Labyrinths by Jorge Luis Borges (1962)

The metaphysicians of Tlön do not seek for the truth or even for verisimilitude, but rather for the astounding.

There is no pleasure more complex than that of thought.

In the course of a life dedicated to letters and (at times) to metaphysical perplexity…

Borges wrote a surprising amount (some 70 books in Spanish) and yet he is principally known in the Anglo-Saxon world for just one work published 60 years ago, Labyrinths, a breath-taking collection of 40 mind-bending short stories, short essays, and ‘parables’, all of which reference, quote and play with a multitude of obscure and arcane texts and ideas derived from philosophy, theology and mysticism.

Penguin went on to publish a flotilla of four or five other volumes by Borges, but none of them hold a candle to Labyrinths which is one of the most important volumes of short stories in English in the second half of the 20th century. It is a scandal that, to this day, only a fraction of Borges’s output has been translated into English.

Adventures among books and ideas

Labyrinths consists of 23 ficciones, ten essays and eight ‘parables’. All the stories were written and first published in Borges’s native Spanish in Argentine literary magazines between 1941 and 1956. The first 13 stories are taken from a previous collection, Ficciones, published in 1945, which was expanded in successive editions, and the remaining ten were published in a collection titled The Aleph, published in 1949, and also added to in later editions. That’s a long time ago but when you look at individual stories it’s striking to see that most of them were first published in literary magazines much earlier, most of them at the very end of the 1930s, during the Second World War and in the immediate post-war years. Although he carried on writing into the 1980s, his greatest hits were composed in the 1940s.

Before I exhaust myself giving brief summaries of each of the pieces, let me make a simple point which is that, rereading Borges’s stories made me realise that possibly his major discovery was that, for the purposes of writing a short fiction, you can replace plot with ideas.

What I mean is that the best stories discuss philosophical and metaphysical or mystical ideas and, in doing so, refer to scores of obscure Latin and Greek, or Christian or Islamic texts and sources – and that it is this, rather than plots, character or dialogue, which fills his stories.

Most adventures are, almost by definition, about people, about named characters. Borges’s short fictions are adventures whose protagonists are ideas, ideas characterised by their multi-layered bookishness and whose explanation requires multiple references to all manner of arcane texts – and whose ‘adventure’ consists in the logical unfolding of far-fetched premises to even more-mind-boggling conclusions: such as the man who discovers he is a dream created by someone else; or that the entire universe is made up of an infinite library; or that all human activity is determined by a secret lottery; and so on.

It is immensely characteristic of this preference for ideas over psychology or emotions or feelings that, when the narrator of Tlön, Uqbar, Orbis Tertius stumbles across an encyclopedia purporting to catalogue the fictitious planet of Tlön, he experiences a moment of delirious happiness i.e. emotion, feeling – but quickly stifles it:

I began to leaf through [the encyclopedia] and experienced an astonished and airy feeling of vertigo which I shall not describe, for this is not the story of my emotions but of Uqbar and Tlön and Orbis Tertius.

In fact various emotions do occur in the stories, there are characters and events, but this moment can stand as a symbol of the way that fiction’s traditional concerns for character and emotion and plot are, on the whole, in Borges’s stories, repressed or sidelined in order to make way for the adventures of ideas and books.

Borges’s bookishness is not for everyone

And I suppose there’s a point that’s so obvious that it’s easy to miss which is that you have to be fairly learnèd and scholarly, or at least fairly well-read, in order to really enjoy these works. On the first page alone of Deutsches Requiem Borges mentions Brahms and Schopenhauer and Shakespeare and Nietzsche and Spengler and Goethe and Lucretius. Now I not only know who these guys all are, but I have read some or much of all of them (a lot of Shakespeare and Nietszche, a book of Schopenhauer’s, some Goethe and Spengler) and so the mental edifice which invoking their names creates, the structure and framework of the story, are all entirely familiar to me and so I can enjoy how Borges plays with their names and references.

But I suppose there will be many readers who haven’t read (or listened to, in the case of Brahms) these authors and composers, and so might have to stop and Google each of them and, I suppose, this might well put off a lot of potential readers. It’s not that the stories are intrinsically ‘difficult’ (though sometimes they juggle with ideas on the edge of comprehension) so much as that the entire atmosphere of intense bookishness and scholarly whimsy which they evoke might well deter as many unbookish readers as it fanatically attracts fans and devotees among the literary-minded.

Contents – Fictions

Tlön, Uqbar, Orbis Tertius (1940)

Uqbar is a mythical land which the narrator and friends find mentioned in a ‘pirated’ edition of Volume XLVI of the Anglo-American Cyclopaedia, but can find referred to nowhere else, despite ransacking the reference books of numerous libraries. The article explains that the literature of Uqbar was one of fantasy, featuring epics and legends set in two imaginary regions, Mlejnas and Tlön. In part 2 of the story we learn that Tlön is less an imaginary realm than an entire ‘planet’.

At first it was believed that Tlön was a mere chaos, an irresponsible license of the imagination; now it is known that it is a cosmos and that the intimate laws which govern it have been formulated, at least provisionally

Once he has posited the existence of this ‘planet’, the narrator goes on to recount the dizzying nature of its language and its many schools of philosophy:

  • one of the schools of Tlön goes so far as to negate time: it reasons that the present is indefinite, that the future has no reality other than as a present hope, that the past has no reality other than as a present memory
  • another school declares that all time has already transpired and that our life is only the crepuscular and no
    doubt falsified and mutilated memory or reflection of an irrecoverable process
  • another, that the history of the universe — and in it our lives and the most tenuous detail of our lives — is the scripture produced by a subordinate god in order to communicate with a demon
  • another, that the universe is comparable to those cryptographs in which not all the symbols are valid and that only what happens every three hundred nights is true
  • another, that while we sleep here, we are awake elsewhere and that in this way every man is two men

This is what makes Borges’s stories so phenomenally packed and mind-bending: that each individual sentence is capable of introducing to an entirely new way of thinking about the world.

The postscript to the story describes the narrator stumbling on a letter which purports to summarise the process whereby magi in the early 17th century decided to invent a country, how the idea was handed down as the texts proliferate, till an early Victorian American decided they needed to be more ambitious and describe an entire planet. In 1914 the last volume of a projected 40-volume encyclopedia of Tlön was distributed to the cabal of experts. It is estimated it will become the Greatest Work of Mankind, but it was decided this vast undertaking would itself be the basis of an even more detailed account which was provisionally titled the Orbus Tertius. Slowly, the narrator claims, mysterious objects from Tlön have appeared in our world. This last part is set two years in the future and describes a world in which news of Tlön has become widespread and artefacts from the imaginary planet are appearing all over the world and beginning to replace our own.

The contact and the habit of Tlön have disintegrated this world…Already the schools have been invaded by the (conjectural) “primitive language” of Tlön; already the teaching of its harmonious history (filled with moving episodes) has wiped out the one which governed in my childhood; already a fictitious past occupies in our memories the place of another, a past of which we know nothing with certainty — not even that it is false… A scattered dynasty of solitary men has changed the face of the world. Their task continues. If our forecasts are not in error, a hundred years from now someone will discover the hundred volumes of the Second Encyclopedia of Tlön. Then English and French and mere Spanish will disappear from the globe. The world will be Tlön.

So it is, on a fairly obvious level, a kind of science fiction disaster story in which our world will eventually be taken over and/or destroyed by the imaginary creation of the cabal.

The Garden of Forking Paths (1941)

A story which opens with a book and is about a book. Its first sentence is:

On page 22 of Liddell Hart’s History of World War I you will read that an attack against the Serre-Montauban line by thirteen British divisions (supported by 1,400 artillery pieces), planned for the 24th of July, 1916, had to be postponed until the morning of the 29th….

The story is the account of Dr. Yu Tsun, former professor of English at the Hochschule at Tsingtao, a spy acting for the Germans, based in England, in Staffordshire, but is rumbled by a British officer, Captain Madden, so makes his way by train to the village of Ashgrove and the house of one Dr Stephen Albert, who describes the efforts of Yu’s ancestor, ‘Ts’ui Pên who was governor of Yunnan and who renounced worldly power in order to write a novel that might be even more populous than the Hung Lu Meng and to construct a labyrinth in which all men would become lost’. The story reveals that this labyrinth is metaphorical: it actually stands for the scattered manuscript of an incomplete book. The garden of forking paths is the novel promised by never completed. But the nature of the fragments is deliberate:

The Garden of Forking Paths is an incomplete, but not false, image of the universe as Ts’ui Pên conceived it. In contrast to Newton and Schopenhauer, your ancestor did not believe in a uniform, absolute time. He believed in an infinite series of times, in a growing, dizzying net of divergent, convergent and parallel times. This network of times which approached one another, forked, broke off, or were unaware of one another for centuries, embraces all possibilities of time.

So it’s about a book which encompasses all time, and all possible permutations of time.

The Lottery in Babylon (1941)

Tells the story of the development of a hyper-complex lottery run by the all-powerful ‘Company’ in a fictional version of ‘Babylon’, which ends up becoming the basis for everything which happens, for every event in everybody’s lives.

Pierre Menard, Author of the Quixote (1939)

This purports to be a brief article by a follower of the now deceased writer Pierre Menard. It starts by listing the complete works of the defunct writer, some 19 in all, thus establishing the hyper-bookish context; then goes on to describe the unprecedented attempt by Pierre Menard to rewrite (sections of) Don Quixote as if by himself, as if for the first time, as if written by a 20th century author, and the complexity and strangeness of the result.

The Circular Ruins (1940)

The unnamed man arrives in a canoe from the south, beaches it in the mud and climbs to the ancient ruins.

The purpose which guided him was not impossible, though it was supernatural. He wanted to dream a man: he wanted to dream him with minute integrity and insert him into reality

He devotes years to dreaming, piece by piece, a perfect young man, who he then teaches in his dreams and who then finally becomes a real entity in the real world, who can pass painlessly though fire. But when a forest fire rages towards the ruins where he has been living the man walks boldly towards them – only not to feel a thing and to realise, that he himself is a dream-man who has been dreamed, in his turn, by someone else.

The Library of Babel (1941)

The narrator lives inside a library so huge, made up of infinite levels and extending through infinite galleries of hexagonal rooms, that he and all the other inhabitants regard it as the known universe. From this perspective, of an inhabitant of the infinite library, he shares with us the discoveries and/or theories of various other inhabitants who, through the centuries, have explored deeper into the infinite library, made discoveries and come up with theories as to its origin and purpose, for example the theories of the idealists (‘the hexagonal rooms are a necessary form of absolute space’) or the mystics (‘The mystics claim that their ecstasy reveals to them a circular chamber containing a great circular book, whose spine is continuous and which follows the complete circle of the walls’) origin stories (‘Man, the imperfect librarian, may be the product of chance or of malevolent demiurgi’), those who have given up trying to find meaning (‘I know of an uncouth region whose librarians repudiate the vain and superstitious custom of finding a meaning in books and equate it with that of finding a meaning in dreams or in the chaotic lines of one’s palm’).

Five hundred years before his birth the momentous discovery was made that the library contains all possible combinations of their language’s 25 symbols, in other words, contains all human knowledge, and much more, contains the history and future of everyone. This led to a wave of optimism and pride. This gave rise to a category of men named inquisitors who travel far and wide in search of these phantom volumes which will explain everything, and are named the Vindications. This was followed by the depressing realisation that, although these books certainly exist, in a library infinitely large anyone’s chances of finding them are infinitely small. Which gave rise to a semi-religious movement of nihilists, the Purifiers, who set out to examine and destroy all books which are not Vindications. But even their senseless destruction of millions of books made little difference in a library which is infinite in size.

The knowledge that everything has already been written has had a negative effect. Some have become religious hysterics. Suicides have become more common. The population of the hexagonal rooms has been depleted. He wonders whether the human species will be extinguished.

