, but it doesn’t because the inventors generally turn out to be polymaths who also made major contributions to all kinds of other areas of science. Being told a list of Paul Dirac’s other major contributions to 20th century science is not a good way for preparing your mind to then try and understand his one intervention on universe-modelling (which turned, in any case, out to be impractical and lead nowhere).

Another drawback of the ‘comprehensive’ approach is that a lot of these models have been rejected or barely saw the light of day before being disproved or – more complicatedly – were initially disproved but contained aspects or insights which turned out to be useful forty years later, and were subsequently recycled into revised models. It gets a bit challenging to try and hold all this in your mind.

In The Origin of the Universe Barrow sticks to what you could call the canonical line of models, each of which represented the central line of speculation, even if some ended up being disproved (like Hoyle and Gold and Bondi’s model of the steady state universe). Given that all of this material is pretty mind-bending, and some of it can only be described in advanced mathematical formulae, less is definitely more. I found The Book of Universes simply had too many universes, explained too quickly, and lost amid a lot of biographical bumpf summarising people’s careers or who knew who or contributed to who’s theory. Too much information.

One last drawback of the comprehensive approach is that quite important points – which are given space to breathe and sink in in The Origin of the Universe are lost in the flood of facts in The Book of Universes.

I’m particularly thinking of Einstein’s notion of the cosmological constant which was not strictly necessary to his formulations of relativity, but which Einstein invented and put into them solely in order to counteract the force of gravity and ensure his equations reflected the commonly held view that the universe was in a permanent steady state.

This was a mistake and Einstein is often quoted as admitting it was the biggest mistake of his career. In 1965 scientists discovered the cosmic background radiation which proved that the universe began in an inconceivably intense explosion, that the universe was therefore expanding and that the explosive, outward-propelling force of this bang was enough to counteract the contracting force of the gravity of all the matter in the universe without any need for a hypothetical cosmological constant.

I understand this (if I do) because in The Origin of the Universe it is given prominence and carefully explained. By contrast, in The Book of Universes it was almost lost in the flood of information and it was only because I’d read the earlier book that I grasped its importance.

The Book of Universes

Barrow gives a brisk recap of cosmology from the Sumerians and Egyptians, through the ancient Greeks’ establishment of the system named after Ptolemy in which the earth is the centre of the solar system, on through the revisions of Copernicus and Galileo which placed the sun firmly at the centre of the solar system, on to the three laws of Isaac Newton which showed how the forces which govern the solar system (and more distant bodies) operate.

There is then a passage on the models of the universe generated by the growing understanding of heat and energy acquired by Victorian physicists, which led to one of the most powerful models of the universe, the ‘heat death’ model popularised by Lord Kelvin in the 1850s, in which, in the far future, the universe evolves to a state of complete homegeneity, where no region is hotter than any other and therefore there is no thermodynamic activity, no life, just a low buzzing noise everywhere.

But this is all happens in the first 50 pages and is just preliminary throat-clearing before Barrow gets to the weird and wonderful worlds envisioned by modern cosmology i.e. from Einstein onwards.

In some of these models the universe expands indefinitely, in others it will reach a peak expansion before contracting back towards a Big Crunch. Some models envision a static universe, in others it rotates like a top, while other models are totally chaotic without any rules or order.

Some universes are smooth and regular, others characterised by clumps and lumps. Some are shaken by cosmic tides, some oscillate. Some allow time travel into the past, while others threaten to allow an infinite number of things to happen in a finite period. Some end with another big bang, some don’t end at all. And in only a few of them do the conditions arise for intelligent life to evolve.

The Book of Universes then goes on, in 12 chapters, to discuss – by my count – getting on for a hundred types or models of hypothetical universes, as conceived and worked out by mathematicians, physicists, astrophysicists and cosmologists from Einstein’s time right up to the date of publication, 2011.

