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Psychohistorical Crisis (2001)
Donald Kingsbury
Note: This work of mathematical fiction is recommended by Alex for hardcore fans of science fiction.

In the far future, a group of "psychohistorians" controls the fate of humanity using the mathematical theory of "the founder" in this unauthorized "sequel" to Asimov's Foundation series. Kingsbury's lengthy novel elaborates upon some interesting ideas that were not fully explored elsewhere, such as the relationship between psychohistorical predictions and "free will" and what would happen if another group was to use the Founder's ideas to try to subvert the goals of the psychohistorians.

While training to be a psychohistorian, our hero Eron Scogil tries to use the Founder's math to study the ancient history of the planet "Rith" [Earth]. (It is both humorous and depressing to see a believable presentation of how little our world would be remembered and understood by our descendants if they inhabit other planets 70,000 years from now.) In doing so, he discovers a modification to the "classical" mathematical techniques used by others which reveals both the role that secrecy plays in maintaining the status quo and the danger posed to the "Pscholars" by the possible existence of other groups who know these secrets. His reward for bringing this knowledge to the attention of his teachers and mentors is a type of capital punishment: the electronic computer that has been part of his brain since his youth is removed and destroyed, leaving him "just an animal" like his ancient human ancestors. (No offense intended to any humans who might be reading this novel, I assume.) And, that's where this story starts. The book is weighty and difficult to get through, but I highly recommend it.

Of course, there are quite a few other books with similar themes. Aside from the already mentioned Foundation, there is The Chimera Prophesies (by a professor of math education), The Dark Side of the Sun (where the math is more a part of a joke than a serious statement of any kind), and In the Country of the Blind. Of these, the last is actually the most similar since it puts a lot of focus on the math itself (and because it is used in Eifelheim to look to the past rather than the future, as it is here).

Since the author taught mathematics at McGill University in Montreal for many years, there is reason to have high hopes for the mathematical content in this book. In fact, mathematics is discussed with great frequency. However, in most cases it is just vague comments about how important math is, how talented the main characters are as mathematicians, and so on without any details.

A more mathematical part of the book occurs when the protagonist arrives at university to study psychohistory. The reader is presented with some hints of what he is studying (e.g. category theory which I think would be unlikely to be useful for predicting human behavior) and quotes from some of his textbooks (I love the one from his physics text).

In addition, some of the other chapters begin with quotations from the writings of the Founder himself, which often contain interesting mathematical ideas:

(quoted from Psychohistorical Crisis)

There is a substantive computational difference between

  1. macro events such as wind or temperature or healthy economy and
  2. micro events like the velocity of an air molecule or a single bankruptcy.
Microevents can be summed over to tell us all we need to know about a macroevent. The velocities of individual air molecules can add up to a wind or a cyclone or a temperature reading. The exchanges between buyer and seller can add up to an economy.p> The process is not reverisible. No macroevent can be broken down into its individual microevents. Important information is destroyed by summation and cannot be recovered. No weather report will tell you the velocity of a particular molecule. No economic index will tell you who bought what, when and where. No psychohisotircal prediction will tell you the fate of the individuals who will act together to generate that future.

-- Excerpt from the Founder's Psychohistorical Tools for Making a Future

When we later learn a bit about his modifications to the "classical" math, it is framed in terms of dynamical systems:

(quoted from Psychohistorical Crisis)

The dynamics of those simple laws were interesting.

When Eron attached (to the methods of prediction) a high coefficient of secrecy, each node, whether community or individual, tended to optimize only its own future. Nonoptimal falsification of negative predictions dominated.


When Eron set the same coefficient of secrecy low enough so that all nodes were sharing each other's negative predictions, quite another dynamics took over: predictive iteration accelerated faster than falsifying action. .... The equations converged to either of two stable states...

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Works Similar to Psychohistorical Crisis
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. Strange Attractors by Charles Soule (author) / Greg Scott (Illustrator)
  2. Foundation by Isaac Asimov
  3. In The Country of the Blind by Michael Flynn
  4. The Dark Side of the Sun by Terry Pratchett
  5. The Chimera Prophesies by Elliott Ostler
  6. The Ah of Life by Banks Helfrich (Writer and Director)
  7. Dark Integers by Greg Egan
  8. Schild's Ladder by Greg Egan
  9. Improbable by Adam Fawer
  10. Dark as Day by Charles Sheffield
Ratings for Psychohistorical Crisis:
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:
3.5/5 (2 votes)
Literary Quality:
4/5 (2 votes)

GenreScience Fiction,
MotifCool/Heroic Mathematicians, Future Prediction through Math, Math as Beautiful/Exciting/Useful,
TopicMathematical Physics, Fictional Mathematics,

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(Maintained by Alex Kasman, College of Charleston)