Funes the Memorious (1942)

Ireneo Funes was a dark, Indian-looking man from Uruguay. He died in 1889. The author of this piece is contributing a memoir of him to a volume to be published in his honour. Funes was a perfectly ordinary young man till a horse threw him aged 19. From that point onwards, he remembers everything which happens to him, every single impression, sight, sound and smell which his senses register, is recorded in the fine instrument of his memmory.

The two projects I have indicated (an infinite vocabulary for the natural series of numbers, a useless mental catalogue of all the images of his memory) combine in this dazzling idea. Not just memory, he notices everything.

He was the solitary and lucid spectator of a multiform, instantaneous and almost intolerably precise world

And the ‘story’, really an essay based on a fictional premise, explores what it would mean to live in this state.

To think is to forget differences, generalize, make abstractions. In the teeming world of Funes, there were only details, almost immediate in their presence.

The Shape of the Sword (1942)

Not a bookish brain-teaser, this is a much more straightforward story. The narrator, who is referred to as Borges, is forced when travelling in the North to stay in the house of a man who has a reputation as a martinet and occasional drunk who is disfigured by a half-moon-shaped scar on his forehead. The man treats Borges to dinner then they get talking and finally the man tells him his story: how he was a fighter with the IRA during the Irish Civil War, and helped mentor and protect a vehement young recruit, one John Vincent Moon, a committed communist who shut down every discussion with his fervent ideology. On a patrol they were caught by a guard who shot and nicked Moon’s shoulder. They break into the abandoned house of an old Indian officer, to hide out. When the town they were hiding in was taken by the Black and Tans, he returned to the house to overhear Moon betraying him to the authorities on the promise of his own safe passage, whereupon he chased Moon round the house brandishing one of the swords belonging to its absent owner until he caught him and branded his face with the half moon with a sword.

All through the story you’d been led to believe the narrator was the strong man. Only at the end does he break down and confess that it was he who was the betraying coward, John Vincent Moon. And hence the scar cut into his face.

Theme of the Traitor and the Hero (1944)

A very short story which foregrounds its own fictiveness, as Borges admits it’s an idea for a story which could be set anywhere, then arbitrarily settles on Ireland where, he says, a man named Ryan is researching the famous assassination of an eminent Irish patriot, his great-grandfather, Fergus Kilpatrick, in a theatre in 1824. His researches show him that Kilpatrick’s assassination shared many details with that of Julius Caesar, the parallels so eerie that for a while he develops a theory of ‘the existence of a secret form of time, a pattern of repeated lines’, and invokes the theories of Condorcet, Hegel, Spengler and Vico to back him up.

But then a stranger reality emerges. He discovers the oldest and closest of Kilpatrick’s companions, James Alexander Nolan, had translated the main plays of Shakespeare back in 1814. Finally the story that emerges is this: the conspirators kept being betrayed to the police so Kilpatrick had tasked his oldest comrade, Nolan, with identifying the traitor. At a secret meeting of the patriots Nolan announced that it was Kilpatrick himself. The great patriot admitted it. They discussed how to deal with him. They came up with a drama, a play, a theatrical event, which would ensure Kilpatrick’s punishment and death, and yet if he was said to have been assassinated at the theatre, people’s illusions about him, and the Cause in general, would be preserved. And so Nolan, the Shakespeare translator, arranged it all, even borrowing certain events (the unheeded warning) in order to make the ‘assassination’ more melodramatic and memorable.

And also, his disillusioned great grandson and biographer speculates, to leave messages to posterity. Some of the allusions were pretty crass. Maybe he, Ryan, was intended to discover the truth. After weighing the pros and cons, Ryan decides to suppress what he has learned, and write a straightforward biography climaxing in the great man’s tragic assassination. Maybe that, too, was part of the plan.

Death and the Compass (1942)

This is a murder mystery of a particularly arch and contrived tone, but reading it makes you realise Borges’s debt to the English yarn tellers of the 1890s, to Robert Louis Stevenson and especially Conan Doyle. We are introduced to Erik Lönnrot, another in the long line of hyper-intellectual freelance detectives with a taste for paradox and irony i.e. an entirely literary creation, who also, as per the tradition, plays off a phlegmatic police inspector, Franz Treviranus.

At the Third Talmudic Congress held in the Hotel du Nord, Rabbi Marcel Yarmolinsky goes to bed one night and his body is found dead, stabbed in the chest, the next morning. The dead man, of course, had a number of rare and arcane books of theology in his room. Which Lönnrot takes away and reads:

One large octavo volume revealed to him the teachings of Israel Baal Shem Tobh, founder of the sect of the Pious; another, the virtues and terrors of the Tetragrammaton, which is the unutterable name of God; another, the thesis that God has a secret name, in which is epitomized (as in the crystal sphere which the Persians ascribe to Alexander of Macedonia) his ninth attribute, eternity — that is to say, the immediate knowledge of all things that will be, which are and which have been in the universe…

Books books books. But then more bodies turn up dead – small-time crook Daniel Simon Azevedo, then the kidnapping and murder of one Gryphius. We know the three murders are linked because at the scene three sentences are written, ‘The first letter of the Name has been uttered’, and the second and the third.

After the third the police are anonymously sent a letter sent by ‘Baruch Spinoza’ asserting that a fourth murder will not be carried out. But Lönnrot has seen through all this. He Dandy Red Scharlach set out

to weave a labyrinth around the man who had imprisoned my brother. I have woven it and it is firm: the ingredients are a dead heresiologist, a compass, an eighteenth-century sect, a Greek word, a dagger, the diamonds of a paint shop.

The Secret Miracle (1943)

Hladik had rounded forty. Aside from a few friendships and many habits, the problematic exercise of literature constituted his life…

Jaromir Hladik is an author of, among others, an unfinished drama entitled The Enemies, of Vindication of Eternity (which discusses immutable Being of Parmenides, the modifiable Past of Hinton, and the idealist philosopher, Francis Bradley) and of a study of the indirect Jewish sources of Jakob Böhme, he has translated the Sepher Yezirah and published studies of the work of Böhme, of Ibn Ezra, and of Fludd. He is another of Borges’s hyper-bookish heroes.

The Nazis take Prague and seize Hladik who is identified as a Jewish author and condemned to death. The story deals with the feverishly philosophical ideas which flood his mind during the days and nights he spends in his prison cell leading up to his sentence of death by firing squad, in which he discusses with himself various aspects of time and reality and God, and has a dream that God’s word is vouchsafed to him through a random book in a library, and in which he goes through the elaborate plot of his verse drama, The Enemies, which is itself a drama about reality and illusion. He begs God for a year to finish the work in order to justify himself and Him.

Finally he is led out to the shabby yard where the soldiers are hanging round bored, are rallied by their sergeant and line up to shoot him but, just as the order is given, time freezes, completely, but Hladik’s consciousness continues, observing the frozen world about him from his frozen body, at first in panic, and then realising that God heard his plea and has given him a year to complete his drama. And the final page of the drama describes how he does that, not needing food or water or bodily functions, but devoting a year of time to bringing the verse drama to complete perfection, And as the last phrase of it is completed in his mind, the world resumes, the firing squad fires, and Hladik slumps, dead.

Three Versions of Judas (1944)

Borges’s fiction is above all hyper-bookish, made out of references to arcane philosophical or theological texts from the Middle Ages or Antiquity. Most (if not quite all) the ‘stories’ mimic the style and approach of an old-fashioned scholarly article, not least in having textual footnotes which cite other scholarly volumes or references.

Instead of a description of a city or house or street or natural location, a time of day, or the physical appearance of a protagonist, Borges’s fictions set their scene amid books and references.

In Asia Minor or in Alexandria, in the second century of our faith, when Basilides disseminated the idea that the cosmos was the reckless or evil improvisation of deficient angels, Nils Runeberg would have directed, with singular intellectual passion, one of the Gnostic conventicles. Dante would have assigned him, perhaps, a fiery grave; his name would extend the list of lesser heresiarchs, along with Satornilus and Carpocrates; some fragment of his preachings, embellished with invective, would survive in the apocryphal Liber adversus omnes haereses or would have perished when the burning of a monastery library devoured the last copy of the Syntagma. Instead, God afforded Runeberg the twentieth century and the university town of Lund. There, in 1904, he published the first edition of Kristus och Judas and, in 1909, his major book, Den hemlige Frälsaren. (Of the latter there is a German translation, made in 1912 by Emil Schering; it is called Der heimliche Heiland.)

Amid a dense forest of allusions to obscure works of theology and scores of beliefs held by the orthodox and heretical, Borges articulates the three theories developed by Danish theologian, namely:

  1. In his book Kristus och Judas, Runeberg asserts that Judas was a kind of ‘reflection’ of Jesus in the human world; just as Jesus was sent from heaven, so Judas took up the burden of being human in order to pave the way for Jesus to take the path to the crucifixion and salvation of humanity.
  2. Meeting fierce criticism from fellow theologians, Runeberg rewrites the book to assert that it was Judas who sacrificed more than Jesus, mortifying his spirit for the greater good.
  3. Then in his final book, Den hemlige Frälsaren, Runeberg develops this idea to its logical conclusion, which is that it was Judas not Jesus who made the ultimate sacrifice and truly laid down his life for humanity. Jesus hung on the cross for 6 hours but then he was translated to heaven, whereas Judas committed suicide, taking upon himself not only an eternal reputation for treachery and betrayal, but condemning his own soul to eternity in hell. Which one made the greater sacrifice? Therefore, Runeberg asserts, it was Judas who was the true incarnation of a God determined to make the most complete identification with humanity possible, even to the uttermost depths of human depravity and damnation.

The Sect of the Phoenix (1952)

Those who write that the sect of the Phoenix had its origin in Heliopolis and derive it from the religious restoration following upon the death of the reformer Amenophis IV, cite texts from Herodotus, Tacitus and the monuments of Egypt, but they ignore, or prefer to ignore, that the designation ‘Phoenix’ does not date before Hrabanus Maurus and that the oldest sources (the Saturnales of Flavius Josephus, let us say) speak only of the People of the Custom or of the People of the Secret.

Repeatedly the stories invoke the same kind of imaginative world, a world of arcane books and abstruse learning, which revolves not so much around pure philosophy – the academic subject of Philosophy which concerns rather mundane discussions of language or ethics which bothered Plato and Locke – but the swirling multi-coloured world of abstruse theologies and mystical visions of the divinity and cults and lost texts, of heresiarchs (‘the founder of a heresy or the leader of a heretical sect’) and patriarchs, sectarians and mystagogues, Talmudists and Confucians, Gnostics and alchemists, adepts in secret rituals and concealed knowledge, and which has adherents down to the present day such as the heretical theologian Nils Runeberg from The Three Versions of Judas or the learned Rabbi Marcel Yarmolinsky in Death and The Compass, intense bookish eccentric figures who carry the convoluted world of medieval theology into obscure corners of our workaday world.

This brief story is an ostensible short scholarly essay by a narrator who claims:

I have collated accounts by travelers, I have conversed with patriarchs and theologians… I have attained on three continents the friendship of many devotees of the Phoenix

And so is in a position to know that devotees of ‘the sect of the Phoenix’ are everywhere, of all creeds and colours, speaking all languages, often not even realising it themselves. I think the essay is an answer to the question, What if there was a religion so widespread that its adherents didn’t even realise they followed it?

The Immortal (1949)

A princess (!) buys a second hand edition of Alexander Pope’s translation of The Iliad off a book dealer, Joseph Cartaphilus, in London and later finds in the leaves of the last volume a manuscript, which then makes up the body of the story. It is a first person narrative by Marcus Flaminius Rufus, military tribune of one of Rome’s legions, who hears rumours of a land to the West where sits the City of the Immortals and so sets off with a troop of 200 soldiers and sundry mercenaries all of whom desert him in the face of all kinds of adversity, until he comes to consciousness in a settlement of speechless troglodytes before staggering on, exhausted, hungry, thirsty towards a high rocky plateau on which is built a mysterious city, but when he finally gains entrance he discovers it is not only abandoned and deserted, but built with an excess of useless passages and windows and balconies and details amid he becomes lost and then overwhelmed by its size and complexity and horrifying pointlessness.

