Mathematics in literature

[bluevictim]

Amidst all the fuss about the new Alice in Wonderland movie, I came across the following article postulating that many of the wacky scenes are parodies of new developments in mathematics in Lewis Carroll's day.

As I embarked on my DPhil investigating Victorian literature, I wanted to know what inspired these later additions. The critical literature focused mainly on Freudian interpretations of the book as a wild descent into the dark world of the subconscious. There was no detailed analysis of the added scenes, but from the mass of literary papers, one stood out: in 1984 Helena Pycior of the University of Wisconsin-Milwaukee had linked the trial of the Knave of Hearts with a Victorian book on algebra. Given the author's day job, it was somewhat surprising to find few other reviews of his work from a mathematical perspective. Carroll was a pseudonym: his real name was Charles Dodgson, and he was a mathematician at Christ Church College, Oxford.

The 19th century was a turbulent time for mathematics, with many new and controversial concepts, like imaginary numbers, becoming widely accepted in the mathematical community. Putting Alice's Adventures in Wonderland in this context, it becomes clear that Dodgson, a stubbornly conservative mathematician, used some of the missing scenes to satirise these radical new ideas.

...

As someone who gets excited at the mention of quaternions, I found the article very interesting, and I thought it might make for a good excuse to start a thread about mathematics in literature.

Many examples can be found, from Zamyatin's We, with its use of mathematics to symbolize a threatening rational rigidity, to Tom Stoppard's Arcadia, in which ideas from dynamical systems and chaos play a large role, to Pynchon's information theory-soaked The Crying of Lot 49. And of course mathematical concepts regularly show up in science-fiction. I even found a webpage cataloging mathematical fiction.

Has someone come across a particularly nice example of mathematics in literature? Was there something about math that puzzled you in some book? Was there a particularly clueless treatment of math to laugh at? I know there are many people here with technical backgrounds, so I hope there is good potential for a stimulating discussion.

[Modest Proposal]

My dad is a MD but also a talented amateur mathematician and is always giving me obscure but interesting mathematical concepts to explore in my fiction.

As far as more famous authors who do this, Abbott's "Flatland" is a great older text to merge/blur the boundaries between scientific concepts and narrative.

Vernor Vinge is a famous name in SF, having won 5 Hugo Awards (SF's biggest prize) and starting the incredibly popular Cyberpunk genre with "True Names", and was a mathematics professor at San Diego State U. As I'm only in San Diego for a short time now, I'm setting up a meeting with him before I leave--we have some mutual colleges at SDSU.

[kiki1982]

Euclid in The Mill on the Floss! That was hilarious!

Father Tulliver: 'Well, my lad, [...] you look rarely! School agrees with you.'
Tom Tulliver: 'I don't think I am well, father. I wish you'd ask Mr Stelling [the teacher] not to let me do Euclid. - It brings on the tootrhache, I think.'
Father: 'Eclid, my lad - why, what's that?'
Son: 'Oh, I don't know; it's definitions, and axioms, and triangles, and things. It's a book I've got to learn in - there's no sense in it.'



And the poor father wanted his son to get 'an edication' so that he became clever... It brought him nowhere, but Euclid bringing on the tootheache...

I'm sure it didn't occur to Euclid himself when he was busy.

[billl]

I am gonna be lazy and simply trumpet a biography of a mathematician that I found pretty interesting and moving:

http://www.amazon.com/Man-Who-Knew-I...8207538&sr=8-1

about a self-taught genius
http://en.wikipedia.org/wiki/Srinivasa_Ramanujan

who came up with some (apparently) amazingly unorthodox mathematics, AND lived a very interesting life, as a person strewn between cultures and between responsibilities towards profession, family, and curiosity towards the most abstract truths.

It is a FANTASTIC read, if you might be interested in the life of a mathematical genius. (with some insight, I think, into 20th-Century Indian culture and expectations, in the light of the British Empire, etc. ... Hope I'm not getting anything offensively wrong, in my characterization here...)

[mal4mac]

Bertrand Russell's autobiography has (unsurprisingly!) a lot of interesting asides on mathematics, his account of his encounter with Euclid, when he was a young boy, is especially memorable. As Russell won the Nobel prize for Literature, I guess it counts as literature, although Russell doesn't make it into many canonical lists - maybe Bloom tried his technical works and couldn't understand them, or (like me) was dismayed by his rushed pot-boilers ("History of Western Philosophy", etc, etc).

