The Master and Margarita (3 of 5) & The Brothers Karamazov (5 of 16)
Lines, trees & sunlight
Dear classics reader,
In this week’s haunted apartment you will find:
Our discussion of The Brothers Karamazov Book Five, Chapters 1-4 – with a note on non-Euclidian geometry;
Birthday wishes to Bulgakov, Schnitzler & Porter;
A preview of coming attractions and other notices;
And for paid subscribers:
The week’s new classics – including the first English translation of Tree by Aya Kōda;
And our third discussion of The Master and Margarita – with a tour of literary Kyiv.
This newsletter may be too long for your email inbox. If so, please click ‘View entire message’ at the bottom – or visit Substack.
The Brothers Karamazov (5 of 16)
This month we’re reading Book Five of The Brothers Karamazov – ‘Pros and Cons’. Here are my thoughts on Chapters 1-4:
I’d love to hear yours in the comments!
In chapter 3, Ivan surprises Alyosha (and us) by declaring:
‘I accept God purely and simply.’
This is the opposite of the view he expressed at his father’s house. He continues:
‘We have to accept the fact that if God exists and if He really did create the world, He created it, as we know full well, according to Euclidean geometry, and gave man a mind that can understand only three dimensions of space.’
Here, Ivan is referring, of course, to the Ancient Greek philosopher and mathematician Euclid, who lived around 300 BC.
Euclid is best remembered for the Elements, his treatise on geometry. At the start of the Elements, Euclid provides 23 axiomatic definitions, the last of which is:
‘Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet each other in either direction.’
He then develops this definition in his ‘fifth postulate’.
Ivan says, however, that:
‘there have been, and are even now, even amongst the most eminent mathematicians and philosophers, some who question whether the whole universe or, to take it even further, the whole of existence, was created purely according to Euclidean theory; they even venture to suggest that two parallel lines, which according to Euclid cannot meet on earth under any circumstances, will perhaps meet somewhere at infinity.’
Ivan is referring to the Russian and Hungarian mathematicians Nikolai Lobachevsky and János Bolyai, the founders of non-Euclidean geometry.
From the moment that Euclid formulated his ‘parallel postulate’ in the 4th-century BC, subsequent mathematicians were unable to prove convincingly that parallel lines do not meet. Great minds from Ptolemy (2nd century AD) and Proclus (5th century AD) to Ibn-al-Khaitam of Iraq (c. 1000), Giovanni Saccheri (1733) and J. H. Lambert (1766) tried and failed.
Ignat Avsey quotes the Encyclopaedia Britannica in his endnote:
‘In 1763 the German mathematician Georg Simon Klügel listed nearly 30 attempts to prove axiom 5 and concluded that the alleged proofs were all unsound. Fifty years later a new generation of geometers, still working on the same problem, were becoming more and more frustrated. One of them, a Hungarian named Farkas Bolyai, wrote in a letter to his son János: “I entreat you, leave the science of parallels alone . . . I have travelled past all reefs of this infernal Dead Sea and have always come back with a broken mast and torn sail.” The son, refusing to heed this warning, continued to think about parallels until, in 1823, he saw the whole truth and declared, in his youthful enthusiasm, “I have created a new universe from nothing.”’
János Bolyai published his ground-breaking observations in a 24-page appendix to his father’s 1832 textbook, which the American mathematician George Bruce Halstead hailed as ‘the most extraordinary two dozen pages in the whole history of thought’.
In fact, the first person to publish on non-Euclidean geometry was Nikolai Lobachevsky in 1829-30. In Avsey’s words, Lobachevsky ‘did to Euclidean geometry what Einstein did to Newtonian physics’.
Lobachevskian geometry was further extended in the mid-19th century by the German mathematician Bernhard Riemann, as Avsey explains:
‘Riemann . . . concluded that the non-Euclidean approach to the principle of parallelism must imply ultimate curvature of space, or, to put it graphically, an astronomer looking out into space through an infinitely powerful telescope would see the back of his head. Hence space – the universe, in fact – is unbounded rather than being infinite.’
Ivan, however, declares that these new theories are beyond his ken in the same way that God is beyond his understanding:
‘I have a Euclidean mind, a terrestrial mind, and so I maintain that we cannot decide questions that are not of this world.’
But then he surprises Alyosha (and us) again, when he says:
‘I reject this God-created universe, and although I know it exists, I reject it out of hand.’
