MATHEMATICAL FICTION:

a list compiled by Alex Kasman (College of Charleston)

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Machines Like Me (2019)
Ian McEwan
(click on names to see more mathematical fiction by the same author)
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Note: This work of mathematical fiction is recommended by Alex for literati.

There are many ways to describe this book without mentioning mathematics: It is a romance between Charlie (a slacker who dabbles in day-trading) and Miranda (the law student who lives in the apartment above his). There are shades of McEwan's Atonement in the subplot concerning the quest for justice in a case involving rape, suicide, and perjury. And there is philosophical inquiry into the nature of consciousness as the couple become "parents" to an artificially intelligent android. But, a famous mathematician and his mathematical research play an important role in the background.

This book takes place in an alternate universe where things turned out slightly differently than they did in our own. The Beatles released a reunion album in the 1980s. The UK suffered a bitter defeat in the Falkland Islands. And, most significantly, rather than submitting to chemical castration and committing suicide, mathematician Alan Turing chooses to go to prison after his arrest for homosexual activity.

The consequences of Turing living beyond 1954 are far reaching. Turing becomes a wealthy entrepreneur (like the famous silicon valley CEOs of today). The internet and associated technologies that we think of as being 21st century inventions are commonplace in the last quarter of the 20th. And, the artificial intelligence capabilities available to people in that world in the 1980s are well beyond anything we have achieved in reality in 2019.

The advances in artificial intelligence are specifically attributed to Turing's mathematical research into the "P vs. NP Problem". For those who may not know, this is a real open question at the intersection of mathematics and computer science about how many steps it would take to answer certain sorts of questions involving n objects, where n some positive whole number. (Think, for example, about factoring a number with n digits or figuring out the shortest path that takes you to n different locations.) In general, increasing n also increases the number of steps required to find a solution, but the open question is whether it always grows like a polynomial in n or whether some problems grow so quickly in complexity that it grows faster than any polynomial. As far as I know, the real Alan Turing never worked on that problem. But, in Machines Like Me, he begins thinking about it while in prison and many years later proves that "P=NP". In other words, he (together with unnamed co-authors) has proved that indeed the number of steps to answer the question can grow at most as a polynomial in n. This, in turn, implies that there is some short and effective way to answer questions that we currently think are too time consuming for a computer to answer in practice. Moreover, his proof apparently revealed how to do these computations quickly, and his ability to create amazing artificial intelligences is a consequence:

(quoted from Machines Like Me)

[Turing:] "...Simple statements need external information to be understood because language is as open a system as life. I hunted the bear with my knife. I hunted the bear with my wife. Without thinking about it, you know that you can't use your wife to kill a bear. The second sentence is easy to understand, even though it doesn't contain all of the necessary information. A machine would struggle.

"And for some years so did we. At last we broke through by finding the positive solution to P versus NP -- I don't have time now to explain it. You can look it up for yourself. In a nutshell, some solutions to problems can be easily verified once you've been given the right answer. Does that mean therefore that it's possible to solve them in advance? At last the mathematics was staying yes, it's possible, and here's how. Our computers no longer had to sample the world on a trial-and-error basis and correct for best solutions. We had a means of instantly predicting the best routes to an answer. It was liberation. The floodgates opened. Self-awareness and every emotion came within our technical reach..."

For the first half of the book, Turing does not appear as a character but only as someone who clearly shaped the world in which the story unfolds. But, through Charlie, we get to meet Turing on three occasions: a chance encounter at a restaurant, an invitation to Turing's house to discuss the sad fact that many of the artificially intelligent androids are choosing to commit suicide, and one more time (which I won't describe in greater detail to avoid spoilers) at the very end of the book, giving Turing the opportunity to review and bring closure to some of the philosophical themes of the book.

I spotted many ironies associated with Turing, which I assume the author intended. The suicides of the androids whose minds run on the fictional Turing's algorithms are surely some a reference to the suicide of the real Alan Turing. The narrator does mention Turing's role in the Allied victory in World War II (something that is also true in reality, although his role has been diminished in recent years as the contribution of others has come to light), but the book also attributes the British loss in the Falklands to Turing in that the Argentinian weapons used algorithms that he developed and released for free public use. The book never specifically mentions the Turing Test, but there is a scene in which Miranda brings Charlie (her fiancé) and Adam (their android) to meet her father and even after the visit the father is under the misimpression that Adam is the human fiancé and Charlie is artificially intelligent. Charlie eventually realizes that he has been mistaken for a robot and has some fun playing along with the error in a sort of reverse "imitation game".

Alan Turing appears in quite a few works of mathematical fiction (see here), and it is interesting to see where this novel fits in with that specific body of literature. There are some in which he is portrayed as being especially autistic or mentally unstable, with two extreme examples of that being the recent film Imitation Game and the novel A Madman Dreams of Turing Machines. There is none of that here; McEwan's Turing seems quite "normal". It is also worth mentioning that this is not the only work of speculative fiction to imagine Turing somehow living on beyond 1954 in some form or other. (See also Oracle, Tangents and Turing (A Novel About Computation).)

There is a tiny bit more mathematics in this novel than what I mentioned above. Adam, the android, twice explains how he uses Bayesian probability models, not only to improve Charlie's investments but also to make predictions about the outcomes of future events in their own lives. Charlie tries to read about P vs. NP, noting the use of the technical notation "iff" and quoting a Field's medalist, but in the end doesn't really understand it. He briefly ponders going to university to earn a degree in mathematics. And at one point he thinks of Miranda in mathematical metaphors:

(quoted from Machines Like Me)

Then might she resemble a counter-intuitive Euclidean proof? I couldn't think of one. But after half an hour of fast walking, I thought I'd found the mathematical expression for her: her psyche, her desires and motives were inexorable, like prime numbers, simply and unpredictably there. More old hat, dressed as logic. I was in knots.

This novel masterfully fits together many different pieces, some of which have connections to mathematics, to produce a lovely and thought provoking whole.


Note: I've written a joint review of this novel along with A Universe of Sufficient Size that covers many details not mentioned in this post. It is to appear in the Notices of the American Mathematical Society.

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(Note: This is just one work of mathematical fiction from the list. To see the entire list or to see more works of mathematical fiction, return to the Homepage.)

Works Similar to Machines Like Me
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. Turing (A Novel About Computation) by Christos Papadimitriou
  2. Oracle by Greg Egan
  3. Tangents by Greg Bear
  4. The Discrete Charm of the Turing Machine by Greg Egan
  5. A Doubter's Almanac by Ethan Canin
  6. A Universe of Sufficient Size by Miriam Sved
  7. The Tenth Muse by Catherine Chung
  8. The Invention of Ana [Forestillinger om Ana Ivan] by Mikkel Rosengaard
  9. The Proof of Love by Catherine Hall
  10. The Wild Numbers by Philibert Schogt
Ratings for Machines Like Me:
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)
.

Categories:
GenreScience Fiction,
MotifProving Theorems, Real Mathematicians, Romance, Turing,
TopicComputers/Cryptography, Real Mathematics, Mathematical Finance, Probability/Statistics,
MediumNovels,

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(Maintained by Alex Kasman, College of Charleston)