"My Philosophical Development" is another great book by Russell - I remember a golden summer at college that started with me reading this after my exams (Maths, Physics,...) It sort of pulled together why these subjects might be worth studying! At least it kept me going for another two years

Ramanujan is a fascinating character, who makes a vivid appearance in "A Mathematician's Apology (Canto)" by G.H. Hardy. But I most remember his account of spending a few hours each morning doing mathematics with pencil and paper and then spending the afternoons sauntering round "the backs", pausing to watch the ladies play tennis. Then over dinner (and good wine) he might discuss with the dean how they could get Ramanujan a research position... Parts of Russell's biography reads a bit like that... dreaming spires indeed... Wish jobs like that were easy to get

Another book I would recommend is Mathematics: A Very Short Introduction by Timothy Gowers. This is a bang up to date overview by a top mathematician, a great read. It's a bit dry compared to Hardy and Russell, though!

If you want to avoid dry, try "Surely You're Joking, Mr.Feynman!: Adventures of a Curious Character" by Ralph Leighton, Richard P. Feynman, and Edward Hutchings. It's as funny, interesting and easy to read as any comic novels I've read, besides having a lot of useful things to say about physics and mathematics. (But is it literature?...)

You might be about to accuse me of deviating from the thread focus of "mathematics in literature". But I'm not really, they are books about mathematics that *are* (or might be!) literature, therefore they are literature in which there is a lot of mathematics!

[bluevictim]

As far as more famous authors who do this, Abbott's "Flatland" is a great older text to merge/blur the boundaries between scientific concepts and narrative.

Flatland is definitely a classic work of mathematical fiction. It's also very appropriate for Bayley's article about Dodgson's attitude to "new" mathematics. Abbott's Flatland is essentially an argument against dismissing unintuitive concepts as nonsense. Indeed, Bayley's description of Dodgson calling abstract mathematics "semi-colloquial" and "semi-logical" makes him look like a Flatlander calling the third-dimension impossible.

Euclid in The Mill on the Floss! That was hilarious!

Father Tulliver: 'Well, my lad, [...] you look rarely! School agrees with you.'
Tom Tulliver: 'I don't think I am well, father. I wish you'd ask Mr Stelling [the teacher] not to let me do Euclid. - It brings on the tootrhache, I think.'
Father: 'Eclid, my lad - why, what's that?'
Son: 'Oh, I don't know; it's definitions, and axioms, and triangles, and things. It's a book I've got to learn in - there's no sense in it.'

Euclid's reign in mathematical education is quite impressive. For around two thousand years his Elements was the textbook on geometry. His great influence is attested by the famous poem by Edna St. Vincent Millay:

Euclid Alone Has Looked On Beauty Bare

Euclid alone has looked on Beauty bare.
Let all who prate of Beauty hold their peace,
And lay them prone upon the earth and cease
To ponder on themselves, the while they stare
At nothing, intricately drawn nowhere
In shapes of shifting lineage; let geese
Gabble and hiss, but heroes seek release
From dusty bondage into luminous air.
O blinding hour, O holy, terrible day,
When first the shaft into his vision shone
Of light anatomized! Euclid alone
Has looked on Beauty bare. Fortunate they
Who, though once only and then but far away,
Have heard her massive sandal set on stone.

I am gonna be lazy and simply trumpet a biography of a mathematician that I found pretty interesting and moving:

http://www.amazon.com/Man-Who-Knew-I...8207538&sr=8-1

about a self-taught genius
http://en.wikipedia.org/wiki/Srinivasa_Ramanujan

who came up with some (apparently) amazingly unorthodox mathematics, AND lived a very interesting life, as a person strewn between cultures and between responsibilities towards profession, family, and curiosity towards the most abstract truths.

Very interesting, indeed.

"My Philosophical Development" is another great book by Russell - I remember a golden summer at college that started with me reading this after my exams (Maths, Physics,...) It sort of pulled together why these subjects might be worth studying! At least it kept me going for another two years

The cross-pollination between mathematics and philosophy, especially since the 19th century, has led to profound advances in both disciplines. Unfortunately, as you observe, literary circles seem to have largely isolated themselves from these developments. I guess it's no surprise that humanists like Harold Bloom don't see the appeal of mathematics; they simply have no training in logically rigorous thinking.

You might be about to accuse me of deviating from the thread focus of "mathematics in literature". But I'm not really, they are books about mathematics that *are* (or might be!) literature, therefore they are literature in which there is a lot of mathematics!

