# Counting heads

Mathematical sf isn’t very common, but it can be very good indeed – as I was reminded when I recently read Vandana Singh’s “Infinities” in the Hartwell/Cramer *Year’s Best SF 15*. There are a couple of theme anthologies on the subject – Rudy Rucker’s *Mathenauts* (1987) and Clifton Fadiman’s *Fantasia Mathematic*a (1958) and *The Mathematical Magpie* (1962). Since the Rucker book, several writers have emerged who write around mathematical themes a lot – Greg Egan and Ted Chiang are the obvious names – but unless I’ve missed something, there hasn’t been a dedicated anthology on the subject since 1987.

So this is a first attempt to put together a current bibliography of mathematical sf. Additions are welcomed in the comments. Let me try, though, to suggest a couple of guidelines: 1) Don’t duplicate the stories carried in the three anthologies mentioned above (follow the links for full contents); 2) Stories must be clearly sf (so no, eg, math puzzles with sf elements); 3) Stories must be professionally published; 4) If you can give a book publication, that’s better (because more accessible) than a magazine publication; 5) I’m really looking for stories with mathematics as a central element rather than just a part – so no stories about, say, the Singularity unless they have a specific mathematical extra element. And if they’re good stories, all the better.

- Abbott, Edwin, A. (1884)
*Flatland* - Chiang, Ted (2002)
*Stories of Your Life and Others* - Egan, Greg – just about everything, esp
*Axiomatic*(1995)*Luminous*(1998)*, Schild’s Ladder*(2002)*, Incandescence*(2008)*.* - Fadiman, Clifton –
*Fantasia Mathematica*(1958) and*The Mathematical Magpie*(1962). - Heinlein, Robert A (1941) “And He Built a Crooked House” (
*Astounding*) - Kingsbury, Donald (2002)
*Psychohistorical Crisis* - Langford, David (1987) “BLIT” (
*Interzone*, collected in*Different Kinds of Darkness*) - Le Guin, Ursula (1974)
*The Dispossessed* - Priest, Christopher (1974)
*Inverted World* - Robinson, Kim Stanley (1987) “The Blind Geometer” (
*Asimov’s*, later published as a Tor Double) - Rucker, Rudy – just about everything, but especially
*White Light*(1980),*Mathematicians in Love (2006)*, and*Mathenauts*(ed) (1987). - Singh, Vandana (2009), “Infinities” (
*The Woman Who Thought She Was a Planet*) - Stephenson, Neal (1999)
*Cryptonomicon* - Stross, Charles – many stories, such as “Antibodies” (2001)
- Zindell, David (1988)
*Neverness*[and sequels]

By the way, the three contents lists linked to above are part of a much larger site called Mathfiction. It’s a very useful resource, but takes a somewhat broader view of the field than I have above – including non-sf works like *The 39 Steps* and sf works like Harrison’s *Bill the Galactic Hero* which reference maths only in passing.

How about Barrington Bayley? I’m thinking “The Exploration of Space”, from New Worlds, collected in The Knights of the Limits.

How about (Tom Godwin’s?) The Cold Equations? A good one beacuse of the unbreakable link between the “cold” mathematical facts and the tragic human consequences that ensue from them. I know it’s been anthologized many times over the years. Also, would Ringworld and Mission of Gravity count under your terms? I think they would.

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Actually I’ve only published two works

aboutmathematics: the short stories “Luminous” and “Dark Integers”. At a stretch, “The Infinite Assassin” could be included. ButSchild’s LadderandIncandescenceare about physics. Since Newton, if not earlier, it’s been plain that physical laws are best expressed through mathematics, but do you really want to subsume all works that include mathematically literate treatments of physics into “mathematical SF”? That’s a bit like subsuming all works where the characters speak grammatically into “linguistic SF”.Would you count Terry Pratchett’s

Pyramids? It is fantasy rather than SF, but mathematics (of a sort) plays a very significant role.Some of Miles Brewer’s stories (collected in The Man With The Strange Head) are mathematical. Unfortunately, they’re also not very good, so after reading three or four I sent my copy of the book out into the Brooklyn stoop circuit, and can’t cite any specific examples. But I know there were others than the one featured in the anthology mentioned above.

