Culture
Could Monkeys Really Type All of Shakespeare?
Science doesn’t usually tolerate frivolity, but the infinite monkey theorem enjoys an exception. The question it poses is thoroughly outlandish: Could an infinite number of monkeys, each given an infinite amount of time to peck away at a typewriter (stocked with an infinite supply of paper, presumably) eventually produce, by pure chance, the complete works of William Shakespeare?
The problem was first described in a 1913 paper by the French mathematician Émile Borel, a pioneer of probability theory. As modernity opened new scientific fronts, approaches to the theorem also evolved. Today, the problem pulls in computer science and astrophysics, among other disciplines.
In 1979, The New York Times reported on a Yale professor who, using a computer program to try to prove this “venerable hypothesis,” managed to produce “startlingly intelligible, if not quite Shakespearean” strings of text. In 2003, British scientists put a computer into a monkey cage at the Paignton Zoo. The outcome was “five pages of text, primarily filled with the letter S,” according to news reports. In 2011, Jesse Anderson, an American programmer, ran a computer simulation with much better results, albeit under conditions that — like the Yale professor’s — mitigated chance.
A new paper by Stephen Woodcock, a mathematician at the University of Technology Sydney, suggests that those efforts may have been for naught: It concludes that there is simply not enough time until the universe expires for a defined number of hypothetical primates to produce a faithful reproduction of “Curious George,” let alone “King Lear.” Don’t worry, scientists believe that we still have googol years — 10¹⁰⁰, or 1 followed by 100 zeros — until the lights go out. But when the end does come, the typing monkeys will have made no more progress than their counterparts at the Paignton Zoo, according to Dr. Woodcock.
“It’s not happening,” Dr. Woodcock said in an interview. The odds of a monkey typing out the first word of Hamlet’s famous “To be or not to be” soliloquy on a 30-key keyboard was 1 in 900, he said. Not bad, one could argue — but every new letter offers 29 fresh opportunities for error. The chances of a monkey spelling out “banana” are “approximately 1 in 22 billion,” Dr. Woodcock said.
The idea for the paper came to Dr. Woodcock during a lunchtime discussion with Jay Falletta, a water-usage researcher at the University of Technology Sydney. The two were working on a project about washing machines, which strain Australia’s extremely limited water resources. They were “a little bit bored” by the task, Dr. Woodcock acknowledged. (Mr. Falletta is a co-author on the new paper.)
If resources for washing clothes are limited, why shouldn’t typing monkeys be similarly constrained? By neglecting to impose a time or monkey limit on the experiment, the infinite monkey theorem essentially contains its own cheat code. Dr. Woodcock, on the other hand, opted for a semblance of reality — or as much reality as a scenario featuring monkeys trying to write in iambic pentameter would allow — in order to say something about the interplay of order and chaos in the real world.
Even if the life span of the universe were extended billions of times, the monkeys would still not accomplish the task, the researchers concluded. Their paper calls the infinite monkey theorem “misleading” in its fundamental assumptions. It is a fitting conclusion, perhaps, for a moment when human ingenuity seems to be crashing hard against natural constraints.
Low as the chances are of a monkey spelling out “banana,” they are still “an order of magnitude which is in the realm of our universe,” Dr. Woodcock said. Not so with longer material such as the children’s classic “Curious George” by Margret Rey and H.A. Rey, which contains about 1,800 words. The chances of a monkey replicating that book are 1 in 10¹⁵⁰⁰⁰ (a 1 followed by 15,000 zeros). And, at nearly 836,000 words, the collected plays of Shakespeare are about 464 times longer than “Curious George.”
“If we replaced every atom in the universe with a universe the size of ours, it would still be orders of magnitude away from making the monkey typing likely to succeed,” Dr. Woodcock said.