When he emerges he discovers one of the speechless troglodytes has followed him like a loyal dog. He nicknames him Argos after Odysseus’s loyal dog and over the next few weeks tries to teach him to speak. Then, one day, there is a ferocious downpour of rain, and Argos suddenly speaks, responds to the name, recognises the classical allusion and, to the narrator’s astonishment, reveals that he is Homer, author of the Iliad and the Odyssey and that the other haggard, grimy, speechless troglodytes, they are the Immortals, who long ago wrecked their beautiful city, rebuilding it as a surrealist testament to the unknown and irrational forces which control our fates, and withdrew to the caves and lives of inarticulate resignation.

Because he has drunk of the river that runs past the troglodytes’ caves he is now immortal and the narrative briefly covers his wandering life for the following centuries, until in 1929 he drinks from a stream in Eritrea and realises, with enormous relief, that it has restored his mortality.

The Theologians (1947)

An orgy of theological minutiae describing the academic rivalry between two sixth century theologians, Aurelian of Aquileia and John of Pannonia, who compete with each other in refuting the heresy of the so-called Monotones (namely that history is cyclical and all people and events recur again and again), which twists via a dense undergrowth of theological quotes and references to a climax in which Aurelian witnesses John being burned at the stake for the very heresy he had set out to refute, and then the two rival theologians meet up in heaven where, in true Borgesian fashion, they are revealed to be two aspects of the same person.

Story of the Warrior and the Captive (1940)

Droctulft was an eighth century Lombard warrior who, during the siege of Ravenna, left his companions and died defending the city he had previously attacked. Borges imagines this pallid denizen of the pagan forests and the boar hunt arriving at a city, his dazzlement at the order and clarity and architecture and gardens, and suddenly throwing in his lot with the citizens, fighting against his former comrades.

And this reminds him of his grandmother who was from England. She lived out on the borderlands. One day she was introduced to a young woman Indian who, it transpires, was English, from Yorkshire, her parents emigrated and were killed in an Indian raid and she was stolen away and married to a chieftain who she has already borne two children. Borges’s grandmother offers to take her away, to return her to civilisation, but the Englishwoman-gone-native refuses. She, like Droctulft, has made a deep choice.

Emma Zunz (1948)

Emma’s father commits suicide because he was swindled out of his share of the factory he set up. She vows to be revenged on the swindler, Aaron Loewenthal (all the characters in this story are Jewish) and, a shy 19, dresses up, goes hanging round in bars, in order to lose her virginity to some rough foreigner. This is to nerve her for the assassination, when she presents herself to Loewenthal in the guise of a stoolpigeon for the ringleaders of the disgruntled workers in the factory but, when he rises to fetch her a glass of water, impulsively shoots him, though she’s not very good at it and takes three shots. She then calls the police and pleads a story that Lowenthal tried to rape and outrage her, which, Borges says, is true, in spirit if not in detail, and her genuine outrage and sense of shame and hate secures her an acquittal at her subsequent trial.

The House of Asterion (1947)

The world seen from the perspective of the Minotaur. (The idea is related to the brief one-page summary Borges gives of a story he planned to write about the world seen from the point of view of Fafnir, the gold-guarding dragon in the Nibelung legend. You can see how you could quickly generate a list of stories ‘from the point of’ figures from myth and legend.)

Deutsches Requiem (1946)

Otto Dietrich zur Linde is a Nazi and a devout follower of Schopenhauer and his doctrine that nothing that happens to us is accidental (it is a happy coincidence that I’ve recently been reading Samuel Beckett, who was also very influenced by Schopenhauer, in particular by his attitude of quietism).

As the Second World War breaks out Otto Dietrich zur Linde is involved in a shootout which leads to the amputation of one of his legs. As a good Nazi he is eventually rewarded by being made, in 1941, subdirector of the concentration camp at Tarnowitz.

When the wonderful Jewish poet David Jerusalem is sent to the camp, zur Linde sets about systematically destroying him because, by doing so, he is destroying the compassion in his own soul which keeps him down among ordinary humans, prevents him from becoming Nietzsche’s Overman.

As the tide of war turns against the Germans, zur Linde speculates why and what it means before realising that Germany itself must be destroyed so that the New Order it has helped to inaugurate can come fully into being. This short text turns into quite a disturbing hymn to Nazism:

Many things will have to be destroyed in order to construct the New Order; now we know that Germany also was one of those things. We have given more than our lives, we have sacrificed the destiny of our beloved Fatherland. Let others curse and weep; I rejoice in the fact that our destiny completes its circle and is perfect.

Averroes’ Search (1947)

A classic example of Borges’s fascination with the byways of medieval mystical theology, and his ability to spin narratives out of it.

Abulgualid Muhammad Ibn-Ahmad ibn-Muhammad ibnRushd (a century this long name would take to become Averroes, first becoming Benraist and Avenryz and even Aben-Rassad and Filius Rosadis) was writing the eleventh chapter of his work Tahafut-ulTahafut (Destruction of Destruction), in which it is maintained, contrary to the Persian ascetic Ghazali, author of the Tahafut-ulfalasifa (Destruction of Philosophers), that the divinity knows only the general laws of the universe, those pertaining to the species, not to the individual…

It is a complex text, woven with multiple levels of references, which revolves round a dinner party attended in the then-Muslim city of Cordoba in Muslim Spain by the great medieval Muslim commentator on the ancient Greek philosopher, Aristotle, and some colleagues and friends including one who claims to have travelled as far as the fabled land of Sin (China). When he was there he recounts being taken to a large hall with tiered banks of seats where many people on a raised platform acted out events. The other diners agree how ridiculous this sounds and we learn that, apparently, the traditions and culture of Islam did not have or understand the entire concept of the theatre and the drama.

The essay focuses on the way this conversation was relevant for Averroes because he was that day working on a translation of Aristotle and puzzled by two words he had come across, ‘tragedy’ and ‘comedy’ which have no parallel in the world of Islam.

This is all fascinating and beautifully described amid the gardens and roses and civilised calm of the Muslim city, but on the last half page Borges twists the story onto a different level altogether by intruding himself as the author and declaring he only told this story as an attempt to describe a certain kind of failure to imagine something, and that, as the story progressed, he, Borges, realised that he was failing to imagine his own story, thus the story and the writing of the story, both addressed the same subject, in a kind of duet.

I felt, on the last page, that my narration was a symbol of the man I was as I wrote it and that, in order to compose that narration, I had to be that man and, in order to be that man, I had to compose that narration, and so on to infinity. (The moment I cease to believe in him, ‘Averroes’ disappears.)

Wow.

The Zahir (1947)

Clementina Villar was a model and celebrity, always appearing at the right place at the right time dressed in the height of fashion. She dies in a slummy suburb and Borges attends her wake. Decomposition makes her look younger. On the rebound from his grief he drops into a neighbourhood bar, orders a brandy and is given the Zahir among his change. The Zahir is an everyday coin but:

people (in Muslim territories) use it to signify ‘beings or things which possess the terrible property of being unforgettable, and whose image finally drives one mad.’

He can’t stop looking at it, he takes it home, he turns it over and over, it obsesses his sleep, eventually he gets lots in a maze of streets, slips into another bar and pays for a drink handing the coin over, goes home and has his first good night’s sleep in weeks.

The Waiting (1950)

An unnamed man checks into a boarding house in a suburb of Buenos Aires and tries to lead a completely anonymous life while he waits for his assassins to track him down and kill him.

The God’s Script

The story is told by Tzinacán, magician of the pyramid of Qaholom, an Aztec priest whose city was conquered and burned down by the conquistador Pedro de Alvarado who tortured and mangled him to try and extract the secret of where all the native gold and treasure was hidden. Now he lies in a dungeon where he has been subsisting for years, but it is a strange prison because on the other side of the wall is kept a jaguar which paces up and down in his cell. Only at certain hours of the day, when the light is right, can Tzinacán see it. Over the years Tzinacán becomes obsessed with the idea that his god Qaholom must have foreseen the disaster which overcame his people,

The god, foreseeing that at the end of time there would be devastation and ruin, wrote on the first day of Creation a magical sentence with the power to ward off those evils. He wrote it in such a way that it would reach the most distant generations and not be subject to chance. No one knows where it was written nor with what characters, but it is certain that it exists, secretly, and that a chosen one shall read it.

So it is another story about a kind of secret knowledge, known only to adepts, occult and hidden. To cut a long story short, Tzinacán has a revelation which is indistinguishable from going mad, as he ponders the nature of this message from the gods, as he ponders at length what the language of a god would be like, how it would contain the whole world, not even in a sentence, but in one infinite word, and he suddenly perceives it in the shape of an infinite wheel, on all sides of him, made of fire and water, the secret of the world is contained in fourteen words of forty syllables, if he said them out loud the prison would disappear and he would be master of the land of Moctezuma – but he never will because he has ceased to be Tzinacán, he has ceased to have his concerns or aims, and therefore he knows the secret of divine power, but the very knowledge of it means he never has to use it.

Essays

The Argentine Writer and Tradition (1951)

The problems of national identity and literary heritage faced by the writer in Argentina are not something most of us have spent much time worrying about. Reading Borges’s essay on the subject mostly confirms that I know nothing whatsoever about Latin American literature. For my generation this meant entirely the magical realism school pioneered by Gabriel Garcia Marquez and a cluster of related writers such as Mario Vargas Llosa and, fashionable among feminists, Isabel Allende. I’m fairly well read but I’d never heard of any of the names or works Borges refers to, for example I had no idea the great Argentine epic poem is El gaucho Martín Fierro by Jose Hernandez which is, apparently, packed with gaucho colloquialisms.

Initially the essay dwells on obscure questions about the relative merits of ‘gauchesque’ poetry (which he takes to be the contrived nationalistic poetry of literary circles of Buenos Aires) vis-a-vis the poetry of payadas (improvised musical dialogues on philosophical themes which reveal their true nationalism precisely by the absence of localising dialect) but both of which are almost meaningless to me since I can’t read Spanish and had never heard of Martín Fierro. (Borges had published in 1950 a study of the gauchesque, Aspectos de la literatura gauchesca and in 1953 an essay on Martín Fierro.)

But slowly emerges his main point which is more comprehensible, namely that ‘national’ poetry or literature does not at all need to limit itself to local colour and national subjects: witness Shakespeare who wrote about Italians and Danes, and Racine whose works are entirely set in the world of Greek myth. Thus:

The idea that Argentine poetry should abound in differential Argentine traits and Argentine local colour seems to me a mistake.

In Borges’s opinion, there are other elements of the Argentine character which distinguish their literature, among which he mentions: ‘ the Argentine’s reticence, his constraint’, ‘Argentine reserve, distrust and reticence, of the difficulty we have in making confessions, in revealing our intimate nature’. In demonstrating the unnecessity of having local colour, he cites the fact (observed by Gibbon) that there are no references to camels in the Koran. This is because Mohammed, as an Arab, so lived in the culture of camels that he didn’t even have to mention them. That is how local colour should be conveyed – by the subtlety of its absence. Thus when Borges reads Argentine nationalists prescribing that Argentine writers should write about the Argentine national scene using local colour and local words, he thinks they are dead wrong.

He goes on to speculate about the role of the Jews in European literature, and the Irish in English literature, both of which are over-represented, and it’s because they are outsiders and so not tied by tradition; they can be innovators.

For that reason I repeat that we should not be alarmed and that we should feel that our patrimony is the universe; we should essay all themes, and we cannot limit ourselves to purely Argentine subjects in order to be Argentine; for either being Argentine is an inescapable act of fate — and in that case we shall be so in all events — or being Argentine is a mere affectation, a mask.

(In Labyrinths this appears as rather a one-off work, but in fact Borges wrote extensively throughout his career on Argentine subject matter, including Argentine culture (‘History of the Tango’, ‘Inscriptions on Horse Wagons’), folklore (‘Juan Muraña’, ‘Night of the Gifts’), literature (‘The Argentine Writer and Tradition’, ‘Almafuerte’, ‘Evaristo Carriego’), and national concerns (‘Celebration of the Monster’, ‘Hurry, Hurry’, ‘The Mountebank’, ‘Pedro Salvadores’).