A list of names

Barrow namechecks and briefly explains the models of the universe developed by the following (I am undertaking this exercise partly to remind myself of everyone mentioned, partly to indicate to you the overwhelming number of names and ideas the reader is bombarded with):

  • Aristotle
  • Ptolemy
  • Copernicus
  • Giovanni Riccioli
  • Tycho Brahe
  • Isaac Newton
  • Thomas Wright (1771-86)
  • Immanuel Kant (1724-1804)
  • Pierre Laplace (1749-1827) devised what became the standard Victorian model of the universe
  • Alfred Russel Wallace (1823-1913) discussed the physical conditions of a universe necessary for life to evolve in it
  • Lord Kelvin (1824-1907) material falls into the central region of the universe and coalesce with other stars to maintain power output over immense periods
  • Rudolf Clausius (1822-88) coined the word ‘entropy’ in 1865 to describe the inevitable progress from ordered to disordered states
  • William Jevons (1835-82) believed the second law of thermodynamics implies that universe must have had a beginning
  • Pierre Duhem (1961-1916) Catholic physicist accepted the notion of entropy but denied that it implied the universe ever had a beginning
  • Samuel Tolver Preson (1844-1917) English engineer and physicist, suggested the universe is so vast that different ‘patches’ might experience different rates of entropy
  • Ludwig Boltzmann and Ernst Zermelo suggested the universe is infinite and is already in a state of thermal equilibrium, but just with random fluctuations away from uniformity, and our galaxy is one of those fluctuations
  • Albert Einstein (1879-1955) his discoveries were based on insights, not maths: thus he saw the problem with Newtonian physics is that it privileges an objective outside observer of all the events in the universe; one of Einstein’s insights was to abolish the idea of a privileged point of view and emphasise that everyone is involved in the universe’s dynamic interactions; thus gravity does not pass through a clear, fixed thing called space; gravity bends space.

The American physicist John Wheeler once encapsulated Einstein’s theory in two sentences:

Matter tells space how to curve. Space tells matter how to move. (quoted on page 52)

  • Marcel Grossmann provided the mathematical underpinning for Einstein’s insights
  • Willem de Sitter (1872-1934) inventor of, among other things, the de Sitter effect which represents the effect of the curvature of spacetime, as predicted by general relativity, on a vector carried along with an orbiting body – de Sitter’s universe gets bigger and bigger for ever but never had a zero point; but then de Sitter’s model contains no matter
  • Vesto Slipher (1875-1969) astronomer who discovered the red shifting of distant galaxies in 1912, the first ever empirical evidence for the expansion of the galaxy
  • Alexander Friedmann (1888-1925) Russian mathematician who produced purely mathematical solutions to Einstein’s equation, devising models where the universe started out of nothing and expanded a) fast enough to escape the gravity exerted by its own contents and so will expand forever or b) will eventually succumb to the gravity of its own contents, stop expanding and contract back towards a big crunch. He also speculated that this process (expansion and contraction) could happen an infinite number of times, creating a cyclic series of bangs, expansions and contractions, then another bang etc
A graphic of the oscillating or cyclic universe (from Discovery magazine)

A graphic of the oscillating or cyclic universe (from Discovery magazine)

