a list compiled by Alex Kasman (College of Charleston)

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Doctor Who: The Turing Test (2000)
Paul Leonard

Mathematician Alan Turing appears as a primary character in this unusual Doctor Who novel, and narrates the first third of it. (The other two thirds are narrated by authors Graham Greene and Joseph Heller respectively!)

Turing, Greene, Heller, and the Doctor get caught up in a conflict between three non-humans sending some mysterious signals from Dresden (where they are posing as Nazis) and two who are hunting them down (one of them posing as a high ranking British officer and the other playing the role of the femme fatale).

The facts that the book is told from the perspective of three real historical figures of the 20th century, that the Doctor himself only appears occasionally, that it somewhat explicitly describes horrific deaths and lustful sex, and that moral relativism is the predominant theme are why I have described this as an unusual Doctor Who book. It is certainly unlike any of the two dozen or so other books about the Gallifreyan Time-Lord that I've read. (Perhaps these features are more common in the Eighth Doctor Adventures; this is the only book I've read from among those.)

I am impressed with the author's attempt to imitate the different styles of the three narrators, even if each has been reduced to a caricature. Turing is portrayed as being earnest, rational (to a fault), naive, child-like, and madly in love with the Doctor. Greene, who is portrayed here during his time working for Kim Philby, is much more jaded and obsessed with religion. The tone switches to a madcap comedy when Heller takes over the narration, but somehow it all fits together into a whole that has a surprising philosophical depth for a Doctor Who novel.

Let me say a bit about the ways that math arises in the book:

In the first part which is narrated by Turing, math arises frequently as a practical matter in his discussion of his daily activities or in metaphors. For example:

(quoted from Doctor Who: The Turing Test)

I was to give a lecture on Computable Numbers at St. John's.

(quoted from Doctor Who: The Turing Test)

The white stony paths were as straight as solved equations, the sharp winter sun-shadows crossing the lawn as sharply defined as the boundaries of sets, the toothed walls of the College and its Chapel approaching me were like huge stone gear wheels frozen in the middle of a suddenly comprehended calculation.

On page 18, Turing tests the Doctor by saying "There's a problem with Hilbert's theory of groups that has always troubled me." Turing is suitably impressed by the Doctor's answer. (Was this intended to be a reference to Hilbert's Fifth Problem? Other than that, I don't really associate David Hilbert with group theory.)

Page 29 begins with an analogy between the trust on which friendships depend and the axioms that underlie mathematical theories which then morphs into a brief discussion of Turing's work on computable numbers. A longer discussion of computable numbers appears on page 53. It's actually a pretty nice description of the math whose only real fault is that it exaggerates the importance of the result by failing to mention Gödel's closely related work which preceded it.

Math becomes especially important to the plot in the third portion narrated by Heller when Turing explains how the Doctor's plan relies on the mathematical nature of reality itself:

(quoted from Doctor Who: The Turing Test)

"You're telling me that they're made of equations?" I asked him.

"Well, in a sense we're all made of equations. This flesh -" he pinched his hand - "is the effect of a wave on a particle. It isn't 'solid', except in a theoretical, geometrical sense. Changing the nature of the mathematics that describes my hand would change the nature of its reality -"

I interrupted quickly, before he became completely incomprehensible. "So, the world is just arithmetic made flesh."


"And that makes a difference?"

He stared at me. "Of course it makes a difference! If the world can be explained entirely in terms of mathematics, and you can alter that description, then you can do anything you like!"

Finally, although I don't really consider this to be mathematical, Turing is inspired by his encounter with the Doctor and the other aliens to devise a test involving someone trying to decide whether something is "human", thereby justifying the title.

Note: It was Vijay Fafat who told me about this work of mathematical fiction way back in 2012. However, his e-mail message arrived at an unfortunate time and was misplaced. I only rediscovered that message in 2021 and am working my way through the many suggestions it contained. I am very grateful to Vijay for the suggestion and also very sorry that it has taken me so long to act upon it.

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Works Similar to Doctor Who: The Turing Test
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. Cryptonomicon by Neal Stephenson
  2. Doctor Who: The Algebra of Ice by Lloyd Rose (pseudonym of Sarah Tonyn)
  3. To Say Nothing of the Dog by Connie Willis
  4. The End of Mr. Y by Scarlett Thomas
  5. The Smithsonian Institution by Gore Vidal
  6. The Pythagoras Problem by Trevor Baxendale
  7. Doctor Who (Episode: Logopolis) by Christopher Bidmead
  8. Mathematica by John Russell Fearn
  9. The Atrocity Archives by Charles Stross
  10. Oracle by Greg Egan
Ratings for Doctor Who: The Turing Test:
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:
4/5 (1 votes)

GenreHistorical Fiction, Humorous, Science Fiction,
MotifAliens, Real Mathematicians, War, Time Travel, Turing,

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Exciting News: The total number of works of mathematical fiction listed in this database recently reached a milestone. The 1,500th entry is The Man of Forty Crowns by Voltaire. Thanks to Vijay Fafat for writing the summary of that work (and so many others). I am also grateful to everyone who has contributed to this website. Heck, I'm grateful to everyone who visited the site. Thank you!

(Maintained by Alex Kasman, College of Charleston)