The Wall and the Books

A meditation on the fact that the Chinese emperor, Shih Huang Ti, who commissioned the building of the Great Wall but also ordered the burning of all the books and libraries. It allows Borges one of his characteristic series of dreamy speculations. It is recorded that Shih Huang Ti’s mother was a libertine whom he banished. Maybe burning the books was a symbolically Freudian attempt to abolish the entire past which contained his personal shame. Maybe the wall was a psychological wall to keep out his guilt. He also forbade death to be mentioned and sought an elixir for immortality, so maybe fire and wall were to keep death at bay. If he ordered the building of the wall first then the burning of the books, we have the image of an emperor who set out to create, gave up, and resigned himself to destroying; if the order is reverse, we have the image of an emperor who set out to destroy everything, gave up, and dedicated himself to endless building. Dreamy speculations:

Perhaps the wall was a metaphor, perhaps Shih Huang Ti sentenced those who worshiped the past to a task as immense, as gross and as useless as the past itself. Perhaps the wall was a challenge and Shih Huang Ti thought: “Men love the past and neither I nor my executioners can do anything against that love, but someday there will be a man who feels as I do and he will efface my memory and be my shadow and my mirror and not know it.” Perhaps Shih Huang Ti walled in his empire because he knew that it was perishable and destroyed the books because he understood that they were sacred books, in other words, books that teach what the entire universe or the mind of every man teaches. Perhaps the burning of the libraries and the erection of the wall are operations which in some secret way cancel each other.

A lazy Sunday afternoon of perhapses. The essay ends with a thunderclap, the notion that the way these two contrasting facts seem about to deliver some kind of revelation which never, in fact, arrives, the sense of a great meaning, which is never made clear:

this imminence of a revelation which does not occur is, perhaps, the aesthetic phenomenon.

The Fearful Sphere of Pascal

‘It may be that universal history is the history of a handful of metaphors.’ In which case he is examining one particular metaphor, that of the infinite sphere whose centre is nowhere, and pursues it through the works of Xenophanes of Colophon, Plato, Parmenides, Empedocles, Alain de Lille, the Romance of the Rose, Rabelais, Dante, Copernicus, Giordano Bruno, John Donne, John Milton, Glanville, Robert South, Pascal.

This very brief trot through the different expressions of the same metaphor suggest very strongly a sense of the rise and rise in optimism in human thought up to a kind of breakthrough in the Renaissance, summed up in Bruno’s attitude, which then crumbles into the sense of fear and isolation expressed by Pascal. I.e. this tiny essay gives a powerful sense of the changing moods and contexts of Western civilisation.

Partial Magic in the Quixote

It starts by asserting that Cervantes set out to write an utterly disenchanted account of the sordid reality of the Spain of his day yet certain moments of magic and romance nonetheless intrude; but this fairly simple point then unfolds into something much stranger as Borges zeroes in on the fact that in part two of Don Quixote the characters have read part one and comment on their own existence as characters. Borges then lists a number of other examples of fictions which appear within themselves such the Ramayana of Valmiki which, late on, features an appearance of the Ramayana of Valmiki as a major part of the plot. Similarly, on the 602nd night of the Thousand and One Nights, Scheherezade summarises the history of the king which includes his encounter with her and her telling of the stories which make up the nights, including the telling of the 602nd night, which includes the telling of the king’s own story, which includes his meeting with her and her telling of all the stories over again, including the telling of the 602nd night, and so on, forever.

What is it that intrigues and disturbs us about these images of infinite recursion?

I believe I have found the reason: these inversions suggest that if the characters of a fictional work can be readers or spectators, we, its readers or spectators, can be fictitious.

Valéry as Symbol

This brief note appears to be an obituary for the French poet Paul Valéry who died in 1945. Borges takes the surprising tack of comparing the French poet with the American poet Walt Whitman. On the face of it no two figures could be more different, Whitman loud, brash, confident, chaotic, contradictory, is morning in America, while Valéry, careful, sensitive, discreet, reflects the ‘delicate twilight’ of Europe. What they have in common is they created fictional images of themselves, made themselves symbolic of particular approaches.

Paul Valéry leaves us at his death the symbol of a man infinitely sensitive to every phenomenon and for whom every phenomenon is a stimulus capable of provoking an infinite series of thoughts.. Of a man whose admirable texts do not exhaust, do not even define, their all-embracing possibilities. Of a man who, in an age that worships the chaotic idols of blood, earth and passion, preferred always the lucid pleasures of thought and the secret adventures of order.

Kafka and His Precursors

A sketch at identifying precursors of Kafka’s ‘atrocious thought’, Borges finds precursors in Zeno’s paradoxes; in the ninth century Chinese writer, Han Yu; Kierkegaard; a poem by Browning; a short story by Léon Bloy; and one by Lord Dunsany. We would never have noticed the Kafkaesque in all these texts had Kafka not created it. Thus each author modifies our understanding of all previous writing.

The fact is that every writer creates his own precursors. His work modifies our conception of the past, as it will modify the future.

Avatars of the Tortoise

There is a concept which corrupts and upsets all others. I refer not to Evil, whose limited realm is that of ethics; I refer to the infinite.

He tells us that he once meditated a Biography of the Infinite but it would have taken forever to write. (Borges did in fact publish Historia de la eternidad in 1936.) Instead he gives us this fragment, a surprisingly thorough and mathematically-minded meditation on the second paradox of Zeno, the tortoise and Achilles. It is an intimidating trot through philosophers from the ancient Greek to F.H. Bradley and Bertrand Russell, in each one finding reformulations of the same problem in logic and various ways round it.

Only in the concluding paragraph does it become a bit more accessible when Borges brings out the meaning of Idealistic philosophy, that the world may be entirely the product of our minds and, as so often, ends on a bombshell of an idea:

We (the undivided divinity operating within us) have dreamt the world. We have dreamt it as firm, mysterious, visible, ubiquitous in space and durable in time; but in its architecture we have allowed tenuous and eternal crevices of unreason which tell us it is false.

In this view, Zeno’s paradoxes are among a putative small collection of problems or paradoxes or unnerving insights which are like cracks in the surface of the world we have made, cracks which gives us a glimpse of the utterly fictitious nature of ‘reality’.

The Mirror of Enigmas

A note on the verse from the Bible, First Letter to the Corinthians 13:12 in which Saint Paul writes: ‘For now we see through a glass, darkly; but then face to face: now I know in part; but then shall I know even as also I am known.’ He considers half a dozen meditations on it by the author Léon Bloy which I found obscure. I preferred the final passage where he describes the thinking underlying the intellectual activity of the Cabbalists:

Bloy did no more than apply to the whole of Creation the method which the Jewish Cabalists applied to the Scriptures. They thought that a work dictated by the Holy Spirit was an absolute text: in other words, a text in which the collaboration of chance was calculable as zero. This portentous premise of a book impenetrable to contingency, of a book which is a mechanism of infinite purposes, moved them to permute the scriptural words, add up the numerical value of the letters, consider their form, observe the small letters and capitals, seek acrostics and anagrams and perform other exegetical rigours which it is not difficult to ridicule. Their excuse is that nothing can be contingent in the work of an infinite mind

A Note on (toward) Bernard Shaw

A book is more than a verbal structure or series of verbal structures; it is the dialogue it establishes with its reader and the intonation it imposes upon his voice and the changing and durable images it leaves in his memory. This dialogue is infinite… Literature is not exhaustible, for the sufficient and simple reason that no single book is. A book is not an isolated being: it is a relationship, an axis of innumerable relationships…

I didn’t quite understand the thrust of this essay which begins by refuting the notion that literature is purely a game, and asserts that it involves and tone of voice and relationship with a reader, and then seems to go on to say that this is in some measure proven by the works of George Bernard Shaw whose philosophy may be derivative (Butler and Schopenhauer) but whose prolific invention of character is unprecedented in his time. The sardonic Irishman is an odd choice for the sly Argentinian to single out for praise.

A New Refutation of Time

Consists of two essays written in the 1940s. They are complex and hard to follow but I think he begins with the philosophical doctrine of Idealism which claims the human mind consists of a succession of sense perceptions and doesn’t require there to be a ‘real world’ out there, behind them all. Borges is, I think, trying to go one step further and assert that there need not be a succession of sense perceptions, there is no logical necessity for these impressions to be in the series which we call time. There is only the present, we can only exist in the present, therefore there is no time.

Parables

A series of very short thoughts, images, moments or insights which inspire brief narratives pregnant with meaning or symbolism. Kafka, of course, also wrote modern parables, parables with no religious import but fraught with psychological meaning.

Inferno, 1, 32

God sends a leopard kept in a cage in late 13th century Italy a dream in which he explains that his existence, his life history and his presence in the zoo are all necessary so that the poet Dante will see him and place him at the opening of his poem, The Divine Comedy.

Paradiso, XXXI, 108

Who of us has never felt, while walking through the twilight or writing a date from his past, that something infinite had been lost?

Maybe the mysterious thing which St Paul and the mystics saw and could not communicate appears to all of us every day, in the face of the street lottery ticket seller. Perhaps the face of Jesus was never recorded so that it could become the face of all of us.

Ragnarök

He has a dream. He was in the School of Philosophy and Letters chatting with friends when a group breaks free from the mob below to cries of ‘The gods! The gods’ who take up their place on the dais after centuries of exile. But during that time they have become rough and inhuman, they cannot actually talk but squeak and grunt.

Centuries of fell and fugitive life had atrophied the human element in them; the moon of Islam and the cross of Rome had been implacable with these outlaws. Very low foreheads, yellow teeth, stringy mulatto or Chinese moustaches and thick bestial lips showed the degeneracy of the Olympian lineage. Their clothing corresponded not to a decorous poverty but rather to the sinister luxury of the gambling houses and brothels of the Bajo. A carnation bled crimson in a lapel and the bulge of a knife was outlined beneath a close-fitting jacket. Suddenly we sensed that they were playing their last card, that they were cunning, ignorant and cruel like old beasts of prey and that, if we let ourselves be overcome by fear or pity, they would finally destroy us. We took out our heavy revolvers (all of a sudden there were revolvers in the dream) and joyfully killed the Gods.

Parable of Cervantes and the Quixote

How could Miguel de Cervantes ever have guessed that his attempt to mock and undermine the glorious myths of the Age of Chivalry in his fictitious character, Don Quixote, would itself become a larger-than-life myth? (Well, anyone who has studied a bit of human nature and knows that humans are the myth-making species, constantly rounding out narratives, creating stories which explain everything in which larger-than-life figures either cause all evil or all good.)

The Witness

Borges imagines the last pagan Anglo-Saxon, the last eye-witness of the sacrifices to the pagan gods, living on into the new age of Christianity. What memories and meanings will be lost at his death? Which makes him reflect on what will be lost when he himself dies.

A Problem

A very abstruse problem: Cervantes derives Don Quixote from an Arab precursor, the Cide Hamete Benengeli. Imagine a scrap of manuscript is discovered in which his knightly hero discovers that in one of his fantastical conflicts he has actually killed a man. How would Quixote respond? And Borges imagines four possible responses.

Borges and I

The narrator, Borges, speculates about the other Borges. On a first reading I take this to be the Borges of literature, the Borges who both writes the stories and is conjured into existence by the stories, who is not the same as the flesh and blood Borges who walks the streets.

Little by little, I am giving over everything to him, though I am quite aware of his perverse custom of falsifying and magnifying things

Everything and Nothing

A moving and beautiful meditation on the life of William Shakespeare which paints him as a hollow man, plagued by his own emptiness, who seeks to fill it with books, then with sex with an older woman (marriage to Anne Hathaway), moving to the big city, and involvement in about the most hurly-burly of professions, acting, before someone suggests he writes plays as well as acting in them, and he fills his soul with hundreds of characters, giving them undreamed-of speeches and feelings, before, an exhausted middle aged man he retires back to his provincial birthplace, and renounces all poetry for the gritty reality of lawsuits and land deals before dying young.

