a list compiled by Alex Kasman (College of Charleston)

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Schild's Ladder (2002)
Greg Egan
(click on names to see more mathematical fiction by the same author)
Highly Rated!
Note: This work of mathematical fiction is recommended by Alex for hardcore fans of science fiction.

Far in the future, the mathematical theory of "quantum graph theory" is the theory of physics. Unlike the current theories of relativity and quantum physics, which are obviously approximations that fall apart when pushed too far, QGT seems to be an entirely correct description of reality from the beginning of the universe onwards: a true theory of everything. And so everyone is surprised when an experiment -- one that QGT predicts to be entirely safe -- goes wrong, producing an expanding "novo-vacuum" that will apparently destroy our universe. The main focus of the book is the moral and scientific questions surrounding the attempts to stop this disaster.

It doesn't take long for this book to get into the mathematics; We see it right on the first page! As in several of Egan's other books, a form of mathematical physics that builds on current theories of quantum gravity is the focal point. The so-called "quantum graph theory" is described in interesting and believable detail. Unlike some other mathematical fiction where the mathematics comes off sounding obviously fake, Egan is able to capture the essence and cadence of mathematical dialogue while saying things that, presumably, are equally fake. Here, for instance, the scientists brainstorm to try to figure out where they went wrong and eventually come up with an explanation that parallels the current attempts to explain the quantum measurement problem in terms of decoherence.

It is always difficult for me, personally, to read SF stories that take place so far in the future that the characters no longer really seem to be human. In this book, for example, bodies have become optional. The fact that I find it more difficult to identify with these characters however is counter-balanced by two wonderful consequences of this plot twist:

  • Egan makes use of this to bring up some interesting questions surrounding the question of "identity" in philosophy. Suppose we could just leave our bodies like a person stepping out of a car, and have a new one what extent do we then identify with our bodies? More mathematically, the title of the book is brought to bear on this old philosophical question. I must admit, I'd never heard of "Schild's Ladder" before, but it is apparently a constructive explanation of the notion of parallel transport of vectors on a manifold. The modern notion of "tangent vectors" in mathematics involves a "tangent bundle", which is to say a separate "tangent space" at each point on the manifold. Although this works well in general, it becomes difficult to say when the tangent vector at one point is the same vector that appears at another. So, the notion of "carrying" a vector around on a manifold becomes a subtle one of practical importance. Here, not only is this notion used to explain (by analogy) how we can tell from moment to moment whether we are the same person, but the mathematical fact that sometimes parallel transport of the same starting vector around different paths with the same endpoints will produce different resulting vectors!
  • One character who has only temporarily taken on the form of a physical human body, is asked by some colleagues about what it was like where he grew up. His response is my favorite line in the book. He explains that he was raised in CP4 (which looks locally like a 4 dimensional complex vector space but has a very different global topology) and that he only sometimes visited 3 dimensional spaces to work on certain bizarre physics problems...but even then, he prefers working in symplectic manifolds where you can separate the positions and momenta!

Contributed by John C. Konrath

I found this work intellectually satisfying. Mr. Egan challenges the reader with plentiful mathematical, physical and biological theories, as well as raising several philosophical questions. This story is an entertaining blend of science-fiction, adventure and mystery. While the characters are unremarkable and at times the plot stretches beyond the believable, overall this book is well worth reading.

Contributed by Scott Guerin

One of my favorite science fiction novels. I go back to reading Clarke and Asimov in the mid 1960s in grade school but this one really sticks with me in its profundity. I need to read it again as I seem to remember Cass and a friend discovered some alien slime mold in their youth but didn't tell anyone about it as they'd have had to evacuate their home I misremembering?

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Works Similar to Schild's Ladder
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. The Arrows of Time [Orthogonal Book Three] by Greg Egan
  2. Dark Integers by Greg Egan
  3. Diaspora by Greg Egan
  4. Distress by Greg Egan
  5. Border Guards by Greg Egan
  6. 3-adica by Greg Egan
  7. Singleton by Greg Egan
  8. The Exception by Alex Kasman
  9. Luminous by Greg Egan
  10. Oracle by Greg Egan
Ratings for Schild's Ladder:
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:
4.37/5 (11 votes)
Literary Quality:
3.73/5 (11 votes)

GenreScience Fiction,
MotifProving Theorems,
TopicGeometry/Topology/Trigonometry, Mathematical Physics, Real Mathematics, Fictional Mathematics,

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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)