Computer-generated nonsense accepted for publication by a mathematics journal

The strike back against Alan Sokal has been 15 years coming.

In 1998, physicist Alan Sokal decided to prove that the impenetrable language used by various post-modernists rendered their work incomprehensible, not only to the public at large, but even to other post-modernists.

Sokal submitted an article, intended as a joke, to an American academic journal called Social Text. John Sturrock, writing in the LRB in 1999, summed up Sokal's aim:

This Duke University periodical likes, by the sound of it, to give air-space to the arguments of the epistemic relativists and other anti-foundationalists. Sokal knew the sort of thing the editors favoured, and he sent them a ‘parody’, as he puts it, entitled ‘Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity’. The text of this reappears as an Appendix in Intellectual Impostures, though by the time you get to it, whatever life might have been left in the joke has been well and truly eroded by the content of the earlier chapters. The ‘parody’ makes relativist claims – for, to take an example more glaring than most, a ‘relational and contextual concept of geometry’ – so far out, as Sokal sees it, for the editors of Social Text to have realised that they were being had and to have turned it down.

While Sturrock mounted an admirable defence of Social Text's editors, the hoax was widely seen as an embarrassment for the publication, and a killer blow from Sokal in his self-declared "science wars".

If there ever was such a thing, however, fifteen years later it appears that the humanities may be equalising the score. The LRB blog reports:

Last month That’s Mathematics! reported another landmark event in the history of academic publishing. A paper by Marcie Rathke of the University of Southern North Dakota at Hoople had been provisionally accepted for publication in Advances in Pure Mathematics.

The paper, "Independent, Negative, Canonically Turing Arrows of Equations and Problems in Applied Formal PDE" has the abstract:

Let ρ = A. Is it possible to extend isomorphisms? We show that D´ is stochastically orthogonal and trivially affine. In [10], the main result was the construction of p-Cardano, compactly Erdős, Weyl functions. This could shed important light on a conjecture of Conway–d’Alembert.

And concludes:

Now unfortunately, we cannot assume that                              

                      

The LRB's Paul Taylor explains:                       

Baffled? You should be. Each of these sentences contains mathematical nouns linked by the verbs mathematicians use, but the sentences scarcely connect with each other. The paper was created using Mathgen, an online random maths paper generator. Mathgen has a set of rules that define how papers are arranged in sections and what kinds of sentence make up a section and how those sentences are made up from different categories of technical and non-technical words. It creates beautifully formatted papers with the conventional structure, complete with equations and citations but, alas, totally devoid of meaning.

A computer. Not the one which wrote the article. Photograph: Getty Images

Alex Hern is a technology reporter for the Guardian. He was formerly staff writer at the New Statesman. You should follow Alex on Twitter.

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Mind-reader, lover and crazed zealot – why the enigmatic power of Rasputin endures

As Douglas Smith wisely surmises in his new book, trying to separate the mythology of Rasputin from the man himself is nearly impossible.

The first would-be murderer to land a blow on Grigory Rasputin was a peasant woman named Khioniya Guseva, whose nose had been eaten away by a disease (not syphilis, she told her interrogators emphatically) and who had been a devotee of Rasputin’s rival Iliodor, the self-styled “Mad Monk”. In June 1914 Guseva pursued Rasputin through Pokrovskoye, the Siberian village that was his home, and stabbed him with a 15-inch dagger.

Rasputin recovered. From thenceforward, though, death dogged him. As confidant and adviser to the tsar and tsarina of Russia, he was detested by monarchists and revolutionaries alike. By the time he was killed, two and a half years later, myriad plots had been hatched against his life. The minister of the interior had tried sending him on a pilgrimage accompanied by a priest: the priest had instructions to throw Rasputin from a moving train. A colonel in the secret services planned to lure him into a car with promises to introduce him to a woman, then drive to an isolated spot and strangle him. His madeira (Raputin’s fav­ourite drink) was to be poisoned. Peasants were bribed to lead him into ambushes. A strange lady turned up at his flat (as strange ladies often did) and showed him a revolver: she had brought it to kill him with, she told him, but had changed her mind after gazing into his eyes. No wonder that by the time Prince Felix Yusupov invited him to come by night to the cellar beneath the Yusupov Palace Rasputin was suspicious and fearful, and had all but given up the noisy, night-long parties he used to enjoy.