Like other monkey theorem enthusiasts, Dr. Woodcock mentioned a famous episode of “The Simpsons,” in which the crusty plutocrat C. Montgomery Burns tries the experiment, only to fly into a fury when a monkey mistypes the opening sentence of Charles Dickens’s “A Tale of Two Cities.” In reality, the monkey’s achievement (“It was the best of times, it was the blurst of times”) would have been a stunning triumph over randomness.
Outside cartoons, such successes are unlikely. First, there is cosmic death to consider. Many physicists believe that in 10¹⁰⁰ years — a much larger number than it might seem in type — entropy will have caused all the heat in the universe to dissipate. Far away as that moment may be, experts do think it is coming.
Then there’s the availability of monkeys. Of the more than 250 possible species, Dr. Woodcock selected chimpanzees, our closest genomic kin, to mimic the Bard. He enlisted 200,000 — the entire population of chimps currently on Earth — until the end of time. (Optimistically, he did not to plan for the species’ dwindling or extinction. Nor did he consider constraints like the availability of paper or electricity; the study does not specify which platform the monkeys might use.)
Monkeys intent on recreating Shakespeare would also need editors, with a strict reinforcement training regimen that allowed for learning — and a lot of it, since Dr. Woodcock set each monkey’s life span at 30 years. “If it’s cumulative, obviously, you can get somewhere,” said Richard Dawkins, the evolutionary biologist, who discusses the typing monkeys in “The Blind Watchmaker,” his 1986 book about evolution. Unless the typing were “iterative,” though, Dr. Dawkins said in an interview, progress would be impossible.
The new paper has been mocked online because the authors purportedly fail to grapple with infinity. Even the paper’s title, “A numerical evaluation of the Finite Monkeys Theorem,” seems to be a mathematical bait-and-switch. Isn’t infinity a basic condition of the infinite monkey theorem?
It shouldn’t be, Dr. Woodcock seems to be saying. “The study we did was wholly a finite calculation on a finite problem,” he wrote in an email. “The main point made was just how constrained our universe’s resources are. Mathematicians can enjoy the luxury of infinity as a concept, but if we are to draw meaning from infinite-limit results, we need to know if they have any relevance in our finite universe.”
This conclusion circles back to the French mathematician Borel, who took an unlikely turn into politics, eventually fighting against the Nazis as part of the French Resistance. It was during the war that he introduced an elegant and intuitive law that now bears his name, and which states: “Events with a sufficiently small probability never occur.” That is where Dr. Woodcock lands, too. (Mathematicians who believe the infinite monkey theorem holds true cite two related, minor theorems known as the Borel-Cantelli lemmas, developed in the prewar years.)
The new paper offers a subtle comment on the seemingly unbridled optimism of some proponents of artificial intelligence. Dr. Woodcock and Mr. Falletta note, without truly elaborating, that the monkey problem could be “very pertinent” to today’s debates about artificial intelligence.
For starters, just as the typing monkeys will never write “Twelfth Night” without superhuman editors looking over their shoulders, so increasingly powerful artificial intelligences will require increasingly intensive human input and oversight. “If you live in the real world, you have to do real-world limitation,” said Mr. Anderson, who conducted the 2011 monkey experiment.
There is no free lunch, so to speak, said Eric Werner, a research scientist who runs the Oxford Advanced Research Foundation and has studied various forms of complexity. In a 1994 paper about ants, Dr. Werner laid out a guiding principle that, in his view, applies equally well to typing monkeys and today’s language-learning models: “Complex structures can only be generated by more complex structures.” Lacking constant curation, the result will be a procession of incoherent letters or what has come to be known as “A.I. slop.”
A monkey will never understand Hamlet’s angst or Falstaff’s bawdy humor. But the limits of A.I. cognition are less clear. “The big question in the industry is when or if A.I. will understand what it is writing,” Mr. Anderson said. “Once that happens, will A.I. be able to surpass Shakespeare in artistic merit and create something as unique as Shakespeare created?”
And when that day comes, “Do we become the monkeys to the A.I.?”
