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Beyond Infinity (2004)
Gregory Benford
(click on names to see more mathematical fiction by the same author)

Cley is one of the few "original" humans left in a future where most of the characters are genetically enhanced. These engineered lifeforms, whether they are Supras (a highly advanced humanoid) or based on some other natural species, look upon Cley as hopelessly primitive.

There are some discouraging words about mathematics right at the bottom of the first page:

(quoted from Beyond Infinity)

This gave her a kind of status. Not many true Originals walked the Earth, though the historians who pestered her early education said there had once been billions of them afoot. Billions! There were hardly a tenth that many now in all Earthly humanitarian's. Not that she cared much about such numbers. Mathematics was a fossil art. Few in her time bothered to scale those heights of analysis with their majestic, abstruse peaks that the ancient civilizations had climbed, marked as their own, and finally abandoned as too chilly, remote, and even inhuman.

The main plot of the book involves a devastating attack by immaterial beings who desperately wish to eliminate all "originals" like Cley. She is saved by "Seeker", a genetically engineered raccoon who seems to know quite a bit of math himself. Twice when Supras mention something about infinite, Seeker shows off by commenting on the different sizes of transfinite cardinals. It turns out that the attackers know advanced mathematical physics which sounds a lot like String Theory. Coincidentally, Cley and the Supra librarians she was working with were investigating the ancient Earth culture that discovered it. Here she discusses it with a Supra who taught Cley to communicate telepathically:

(quoted from Beyond Infinity)

Cley frowned. "What's beyond the stars?

Spaces, geometries -- beyond infinity, in a way.

Cley sent, Beyond our universe?

Other dimensions, other....surfaces, in those dimensions. Membranes. It is difficult to explain without training in the topologies of space-time.

Seeker seems to know a lot about it also:

(quoted from Beyond Infinity)

[Seeker:] "I suspect it will be a morph form that manifests in this geometry as more cylindrical, to match the boundary conditions."

Cley blinked. "You we're once a mathist, weren't you?"

"All procyons [i.e. genetically engineered raccoons] are, as children."

"I didn't learn words like `symmetry principle.' mathists do."

(quoted from Beyond Infinity)

All this seemed like abstract fictions to Cley, even when Seeker had explained that the idea had led to mathematics that nicely packaged up the fundamental forces, starting with gravity. In theory, the forces then all merged "naturally" -- for the mathematically minded. To Cley, this had verged on the theological... ...But even those ancient mathists had not envisioned a place like this Tubeworld, a dimension simultaneously near infinite along it cylindrical length, but small enough across to walk around in an hour.

There is one place where Cley demonstrates she isn't completely incapable of thinking mathematically (imagining a reversal of chirality of a 3D-object following a rotation in 4D-space). She achieved this with lots of hints from Seeker who seemed very proud of her after she did this. But, often the point seemed to be to emphasize how bad at math and uninterested in it this "Original" was. (I started finding this mathematical paternalism quite annoying.)

At one point Seeker tosses in an insult to the mathematical (in)abilities of "Ur"-humans like Cley along with a discussion of the fact that deterministic theories of mathematical physics do not necessarily lead to effective predictions:

(quoted from Beyond Infinity)

Seeker said, "The Ur-humans found all such laws -- the work was that elementary. But, to know how gravity pulls upon a body does not mean even in principle that you can force how many such bodies will move."

Here is one more mathematical quote, in which one of the Supras explains how the bad guys discovered faster-than-light travel:

(quoted from Beyond Infinity)

On average, empty space has zero energy. But by enclosing a volume with a sphere of conducting g plasma, the Malign prevented the creation of waves with wavelengths larger than that volume. These missing waves gave the vacuum a net negative energy and allowed formation of a wormhole in space-time. All such processes are ruled by probabilities requiring great calculation. Yet through that hole the Maling slithered.

This science fiction novel is written in an unusual style that the author calls "transcendental adventure". To me, it seemed to be little more than a drug-fueled delusion sprinkled nonsensically with mathematical terminology. That description could also fit much of Rudy Rucker's writings, but in my opinion Rucker is much better at it than Benford. I found this novel nearly unreadable. But, you might love it. If you've read this book and would like to see this forum to say positive things about it, used the "ratings" feature below to enter your own ratings and comments.

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Works Similar to Beyond Infinity
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. Diamond Dogs by Alastair Reynolds
  2. The Eighth Room by Stephen Baxter
  3. Distances by Vandana Singh
  4. Schild's Ladder by Greg Egan
  5. The Exception by Alex Kasman
  6. Artifact by Gregory Benford
  7. From the Earth to the Moon [De la Terre à la Lune, trajet direct en 97 heures 20 minutes] by Jules Verne
  8. Catch the Lightning [Lightning Strikes Vols. I-II] by Catherine Asaro
  9. Light by M. John Harrison
  10. Applied Mathematical Theology by Gregory Benford
Ratings for Beyond Infinity:
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 (2 votes)
Literary Quality:
2/5 (1 votes)

GenreScience Fiction,
TopicGeometry/Topology/Trigonometry, Infinity, Mathematical Physics,

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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)