In a fantastical coda, he arrives in heaven and complains to God that all he wants is to have an identity, to be a complete man instead of a hollow man, but God surprises him with his reply.

After dying he found himself in the presence of God and told Him: ‘I who have been so many men in vain want to be one and myself.’ The voice of the Lord answered from a whirlwind: ‘Neither am I anyone; I have dreamt the world as you dreamt your work, my Shakespeare, and among the forms in my dream are you, who like myself are many and no one.’


Labyrinths

A labyrinth is a structure compounded to confuse men; its architecture, rich in symmetries, is subordinated to that end. (The Immortal)

The choice of this word for the title of the volume is no accident. The metaphor of the labyrinth, referring to endless tangles of intellectual speculation, crops up in most of the stories and many of the essays. It is a founding metaphor of his work.

  • Tlön is surely a labyrinth, but it is a labyrinth devised by men, a labyrinth destined to be deciphered by men.
  • Haslam has also published A General History of Labyrinths
  • I have some understanding of labyrinths: not for nothing am I the great grandson of that Ts’ui Pên who was governor of Yunnan and who renounced worldly power in order to write a novel that might be even more populous than the Hung Lu Meng and to construct a labyrinth in which all men would become lost.
  • I thought of a labyrinth of labyrinths, of one sinuous spreading labyrinth that would encompass the past and the future and in some way involve the stars
  • Once initiated in the mysteries of Baal, every free man automatically participated in the sacred drawings, which took place in the labyrinths of the god every sixty nights (Babylon)
  • Another [book] (very much consulted in this area) is a mere labyrinth of letters (Babel)
  • He is rescued from these circular labyrinths by a curious finding, a finding which then sinks him into other, more inextricable and heterogeneous labyrinths (Theme of the Traitor and the Hero)
  • I felt that the world was a labyrinth, from which it was impossible to flee… (Death and the Compass)
  • On those nights I swore by the God who sees with two faces and by all the gods of fever and of the mirrors to weave a labyrinth around the man who had imprisoned my brother (Death and the Compass)
  • Meticulously, motionlessly, secretly, he wrought in time his lofty, invisible labyrinth (The Secret Miracle)
  • Intolerably, I dreamt of an exiguous and nitid labyrinth: in the center was a water jar; my hands almost touched it, my eyes could see it, but so intricate and perplexed were the curves that I knew I would die before reaching it. (The Immortal)
  • There were nine doors in this cellar; eight led to a labyrinth that treacherously returned to the same chamber; the ninth (through another labyrinth) led to a second circular chamber equal to the first. (The Immortal)
  • You are not lighting a pyre, you are lighting a labyrinth of flames. (The Theologians)

The most labyrinthine story is The Garden of Forking Paths in which the word occurs 18 times.

The labyrinth is a metaphor for the mind and the way it never stops speculating, creating unending streams of interpretation, of our lives, of the world, of each other, of everything, each more entrancing and futile than the one before (among which are ‘the intimate delights of speculative theology’). Thus many of his ‘stories’ feature hardly any characters, events or dialogue – all the energy goes toward capturing the beguiling, phosphorescent stream-of-ideas of an extremely learned, religio-philosophical, fantastical mind:

I thought that Argos and I participated in different universes; I thought that our perceptions were the same, but that he combined them in another way and made other objects of them; I thought that perhaps there were no objects for him, only a vertiginous and continuous play of extremely brief impressions. I thought of a world without memory, without time; I considered the possibility of a language without nouns, a language of impersonal verbs or indeclinable epithets. (The Immortal)

And this endless stream of ideas reflects the way a mature world is full of infinite iterations of any given object. Looking at a coin in his hand:

I reflected that every coin in the world is a symbol of those famous coins which glitter in history and fable. I thought of Charon’s obol; of the obol for which Belisarius begged; of Judas’ thirty coins; of the drachmas of Laï’s, the famous courtesan; of the ancient coin which one of the Seven Sleepers proffered; of the shining coins of the wizard in the 1001 Nights, that turned out to be bits of paper; of the inexhaustible penny of Isaac Laquedem; of the sixty thousand pieces of silver, one for each line of an epic, which Firdusi sent back to a king because they were not of gold; of the doubloon which Ahab nailed to the mast; of Leopold Bloom’s irreversible florin; of the louis whose pictured face betrayed the fugitive Louis XVI near Varennes. (The Zahir)

And:

Money is abstract, I repeated; money is the future tense. It can be an evening in the suburbs, or music by Brahms; it can be maps, or chess, or coffee; it can be the words of Epictetus teaching us to despise gold; it is a Proteus more versatile than the one on the isle of Pharos. It is unforeseeable time, Bergsonian time, not the rigid time of Islam or the Porch.

Everything relates to everything else. Everything is a symbol of everything else, including the most profound categories of thought, hundreds, thousands of which have been dreamt up by the centuries full of metaphysicians and mystics. Anything can stand for anything else and that is, or should be, the freedom of literature, showing us how the infinite nature of human thought can liberate us, at every moment.

Tennyson once said that if we could understand a single flower, we should know what we are and what the world is. Perhaps he meant that there is no fact, however insignificant, that does not involve universal history and the infinite concatenation of cause and effect. Perhaps he meant that the visible world is implicit in every phenomenon, just as the will, according to Schopenhauer, is implicit in every subject… (The Zahir)

Or perhaps something else again, and something else again, and on forever, as long as we breathe, as long as we have consciousness, which consists of impressions, connections, moods, feelings and thoughts endlessly unfurling. Hence his interest in The Infinite, which is the subject of many of the stories (The Library of Babel) and the essay on Achilles and the tortoise which examines the infinitely recursive nature of intelligence. Speaking of the paradox, he writes:

The historical applications do not exhaust its possibilities: the vertiginous regressus in infinitum is perhaps applicable to all subjects. To aesthetics: such and such a verse moves us for such and such a reason, such and such a reason for such and such a reason…

And so on, forever.

Labyrinths as a labyrinth

I began to note how certain names and references recur in many of the stories, for example the name and works of Kafka or the paradox of Achilles and the tortoise, Schopenhauer’s notion of the world as a fantasy, Spinoza’s that all things long to persist as themselves – when it occurred to me that these references and motifs which recur across so many stories and essays themselves create a matrix or web which links the texts subterraneanly, so to speak, and themselves create a kind of labyrinth out of the text of Labyrinths. That the totality of the book Labyrinths is itself a labyrinth.

And, rereading that definition – ‘A labyrinth is a structure compounded to confuse men’ – maybe the enjoyment of this awesome book comes from savouring pleasurable confusions; maybe it is about entering a world of carefully controlled and contrived intellectual bewilderments.

The Borgesian

There’s an adjective, apparently, Borgesian, which means: ‘reminiscent of elements of Borges’ stories and essays, especially labyrinths, mirrors, reality, identity, the nature of time, and infinity’.

In his preface, André Maurois, in an attempt to convey the sense Borges’s stories give us of a vast erudition, says that Borges has read everything, but this isn’t quite true. His fictions very cannily give the impression that he has read widely, but it becomes clear fairly quickly that he has read widely in a very particular kind of text, in a certain kind of semi-mystical philosophy and metaphysics, often venturing from the fairly reputable works of Berkeley or Hume or Schopenhauer out into the arcane and mysterious byways of Christian and Islamic and Judaic theology, with the occasional excursion into the wisdom of Chinese magi.

These attributes – the combination of reputable Western philosophers with obscure religious mystics, and the casual mingling of Western texts with dicta from the Middle East or China – are exemplified in probably most famous of all Borges’s stories, Tlön, Uqbar, Orbis Tertius. Here’s a complete list of all the books and ideas referred to in just this one short essay:

Books

  • The Anglo-American Cyclopaedia (New York, 1917)
  • Ritter’s Erdkunde
  • Justus Perthes’ atlases
  • Silas Haslam: History of the Land Called Uqbar (1874)
  • Silas Haslam: A General History of Labyrinths
  • Lesbare und lesenswerthe Bemerkungen über das Land Ukkbar in Klein-Asien (1641) by Johannes Valentinus Andreä
  • Thomas De Quincey (Writings, Volume XIII)
  • Bertrand Russell: The Analysis of Mind (1921)
  • Schopenhauer: Parerga und Paralipomena (1851)
  • Hydriotaphia, Urn Burial, or a Discourse of the Sepulchral Urns lately found in Norfolk by Sir Thomas Browne (1658)

References

  • the Gnostic philosophers’ belief that the world is a pale parody of the real Creation
  • the Islamic tradition of the marvellous Night of Nights
  • David Hume’s comments on the philosophy of George Berkeley
  • Meinong’s theory of a subsistent world
  • Spinoza’s attribution to the Almighty of the attributes of time and extension
  • a heresiarch of the eleventh century
  • Zeno’s paradoxes
  • The Tao Te Ching
  • The 1001 Nights
  • hermetic philosophy

And then there are the hoaxes for which Borges acquired quite a reputation. Silas Haslam does not exist, is merely a fictional author and, scattered throughout these 40 texts, among the pedantic footnotes citing genuine works of philosophy or theology, are scattered other fictional authors, thinkers and ideas. In Borges’s hands the worlds of fiction and ‘reality’ meet and mingle on equal terms. They are, after all, situated in the realm of discourse, and can there be anything more imaginary than that?


Related links

Borges reviews

A Brief History of Time: From the Big Bang to Black Holes by Stephen Hawking (1988)

The whole history of science has been the gradual realisation that events do not happen in an arbitrary manner, but that they reflect a certain underlying order. (p.122)

This book was a publishing phenomenon when it was published in 1988. Nobody thought a book of abstruse musings about obscure theories of cosmology would sell, but it became a worldwide bestseller, selling more than 10 million copies in 20 years. It was on the London Sunday Times bestseller list for more than five years and was translated into 35 languages by 2001. So successful that Hawking went on to write seven more science books on his own, and co-author a further five.

Accessible As soon as you start reading you realise why. From the start is it written in a clear accessible way and you are soon won over to the frank, sensible, engaging tone of the author. He tells us he is going to explain things in the simplest way possible, with an absolute minimum of maths or equations (in fact, the book famously includes only one equation E = mc²).

Candour He repeatedly tells us that he’s going to explain things in the simplest possible way, and the atmosphere is lightened when Hawking – by common consent one of the great brains of our time – confesses that he has difficulty with this or that aspect of his chosen subject. (‘It is impossible to imagine a four-dimensional space. I personally find it hard enough to visualise three-dimensional space!’) We are not alone in finding it difficult!

Historical easing Also, like most of the cosmology books I’ve read, it takes a deeply historical view of the subject. He doesn’t drop you into the present state of knowledge with its many accompanying debates i.e. at the deep end. Instead he takes you back to the Greeks and slowly, slowly introduces us to their early ideas, showing why they thought what they thought, and how the ideas were slowly disproved or superseded.

A feel for scientific change So, without the reader being consciously aware of the fact, Hawking accustoms us to the basis of scientific enquiry, the fundamental idea that knowledge changes, and from two causes: from new objective observations, often the result of new technologies (like the invention of the telescope which enabled Galileo to make his observations) but more often from new ideas and theories being worked out, published and debated.

Hawking’s own contributions There’s also the non-trivial fact that, from the mid-1960s onwards, Hawking himself has made a steadily growing contribution to some of the fields he’s describing. At these points in the story, it ceases to be an objective history and turns into a first-person account of the problems as he saw them, and how he overcame them to develop new theories. It is quite exciting to look over his shoulder as he explains how and why he came up with the new ideas that made him famous. There are also hints that he might have trodden on a few people’s toes in the process, for those who like their science gossipy.