Culture
Famous Authors’ Less Famous Books
Literature
‘Romola’ (1863) by George Eliot
Who knew that there’s a major George Eliot novel that neither I nor any of my friends had ever heard of?
“Romola” was Eliot’s fourth novel, published between “The Mill on the Floss” (1860) and “Middlemarch” (1870-71). If my friends and I didn’t get this particular memo, and “Romola” is familiar to every Eliot fan but us, please skip the following.
“Romola” isn’t some fluky misfire better left unmentioned in light of Eliot’s greater work. It’s her only historical novel, set in Florence during the Italian Renaissance. It embraces big subjects like power, religion, art and social upheaval, but it’s not dry or overly intellectual. Its central character is a gifted, freethinking young woman named Romola, who enters a marriage so disastrous as to make Anna Karenina’s look relatively good.
It probably matters that many of Eliot’s other books have been adapted into movies or TV series, with actors like Hugh Dancy, Ben Kingsley, Emily Watson and Rufus Sewell. The BBC may be doing even more than we thought to keep classic literature alive. (In 1924, “Romola” was made into a silent movie starring Lillian Gish. It doesn’t seem to have made much difference.)
Anthony Trollope, among others, loved “Romola.” He did, however, warn Eliot against aiming over her readers’ heads, which may help explain its obscurity.
All I can say, really, is that it’s a mystery why some great books stay with us and others don’t.
‘Quiet Dell’ (2013) by Jayne Anne Phillips
This was an Oprah Book of the Week, which probably disqualifies it from B-side status, but it’s not nearly as well known as Phillips’s debut story collection, “Black Tickets” (1979), or her most recent novel, “Night Watch” (2023), which won her a long-overdue Pulitzer Prize.
Phillips has no parallel in her use of potent, stylized language to shine a light into the darkest of corners. In “Quiet Dell,” her only true-crime novel, she’s at the height of her powers, which are particularly apparent when she aims her language laser at horrific events that actually occurred. Her gift for transforming skeevy little lives into what I can only call “Blade Runner” mythology is consistently stunning.
Consider this passage from the opening chapter of “Quiet Dell”:
“Up high the bells are ringing for everyone alive. There are silver and gold and glass bells you can see through, and sleigh bells a hundred years old. My grandmother said there was a whisper for each one dead that year, and a feather drifting for each one waiting to be born.”
The book is full of language like that — and of complex, often chillingly perverse characters. It’s a dark, underrecognized beauty.
‘Solaris’ (1961) by Stanislaw Lem
You could argue that, in America, at least, the Polish writer Stanislaw Lem didn’t produce any A-side novels. You could just as easily argue that that makes all his novels both A-side and B-side.
It’s science fiction. All right?
I love science and speculative fiction, but I know a lot of literary types who take pride in their utter lack of interest in it. I always urge those people to read “Solaris,” which might change their opinions about a vast number of popular books they dismiss as trivial. As far as I know, no one has yet taken me up on that.
“Solaris” involves the crew of a space station continuing the study of an aquatic planet that has long defied analysis by the astrophysicists of Earth. Part of what sets the book apart from a lot of other science-fiction novels is Lem’s respect for enigma. He doesn’t offer contrived explanations in an attempt to seduce readers into suspending disbelief. The crew members start to experience … manifestations? … drawn from their lives and memories. If the planet has any intentions, however, they remain mysterious. All anyone can tell is that their desires and their fears, some of which are summoned from their subconsciousness, are being received and reflected back to them so vividly that it becomes difficult to tell the real from the projected. “Solaris” has the peculiar distinction of having been made into not one but two bad movies. Read the book instead.
