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The Planck Dive (1998)
Greg Egan
(click on names to see more mathematical fiction by the same author)

This short story describes a bizarre experiment in which researchers are cloned (quantum cloning, not the genetic kind; these researchers aren't "fleshers") and sent into a black hole. Their goal is to attempt to achieve "infinite computation". Both the foundational mathematics of computability theory and mathematical physics play a role.

There is also quite a lot of mathematical name dropping. The city in which they live and the vessel in which they will travel are both named "Cartan", and they even specify which Cartan they are named after:

(quoted from The Planck Dive)

"Cartan Null? What's wrong with that? Cartan was a great flesher mathematician, who clarified the meaning and consequences of Einstein's work. Null because it's built of null geodesics, the paths followed by light rays."

"Posterity," Prospero declared, "will like it better as `The Falling City' -- its essence unencumbered by your infelicitious words."

Tiet said cooly, "We named this polis after Elie Cartan. Its clone inside Chandrasekhar will be named after Elie Cartan. If you're unwilling to respect that, you might as well head back to Athena right now, because no one here is going to offer you the slightest co-operation."

You may have noticed in the quote above that the black hole they are visiting is named after Nobel laureate Subramaniam Chandrashekhar, author of "The Mathematical Theory of Black Holes".

Although it is sometimes hard to delineate between mathematics and physics in science fiction, the description of the physics here is sufficiently mathematical that I believe it qualifies as "mathematical fiction". For instance:

(quoted from The Planck Dive)

"That's assuming a perfectly symmetrical Schwarzschild black hole, which is what we're simulating. And an ancient hole like Chandrasekhar probably has settled down to a fair approximation of the Schwarzschild geometry. But close to the singularity, even in falling starlight would be blue-shifted enough to disrupt it, and anything more massive -- like us if we were really here -- would cause chaotic changes even sooner." She instructed the scape to switch to Belinsky-Khalatinikov-Lifshitz geometry, then restarted time.

Computability theory is full of limitations on what we can determine (and what we can know) due to the finiteness of our computations. However, the story mentions "Tiplerian theology", a clear reference to the theological writings of mathematician Frank J. Tipler. According to this (presumably fictional) philosophy, our goal should be to alter the universe to allow for infinite computation. This is at least one of the goals of the researchers in their "Planck Dive".

(quoted from The Planck Dive)

The two bundles of rays oscillated between circular and elliptical cross-sections as the curvature stretched and squeezed them. Cordelia created a magnifying glass and followed them "in": forwards in time, towards the singularity. She said, "If the orbital periods form a geometric series, there's no limit to the number of orbits you could fit in before the singularity. And the wavelength is blue-shifted in proportion to the size of the orbit, so diffraction effects never take over. So, what's there to stop you doing infinite computation?"

Originally published in Asimov's magazine, February 1998 and reprinted in the anthology "Luminous".

More information about this work can be found at
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Works Similar to The Planck Dive
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. Perturbation - For Nature Computes On A Straight Line (In Seven Balancing Acts) by Vijay Fafat
  2. Location, velocity, end point by Matt Tighe
  3. Planck Zero by Stephen Baxter
  4. Approaching Perimelasma by Geoffrey A. Landis
  5. Diaspora by Greg Egan
  6. Border Guards by Greg Egan
  7. Oracle by Greg Egan
  8. Singleton by Greg Egan
  9. The Arrows of Time [Orthogonal Book Three] by Greg Egan
  10. Transition Dreams by Greg Egan
Ratings for The Planck Dive:
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,
MotifTime Travel, Religion,
TopicComputers/Cryptography, Infinity, Mathematical Physics, Logic/Set Theory,
MediumShort Stories,

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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)