Yes, I did have in mind works that fit more squarely within what LitNetters consider "literature" (works like plays, novels, and poems), but hey, it's the internet so it's not like there are rules or anything. There are indeed many good books out there about mathematics and mathematicians.

[annatak]

Just a layperson here, but this book was so beautifully written. The characters didn't even need names! The professor suffers from a condition where he has no short-term memory (everything resets after 60 or 80 minutes). He takes a liking to the housekeeper's son and calls him "Root" because he resembles the square root symbol! The beauty of numbers is so well written - do take a look!

[sixsmith]

Ratner's Star - Don DeLillo http://www.nytimes.com/books/97/03/1...-r-ratner.html

[mal4mac]

I guess it's no surprise that humanists like Harold Bloom don't see the appeal of mathematics; they simply have no training in logically rigorous thinking.

Stop trying to upset the nice LitNet humanists I'm sure they've read their Aristotle, some of them in the original Greek...

[Babbalanja]

Mathematician John Allen Paulos wrote a fascinating book called Once Upon a Number which examines the way statistics and storytelling are intricately connected. That is, for mathematical analyses we need some sort of narrative context. However, narratives that aren't informed by statistics can reinforce unrealistic biases.

As a bean counter who loves literature, I get a lot out of statistical puzzles and mathematical games. I feel sorry for people who look with dread on math-related subjects or logic, the same way I pity people who can't appreciate music or poetry.

Regards,

Istvan

[papayahed]

This really isn't a literature book but it is fun:

http://www.amazon.com/Archimedes-Rev...411285&sr=8-43

[AuntShecky]

What an intriguing thread! It's going into my "save" file right now!

[bluevictim]

Just a layperson here, but this book was so beautifully written. The characters didn't even need names! The professor suffers from a condition where he has no short-term memory (everything resets after 60 or 80 minutes). He takes a liking to the housekeeper's son and calls him "Root" because he resembles the square root symbol! The beauty of numbers is so well written - do take a look!

Ratner's Star - Don DeLillo http://www.nytimes.com/books/97/03/1...-r-ratner.html

This really isn't a literature book but it is fun:

http://www.amazon.com/Archimedes-Rev...411285&sr=8-43

Thanks for the suggestions!

Stop trying to upset the nice LitNet humanists

Of course I didn't mean to upset anyone. Surely the only people that would take offense are those that value logical rigor, but those people can either a) smile and be satisfied that they have plenty of training in logic, thank you very much, or b) realize their logic skills are insufficiently developed and find themselves in agreement with me anyways.

I'm sure they've read their Aristotle, some of them in the original Greek...

I do hope they identify themselves and chime in!

Mathematician John Allen Paulos wrote a fascinating book called Once Upon a Number which examines the way statistics and storytelling are intricately connected. That is, for mathematical analyses we need some sort of narrative context. However, narratives that aren't informed by statistics can reinforce unrealistic biases.

This looks very interesting indeed. Here's a pretty nice review of Once Upon a Number. I really don't think people who dislike math are in need of too much pity; I'm sure they find plenty of other enriching activities to engage in. Life is simply too wonderful for anyone to be able to fully experience everything (in my opinion).

What an intriguing thread! It's going into my "save" file right now!

I'm glad you are enjoying it! Have you come across any intersections of math and literature lately?

[mal4mac]

Dostoevsky was steeped in Mathematics in his youth, and it pops up in much of his work, often as a very negative symbol!

For instance, The Underground Man asserts the right to the subjectivity of his own consciousness: "I stand for my own caprice and that it be guaranteed me when necessary". The symbol for this in the text is his view of arithmetic, the Platonic forms, the world of mathematics: objectivity.

Dostoevsky studied mathematics at university, and displayed a gift for it, but he detested it, and ploughed that hatred into the views of the Underground Man: "two times two is four has a cocky look; it stands across your path, arms akimbo and spits. I agree that two times two is four is an excellent thing, but if we’re going to start praising everything, then two times two is five is also sometimes a most charming little thing… Consciousness, for example, is infinitely higher than two times two."

Non-Euclidean geometry makes it into "The Brothers Karamazov". Good article here:

http://www.utoronto.ca/tsq/DS/08/073.shtml

Summary: The discovery of non-Euclidean geometry was a psychological breakthrough. Euclidean geometry was no longer identical with Reality. The non-Euclidean plane was a new world. Ivan uses non-Euclidean geometry to reduce the human mind. But, for Dostoevsky, to diminish a human being is necessarily to diminish God, and to condemn us to Hell on Earth.