Thus it is that Hawking starts nice and slow with the ancient Greeks, with Aristotle and Ptolemy and diagrams showing the sun and other planets orbiting round the earth. Then we are introduced to Copernicus, who first suggested the planets orbit round the sun, and so on. With baby steps he takes you through the 19th century idea of the heat death of the universe, on to the discovery of the structure of the atom at the turn of the century, and then gently introduces you to Einstein’s special theory of relativity of 1905. (The special theory of relativity doesn’t take account of gravity, the general theory of relativity of 1915, does, take account of gravity).

Chapter 1 Our Picture of the Universe (pp.1-13)

Aristotle thinks earth is stationary. Calculates size of the earth. Ptolemy. Copernicus. In 1609 Galileo starts observing Jupiter using the recently invented telescope. Kepler suggests the planets move in ellipses not perfect circles. 1687 Isaac newton publishes Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) ‘probably the most important single work ever published in the physical sciences’, among many other things postulating a law of universal gravity. One implication of Newton’s theory is that the universe is vastly bigger than previously conceived.

In 1823 Heinrich Olbers posited his paradox which is, if the universe is infinite, the night sky out to be as bright as daylight because the light from infinite suns would reach us. Either it is not infinite or it has some kind of limit, possibly in time i.e. a beginning. The possible beginning or end of the universe were discussed by Immanuel Kant in his obscure work A Critique of Pure Reason  (1781). Various other figures debated variations on this theme until in 1929 Edwin Hubble made the landmark observation that, wherever you look, distant galaxies are moving away from us i.e. the universe is expanding. Working backwards from this observation led physicists to speculate that the universe was once infinitely small and infinitely dense, in a state known as a singularity, which must have exploded in an event known as the big bang.

He explains what a scientific theory is:

A theory is just a model of the universe, or a restricted part of it, and a set of rules that relate quantities in the model to observations that we make… A theory is a good theory if it satisfies two requirements: it must accurately describe a large class of observations on the basis of a model that contains only a few arbitrary elements, and it must make definite predictions about the results of future observations.

A theory is always provisional. The more evidence proving it, the stronger it gets. But it only takes one good negative observation to disprove a theory.

Today scientists describe the universe in terms of two basic partial theories – the general theory of relativity and quantum mechanics. They are the great intellectual achievements of the first half of this century.

But they are inconsistent with each other. One of the major endeavours of modern physics is to try and unite them in a quantum theory of gravity.

Chapter 2 Space and Time (pp.15-34)

Aristotle thought everything in the universe was naturally at rest. Newton disproved this with his first law – whenever a body is not acted on by any force it will keep on moving in a straight line at the same speed. Newton’s second law stats that, When a body is acted on by a force it will accelerate or change its speed at a rate that is proportional to the force. Newton’s law of gravity states that every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. But like Aristotle, Newton believed all the events he described took place in a kind of big static arena named absolute space, and that time was an absolute constant. The speed of light was also realised to be a constant. In 1676 Danish astronomer Ole Christensen estimated the speed of light to be 140,000 miles per second. We now know it is 186,000 miles per second. In the 1860s James Clerk Maxwell unified the disparate theories which had been applied to magnetism and electricity.

In 1905 Einstein published his theory of relativity. It is derived not from observation but from Einstein working through in his head the consequences and shortcomings of the existing theories. Newton had posited a privileged observer, someone outside the universe who was watching it as if a play on a stage. From this privileged position a number of elements appeared constant, such as time.

Einstein imagines a universe in which there is no privileged outside point of view. We are all inside the universe and all moving. The theory threw up a number of consequences. One is that energy is equal to mass times the speed of light squared, or E = mc². Another is that nothing may travel faster than the speed of light. Another is that, as an object approaches the speed of light its mass increases. One of its most disruptive ideas is that time is relative. Different observes, travelling at different speeds, will see a beam of light travel take different times to travel a fixed distance. Since Einstein has made it axiomatic that the speed of light is fixed, and we know the distance travelled by the light is fixed, then time itself must appear different to different observers. Time is something that can change, like the other three dimensions. Thus time can be added to the existing three dimensions to create space-time.

The special theory of relativity was successful in explaining how the speed of light appears the same to all observers, and describing what happens to things when they move close to the speed of light. But it was inconsistent with Newton’s theory of gravity which says objects attract each other with a force related to the distance between them. If you move on of the objects the force exerted on the other object changes immediately. This cannot be if nothing can travel faster than the speed of light, as the special theory of relativity postulates. Einstein spent the ten or so years from 1905 onwards attempting to solve this difficulty. Finally, in 1915, he published the general theory of relativity.

The revolutionary basis of this theory is that space is not flat, a consistent  continuum or Newtonian stage within which events happen and forces interact in a sensible way. Space-time is curved or warped by the distribution of mass or energy within it, and gravity is a function of this curvature. Thus the earth is not orbiting around the sun in a circle, it is following a straight line in warped space.

The mass of the sun curves space-time in such a way that although the earth follows a straight line in four-dimensional pace-time, it appears to us to move along a circular orbit in three-dimensional space. (p.30)

In fact, at a planetary level Einstein’s maths is only slightly different from Newton’s but it predicts a slight difference in the orbit of Mercury which observations have gone on to prove. Also, the general theory predicts that light will bend, following a straight line but through space that is warped or curved by gravity. Thus the light from a distant star on the far side of the sun will bend as it passes close to the sun due to the curvature in space-time caused by the sun’s mass. And it was an expedition to West Africa in 1919 to observe an eclipse, which showed that light from distant stars did in fact bend slightly as it passed the sun, which helped confirm Einstein’s theory.

Newton’s laws of motion put an end to the idea of absolute position in space. The theory of relativity gets rid of absolute time.

Hence the thought experiment popularised by a thousand science fiction books that astronauts who set off in a space ship which gets anywhere near the speed of light will experience a time which is slower than the people they leave behind on earth.

In the theory of relativity there is no unique absolute time, but instead each individual has his own personal measure of time that depends on where he is and how he is moving. (p.33)

Obviously, since most of us are on planet earth, moving at more or less the same speed, everyone’s personal ‘times’ coincide. Anyway, the key central implication of Einstein’s general theory of relativity is this:

Before 1915, space and time were thought of as a fixed arena in which events took place, but which was not affected by what happened in it. This was true even of the special theory of relativity. Bodies moved, forces attracted and repelled, but time and space simply continued, unaffected. It was natural to think that space and time went on forever.

the situation, however, is quite different in the general theory of relativity. Space and time are now dynamic quantities. : when a body moves, or a force acts, it affects the curvature of space and time – and in turn the structure of space-time affects the way in which bodies move and forces act. Space and time not only affect but also are affected by everything that happens in the universe. (p.33)

This view of the universe as dynamic and interacting, by demolishing the old eternal static view, opened the door to a host of new ways of conceiving how the universe might have begun and might end.

Chapter 3 The Expanding Universe (pp.35-51)

Our modern picture of the universe dates to 1924 when American astronomer Edwin Hubble demonstrated that ours is not the only galaxy. We now know the universe is home to some hundred million galaxies, each containing some hundred thousand million stars. We live in a galaxy that is about one hundred thousand light-years across and is slowly rotating. Hubble set about cataloguing the movement of other galaxies and in 1929 published his results which showed that they are all moving away from us, and that, the further away a galaxy is, the faster it is moving.

The discovery that the universe is expanding was one of the great intellectual revolutions of the twentieth century. (p.39)

From Newton onwards there was a universal assumption that the universe was infinite and static. Even Einstein invented a force he called ‘the cosmological constant’ in order to counter the attractive power of gravity and preserve the model of a static universe. It was left to Russian physicist Alexander Friedmann to seriously calculate what the universe would look like if it was expanding.

In 1965 two technicians, Arno Penzias and Robert Wilson, working at Bell Telephone Laboratories discovered a continuous hum of background radiation coming from all parts of the sky. This echoed the theoretical work being done by two physicists, Bob Dicke and Jim Peebles, who were working on a suggestion made by George Gamow that the early universe would have been hot and dense. They posited that we should still be able to see the light from this earliest phase but that it would, because the redshifting, appear as radiation. Penzias and Wilson were awarded the Nobel Prize in 1987.

How can the universe be expanding? Imagine blowing up a balloon with dots (or little galaxies) drawn on it: they all move apart from each other and the further apart they are, the larger the distance becomes; but there is no centre to the balloon. Similarly the universe is expanding but not into anything. There is no outside. If you set out to travel to the edge you would find no edge but instead find yourself flying round the periphery and end up back where you began.

There are three possible states of a dynamic universe. Either 1. it will expand against the contracting force of gravity until the initial outward propulsive force is exhausted and gravity begins to win; it will stop expanding, and start to contract. Or 2. it is expanding so fast that the attractive, contracting force of gravity never wins, so the universe expands forever and matter never has time to clump together into stars and planets. Or 3. it is expanding at just the right speed to escape collapsing back in on itself, but but so fast as to make the creation of matter impossible. This is called the critical divide. Physicists now believe the universe is expanding at just around the value of the critical divide, though whether it is just under or just above (i.e. the universe will eventually cease expanding, or not) is not known.

Dark matter We can calculate the mass of all the stars and galaxies in the universe and it is a mystery that our total is only about a hundredth of the mass that must exist to explain the gravitational behaviour of stars and galaxies. In other words, there must a lot of ‘dark matter’ which we cannot currently detect in order for the universe to be shaped the way it is.

So we don’t know what the likely future of the universe is (endless expansion or eventual contraction) but all the Friedmann models do predict that the universe began in an infinitely dense, infinitely compact, infinitely hot state – the singularity.

Because mathematics cannot really handle infinite numbers, this means that the general theory of relativity… predicts that there is a point in the universe where the theory itself breaks down… In fact, all our theories of science are formulated on the assumption that space-time is smooth and nearly flat, so they break down at the big bang singularity, where the curvature of space-time is infinite. (p.46)

Opposition to the theory came from Hermann Bondi, Thomas Gold and Fred Hoyle who formulated the steady state theory of the universe i.e. it has always been and always will be. All that is needed to explain the slow expansion is the appearance of new particles to keep it filled up, but the rate is very low (about one new particle per cubic kilometre per year). They published it in 1948 and worked through all its implications for the next few decades, but it was killed off as a theory by the 1965 observations of the cosmic background radiation.

He then explains the process whereby he elected to do a PhD expanding Roger Penrose’s work on how a dying star would collapse under its own weight to a very small size. The collaboration resulted in a joint 1970 paper which proved that there must have been a big bang, provided only that the theory of general relativity is correct, and the universe contains as much matter as we observe.

If the universe really did start out as something unimaginably small then, from the 1970s onwards, physicists turned their investigations to what happens to matter at microscopic levels.

Chapter 4 The Uncertainty Principle (pp.53-61)

1900 German scientist Max Planck suggests that light, x-rays and other waves can only be emitted at an arbitrary wave, in packets he called quanta. He theorised that the higher the frequency of the wave, the more energy would be required. This would tend to restrict the emission of high frequency waves. In 1926 Werner Heisenberg expanded on these insights to produce his Uncertainty Principle. In order to locate a particle in order to measure its position and velocity you need to shine a light on it. One has to use at least one quantum of energy. However, exposing the particle to this quantum will disturb the velocity of the particle.

In other words, the more accurately you try to measure the position of the particle, the less accurately you can measure its speed, and vice versa. (p.55)

Heisenberg showed that the uncertainty in the position of the particle times the uncertainty in its velocity times the mass of the particle can never be smaller than a certain quantity, which is known as Planck’s constant. For the rest of the 1920s Heisenberg, Erwin Schrödinger and Paul Dirac reformulated mechanics into a new theory titled quantum mechanics. In this theory particles no longer have separate well-defined positions and velocities, instead they have a general quantum state which is a combination of position and velocity.

Quantum mechanics introduces an unavoidable element of unpredictability or randomness into science. (p.56)

Also, particles can no longer be relied on to be particles. As a result of Planck and Heisenberg’s insights, particles have to be thought of as sometimes behaving like waves, sometimes like particles. In 1913 Niels Bohr had suggested that electrons circle round a nucleus at certain fixed points, and that it takes energy to dislodge them from these optimum orbits. Quantum theory helped explain Bohr’s theory by conceptualising the circling electrons not as particles but as waves. If electrons are waves, as they circle the nucleus, their wave lengths would cancel each other out unless they are perfect numbers. The frequency of the waves have to be able to circle the nucleus in perfect integers. This defines the height of the orbits electrons can take.

