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Riding the Crocodile (2005)
Greg Egan
(click on names to see more mathematical fiction by the same author)

Contributed by Vijay Fafat

A couple from the race of “Amalgam” wanted to carry out one project before choosing to die after a life spanning tens of thousands of years: Establishing contact with the elusive race called “Aloof”. While the Amalgam had established an empire spaning the disk of the galaxy, they could never penetrate the central bulge, which had apparently been sealed off by the Aloof, who had no desire to establish any sort of communication with them.

The story chronicles this long chase. At one point, the couple discovers traces of a signal leakage coming from the Aloof space but to get into position to properly observe it, they have to solve a geometric problem:

(quoted from Riding the Crocodile)

He asked the map, “Are there two outposts of the Amalgam lying on a straight line that intersects the beam?” The map replied in a tone of mild incredulity. “No.” “That was too much to hope for. Are there three lying on a plane that intersects the beam?” The map said, “There are about ten-to-the-eighteen triples that meet that condition.” Leila suddenly realised what it was he had in mind. She laughed and squeezed his arm. “You are completely insane!” Jasim said, “Let me get the numbers right first, then you can mock me.” He rephrased his question to the map. “For how many of those triples would the beam pass between them, intersecting the triangle whose vertices they lie on?” “About ten-to-the-sixth.” “How close to us is the closest point of intersection of the beam with any of those triangles — if the distance in each case is measured via the worst of the three outposts, the one that makes the total path longest.”

“Seven thousand four hundred and twenty-six light years.” Leila said, “Collision braking. With three components?” “Do you have a better idea?”

(quoted from Riding the Crocodile)

With standard two-body collision braking, the usual solution was to have the first package, shaped like a cylinder, pass right through a hole in the second package. As it emerged from the other side and the two moved apart again, the magnetic fields were switched from repulsive to attractive. Several “bounces” followed, and in the process as much of the kinetic energy as possible was gradually converted into superconducting currents for storage, while the rest was dissipated as electromagnetic radiation. Having three objects meeting at an angle would not only make the timing and positioning more critical, it would destroy the simple, axial symmetry and introduce a greater risk of instability.

It was dawn before they settled on the optimal design, which effectively split the problem in two. First, package one, a sphere, would meet package two, a torus, threading the gap in the middle, then bouncing back and forth through it seventeen times. The plane of the torus would lie at an angle to its direction of flight, allowing the sphere to approach it head-on. When the two finally came to rest with respect to each other, they would still have a component of their velocity carrying them straight towards package three, a cylinder with an axial borehole. Because the electromagnetic interactions were the same as the two-body case — self-centring, intrinsically stable — a small amount of misalignment at each of these encounters would not be fatal. The usual two-body case, though, didn't require the combined package, after all the bouncing and energy dissipation was completed, to be moving on a path so precisely determined that it could pass through yet another narrow hoop.

This story takes place in the same "universe" as the book Incandescence, in the sense that the same alien species appears in that novel. It was first published in One Million A.D., edited by Gardner Dozois; Science Fiction Book Club, 2005.

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Works Similar to Riding the Crocodile
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. Incandescence by Greg Egan
  2. Diamond Dogs by Alastair Reynolds
  3. Schild's Ladder by Greg Egan
  4. Dichronauts by Greg Egan
  5. The Clockwork Rocket [Orthogonal Book One] by Greg Egan
  6. Diaspora by Greg Egan
  7. Singleton by Greg Egan
  8. Border Guards by Greg Egan
  9. Dark Integers by Greg Egan
  10. Glory by Greg Egan
Ratings for Riding the Crocodile:
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:
3/5 (1 votes)

GenreScience Fiction,
MediumShort Stories, Available Free Online,

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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)