I have the same problem thinking of examples that Greg Egan does : does a story count merely because it contains the phrase, “shut up and multiply?” (yes, referring to arithmetic rather than procreation). Is the Wheel of Time mathematical because to count the number of volumes one must resort to contrivances such as Knuth’s up-arrow notation?

Many comments here – thanks, all. Iain & Rose, I haven’t read the Bayley or Pratchett but will seek them out. Thomas, I don’t think Godwin or Clement count, being really about physics more than anything. Greg, I take your point about your work in general; “The Infinite Assassin”, in using the Cantor Dust seems a pretty clear example of mathematical sf, and I was also half-thinking of “Unstable Orbits in the Space of Lies” because of the maths-made-concrete suggested by the title and enacted in the story. Novalis, I’ve only read the Miles Breuer stories in those anthologies, rather than the collection, but so far as I know his work, your verdict seems pretty accurate…

here’s another: “Godel Numbers,” by J.W. Swanson in the March, 1969 issue of GALAXY MAGAZINE.

A J Deutsch ‘A subway named Moebius’ is a classic story about topology

I haven’t read the book but I think “The Last Theorem” by Arthur C. Clarke and Frederik Pohl might match your criteria.

Rudy and I have been talking for a while about putting together another such anthology, so your discussion is helpful.

I believe that Michael Flynn’s “In the Country of the Blind” was based upon sociometric statistics. By this logic, of course, all of Asimov’s “Foundation” novels count.

There was a story from a couple or three years ago about needing prime numbers for teleportation(?) and using them up (not the primeness, but the other use). It was a depressing but clever story in an anthology that was mostly merely depressing, but it did have somewhat about the difficulties of finding primes. Anyone remember it?

Does Dewdney’s

Nice to see this discussion thread. I’ve found a number of unanthologized maths stories over the years, and maybe someday I will in fact edit a new collection.

There exists a math-story anthology not mentioned here yet, this is Imaginary Numbers, edited by William Frucht.

http://www.amazon.com/Imaginary-Numbers-Anthology-Mathematical-Diversions/dp/0471332445

By the way, I have a fairly recent math story online at Tor.com, “Jack and the Aktuals, or, Physical Applications of Transfinite Set Theory.”

http://www.tor.com/stories/2008/10/jackandtheaktuals

Good idea! From my own work:

Applied mathematical theology in NATURE February 2006

Reasons Not to Publish, NATURE Dec 2007

Anomalies, 2006

Around the Curve of the Cosmos, 2007

It seems I had a run of math stories mid-decade. Some of these are in various Best of Year volumes. It’s about time for another anthology of math sf–Rudy?

Gregory

A lot of Egan’s stories foreground mathematical interpretations of physics, or reified instances of mathematical structures. The tesselated intelligences of “Wang’s Carpets”, the geometric progressions of “Into Darkness”–it just seems more mathematics than physics.

Chan Davis, “The Statistomat Pitch,” 1958. Just reprinted in It Walks in Beauty: Selected prose of Chandler Davis. Described by Kasman: http://kasmana.people.cofc.edu/MATHFICT/mfview.php?callnumber=mf860

1.

Note that the URL in Josh’s comment has a link to a link to a 2008 anthology that includes five pieces of math-related fiction. (This is on the MATHFICT site that Sleight notes in the original post.)

2.