‘Fox 8’ (2013) by George Saunders
If one of the most significant living American writers had become hypervisible with his 2017 novel, “Lincoln in the Bardo,” we’d go back and read his earlier work, wouldn’t we? Yes, and we may very well have already done so with the story collections “Tenth of December” (2013) and “Pastoralia” (2000). But what if we hadn’t yet read Saunders’s 2013 novella, “Fox 8,” about an unusually intelligent fox who, by listening to a family from outside their windows at night, has learned to understand, and write, in fox-English?: “One day, walking neer one of your Yuman houses, smelling all the interest with snout, I herd, from inside, the most amazing sound. Turns out, what that sound is, was: the Yuman voice, making werds. They sounded grate! They sounded like prety music! I listened to those music werds until the sun went down.”
Once Saunders became more visible to more of us, we’d want to read a book that ventures into the consciousness of a different species (novels tend to be about human beings), that maps the differences and the overlaps in human and animal consciousness, explores the effects of language on consciousness and is great fun.
We’d all have read it by now — right?
‘Between the Acts’ (1941) by Virginia Woolf
You could argue that Woolf didn’t have any B-sides, and yet it’s hard to deny that more people have read “Mrs. Dalloway” (1925) and “To the Lighthouse” (1927) than have read “The Voyage Out” (1915) or “Monday or Tuesday” (1921). Those, along with “Orlando” (1928) and “The Waves” (1931), are Woolf’s most prominent novels.
Four momentous novels is a considerable number for any writer, even a great one. That said, “Between the Acts,” her last novel, really should be considered the fifth of her significant books. The phrase “embarrassment of riches” comes to mind.
Five great novels by the same author is a lot for any reader to take on. Our reading time is finite. We won’t live long enough to read all the important books, no matter how old we get to be. I don’t expect many readers to be as devoted to Woolf as are the cohort of us who consider her to have been some sort of dark saint of literature and will snatch up any relic we can find. Fanatics like me will have read “Between the Acts” as well as “The Voyage Out,” “Monday or Tuesday” and “Flush” (1933), the story of Elizabeth Barrett Browning’s cocker spaniel. Speaking for myself, I don’t blame anyone who hasn’t gotten to those.
I merely want to add “Between the Acts” to the A-side, lest anyone who’s either new to Woolf or a tourist in Woolf-landia fail to rank it along with the other four contenders.
As briefly as possible: It focuses on an annual village pageant that attempts to convey all of English history in a single evening. The pageant itself interweaves subtly, brilliantly, with the lives of the villagers playing the parts.
It’s one of Woolf’s most lusciously lyrical novels. And it’s a crash course, of sorts, in her genius for conjuring worlds in which the molehill matters as much as the mountain, never mind their differences in size.
It’s also the most accessible of her greatest books. It could work for some as an entry point, in more or less the way William Faulkner’s “As I Lay Dying” (1930) can be the starter book before you go on to “The Sound and the Fury” (1929) or “Absalom, Absalom!” (1936).
As noted, there’s too much for us to read. We do the best we can.
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Culture
6 Poems You Should Know by Heart
Literature
‘Prayer’ (1985) by Galway Kinnell
Whatever happens. Whatever
what is is is what
I want. Only that. But that.
“I typically say Kinnell’s words at the start of my day, as I’m pedaling a traffic-laden path to my office,” says Major Jackson, 57, the author of six books of poetry, including “Razzle Dazzle” (2023). “The poem encourages a calm acceptance of the day’s events but also wants us to embrace the misapprehension and oblivion of life, to avoid probing too deeply for answers to inscrutable questions. I admire what Kinnell does with only 14 words; the repetition of ‘what,’ ‘that’ and ‘is’ would seem to limit the poem’s sentiment but, paradoxically, the poem opens widely to contain all manner of human experience. The three ‘is’es in the middle line give it a symmetry that makes its message feel part of a natural order, and even more convincing. Thanks to the skillful punctuation, pauses and staccato rhythm, a tonal quality of interior reflection emerges. Much like a haiku, it continues after its last words, lingering like the last note played on a piano that slowly fades.”