  • Arthur Eddington (1882-1944) most distinguished astrophysicist of the 1920s
  • George Lemaître (1894-1966) first to combine an expanding universe interpretation of Einstein’s equations with the latest data about redshifting, and show that the universe of Einstein’s equations would be very sensitive to small changes – his model is close to Eddington’s so that it is often called the Eddington-Lemaître universe: it is expanding, curved and finite but doesn’t have a beginning
  • Edwin Hubble (1889-1953) provided solid evidence of the redshifting (moving away) of distant galaxies, a main plank in the whole theory of a big bang, inventor of Hubble’s Law:
    • Objects observed in deep space – extragalactic space, 10 megaparsecs (Mpc) or more – are found to have a redshift, interpreted as a relative velocity away from Earth
    • This Doppler shift-measured velocity of various galaxies receding from the Earth is approximately proportional to their distance from the Earth for galaxies up to a few hundred megaparsecs away
  • Richard Tolman (1881-1948) took Friedmann’s idea of an oscillating universe and showed that the increased entropy of each universe would accumulate, meaning that each successive ‘bounce’ would get bigger; he also investigated what ‘lumpy’ universes would look like where matter is not evenly spaced but clumped: some parts of the universe might reach a maximum and start contracting while others wouldn’t; some parts might have had a big bang origin, others might not have
  • Arthur Milne (1896-1950) showed that the tension between the outward exploding force posited by Einstein’s cosmological constant and the gravitational contraction could actually be described using just Newtonian mathematics: ‘Milne’s universe is the simplest possible universe with the assumption that the universe s uniform in space and isotropic’, a ‘rational’ and consistent geometry of space – Milne labelled the assumption of Einsteinian physics that the universe is the same in all places the Cosmological Principle
  • Edmund Fournier d’Albe (1868-1933) posited that the universe has a hierarchical structure from atoms to the solar system and beyond
  • Carl Charlier (1862-1934) introduced a mathematical description of a never-ending hierarchy of clusters
  • Karl Schwarzschild (1873-1916) suggested  that the geometry of the universe is not flat as Euclid had taught, but might be curved as in the non-Euclidean geometries developed by mathematicians Riemann, Gauss, Bolyai and Lobachevski in the early 19th century
  • Franz Selety (1893-1933) devised a model for an infinitely large hierarchical universe which contained an infinite mass of clustered stars filling the whole of space, yet with a zero average density and no special centre
  • Edward Kasner (1878-1955) a mathematician interested solely in finding mathematical solutions to Einstein’s equations, Kasner came up with a new idea, that the universe might expand at different rates in different directions, in some parts it might shrink, changing shape to look like a vast pancake
  • Paul Dirac (1902-84) developed a Large Number Hypothesis that the really large numbers which are taken as constants in Einstein’s and other astrophysics equations are linked at a deep undiscovered level, among other things abandoning the idea that gravity is a constant: soon disproved
  • Pascual Jordan (1902-80) suggested a slight variation of Einstein’s theory which accounted for a varying constant of gravitation as through it were a new source of energy and gravitation
  • Robert Dicke (1916-97) developed an alternative theory of gravitation
  • Nathan Rosen (1909-995) young assistant to Einstein in America with whom he authored a paper in 1936 describing a universe which expands but has the symmetry of a cylinder, a theory which predicted the universe would be washed over by gravitational waves
  • Ernst Straus (1922-83) another young assistant to Einstein with whom he developed a new model, an expanding universe like those of Friedman and Lemaître but which had spherical holes removed like the bubbles in an Aero, each hole with a mass at its centre equal to the matter which had been excavated to create the hole
  • Eugene Lifschitz (1915-85) in 1946 showed that very small differences in the uniformity of matter in the early universe would tend to increase, an explanation of how the clumpy universe we live in evolved from an almost but not quite uniform distribution of matter – as we have come to understand that something like this did happen, Lifshitz’s calculations have come to be seen as a landmark
  • Kurt Gödel (1906-1978) posited a rotating universe which didn’t expand and, in theory, permitted time travel!
  • Hermann Bondi, Thomas Gold and Fred Hoyle collaborated on the steady state theory of a universe which is growing but remains essentially the same, fed by the creation of new matter out of nothing
  • George Gamow (1904-68)
  • Ralph Alpher and Robert Herman in 1948 showed that the ratio of the matter density of the universe to the cube of the temperature of any heat radiation present from its hot beginning is constant if the expansion is uniform and isotropic – they calculated the current radiation temperature should be 5 degrees Kelvin – ‘one of the most momentous predictions ever made in science’
  • Abraham Taub (1911-99) made a study of all the universes that are the same everywhere in space but can expand at different rates in different directions
  • Charles Misner (b.1932) suggested ‘chaotic cosmology’ i.e. that no matter how chaotic the starting conditions, Einstein’s equations prove that any universe will inevitably become homogenous and isotropic – disproved by the smoothness of the background radiation. Misner then suggested the Mixmaster universe, the  most complicated interpretation of the Einstein equations in which the universe expands at different rates in different directions and the gravitational waves generated by one direction interferes with all the others, with infinite complexity
  • Hannes Alfvén devised a matter-antimatter cosmology
  • Alan Guth (b.1947) in 1981 proposed a theory of ‘inflation’, that milliseconds after the big bang the universe underwent a swift process of hyper-expansion: inflation answers at a stroke a number of technical problems prompted by conventional big bang theory; but had the unforeseen implication that, though our region is smooth, parts of the universe beyond our light horizon might have grown from other areas of inflated singularity and have completely different qualities
  • Andrei Linde (b.1948) extrapolated that the inflationary regions might create sub-regions in  which further inflation might take place, so that a potentially infinite series of new universes spawn new universes in an ‘endlessly bifurcating multiverse’. We happen to be living in one of these bubbles which has lasted long enough for the heavy elements and therefore life to develop; who knows what’s happening in the other bubbles?
  • Ted Harrison (1919-2007) British cosmologist speculated that super-intelligent life forms might be able to develop and control baby universe, guiding the process of inflation so as to promote the constants require for just the right speed of growth to allow stars, planets and life forms to evolve. Maybe they’ve done it already. Maybe we are the result of their experiments.
  • Nick Bostrom (b.1973) Swedish philosopher: if universes can be created and developed like this then they will proliferate until the odds are that we are living in a ‘created’ universe and, maybe, are ourselves simulations in a kind of multiverse computer simulation

Although the arrival of Einstein and his theory of relativity marks a decisive break with the tradition of Newtonian physics, and comes at page 47 of this 300-page book, it seemed to me the really decisive break comes on page 198 with the publication Alan Guth’s theory of inflation.