Lumping God with non-Euclidean geometry, Ivan, in his overweening pride, takes his own intellect as the measure, as though his incomprehension of God and non-Euclidean geometry were equivalent. Reducing God to the level of his intellect, he deprives God of any "mystic extension".

Ivan, driven by his overriding need to prove the absurdity of existence, constructs the geometric metaphor, using one hypothetical unknown, the meeting of parallel lines, to deny another, ultimate harmony, in order to negate the world, to reinforce the idea that this world is senseless.

Geometry proves nothing about the existence of God. Ivan suggests that since non-Euclidean geometry is not of this world, God is not of this world. What really troubles Ivan is not geometry, but God's remoteness. God is infinitely far away. He is at that place where two parallel lines meet. This means that God has, in effect, abandoned man, equivalent to saying that God is nowhere. This despair is the source of his nihilism, and Non-Euclidean geometry is a symbol for God's absence from this world.

Ivan, listening to the devil, has jeopardized his sanity by thinking about "questions not suitable to a mind created with a conception of only three dimensions".

On the broad scale of history, every major step forward in science has proved a step farther away from God. The discovery of the non-Euclidean plane was not only a "psychological breakthrough", it was a defeat for Euclid's geometry, which conformed to the three dimensional Reality of human sensory perceptions, and was long thought to be the immutable reflection of eternal Truth, of the majesty and harmony of God's creation.

Defining "earthly realism" in determinate, Euclidean mathematical terms, the devil reduces earthly life to an abstraction. Ivan does not love "earthly realism". He rejects this world, hoping for a better one beyond, but has no evidence of it. The devil demolishes Ivan's tenuous hope when he defines his realm beyond the earth in terms of total mathematical indeterminacy. For the devil comes from the infinite reaches where "non-Euclidean geometry" and "indeterminate equations" are the norm, where there are no outlines, and thus no stable images, where there is no up or down, high or low, right or wrong. Formulae and Euclidean geometry admit of reassuring predictions and definite calculations, but "indeterminate equations" have no fixed values, no fixed extensions. In fact, most equations have indeterminate terms. But again, mathematics per se, is not the point. Ivan wants to know, once and for all, does God exist. But from the devil he will get only indeterminate answers. Thus "indeterminate equations" have become a metaphor of indeterminate faith and so mirror Ivan's dilemma. Combining the notion of indeterminacy with the universal quantifier "all", the devil maximizes the temptation to despair.

The devil harrows Ivan, the natural scientist, by taking Ivan's own scientific images and ideas to extremes with the notion of infinity in order to induce maximum despair. The mathematical allusions and images of lifeless matter which mark their speech reflect their abstract, theoretical lives and serve as metaphors for a steadily encroaching materialist world view. With varied motifs of upheaval and extinction, of fragmenting and colliding matter, the devil projects a meaningless universe where nothing holds together.

The devil uses indeterminate equations, which are capable of an infinite number of possible solutions, in order to torture Ivan on his sorest point, his wish to to ascertain the existence of God and immortality. The devil haunts Ivan with visions of emptiness, hopelessness and with indeterminacy he blurs and all but obliterates the divine presence. Instead of using mathematics to clarify, enlighten or prove, the devil perverts it in order to confuse, obscure and sow despair.

[billl]

Ramanujan is a fascinating character, who makes a vivid appearance in "A Mathematician's Apology (Canto)" by G.H. Hardy.

By chance, I stumbled upon this excerpt while reading an excorciating review of an anthology of science writing edited by Richard Dawkins (this quotation is from the introduction to Hardy's book, actually):

On the other hand, there is an excerpt from my favorite piece of writing by C.P. Snow. It is an introduction to G.H. Hardy's classic A Mathematician's Apology. In it Snow talks about Hardy's discovery of the Indian mathematical genius Ramanujan. I have read this many times and always with pleasure. It ends with Hardy's visit to Ramanujan in a London hospital. To cheer him up Hardy tells him that he came in a taxicab with the number 1729 and that he is sure that this is a number of absolutely no interest. Ramanujan immediately corrects him. It is the smallest number than can be expressed in two different ways as the sum of two cubes.

It is a pity that Dawkins does not tell us how this evolved into a problem in number theory. For example 87,539,319, which is known as taxicab 3, is the smallest number that can be expressed as the sum of cubes in three different ways.