“Just as I was entering young adulthood, probably slow to claim romantic feelings, a girlfriend copied out a poem by Pablo Neruda and slipped it into an envelope with red lipstick kisses all over it. In turn, I recited this poem. It took me the remainder of that winter to memorize its lines,” says Jackson. “The poem captures the pitch of longing that defines love at its most intense. The speaker in Shakespeare’s most famous sonnet believes the poem creates the beloved, ‘So long as men can breathe or eyes can see, / So long lives this, and this gives life to thee.’ (Sonnet 18). In Rilke’s expressive declarations of yearning, the beloved remains elusive. Wherever the speaker looks or travels, she marks his world by her absence. I find this deeply moving.”
“Clifton faced many obstacles, including cancer, a kidney transplant and the loss of her husband and two of her children. Through it all, she crafted a long career as a pre-eminent American poet,” says Jackson. “Her poem ‘won’t you celebrate with me’ is a war cry, an invitation to share in her victories against life’s persistent challenges. The poem is meaningful to all who have had to stare down death in a hospital or had to bereave the passing of close relations. But, even for those who have yet to mourn life’s vicissitudes, the poem is instructive in cultivating resilience and a persevering attitude. I keep coming back to the image of the speaker’s hands and the spirit of steadying oneself in the face of unspeakable storms. She asks in a perfectly attuned gorgeously metrical line, ‘what did i see to be except myself?’”
‘Sonnet 94’ (1609) by William Shakespeare
They that have power to hurt and will do none,
That do not do the thing they most do show,
Who, moving others, are themselves as stone,
Unmovèd, cold, and to temptation slow,
They rightly do inherit heaven’s graces
And husband nature’s riches from expense;
They are the lords and owners of their faces,
Others but stewards of their excellence.
The summer’s flower is to the summer sweet,
Though to itself it only live and die;
But if that flower with base infection meet,
The basest weed outbraves his dignity.
For sweetest things turn sourest by their deeds;
Lilies that fester smell far worse than weeds.
“It’s one of the moments of Western consciousness,” says Frederick Seidel, 90, the author of more than a dozen collections of poetry, including “So What” (2024). “Shakespeare knows and says what he knows.”
“It trombones magnificent, unbearable sorrow,” says Seidel.
“It’s smartass and bitter and bright,” says Seidel.
These interviews have been edited and condensed.
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Culture
Classic and Contemporary Literature From France, Japan, India, the U.K. and Brazil
Literature
FRANCE
According to the writer Leïla Slimani, 44, the author of ‘The Country of Others’ (2020).
Classic
‘Essais de Montaigne’ (‘Essays of Montaigne,’ 1580)
“France is a country of nuance with a love of conversation and freedom and an aversion to fanaticism. It’s also a country built on reflexive subjectivity. Montaigne reveals all that, writing, ‘I am myself the matter of my book.’”
Contemporary
‘La Carte et le Territoire’ (‘The Map and the Territory,’ 2010) by Michel Houellebecq
“Houellebecq describes France as a museum, where landscape turns into décor and where rural areas are emptying out. He shows the gap between the Parisian elite and the rest of the population, which he paints as aging and disoriented by modernity. It’s a melancholic and yet ironic novel about a disenchanted nation.”
JAPAN
According to the writer Yoko Ogawa, 64, the author of ‘The Memory Police’ (1994).
Classic
‘Man’yoshu’ (late eighth century)
“‘Man’yoshu,’ the oldest extant collection of Japanese poetry, reflects a diversity of voices — from emperors to commoners. They bow their heads to the majesty of nature, weep at the loss of loved ones and find pathos in death. The pages pulse with the vitality of successive generations.”