Up till the Guth breakthrough, astrophysicists and astronomers appear to have focused their energy on the universe we inhabit. There were theoretical digressions into fantasies about other worlds and alternative universes but they appear to have been personal foibles and everyone agreed they were diversions from the main story.

Inflation

However, the idea of inflation, while it solved half a dozen problems caused by the idea of a big bang, seems to have spawned a literally fantastic series of theories and speculations.

Throughout the twentieth century, cosmologists grew used to studying the different types of universe that emerged from Einstein’s equations, but they expected that some special principle, or starting state, would pick out one that best described the actual universe. Now, unexpectedly, we find that there might be room for many, perhaps all, of these possible universes somewhere in the multiverse. (p.254)

This is a really massive shift and it is marked by a shift in the tone and approach of Barrow’s book. Up till this point it had jogged along at a brisk rate namechecking a steady stream of mathematicians, physicists and explaining how their successive models of the universe followed on from or varied from each other.

Now this procedure comes to a grinding halt while Barrow enters a realm of speculation. He discusses the notion that the universe we live in might be a fake, evolved from a long sequence of fakes, created and moulded by super-intelligences for their own purposes.

Each of us might be mannequins acting out experiments, observed by these super-intelligences. In which case what value would human life have? What would be the definition of free will?

Maybe the discrepancies we observe in some of the laws of the universe have been planted there as clues by higher intelligences? Or maybe, over vast periods of time, and countless iterations of new universes, the laws they first created for this universe where living intelligences could evolve have slipped, revealing the fact that the whole thing is a facade.

These super-intelligences would, of course, have computers and technology far in advance of ours etc. I felt like I had wandered into a prose version of The Matrix and, indeed, Barrow apologises for straying into areas normally associated with science fiction (p.241).

Imagine living in a universe where nothing is original. Everything is a fake. No ideas are ever new. There is no novelty, no originality. Nothing is ever done for the first time and nothing will ever be done for the last time… (p.244)

And so on. During this 15-page-long fantasy the handy sequence of physicists comes to an end as he introduces us to contemporary philosophers and ethicists who are paid to think about the problem of being a simulated being inside a simulated reality.

Take Robin Hanson (b.1959), a research associate at the Future of Humanity Institute of Oxford University who, apparently, advises us all that we ought to behave so as to prolong our existence in the simulation or, hopefully, ensure we get recreated in future iterations of the simulation.

Are these people mad? I felt like I’d been transported into an episode of The Outer Limits or was back with my schoolfriend Paul, lying in a summer field getting stoned and wondering whether dandelions were a form of alien life that were just biding their time till they could take over the world. Why not, man?

I suppose Barrow has to include this material, and explain the nature of the anthropic principle (p.250), and go on to a digression about the search for extra-terrestrial life (p.248), and discuss the ‘replication paradox’ (in an infinite universe there will be infinite copies of you and me in which we perform an infinite number of variations on our lives: what would happen if you came face to face with one of your ‘copies?? p.246) – because these are, in their way, theories – if very fantastical theories – about the nature of the universe and he his stated aim is to be completely comprehensive.

The anthropic principle

Observations of the universe must be compatible with the conscious and intelligent life that observes it. The universe is the way it is, because it has to be the way it is in order for life forms like us to evolve enough to understand it.

Still, it was a relief when he returned from vague and diffuse philosophical speculation to the more solid territory of specific physical theories for the last forty or so pages of the book. But it was very noticeable that, as he came up to date, the theories were less and less attached to individuals: modern research is carried out by large groups. And he increasingly is describing the swirl of ideas in which cosmologists work, which often don’t have or need specific names attached. And this change is denoted, in the texture of the prose, by an increase in the passive voice, the voice in which science papers are written: ‘it was observed that…’, ‘it was expected that…’, and so on.

