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Arcadia (2016)
Iain Pears
(click on names to see more mathematical fiction by the same author)
Note: This work of mathematical fiction is recommended by Alex for literati.

As this clever novel is intentionally a hodge-podge of genres, it is a bit difficult to describe. It involves a British spy brought back from retirement in the 1960s to find a mole, a mathematician in a dystopian future who invents a machine that lets one travel either through times or to different universes, a girl going through a garden gate stored in a basement and ending up in a forest where she is mistaken for a fairy and falls in love with the rightful heir to the throne who is living in hiding with his band of merry men (robbing from the rich, of course) because he is falsely accused of having killed his uncle, and...

As I said, it is a bit complicated. And though it is clearly derivative of other works, such as Tinker Tailor Soldier Spy, The Lion the Witch and the Wardrobe, Robin Hood, romance novels, and even bits of Kurt Vonnegut, Agatha Christie and the Wizard of Oz, the intricate way these familiar tropes and literary allusions are fit together is actually rather original and works surprisingly well.

Another work of mathematical fiction to which this bears some similarity is the play by Tom Stoppard of the same name. For instance, both are complicated and beautifully constructed works of fiction that feature people living in different eras, female mathematicians, and British people digging through ancestral papers to find something of mathematical interest. However, I am not sure whether these similarities are intentional. In more significant ways, this work is very different than Stoppard's play. For one thing, it is much less mathematical. It does not actually mention any real math, while the play involves fractal geometry and chaos theory. And, the math in this novel, though playing a role in the plot, is marginalized while it is a central focus in the play. (This, of course, is not intended as a criticism of the novel. There is no reason math should be a central focus. Still, since this is a site about mathematical fiction, I feel obligated to point it out.) Also, while Stoppard's play is essentially realistic, this novel is definitely a work of science fiction or fantasy. (Again, this particular work is hard to classify, but I would say it is just barely on the SF side of the division between them.)

If that analysis (and the praise the book has received from critics and readers) intrigues you at all, then perhaps you should stop looking at this posting until you've had a chance to read it, because I would hate to spoil it for you. Below, I will focus only on the mathematical aspects of the book, but in doing so I may reveal some of the book's surprises.

One way math arises in this novel is through a paradoxical document called "The Devil's Handwriting" which serves as the novel's MacGuffin. It consists of equations written in a dense mathematical code called "Tsou notation", but is anachronistic in that it seems to have been handwritten long before either the math necessary to understand the equations or the Tsou notation were invented.

There are two interesting bits of fictional mathematics that are discussed just briefly. Each of them takes the form of an identity that the mathematician discovers. In one case, she recognizes that a disturbance in time, like the result of plucking a taut string, will travel both forwards and backwards:

(quoted from Arcadia)

All events displace in both temporal directions simultaneously and equally. The magnitude of displacement is in direct proportion to the mass of the event -- Meerson's second law.

Later, the same mathematician recognizes a possible relationship between two seemingly unrelated probabilities and briefly considers rigorously proving that is true.

The most unusual discussion of mathematics in the book concerns the emotional and biological state of the mathematician Angela Meerson:

(quoted from Arcadia)

"Angela is a psycho-mathematician," Hanslip said. "She works by harnessing emotions to power her calculations, and further enhancing these through the use of powerful stimulants. It is a highly specialized technique but people established centuries ago that many people could do maths by associating complex calculations with things like shapes or colors. It is a sort of controlled insanity and in the right hands it can outperform any computer in intuition. Angela's intuitions then have to be converted into orthodox calculations, of course, but she has done extraordinary work. ...

Her response to her calculations is like a mother defending a child, literally so. When she is one of these states she would die, or kill, to protect whatever she is working on. ...

She was always exceptionally talented but to enhance this she was subjected to a procedure some eighteen years ago. That is, she was put into an artificial coma, and a pregnancy was induced. The complex emotional responses were captured and harnessed."

[Italics added. -ak]

At first glance, there are many disturbing stereotypes in that quoted passage. The ideas that insanity is necessary for mathematical success and that women think emotionally and intuitively rather than rigorously are misconceptions I often complain about at this Website. I also suspect many female researchers would be offended by the suggestion that Meerson had to be motivated by maternal instinct. Many authors make use of these sorts of stereotypes either because they truly believe them or because they simply do not care. However, in this unusual case there is another possible explanation. Note that this sort of sexism was particularly common in the classic science fiction of the mid-twentieth century. Then, in Pears' Arcadia, this could be (and I believe is) yet another literary allusion. And, in the "more enlightened" twenty-first century, such references can be seen as a form of criticism of a discredited prejudice from the past. (At least, that's how I'd like to see it, since that is what I intended when I named a character "Category Theory Girl" in my super-hero parody The Adventures of Topology Man.)

In conclusion, I think this is a magnificent, complex and thought provoking work of fiction that will be especially fun for anyone who would like to see allusions to a wide variety of literary genres. In a sense, it is meta-fiction as much as it is fiction! Mathematics gets mentioned occasionally and technically plays a key role in the plot, but truly this book would not be very different if the math had been left out of it.

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Works Similar to Arcadia
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. How to Live Safely in a Science Fictional Universe by Charles Yu
  2. The Kingdom of Ohio by Matthew Flaming
  3. An Instance of the Fingerpost by Iain Pears
  4. The Lost Books of the Odyssey by Zachary Mason
  5. Stranger than Fiction by Marc Forster (Director) / Zach Helm (Screenplay)
  6. Nullstellen by Dietmar Dath
  7. Napier's Bones by Derryl Murphy
  8. Ninefox Gambit by Yoon Ha Lee
  9. Cryptonomicon by Neal Stephenson
  10. The Square Root of Pythagoras by Paul Di Filippo / Rudy Rucker
Ratings for Arcadia:
RatingsHave you seen/read this work of mathematical fiction? Then click here to enter your own votes on its mathematical content and literary quality or send me comments to post on this Webpage.
Mathematical Content:
3/5 (1 votes)
Literary Quality:
5/5 (1 votes)

GenreHistorical Fiction, Science Fiction, Fantasy, Adventure/Espionage,
MotifFemale Mathematicians, Time Travel, Romance,
TopicFictional Mathematics,

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