His legend has been recounted many times. The peasant who became an all-­powerful figure at the Romanov court. His priapic sexuality and his rumoured affair with Tsarina Alexandra. His “burning” eyes. His ability to hypnotise and beguile. His gift for healing, which miraculously preserved the life of the haemophiliac heir, Tsarevich Alexei. His devilish influence over the imperial couple that led them into repeated mistakes, eventually precipitating the 1917 revolution. His debauchery. His supernatural power, which obliged his murderers to kill him not once, but thrice – with poisoned pink cakes, with gunshots at point-blank range and eventually by drowning him. All of this, everybody who knows anything about Russian history, and many who do not, have heard. Douglas Smith retells the story, pruning it of absurdities, greatly expanding it, and demonstrating how very much more complicated it is than the legend would have us believe.

Rasputin’s public career began in his thirties, when he arrived in St Petersburg in 1905. Smith’s account of his life before his debut in the city is the most fascinating part of this book. It describes a world of isolated peasant communities with few books (in 1900 only about 4 per cent of Siberia’s inhabitants could read) but many holy men. This is the world of Dostoevsky’s Brothers Karamazov: violent, physically harsh, but spiritually ecstatic.

At the age of 28, Rasputin – married with children, still living with his father and helping to farm the family’s smallholding – left home to become a pilgrim. This was not an egregious decision. According to Smith, there were “about a million” pilgrims criss-crossing Russia at the time, walking barefoot, begging for food and lodging, trudging towards the holiest monasteries or seeking out revered starets, or church “elders”.

Rasputin would be away from home for years at a time. He would walk 30 miles a day. For three years he wore fetters, as many pilgrims did. After he laid them aside he went for six months without changing his clothes. He was often hungry, either because he could get no food, or because he was fasting. He was repeatedly robbed by bandits. But, for all his tribulations, on his return he would tell his children that he had seen marvels – cathedrals with golden cupolas and wild forests. He became part of a network of priests and visionaries which spanned the vast empire. He talked with everyone he met on the road, acquiring a knowledge of the narod, the Russian people, that its rulers never had. Smith’s account of his wandering years conjures up a richness of experience that makes the way the nobility later sneered at the “illiterate peasant”, the “nobody” who had got hold of their tsarina, seem indicative not of Rasputin’s shortcomings, but of their own.

In 1905 Rasputin was in the Tatar city of Kazan, drinking tea with a famed healer called Father Gavril. He told Gavril that he intended to walk on to St Petersburg, still hundreds of miles to the west. Gavril said nothing, but thought: “You’ll lose your way in Petersburg.” Rasputin, who already had a reputation as a mind-reader, responded as though he had heard, saying that God would protect him.

He was not the first holy man to be feted in the capital. Four years before he arrived in St Petersburg a French “sage” called Monsieur Philippe was holding séances in the city, and had soon “enraptured” the royal family. Nicholas and Alexandra prayed with Philippe and sat up until the small hours listening to him talk. They called him by the sobriquet they would soon give Rasputin, “Our Friend”, and they counted on him to guide the tsar in crucial talks with Kaiser Wilhelm of Germany. Eventually Nicholas was prevailed upon to send him away, but other starets or “holy fools” succeeded Philippe at court (including Mitya “the Nasal Voice”, whose speech impediment made his words incomprehensible but who was nonetheless credited as a prophet). Rasputin may have been exceptionally charismatic – someone who met him soon after his arrival in the city described him as “a burning torch” – but, as one of his sponsors in high society said, “our Holy Russia abounds in saints” and the ruling class was just as enthralled by them as were the peasantry.

So, what was it about Rasputin? The eyes certainly – there are numerous references in contemporary descriptions to his “compelling”, “mesmeric”, “brilliant” eyes, their “strange phosphorescent light” and the way they stared, as though penetrating another’s mind. There were also his skills as a performer. He would talk eloquently and for hours. Smith quotes some striking accounts of Rasputin at prayer. For him, prayer was not a matter of closed eyes and folded hands and silent communion with God. It was a performance. He vibrated like a taut bow-string. He turned his face towards heaven and then, “with great speed, he would begin to cross himself and bow”.

He was all dynamic energy. He was unpredictable and frightening. His conversation could be bantering and light but then he would turn on someone standing on the fringe of a party and, as though he had read her mind, begin to scold her for having sinful thoughts. Then there was the erotic charge. In this compendious and exhaustively researched book, Smith debunks dozens of untrue stories about his subject, yet there is no denying Rasputin’s propensity for stroking and kissing women he barely knew and (once he was sufficiently celebrated for this to become easy for him) leading them into his bedroom and making love to them while people in the next room continued to drink their tea, pretending not to hear the thumps and moans. He was “so full of love”, he said, that he could not help caressing all those around him. Alternatively, he claimed (and many of his devotees accepted) that his sexual activity was designed to help his female followers overcome their carnal passions: he used sex to free them from sex. Smith treats this belief as being probably sincerely held – if almost comically self-justifying.