Chapter 5 Elementary Particles and Forces of Nature (pp.63-79)

A chapter devoted to the story of how we’ve come to understand the world of sub-atomic particles. Starting (as usual) with Aristotle and then fast-forwarding through Galton, Einstein’s paper on Brownian motion, J.J. Thomson’s discovery of electrons, and, in 1911, Ernest Rutherford’s demonstration that atoms are made up of tiny positively charged nucleus around which a number of tiny positively charged particles, electrons, orbit. Rutherford thought the nuclei contained ‘protons’, which have a positive charge and balance out the negative charge of the electrons. In 1932 James Chadwick discovered the nucleus contains neutrons, same mass as the proton but no charge.

In 1965 quarks were discovered by Murray Gell-Mann. In fact scientists went on to discover six types, up, down, strange, charmed, bottom and top quarks. A proton or neutron is made up of three quarks.

He explains the quality of spin. Some particles have to be spin twice to return to their original appearance. They have spin 1/2. All the matter we can see in the universe has the spin 1/2. Particles of spin 0, 1, and 2 give rise to the forces between the particles.

Pauli’s exclusionary principle: two similar particles cannot exist in the same state, they cannot have the same position and the same velocity. The exclusionary principle is vital since it explains why the universe isn’t a big soup of primeval particles. The particles must be distinct and separate.

In 1928 Paul Dirac explained why the electron must rotate twice to return to its original position. He also predicted the existence of the positron to balance the electron. In 1932 the positron was discovered and Dirac was awarded a Nobel Prize.

Force carrying particles can be divided into four categories according to the strength of the force they carry and the particles with which they interact.

  1. Gravitational force, the weakest of the four forces by a long way.
  2. The electromagnetic force interacts with electrically charged particles like electrons and quarks.
  3. The weak nuclear force, responsible for radioactivity. In findings published in 1967 Abdus Salam and Steven Weinberg suggested that in addition to the photon there are three other spin-1 particles known collectively as massive vector bosons. Initially disbelieved, experiments proved them right and they collected the Nobel Prize in 1979. In 1983 the team at CERN proved the existence of the three particles, and the leaders of this team also won the Nobel Prize.
  4. The strong nuclear force holds quarks together in the proton and neutron, and holds the protons and neutrons together in the nucleus. This force is believed to be carried by another spin-1 particle, the gluon. They have a property named ‘confinement’ which is that you can’t have a quark of a single colour, the number of quarks bound together must cancel each other out.

The idea behind the search for a Grand Unified Theory is that, at high enough temperature, all the particles would behave in the same way, i.e. the laws governing the four forces would merge into one law.

Most of the matter on earth is made up of protons and neutrons, which are in turn made of quarks. Why is there this preponderance of quarks and not an equal number of anti-quarks?

Hawking introduces us to the notion that all the laws of physics obey three separate symmetries known as C, P and T. In 1956 two American physicists suggested that the weak force does not obey symmetry C. Hawking then goes on to explain more about the obedience or lack of obedience to the rules of symmetry of particles at very high temperatures, to explain why quarks and matter would outbalance anti-quarks and anti-matter at the big bang in a way which, frankly, I didn’t understand.

Chapter 6 Black Holes (pp.81-97)

In a sense, all the preceding has been just preparation, just a primer to help us understand the topic which Hawking spent the 1970s studying and which made his name – black holes.

The term black hole was coined by John Wheeler in 1969. Hawking explains the development of ideas about what happens when a star dies. When a star is burning, the radiation of energy in the forms of heat and light counteracts the gravity of its mass. When it runs out of fuel, gravity takes over and the star collapses in on itself. The young Indian physicist Subrahmanyan Chandrasekhar calculated that a cold star with a mass of more than one and a half times the mass of our sin would not be able to support itself against its own gravity and contract to become a ‘white dwarf’ with a radius of a few thousand miles and a density of hundreds of tones per square inch.

The Russian Lev Davidovich Landau speculated that the same sized star might end up in a different state. Chandrasekhar had used Pauli’s exclusionary principle as applied to electrons i.e. calculated the smallest densest state the mass could reach assuming no electron can be in the place of any other electron. Landau calculated on the basis of the exclusionary principle repulsion operative between neutrons and protons. Hence his model is known as the ‘neutron star’, which would have a radius of only ten miles or so and a density of hundreds of millions of tonnes per cubic inch.

(In an interesting aside Hawking tells us that physics was railroaded by the vast Manhattan Project to build an atomic bomb, and then to build a hydrogen bomb, throughout the 1940s and 50s. This tended to sideline large-scale physics about the universe. It was only the development of a) modern telescopes and b) computer power, that revived interest in astronomy.)

A black hole is what you get when the gravity of a collapsing star becomes so high that it prevents light from escaping its gravitational field. Hawking and Penrose showed that at the centre of a black hole must be a singularity of infinite density and space-time curvature.

In 1967 the study of black holes was revolutionised by Werner Israel. He showed that, according to general relativity, all non-rotating black holes must be very simple and perfectly symmetrical.

Hawking then explains several variations on this theory put forward by Roger Penrose, Roy Kerr, Brandon Carter who proved that a hole would have an axis of symmetry. Hawking himself confirmed this idea. In 1973 David Robinson proved that a black hole had to have ‘a Kerr solution’. In other words, no matter how they start out, all black holes end up looking the same, a belief summed up in the pithy phrase, ‘A black hole has no hair’.

What is striking about all this is that it was pure speculation, derived entirely from mathematical models without a shred of evidence from astronomy.

Black holes are one of only a fairly small number of cases in the history of science in which a theory was developed in great detail as a mathematical model before there was any evidence from observations that it was correct. (p.92)

Hawking then goes on to list the best evidence we have for black holes, which is surprisingly thin. Since they are by nature invisible black holes can only be deduced by their supposed affect on nearby stars or systems. Given that black holes were at the centre of Hawking’s career, and are the focus of these two chapters, it is striking that there is, even now, very little direct empirical evidence for their existence.

(Eerily, as I finished reading A Brief History of Time, the announcement was made on 10 April 2019 that the first ever image has been generated of a black hole –

Theory predicts that other stars which stray close to a black hole would have clouds of gas attracted towards it. As this matter falls into the black hole it will a) be stripped down to basic sub-atomic particles b) make the hole spin. Spinning would make the hole acquire a magnetic field. The magnetic field would shoot jets of particles out into space along the axis of rotation of the hole. These jets should be visible to our telescopes.

First ever image of a black hole, captured the Event Horizon Telescope (EHT). The hole is 40 billion km across, and 500 million trillion km away

Chapter 7 Black Holes Ain’t So Black (pp.99-113)

Black holes are not really black after all. They glow like a hot body, and the smaller they are, the hotter they glow. Again, Hawking shares with us the evolution of his thinking on this subject, for example how he was motivated in writing a 1971 paper about black holes and entropy at least partly in irritation against another researcher who he felt had misinterpreted his earlier results.

Anyway, it all resulted in his 1973 paper which showed that a black hole ought to emit particles and radiation as if it were a hot body with a temperature that depends only on the black hole’s mass.

The reasoning goes thus: quantum mechanics tells us that all of space is fizzing with particles and anti-particles popping into existence, cancelling each other out, and disappearing. At the border of the event horizon, particles and anti-particles will be popping into existence as everywhere else. But a proportion of the anti-particles in each pair will be sucked inside the event horizon, so that they cannot annihilate their partners, leaving the positive particles to ping off into space. Thus, black holes should emit a steady stream of radiation!

If black holes really are absorbing negative particles as described above, then their negative energy will result in negative mass, as per Einstein’s most famous equation, E = mc² which shows that the lower the energy, the lower the mass. In other words, if Hawking is correct about black holes emitting radiation, then black holes must be shrinking.

Gamma ray evidence suggests that there might be 300 black holes in every cubic light year of the universe. Hawking then goes on to estimate the odds of detecting a black hole a) in steady existence b) reaching its final state and blowing up. Alternatively we could look for flashes of light across the sky, since on entering the earth’s atmosphere gamma rays break up into pairs of electrons and positrons. No clear sightings have been made so far.

(Threaded throughout the chapter has been the notion that black holes might come in two types: one which resulted from the collapse of stars, as described above. And others which have been around since the start of the universe as a function of the irregularities of the big bang.)

Summary: Hawking ends this chapter by claiming that his ‘discovery’ that radiation can be emitted from black holes was ‘the first example of a prediction that depended in an essential way on both the great theories of this century, general relativity and quantum mechanics’. I.e. it is not only an interesting ‘discovery’ in its own right, but a pioneering example of synthesising the two theories.

Chapter 8 The Origin and Fate of the Universe (pp.115-141)

This is the longest chapter in the book and I found it the hardest to follow. I think this is because it is where he makes the big pitch for His Theory, for what’s come to be known as the Hartle-Hawking state. Let Wikipedia explain:

Hartle and Hawking suggest that if we could travel backwards in time towards the beginning of the Universe, we would note that quite near what might otherwise have been the beginning, time gives way to space such that at first there is only space and no time. Beginnings are entities that have to do with time; because time did not exist before the Big Bang, the concept of a beginning of the Universe is meaningless. According to the Hartle-Hawking proposal, the Universe has no origin as we would understand it: the Universe was a singularity in both space and time, pre-Big Bang. Thus, the Hartle–Hawking state Universe has no beginning, but it is not the steady state Universe of Hoyle; it simply has no initial boundaries in time or space. (Hartle-Hawking state Wikipedia article)

To get to this point Hawking begins by recapping the traditional view of the ‘hot big bang’, i.e. the almost instantaneous emergence of matter from a state of infinite mass, energy and density and temperature.

This is the view first put forward by Gamow and Alpher in 1948, which predicted there would still be very low-level background radiation left over from the bang – which was then proved with the discovery of the cosmic background radiation in 1965.

Hawking gives a picture of the complete cycle of the creation of the universe through the first generation of stars which go supernova blowing out into space the heavier particles which then go into second generation stars or clouds of gas and solidify into things like planet earth.

In a casual aside, he gives his version of the origin of life on earth:

The earth was initially very hot and without an atmosphere. In the course of time it cooled and acquired an atmosphere from the emission of gases from the rocks. This early atmosphere was not one in which we could have survived. It contained no oxygen, but a lot of other gases that are poisonous to us, such as hydrogen sulfide. There are, however, other primitive forms of life that can flourish under such conditions. It is thought that they developed in the oceans, possibly as a result of chance combinations of atoms into large structures, called macromolecules, which were capable of assembling other atoms in the ocean into similar structures. They would thus have reproduced themselves and multiplied. In some cases there would have been errors in the reproduction. Mostly these errors would have been such that the new macromolecule could not reproduce itself and eventually would have been destroyed. However, a few of the errors would have produced new macromolecules that were even better at reproducing themselves. They would have therefore had an advantage and would have tended to replace the original macromolecules. In this way a process of evolution was started that led to the development of more and more complicated, self-reproducing organisms. The first primitive forms of life consumed various materials, including hydrogen sulfide, and released oxygen. This gradually changed the atmosphere to the composition that it has today and allowed the development of higher forms of life such as fish, reptiles, mammals, and ultimately the human race. (p.121)

(It’s ironic that he discusses the issue so matter-of-factly, demonstrating that, for him at least, the matter is fairly cut and dried and not worth lingering over. Because, of course, for scientists who’ve devoted their lives to the origins-of-life question it is far from over. It’s a good example of the way that every specialist thinks that their specialism is the most important subject in the world, the subject that will finally answer the Great Questions of Life whereas a) most people have never heard about the issues b) wouldn’t understand them and c) don’t care.)