  • Edward Tryon (b.1940) American particle physicist speculated that the entire universe might be a virtual fluctuation from the quantum vacuum, governed by the Heisenberg Uncertainty Principle that limits our simultaneous knowledge of the position and momentum, or the time of occurrence and energy, of anything in Nature.
  • George Ellis (b.1939) created a catalogue of ‘topologies’ or shapes which the universe might have
  • Dmitri Sokolov and Victor Shvartsman in 1974 worked out what the practical results would be for astronomers if we lived in a strange shaped universe, for example a vast doughnut shape
  • Yakob Zeldovich and Andrei Starobinsky in 1984 further explored the likelihood of various types of ‘wraparound’ universes, predicting the fluctuations in the cosmic background radiation which might confirm such a shape
  • 1967 the Wheeler-De Witt equation – a first attempt to combine Einstein’s equations of general relativity with the Schrödinger equation that describes how the quantum wave function changes with space and time
  • the ‘no boundary’ proposal – in 1982 Stephen Hawking and James Hartle used ‘an elegant formulation of quantum  mechanics introduced by Richard Feynman to calculate the probability that the universe would be found to be in a particular state. What is interesting is that in this theory time is not important; time is a quality that emerges only when the universe is big enough for quantum effects to become negligible; the universe doesn’t technically have a beginning because the nearer you approach to it, time disappears, becoming part of four-dimensional space. This ‘no boundary’ state is the centrepiece of Hawking’s bestselling book A Brief History of Time (1988). According to Barrow, the Hartle-Hawking model was eventually shown to lead to a universe that was infinitely large and empty i.e. not our one.
The Hartle-Hawking no boundary Hartle and Hawking No-Boundary Proposal

The Hartle-Hawking No-Boundary Proposal

  • In 1986 Barrow proposed a universe with a past but no beginning because all the paths through time and space would be very large closed loops
  • In 1997 Richard Gott and Li-Xin Li took the eternal inflationary universe postulated above and speculated that some of the branches loop back on themselves, giving birth to themselves
The self-creating universe of J.Richard Gott III and Li-Xin Li

The self-creating universe of J.Richard Gott III and Li-Xin Li

  • In 2001 Justin Khoury, Burt Ovrut, Paul Steinhardt and Neil Turok proposed a variation of the cyclic universe which incorporated strong theory and they called the ‘ekpyrotic’ universe, epkyrotic denoting the fiery flame into which each universe plunges only to be born again in a big bang. The new idea they introduced is that two three-dimensional universes may approach each other by moving through the additional dimensions posited by strong theory. When they collide they set off another big bang. These 3-D universes are called ‘braneworlds’, short for membrane, because they will be very thin
  • If a universe existing in a ‘bubble’ in another dimension ‘close’ to ours had ever impacted on our universe, some calculations indicate it would leave marks in the cosmic background radiation, a stripey effect.
  • In 1998 Andy Albrecht, João Maguijo and Barrow explored what might have happened if the speed of light, the most famous of cosmological constants, had in fact decreased in the first few milliseconds after the bang? There is now an entire suite of theories known as ‘Varying Speed of Light’ cosmologies.
  • Modern ‘String Theory’ only functions if it assumes quite a few more dimensions than the three we are used to. In fact some string theories require there to be more than one dimension of time. If there are really ten or 11 dimensions then, possibly, the ‘constants’ all physicists have taken for granted are only partial aspects of constants which exist in higher dimensions. Possibly, they might change, effectively undermining all of physics.
  • The Lambda-CDM model is a cosmological model in which the universe contains three major components: 1. a cosmological constant denoted by Lambda (Greek Λ) and associated with dark energy; 2. the postulated cold dark matter (abbreviated CDM); 3. ordinary matter. It is frequently referred to as the standard model of Big Bang cosmology because it is the simplest model that provides a reasonably good account of the following properties of the cosmos:
    • the existence and structure of the cosmic microwave background
    • the large-scale structure in the distribution of galaxies
    • the abundances of hydrogen (including deuterium), helium, and lithium
    • the accelerating expansion of the universe observed in the light from distant galaxies and supernovae

He ends with a summary of our existing knowledge, and indicates the deep puzzles which remain, not least the true nature of the ‘dark matter’ which is required to make sense of the expanding universe model. And he ends the whole book with a pithy soundbite. Speaking about the ongoing acceptance of models which posit a ‘multiverse’, in which all manner of other universes may be in existence, but beyond the horizon of where can see, he says:

Copernicus taught us that our planet was not at the centre of the universe. Now we may have to accept that even our universe is not at the centre of the Universe.


Reviews of other science books

Chemistry

Cosmology

The environment

Genetics and life

Human evolution

Maths

Particle physics

Psychology

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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