The reason for this ‘rebellion’ against God’s universe – he will go on to explain – is because of the suffering of children and he expresses his paradoxical position by concluding the mathematical metaphor:
‘Let parallel lines meet and let me see it with my own eyes: I will see it and I will say that they have met, and yet at the same time I will not accept it. There, Alyosha, there you have my thesis, the essence of my being.’
On an unrelated note, this conversation between Ivan and Alyosha in Book Five inspired the name of the US indie rock band Ivan & Alyosha.
Ivan & Alyosha was formed in 2007 by Tim Wilson and Ryan Carbary. Their producer, Eli Thomson, suggested the band’s name.
I look forward to discussing the second half of Book Five – Chapters 5-7 – on Friday 5th June, which includes Ivan’s story, ‘The Grand Inquisitor’, the most famous section of the novel.
These chapters were first published in the June 1879 issue of The Russian Messenger.
Here are links to our previous Brothers Karamazov posts:
Different translations (14 November)
The Reading Schedule (28 November)
Fyodor Dostoyevsky (12 December)
0. The Family Tree (2 January)
1. Book One: The Story of a Family – and Father Zosima (23 January)
2. Book Two: An Unseemly Encounter – and Mikhail Rakitin (20 February)
3. Book Three: Sensualists – and Pavel Smerdyakov (27 March)
All the Brothers Karamazov posts are accessible to all subscribers for free, but if you would like to view or contribute to the discussion in the comments section, you will need a paid subscription.
As ever, if you – or anyone you know – can’t afford a paid subscription, just let me know and I’ll send a gift subscription.
Happy Birthday Bulgakov, Schnitzler and Porter
In other news, today was the birthday of both Mikhail Bulgakov and Arthur Schnitzler, authors of our April and May read-alongs this year.
They were born 29 years and 650 miles apart in Vienna in 1862 (Schnitzler) and Kyiv in 1891 (Bulgakov).
Today was also Katherine Anne Porter’s birthday. She was born on this day in 1890 in Indian Creek, Texas.
Callie Russell Porter was two years old when her mother died. She was raised by her paternal grandmother, Catherine Anne Porter, whose name she adopted. She worked as an actress, a singer and a journalist before almost dying in the 1918 flu pandemic; her hair remained white for the rest of her life. She then lived in Mexico, Europe and New York, teaching at a number of universities and divorcing four husbands.
She wrote fewer than thirty stories and only one novel, Ship of Fools (1962), which she published at the age of 72. Robert Penn Warren, however, said that ‘she belongs to the relatively small group of writers [. . .] who have done serious, consistent, original and vital work in the form of short fiction – the group which would include James Joyce, Katherine Mansfield, Sherwood Anderson and Ernest Hemingway.’
Her Collected Stories won both a Pulitzer Prize for Fiction and the National Book Award in 1966.
Pale Horse, Pale Rider by Katherine Anne Porter (1922-39)
From the gothic Old South to revolutionary Mexico, few writers have evoked such a multitude of worlds, both exterior and interior, as powerfully as Katherine Anne Porter. This collection gathers together the best of her Pulitzer Prize-winning short fiction, including ‘Pale Horse, Pale Rider’, where a young woman lies in a fever during the influenza epidemic, her childhood memories mingling with fears for her fiancé on his way to war, and ‘Noon Wine’, a haunting story of tragedy and scandal on a small dairy farm in Texas. In all of the compelling stories collected here, harsh and tragic truths are expressed in prose both brilliant and precise.
[UK] Penguin Modern Classics | 384 pages | introduced by Sarah Churchwell
[US] Mariner Book Classics | 495 pages | as The Collected Stories
Coming Attractions and Other Notices
Future monthly read-alongs
For a sneak preview of our upcoming monthly read-alongs, take a peak here.
June – The Third Policeman
Next month we will be reading Flann O’Brien’s absurd, hilarious, nightmarish The Third Policeman. Join us!
We will be reading over three weeks, starting on Friday 5 June. Here are the details.
Annual book subscription
And if you’re enjoying our read-alongs, why not treat yourself to the Hatchards Classic Book Club annual book subscription?
You (or a friend) can receive all the books we read each month here on Read the Classics, beautifully gift-wrapped and delivered to your door, anywhere in the world, as well as a year’s complimentary subscription to Read the Classics, so you can choose to read along with us, if you wish.
To find out more, follow this link or email Hatchards directly: subscriptions@hatchards.co.uk