Hawking goes on to describe chaotic boundary conditions and describe the strong and the weak anthropic principles. He then explains the theory proposed by Alan Guth of inflation i.e. the universe, in the first milliseconds after the big bang, underwent a process of enormous hyper-growth, before calming down again to normal exponential expansion. Hawking describes it rather differently from Barrow and Davies. He emphasises that, to start with, in a state of hypertemperature and immense density, the four forces we know about and the spacetime dimensions were all fused into one. They would be in ‘symmetry’. Only as the early universe cooled would it have undergone a ‘phase transition’ and the symmetry between forces been broken.

If the temperature fell below the phase transition temperature without symmetry being broken then the universe would have a surplus of energy and it is this which would have cause the super-propulsion of the inflationary stage. The inflation theory:

  • would allow for light to pass from one end of the (tiny) universe to the other and explains why all regions of the universe appear to have the same properties
  • explain why the rate of expansion of the universe is close to the critical rate required to make it expand for billions of years (and us to evolve)
  • would explain why there is so much matter in the universe

Hawking then gets involved in the narrative explaining how he and others pointed out flaws in Guth’s inflationary model, namely that the phase transition at the end of the inflation ended in ‘bubble’s which expanded to join up. But Hawking and others pointed out that the bubbles were expanding so fat they could never join up. In 1981 the Russian Andre Linde proposed that the bubble problem would be solved if  a) the symmetry broke slowly and b) the bubbles were so big that our region of the universe is all contained within a single bubble. Hawking disagreed, saying Linde’s bubbles would each have to be bigger than the universe for the maths to work out, and counter-proposing that the symmetry broke everywhere at the same time, resulting in the uniform universe we see today. Nonetheless Linde’s model became known as the ‘new inflationary model’, although Hawking considers it invalid.

[In these pages we get a strong whiff of cordite. Hawking is describing controversies and debates he has been closely involved in and therefore takes a strongly partisan view, bending over backwards to be fair to colleagues, but nonetheless sticking to his guns. In this chapter you get a strong feeling for what controversy and debate within this community must feel like.)

Hawking prefers the ‘chaotic inflationary model’ put forward by Linde in 1983, in which there is no phase transition or supercooling, but which relies on quantum fluctuations.

At this point he introduces four ideas which are each challenging and which, taken together, mark the most difficult and confusing part of the book.

First he says that, since Einstein’s laws of relativity break down at the moment of the singularity, we can only hope to understand the earliest moments of the universe in terms of quantum mechanics.

Second, he says he’s going to use a particular formulation of quantum mechanics, namely Richard Feynman’s idea of ‘a sum over histories’. I think this means that Feynman said that in quantum mechanics we can never know precisely which route a particle takes, the best we can do is work out all the possible routes and assign them probabilities, which can then be handled mathematically.

Third, he immediately points out that working with Feynman’s sum over histories approach requires the use of ‘imaginary’ time, which he then goes on to explain.

To avoid the technical difficulties with Feynman’s sum over histories, one must use imaginary time. (p.134)

And then he points out that, in order to use imaginary time, we must use Euclidean space-time instead of ‘real’ space-time.

All this happens on page 134 and was too much for me to understand. On page 135 he then adds in Einstein’s idea that the gravitational field us represented by curved space-time.

It is now that he pulls all these ideas together to assert that, whereas in the classical theory of gravity, which is based on real space-time there are only two ways the universe can behave – either it has existed infinitely or it had a beginning in a singularity at a finite point in time; in the quantum theory of gravity, which uses Euclidean space-time, in which the time direction is on the same footing as directions in space it is possible:

for space-time to be finite in extent and yet to have no singularities that formed a boundary or edge.

In Hawking’s theory the universe would be finite in duration but not have a boundary in time because time would merge with the other three dimensions, all of which cease to exist during and just after a singularity. Working backwards in time, the universe shrinks but it doesn’t shrink, as a cone does, to a single distinct point – instead it has a smooth round bottom with no distinct beginning.

The Hartle-Hawking no boundary Hartle and Hawking No-Boundary Proposal

The Hartle-Hawking no boundary Hartle and Hawking No-Boundary Proposal

Finally Hawking points out that this model of a no-boundary universe derived from a Feynman interpretation of quantum gravity does not give rise to all possible universes, but only to a specific family of universes.

One aspect of these histories of the universe in imaginary time is that none of them include singularities – which would seem to render redundant all the work Hawking had done on black holes in ‘real time’. He gets round this by saying that both models can be valid, but in order to demonstrate different things.

It is simply a matter of which is the more useful description. (p.139)

He winds up the discussion by stating that further calculations based on this model explain the two or three key facts about the universe which all theories must explain i.e. the fact that it is clumped into lumps of matter and not an even soup, the fact that it is expanding, and the fact that the background radiation is minutely uneven in some places suggesting very early irregularities. Tick, tick, tick – the no-boundary proposal is congruent with all of them.

It is a little mind-boggling, as you reach the end of this long and difficult chapter, to reflect that absolutely all of it is pure speculation without a shred of evidence to support it. It is just another elegant way of dealing with the problems thrown up by existing observations and by trying to integrate quantum mechanics with Einsteinian relativity. But whether it is ‘true’ or not, not only is unproveable but also is not really the point.

Chapter 9 The Arrow of Time (pp.143-153)

If Einstein’s theory of general relativity is correct and light always appears to have the same velocity to all observers, no matter what position they’re in or how fast they’re moving, THEN TIME MUST BE FLEXIBLE. Time is not a fixed constant. Every observer carries their own time with them.

Hawking points out that there are three arrows of time:

  • the thermodynamic arrow of time which obeys the Second Law of Thermodynamics namely that entropy, or disorder, increases – there are always many more disordered states than ordered ones
  • the psychological arrow of time which we all perceive
  • the cosmological arrow of time, namely the universe is expanding and not contracting

Briskly, he tells us that the psychological arrow of time is based on the thermodynamic one: entropy increases and our lives experience that and our minds record it. For example, human beings consume food – which is a highly ordered form of energy – and convert it into heat – which is a highly disordered form.

Hawking tells us that he originally thought that, if the universe reach a furthest extent and started to contract, disorder (entropy) would decrease, and everything in the universe would happen backwards. Until Don Page and Raymond Laflamme, in their different ways, proved otherwise.

Now he believes that the contraction would not occur until the universe had been almost completely thinned out and all the stars had died i.e. the universe had become an even soup of basic particles. THEN it would start to contract. And so his current thinking is that there would be little or no thermodynamic arrow of time (all thermodynamic processes having come to an end) and all of this would be happening in a universe in which human beings could not exist. We will never live to see the contraction phase of the universe. If there is a contraction phase.

Chapter 10: The Unification of Physics (pp.155-169)

The general theory of relativity and quantum mechanics both work well for their respective scales (stars and galaxies, sub-atomic particles) but cannot be made to mesh, despite fifty of more years of valiant attempts. Many of the attempts produce infinity in their results, so many infinities that a strategy has been developed called ‘renormalisation’ which gets rid of the infinities, although Hawking conceded is ‘rather dubious mathematically’.

Grand Unified Theories is the term applied to attempts to devise a theory (i.e. a set of mathematical formulae) which will take account of the four big forces we know about: electromagnetism, gravity, the strong nuclear force and the weak nuclear force.

In the mid-1970s some scientists came up with the idea of ‘supergravity’ which postulated a ‘superparticle’, and the other sub-atomic particles variations on the super-particle but with different spins. According to Hawking the calculations necessary to assess this theory would take so long nobody has ever done it.

So he moves onto string theory i.e. the universe isn’t made up of particles but of open or closed ‘strings’, which can join together in different ways to form different particles. However, the problem with string theory is that, because of the mathematical way they are expressed, they require more than four dimensions. A lot more. Hawking mentions anywhere from ten up to 26 dimensions. Where are all these dimensions? Well, strong theory advocates say they exist but are very very small, effectively wrapped up into sub-atomic balls, so that you or I never notice them.

Rather simplistically, Hawking lists the possibilities about a complete unified theory. Either:

  1. there really is a grand unified theory which we will someday discover
  2. there is no ultimate theory but only an infinite sequence of possibilities which will describe the universe with greater and greater, but finite accuracy
  3. there is no theory of the universe at all, and events will always seems to us to occur in a random way

This leads him to repeat the highfalutin’ rhetoric which all physicists drop into at these moments, about the destiny of mankind etc. Discovery of One Grand Unified Theory:

would bring to an end a long and glorious chapter in the history of humanity’s intellectual struggle to understand the universe. But it would also revolutionise the ordinary person’s understanding of the laws that govern the universe. (p.167)

I profoundly disagree with this view. I think it is boilerplate, which is a phrase defined as ‘used in the media to refer to hackneyed or unoriginal writing’.

Because this is not just the kind of phrasing physicists use when referring to the search for GUTs, it’s the same language biologists use when referring to the quest to understand how life derived from inorganic chemicals, it’s the same language the defenders of the large Hadron Collider use to justify spending billions of euros on the search for ever-smaller particles, it’s the language used by the guys who want funding for the Search for Extra-Terrestrial Intelligence), it’s the kind of language used by the scientists bidding for funding for the Human Genome Project.

Each of these, their defenders claim, is the ultimate most important science project, quest and odyssey ever,  and when they find the solution it will for once and all answer the Great Questions which have been tormenting mankind for millennia. Etc. Which is very like all the world’s religions claiming that their God is the only God. So a) there is a pretty obvious clash between all these scientific specialities which each claim to be on the brink of revealing the Great Secret.

But b) what reading this book and John Barrow’s Book of Universes convinces me is that i) we are very far indeed from coming even close to a unified theory of the universe and more importantly ii) if one is ever discovered, it won’t matter.

Imagine for a moment that a new iteration of string theory does manage to harmonise the equations of general relativity and quantum mechanics. How many people in the world are really going to be able to understand that? How many people now, currently, have a really complete grasp of Einsteinian relativity and Heisenbergian quantum uncertainty in their strictest, most mathematical forms? 10,000? 1000,000 earthlings?

If and when the final announcement is made who would notice, who would care, and why would they care? If the final conjunction is made by adapting string theory to 24 dimensions and renormalising all the infinities in order to achieve a multi-dimensional vision of space-time which incorporates both the curvature of gravity and the unpredictable behaviour of sub-atomic particles – would this really

revolutionise the ordinary person’s understanding of the laws that govern the universe?

Chapter 11 Conclusion (pp.171-175)

Recaps the book and asserts that his and James Hartle’s no-boundary model for the origin of the universe is the first to combine classic relativity with Heisenberg uncertainty. Ends with another rhetorical flourish of trumpets which I profoundly disagree with for the reasons given above.

If we do discover a complete theory, it should in time be understandable in broad principle by everyone, not just a few scientists. Then we shall all, philosophers, scientists, and just ordinary people, be able to take part in the discussion of the question of why it is that we and the universe exist. If we find the answer to that, it would be the ultimate triumph of human reason. (p.175)

Maybe I’m wrong, but I think this is a hopelessly naive view of human nature and culture. Einstein’s general theory has been around for 104 years, quantum mechanics for 90 years. Even highly educated people understand neither of them, and what Hawking calls ‘just ordinary people’ certainly don’t – and it doesn’t matter. 

Thoughts

Of course the subject matter is difficult to understand, but Hawking makes a very good fist of putting all the ideas into simple words and phrases, avoiding all formulae and equations, and the diagrams help a lot.

My understanding is that A Brief History of Time was the first popular science to put all these ideas before the public in a reasonably accessible way, and so opened the floodgates for countless other science writers, although hardly any of the ideas in it felt new to me since I happen to have just reread the physics books by Barrow and Davies which cover much the same ground and are more up to date.

But my biggest overall impression is how provisional so much of it seems. You struggle through the two challenging chapters about black holes – Hawking’s speciality – and then are casually told that all this debating and arguing over different theories and model-making had gone on before any black holes were ever observed by astronomers. In fact, even when Hawking died, in 2018, no black holes had been conclusively identified. It’s a big shame he didn’t live to see this famous photograph being published and confirmation of at least the existence of the entity he devoted so much time to theorising about.


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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.

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 Hartle and 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.


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