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Paradox (2000)
John Meaney
(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.

Young Tom Corcorigan seems to represent the lowest "caste" in the extremely hierarchical human society of the year 3404. However, his mathematical abilities (he is able to figure out a way around Gödel's theorem) and his chance encounter with one of the mythical "pilots" (who visited the fractally dimensional mu-space) send him on a dangerous "roller coaster ride" - both higher and lower in this hierarchy than he would have ever thought possible.

This second novel by award winning SF author John Meaney is written in an ususual style, but works quite well. It is highly recommended to visitors to this site who enjoy science fiction laced with a good deal of mathematics. It is one of the most mathematical SF novels I have read, in fact. Although the mathematics itself does not make much sense (see below), the feeling of mathematics is well captured by the author (who has an undergraduate degree in physics and has worked in the IT industry) and it is integrated well into the larger plot. The author's interest in martial arts is also exercised in the book. In fact, there is a bit too much focus on karate in the book for my own tastes, but if you like that kind of thing it will be just another positive aspect of this generally quite good tale.

The larger plot concerns the "Oracles" who (apparently due to the reversal of time at the beginning of the "Big Crunch") can sometimes remember the future instead of the past. Like the forecasts of the psychics in "Minority Report", they are used in morally questionable ways by the government, and Tom (who by this point is himself part of this government) becomes involved in a plot to eliminate them.

I sometimes fold down the corners of the pages in the books that I read which make reference to mathematics so that I can easily find them later. Looking now at Paradox, I see 27 such folds. (Perhaps we could make this an official measure of mathematical content on this website.) Just to give you some of the flavor, let me quote one of them. In this passage, Tom is trying to impress an academic panel of royalty with his brilliance. This is difficult since he must follow the brilliant Avernon who has just presented a "theory of everything" that overthrows a thousand years of physics.

(quoted from Paradox)

I know stuff the others don't. Slow exhalation. Use it. "Inspiring, isn't it?" He meant Avernon's theory. "Broad as well as deep."

Striding carefully across the polished floor, he gestured one holodisplay after another into existence.

"So revolutionary, no-one's had time to work through the implications." Animated now, he was surrounded by wafting translucent phase space manifolds: gossamer sheets manifested in light.

"If you think of it" -- causing a burst of new volumes: blue, silver, and a hundred pastel shades -- "it resolves the ancient negentropy question once and for all."

Stillness in the chamber.

Tom drew Avernon-style metavectors into position. The Lords, eyes flickering, descended into deep logosophical trance.


His key display was a simple 3D static image: glistening, roughtly spheroidal, denoting a flat (2D) universe. It started as a point, grew larger to a maximum diameter, then shrank again to another point. The unvierse as a giant pearl; time as a horizontal axis.

Base everything around that.


There were, in effect, two big bangs. Two cosmic histories colliding in the middle, where time switched over from one direction to the other. The concept was called Gold-Sakharov negentropy, and it was so old that Tom was not sure of its origins.

Pause now.

Tom allowed the Lords to meditate on his display.

"Previous arguments," he continued after a few minutes, "have relied on symmetry. Avernon's -- excuse me, Lord Avernon's -- metavector actually requires it" -- he pointed to a twisting manifold -- "for consistency."

Beyond the simple pearl image, more sophistacted imagery showed the cosmos as a hypersphere (subtly different-hued, distorted spheroieds nestling along a notional time-axis) and as a moving construct in 12-space.

"It would be interesting to see how that would map to mu-space--"

Destiny! The lords, stony-faced in logotropic trance, said nothing. What have I revealed?

"-- which I know nothing of, except that its mythical dimensions were supposed to be fractal. As a though experiment, consider the possibility of an infinitely recursive, self-referencing statement, attempting to compete itself."

I'm doing it.

Excited now, almost forgetting the committee, Tom waved golden seas and spongiform black stars into being.

"The number of depths and number of instances are both infinite. But is one infinity a bigger class of infinity than the other?"

He waited a moment, then plunged on.

"By applying the metavector" -- almost dancing, he manoeuvered through his images -- "we see that it negates Gödel's theorem as a direct analogue of negating unidirectional entropic time in realspace."

No questions.

There could not be, for the Lords were too deep in trance to verbalize and Tom had full control of the holos.

"-- Which brings us back to the symmetry arguments. Our realspace cosmos begins from a tiny locus, expands with time until a maximum is reached, then contracts once more to a near-point."

Pearl. Simple image.

"The universe essentially has two origins in time, which grow forwards to meet each other. Two big bangs. We can't know which half of the cosmic life cycle we're in."


"Now the Avernon metavector" -- Tom hid a smile, wondering if he had just coined a name for posterity -- "requires the symmetry. But symmetry cannot be broken at the end points, at the big bang or crunch, any more than at the midpoint. So, in fact, the universal history must look like this."

The universe was no longer a single pearl.

It was a long string of pearls, one after the other.


It was the true cosmic cycle, revealed for the first time.

At some points, the text breaks out into pure mathematical notation (proof-trees). I'm not sure exactly what it says (nothing too deep as far as I can tell), but the author explains that he is using the notation that Woodcock and Davies developed for formal symbolic proof.

More information about this work can be found at
(Note: This is just one work of mathematical fiction from the list. To see the entire list or to see more works of mathematical fiction, return to the Homepage.)

Works Similar to Paradox
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. Light by M. John Harrison
  2. Neverness by David Zindell
  3. The Disposessed by Ursula K. Le Guin
  4. Ninefox Gambit by Yoon Ha Lee
  5. To Hold Infinity by John Meaney
  6. We by Yevgeny Zamyatin
  7. Resolution by John Meaney
  8. Context by John Meaney
  9. The Atrocity Archives by Charles Stross
  10. Diaspora by Greg Egan
Ratings for Paradox:
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:
4/5 (3 votes)
Literary Quality:
4/5 (3 votes)

GenreScience Fiction,
MotifCool/Heroic Mathematicians, Kurt Gödel,
TopicMathematical Physics, Chaos/Fractals, Logic/Set Theory,

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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)