By the end of his life pretty well everyone in Russia believed that Rasputin was having an affair with the empress Alexandra. Everyone, that is, except for Alexandra and her husband. She wrote to Rasputin that it was only when she was leaning on his shoulder that she felt at peace; still, she could see nothing improper in their relationship. Tsar Nicholas, coming home late at night, as he frequently did, to find his wife closeted alone with Rasputin, reacted only with delight that “Our Friend” had blessed them with a visit. Rasputin was accused of “magnetism” – of using a form of hypnotism to dominate others. Whether or not he deliberately did so, he certainly had a magnetic personality.

Yet all these attributes are those of an individual. One of the important themes of Smith’s book is that, remarkable though Rasputin may have been, he could not on his own have brought down the tsarist autocracy, as his murderers thought he had, or saved it, as the tsarina believed he could. He was seen as the heretic who was shaking the foundations of the Orthodox Church, as the corrupter who had rendered the monarchy untenable, as the Satanic sower of discord who broke the ancient and sacred ties that bound the narod to the tsar. He was seen as a peace lover who, as one of his many biographers wrote in 1964, was the “only man in Russia capable of averting” the First World War. Rasputin himself said that it was only his continued existence that kept the tsar on the throne.

When Rasputin’s assassins dumped his body in the Neva, his mourning devotees took pailfuls of water from the icy river, as though his corpse had made it holy, while all over Russia his enemies rejoiced. His murderers – Prince Yusupov, Grand Duke Dmitry and the rest – were hailed as the heroes who had saved the Romanov regime and redeemed Holy Russia. But nothing changed. Two months after Rasputin’s mauled and frozen body was dragged from beneath the ice, the revolution began. The tsar abdicated, and the joke went around that now the royal flag was no longer flying over the imperial palace, but only a pair of Rasputin’s trousers.

Early on in the process of planning his book, Smith writes, he wisely decided that to confine himself to the facts would be absurdly self-limiting. “To separate Rasputin from his mythology, I came to realise, was to completely misunderstand him.” In 1916 an astute observer of Russian politics noted in his diary that: “What really matters is not what sort of influence Grishka [Rasputin] has on the emperor, but what sort of influence the people think he has” (my italics). It’s true, and Smith agrees. “The most important truth about Rasputin,” he writes, “was the one Russians carried around in their heads.”

Smith, accordingly, gives us a plethora of rumours and canards. Over and over again in this book he tells a sensational story, full of salacious or politically complex detail and drawn from an authoritative-sounding contemporary source, only to show in the next paragraph that the story cannot possibly be true. As a result, we get an admirably encyclopaedic account of the fantasy life of early-20th-century Russians, as well as a multifaceted image of the Rasputin of their imagination. We do sometimes, though, get bogged down in the mass of material – factual or fictional – being offered us. This book will be invaluable to all subsequent writers on the subject, but general readers may wish, as I did, that Smith had at times allowed himself a clarifying generalisation rather than piling case history upon unreliable memoir upon clutch of mutually contradictory reports. This is a richly illuminating book, but it is not a lucid one.

At its centre is Rasputin, and for all the multiplicity of contemporary descriptions, and for all Smith’s laudable scholarship, he remains an area of darkness. By the time he came to fame he was no longer illiterate, but his own writings are opaque and incoherent. It is hard to read the man between the lines. Photographs (there are some haunting examples in here) seem to tell us more, but they are enigmatic.

Just occasionally, in this great, rambling edifice of a book, we glimpse him, as though far off down an endless corridor: a young seeker, vibrating with energy and self-mortifying religious fervour; a charismatic celebrity, already talking as he strides into a salon in the shirt an empress has embroidered for him; a hunted man walking home, tailed by a posse of secret agents, and drinking himself into a stupor as he awaits the attack he knew was bound to come.

And yet, for the most part, despite Douglas Smith’s herculean efforts, the man remains inscrutable. “What is Rasputin?” asked the Russian journal the Astrakhan Leaflet in 1914. “Rasputin is a nothing. Rasputin is an empty place. A hole!”

Lucy Hughes-Hallett’s books include “The Pike: Gabriele d’Annunzio – Poet, Seducer and Preacher of War” (Fourth Estate)

Rasputin by Douglas Smith is published by Macmillan (817pp, £25)

This article first appeared in the 01 December 2016 issue of the New Statesman, Age of outrage