Contemporary
‘Tenohira no Shosetsu’ (‘Palm-of-the-Hand Stories,’ 1923-72) by Yasunari Kawabata
“The essence of Japanese literature might lie in brevity: waka [a classical 31-syllable poetry form], haiku and short stories. There’s a tradition of cherishing words that seem to well up from the depths of the heart, imbued with warmth. Kawabata, too, exudes more charm in his short stories — especially these very short ‘palm-of-the-hand’ stories — than in his full-length novels. Good and evil, beauty and ugliness, love and hate — everything is contained in these modest worlds.”
INDIA
According to Aatish Taseer, 45, a T contributing writer and the author of ‘Stranger to History: A Son’s Journey Through Islamic Lands’ (2009).
Classic
‘The Kumarasambhava’ (‘The Birth of Kumara,’ circa fifth century) by Kalidasa
“This is an epic poem by the greatest of the classical Sanskrit poets and dramatists. The gods are in a pickle. They’re being tormented by a monster, but Shiva, their natural protector, is deep in meditation and cannot be disturbed. Kama, the god of love, armed with his flower bow, is sent down from the heavens to waken Shiva. Never a wise idea! The great god, in his fury, opens his third eye and incinerates Kama. But then, paradoxically, the death of the god of love engenders one of the greatest love stories ever told. In the final canto, Shiva and his wife, the goddess Parvati, have the most electrifying sex for days on end — and, 15 centuries on, in our now censorious time, it still leaves one agog at the sensual wonder that was India.”
Contemporary
‘The Complex’ (2026) by Karan Mahajan
“This state-of-the-nation novel, which was published just last month, captures the squalor and malice of Indian family life. Delhi is both my and Mahajan’s hometown and, in this sprawling homage to India’s capital, we see it on the eve of the economic liberalization of the 1990s, as the old socialist city gives way to a megalopolis of ambition, greed and political cynicism.”
THE UNITED KINGDOM
According to the writer Tessa Hadley, 70, the author of ‘The London Train’ (2011).
Classic
‘Jane Eyre’ (1847) by Charlotte Brontë
“Written almost 200 years ago, it remains an insight into our collective soul — or at least its female part. Somewhere at the heart of us there’s a small girl in a wintry room, curled up in the window seat with a book, watching the lashing rain on the window glass: ‘There was no possibility of taking a walk that day. …’ Jane’s solemnity, her outraged sense of justice, her trials to come, the wild weather outside, her longing for something better, for love in her future: All this speaks, perhaps problematically, to something buried in the foundations of our idea of ourselves.”
Contemporary
‘All That Man Is’ (2016) by David Szalay
“Though he isn’t quite completely British (he’s part Canadian, part Hungarian), Szalay is brilliant at catching certain aspects of British men — aspects that haven’t been written about for a while, now updated for a new era. Funny, exquisitely observed and terrifying, this novel reminds us, too, how absolutely our fate and our identity as a nation belong with the rest of Europe.”
BRAZIL
According to the writer and critic Noemi Jaffe, 64, the author of ‘What Are the Blind Men Dreaming?’ (2016).
Classic
‘Memórias Póstumas de Brás Cubas’ (‘The Posthumous Memoirs of Brás Cubas,’ 1881) by Machado de Assis
“Not only is it experimental in style — very short chapters mixed with long ones; different points of view; narrated by a corpse; metalinguistic — but it also introduces an extremely ironic view of the rising bourgeoisie in Rio de Janeiro at the time, revealing the hypocrisy of slave owners, the falsehood of love affairs and the only true reason for all social relationships: convenience and personal interest. After almost 150 years, it’s still modern, both formally and, unfortunately, also in content.”
Contemporary
‘Onde Pastam os Minotauros’ (‘Where Minotaurs Graze,’ 2023) by Joca Reiners Terron
“The two main characters — Cão and Crente — along with some of their colleagues, plan to escape and set fire to the slaughterhouse where they work under exploitative conditions. The men develop sympathy for the animals they kill, and one of them becomes a sort of philosopher, revealing the sheer nonsense of existence and the injustices of society in the deepest parts of Brazil.”
These interviews have been edited and condensed.
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