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Permafrost (2019)
Alastair Reynolds
(click on names to see more mathematical fiction by the same author)

The daughter of the mathematician whose research led to a practical method for time-travel is sent back in time to save the world in this creative science fiction novella.

Although I describe the work as "creative", much of it sounds derivative. The idea that humans would use time-travel to save the world from a future ecological apocalypse is, by now, nearly a cliche. And, the method utilized here (sending the mind of a person from the future into the body of a person in the past) is also not particularly original (see Travelers). However, Reynolds adds more than enough new twists to these familiar ideas to compensate.

Three characters are presented as being mathematicians:

  • Luba Lidova was a mathematical physicist studying a (fictional) sort of quantum entanglement which allows for manipulation of past events.
  • The main protagonist, Valentina Lidova, is Luba's daughter. She is 70 years-old in the book's "present" and teaching math to children, even though she has every reason to believe that the human race will soon be extinct.
  • Margaret Arbetsumian is the mathematical physicist whose job it is to practically apply Lidova's abstract theory for the time-travel project.
Despite the fact that these three characters are mathematicians, there is relatively little actually said about math. Here is one passage in which Lidova's research is discussed in rather vague terms:

(quoted from Permafrost)

"My mother worked on quantum models for single-particle time travel. She showed how an electron -- or anything else, really, provided you could manipulate it, and measure its quantum state -- an electron could be sent back in time, looped back into the past to become a twin of itself in the future, one half of a Luba Pair. if you manipulated either element of the Luba Pair, the other one responded. You could send signals up and down time. But that was all. You couldn't send back anything much larger than an electron -- maybe an atom, a molecule, at the extreme limit, before macroscopic effects collapsed the Luba Pairing. And just as critically, you couldn't observe that time travel had happened. It was like a conjuring trick done in the dark. The moment you tried to observe a Luba Pair in their time-separated state, you got washed out by noise effect."

"Paradox", Margaret said. "Black and white. Either present or absent. If you don't observe, paradox hides its claws. If you attempt to observe, it kills you -- metaphorically, mostly."

I nodded. "That's correct."

"But your mother went beyond binary paradox," Cho said. "She developed a whole class of models in which paradox is a noise effect, a parameter with grey values rather than just black and white."

"She spoke about it less as she got older," I replied. "They hammered her, the whole establishment. Treated her like an idiot. Why the hell should she indulge them anymore?"

"Your mother was correct," Cho said placidly. "This we know. Paradox is inherent in any time-traveling system. But it is containable...treatable. We have learned that there are classes of paradox, layers of paradox."

Margaret made an encouraging gesture int he direction of Director Cho. "Say it. You know you want to."

Cho reached for his beer, smiling at the invitation. "Paradox itself is...not entirely paradoxical."

The most intriguing aspect of Lidova's research is how the paradoxes are handled. According to Lidova's theory, a paradox would ripple through spacetime just as a phonon travels through a crystal, eventually disappearing due to a sort of dispersion. In practice, this means that if you received a message sent from your future self and then decide that you will not send yourself that message, you would at first be shocked at the fact that there was an apparent contradiction -- if you didn't send the message to yourself how did you receive it? However, soon you would start doubting that you had received the message as that reality was replaced with another in which you didn't, and eventually you would not remember anything about the message being received in the first place. The paradox is resolved because it never happened; the "crystal lattice" of spacetime has returned to a stable and contradiction-free state.

(Ironically, I thought about this whenever there was something in the book that I had trouble believing. Of course, one often has to suspend disbelief to some extent when reading science fiction. Here I had a lot of trouble believing in the supposed plan to save the world. [Really, if you had the ability to manipulate the past, is this really the best way to save the world from disaster?] There's also a bit with a dog that didn't quite work for me. And every time a "Luba Pair" was mentioned I thought about how odd it was that Lidova would use her own first name that way. But, because I was enjoying the book and wanted to go on with it, I pushed these concerns to the back of my mind until they were forgotten, and I had the strange feeling that I had personally experienced this phonon-like paradox resolution ; )

Here is another passage from the book that discusses math, but the focus is more on the Lidovas and their relationship than on the mathematics:

(quoted from Permafrost)

We had shared a house since Father died, and my mother had come to depend on me as a sounding board for her wilder ideas, almost as if I were an extension of herself, only a more skeptical, questioning one. That had been flattering to me, when I was in my middle and late teens. To have this celebrated intellect, this world-famous mathematician, treating me as an equal, someone capable of seeing her ideas through fresh eyes, made me very special.

But by the time I was approaching my twenties, I knew I had to strike out on my own. I wasn't going to run off and do anything crazy like join a radical arts collective. I still wanted to be a mathematician, but in my own fresh corner of it, a long way away from my mother's crazy work on time-loops and grey paradox.

I do find it interesting (and encouraging) that all three mathematician characters in this book just happen to be female, an apparently unimportant coincidence that doesn't merit any discussion. And, it is always nice to see math used in fiction for a good cause (which I presume we could agree that saving the world would be). However, aside from these points this book does not really use math or say much about the field of mathematics. So, the fact that it is mathematical fiction may not be much of an incentive to read it (unless mathematical fiction is your hobby, as it is mine).

The reason you should read this book, if you like mind-bending science fiction, is for the climactic scene which is original, beautiful, and worth the wait.

More information about this work can be found at
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Works Similar to Permafrost
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. Eversion by Alastair Reynolds
  2. Limited Wish by Mark Lawrence
  3. One Word Kill by Mark Lawrence
  4. Distress by Greg Egan
  5. Archive (Travelers, Season 3 Episode 8) by Ken Kabatoff / Brad Wright
  6. River of Gods by Ian McDonald
  7. The Arrows of Time [Orthogonal Book Three] by Greg Egan
  8. The Outside by Ada Hoffman
  9. Music of the Spheres by Ken Liu
  10. The Circumference of the World by Lavie Tidhar
Ratings for Permafrost:
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:
2/5 (1 votes)
Literary Quality:
4/5 (1 votes)

GenreScience Fiction,
MotifFemale Mathematicians, Time Travel, Math as Beautiful/Exciting/Useful,
TopicMathematical Physics, Logic/Set Theory,

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Exciting News: The 1,600th entry was recently added to this database of mathematical fiction! Also, for those of you interested in non-fictional math books let me (shamelessly) plug the recent release of the second edition of my soliton theory textbook.

(Maintained by Alex Kasman, College of Charleston)