There is really no need to belabor the point, since it is obvious to most of us these days that mathematics has taken possession, like a demon, of every aspect of our lives. Most of us may not believe in the story of a Devil to whom one can sell one’s soul, but those who must know something about the soul (considering that as clergymen, historians, and artists they draw a good income from it) all testify that the soul has been destroyed by mathematics and that mathematics is the source of an evil intelligence that while making man the lord of the earth has also made him the slave of his machines. ‘The Man Without Qualities’ p 36 – Picador edition (tr. Sophie Wilkins)
Mathematics is a recurring theme in Robert Musil’s oeuvre, and as I have made my way through his catalogue, leading up to his unfinished “masterpiece” ‘The Man Without Qualities’, I have been intrigued by the frequent references to mathematics. As readers of ‘The Man Without Qualities would know, the central character, Ulrich, is a mathematician;
It has already been mentioned that he was a mathematician, and noting more need be said of that for the moment; in every profession followed not for money but for love there comes a moment when the advancing years seem to lead to a void. P16 (Picador edition) (tr. Sophie Wilkins)
However, I am not going to investigate the references to mathematics in his unfinished novel, but will look at his first book ‘The Confusions of Young Törless’ (tr. Mike Mitchell), and his short stories published as ‘Unions’ and ‘Three Women’ (tr. Eithne Wilkins and Ernst Kaiser). The collection of very short observations ‘Posthumous Papers of a Living Author’ (tr. Peter Wortsman) I will use for some other cross reference purposes in a later post.
In ‘The Confusions of Young Törless’, first published in 1906, the protagonist Törless is attending a strict boarding school;
An idea had suddenly occurred to Törless during the maths class.
During the last few days he had followed the lessons in school with especial interest, for he thought to himself:’ If this really is meant to be a preparation for life, as they say, then there must be at least a hint of what I’m looking for.’
It was maths in particular he was thinking of, after the thoughts he’d had about infinity. p81 (Oxford World’s Classics Edition)
This section of the novel then goes on to explore “imaginary numbers”;
‘Yes. It’s not that difficult. You just have to remember that you’re calculating with the square root of minus one.’
‘But that’s just the problem. It doesn’t exist. Every number, whether positive or negative, results in a positive number when it’s squared. That means there can’t be a real number that’s the square root of a negative one.’ P 81
‘…After all, how different is it from irrational numbers? A never-ending division, a fraction the value of which never works out to a final decimal place however long you go on calculating it. And parallel lines meeting in infinity, what do you imagine by that? Pp 81-82
A novel that explores Törless’ coming of age and his exploration of rational thought, the complexity of a world of mathematics, imaginary numbers, irrational numbers, infinity, adds the layer of the unexplorable, a “void” into Törless’ journey for the ultimate truth.
Earlier in the novel, Törless is stretched out on his back in the park, “in vague dreams gazing through the crowns of two trees” at the sky;
And suddenly he noticed – he felt as if it were the first time it had happened – how high the sky actually was.
He felt a kind of sense of alarm. Right above him an unutterable deep little blue hole was shining between the clouds.
It seemed to him as if you ought to be able to climb up into it on a long, long ladder. But the farther he went into it, pulling himself up with his eyes, the more the shining blue background receded. And yet it seemed as if you ought to be able to reach it and hold it fast with your gaze. The desire to do so grew intense to the point of torment.
It was as if his vision, strained to the upmost, were shooting looks like arrows between the clouds, and as if, however far away it set its aim, they always fell a little short.
Now Törless thought about this, making an effort to remain as calm and rational as possible. ‘Of course there’s no end,’ he told himself, ‘things go on and on, father and farther, to infinity.’ Keeping his eyes fixed on the sky, he repeated that to himself, as if trying to test out the power of an incantation. But to no avail; the words said nothing or, rather, they said something quite different, as if they were referring to the same object, but to a different, alien side of it that didn’t concern him at all.
‘Infinity!’ Törless knew the word from maths lessons. It had never meant anything special to him. It kept on cropping up, someone or other had invented it at some time in the past, and since then it has become possible to perform calculations using it that were as reliable as those using anything fixed. It was just what it counted as in the calculation; Törless had never looked for anything beyond that. Pp67-68
The concepts of infinity, parallel lines that will eventually meet, an epiphany for an unfinished masterpiece!?!
‘The Confusions of Young Törless’ was followed by ‘Unions’ in 1911, a collection of two stories, ‘The Perfecting of a Love’ and ‘The Temptation of Quiet Veronica’. My edition appears as part of a collection titled ‘Five Woman’ released by Verba Mundi books, translated by Eithne Wilkins and Ernst Kaiser, which also features the thee novellas that made up Musil’s ‘Three Women’ published in 1924. Between ‘Unions’ and ‘Three Women’ he had written, and had published two plays.
The two works in ‘Unions” are a mystical exploration of emotion to the exclusion of narrative, reviewed at the time as “half-lit, veiled, insubstantially transparent… the mollusk-like fabric of all that is living”, and a recent review at Kirkus reviews says; “Musil’s rather extraordinary, claustrophobic concentration on states of mind and feeling– the attempt to stabilize the most impalpable sensations, intuitions, thoughts, apprehensions.”, these are difficult stories to explore. However, the stories also contain the concept of parallel lines meeting in the infinite;
For although the ordered picture of the world continually crumbled away under her gaze, and although what she felt for things was only the avid love that a mother feels for a child she lacks the strength to guide, still, at times now her languor would begin to vibrate like a string, like a note sounding at once deep within the ear and somewhere in the world, rising in a great vault, kindling a light . . . a light and people whose gestures were a long-drawn yearning, lines extending far, far away and meeting far, far away in the infinite. ‘The Temptation of Quiet Veronica’ p199
‘Three Women’ published in 1914 saw the introduction of more stable narrative plot lines and the stories explore “the relationship between eroticism (generally unhappy) and transcendence” (‘The New Criterion’ February 1996) .The opening paragraph of one of the stories in ’Three Women’, ‘Tonka’ also references infinity;
At a hedge. A bird was singing. And then the sun was somewhere down behind the bushes. The bird stopped singing. It was evening, and the peasant girls were coming across the fields, singing. What little things! Is it petty if such little things cling to a person? Like burrs? That was Tonka. Infinity sometimes flows in drips and drops. P69
Musil’s collection of very short reflections and observations of minutiae ‘Posthumous Papers of a Living Author’ was published in 1936 and contains less mathematical references than these earlier works, however I will explore these short pieces in another blog post about Musil’s work sometime in the future. Possibly something on the art of writing.
I have not referenced Robert Musil’s 1913 essay ‘The Mathematical Man’, which appears in translation in the collection ‘Precision and Soul’ (edited and translated by Burton Pike and David S. Luft), however I will visit that essay in reference to the perceived decline of humanity and the rise of machines, another recurring theme in Musil’s works.
I’ll leave you with a quote from the introduction, by Johnathan Lethem, from ‘The Man Without Qualities’;
Musil’s novel is the literary equivalent of what the ecological critic Timothy Morton calls a “hyperobject”, whose precise boundaries in space and time are impossible to measure, the question with a hyperobject is how to place ourselves in relation to it. Pviii