Consider Joseph Martino’s “Paper Virus” from the mid-Dec. 1993 Analog. Total spoiler follows:

In the course of the story it is discovered that an alien society has quietly infiltrated human society in preparation for a first contact that will not be to our advantage. As part of the prep, they have embedded in our literature erroneous mathematical results in obscure specialties. They know that these specialties are too obscure (now) to draw critical attention; and that lazy mathematicians will use the sabotaged papers as foundation for further work. To understand and respond to the alien technology, humans will need these results suddenly and will not have time to detect the errors, subverting human countermeasures.

With unseen-by-human-eyes electronic submission, high submission volumes and imperfect database security, could this be done? Has it already been done? How do you know?

(Martino cit. from Locus Index to SF http://www.locusmag.com/index/s452.htm)

Thanks for further comments. A couple of specific responses:

– DGH and Rudy Rucker: would be very interested in a new anthology from you. (_Mathenauts II: Mathier_?)

– Kevin: see Greg Egan’s commentary upthread about his own view of mathematical sf. There may be a meta-point here, though: that in some realms of mathematical physics, the theoretical constructs are so abstract, and so divorced from easily visualisable reality, that one person’s physics-based sf may be another person’s math-based sf.

Novalis: just be thankful that, in numbering the Wheel of Time volumes, we don’t have to resort to aleph notation.

This spring McFarlane will publish a book called _Mathematics and Popular Culture_ (eds Sklar and Sklar). Two chapters will be about Egan’s fiction, and other chapters will address a few other figures and films that are sf.

Did M. K. Joseph write some mathematical SF? I confused him with other writers for years, but I have this nagging sense that either THE HOLE IN THE ZERO or a short story of his was about mathematics.

Also, Terry Bisson’s stories in NUMBERS DON’T LIE are missing from your list.

—Gordon V.G.

This site helpfully lists sequels to FLATLAND: http://www.calormen.com/Flatland/

Hilbert Schenck’s 1983 short story “The Geometry of Narrative” is about a Moebius Strip and is itself a textual example of one. It was nominated for both the Hugo and Nebula but has inexplicably never been reprinted anywhere.

Schenck’s story was in the Aug. 1983 ANALOG.

It occurred to me that “Counting the Shapes” by Yoon Ha Lee (June 2001 issue of F&SF) might be considered mathematical fantasy.

—Gordon V.G.

One of my favorite sf math tales is “Four Brands of the Impossible” by Norman L. Kagan, which appeared in F&SF in the mid-60s. He also had a story entitled “The Mathenauts” in IF.

I’m surprised Robert A. Heinlein’s “And He built a Crooked House” wasn’t mentioned. There’s also an old Christopher Anvil story: ‘Cantor’s War”.

Does Ted Cogswell’s “Probability Zero” spoof “Poulation Implosion” count as fiction? First published in Harry Harrison’s 1973 JWC tribute anthology, ASTOUNDING.

It occurred to me today to search the ISFDB.ORG database for stories with “Abacus” in the title. There’s a recent YA novel with that title by Chris McGowan and there are also black, white, and silver ones in story titles. I published the black one in 2002. It’s a computational SF story, though the computational element is mostly the foundation for the story.

Nancy Lebovitz: the story you are looking for is “Mine the Primes” by Julian Todd (Review here.) from The Elastic Book of Numbers. While most of the stories in that anthology aren’t specifically about mathematics (more about the influence of number on our lives), I think Paul Evanby’s “i” also fits Graham’s description.

My story, “A Board in the Other Direction,” about a game of 4-d chess, was in F&SF (January 1974), reprinted in Fred & Joan Saberhagen’s chess-stories-anthology “Pawn to Infinity” (1982). Also a poem, “Cat Math” (on the importance of mathematics to cats) in Asimov’s (August 2008).

There’s a fairytale from early in the 20th century by Ruth Plumly Thompson (best known for her sequels to L. Frank Baum’s Oz books), title something like “The Princess who Slept” about a princess cursed by an ostensibly wicked wizard to sleep for many years, but her prince, inspired by the powerful combination of “love and logarithms,” realizes that the “curse” really isn’t.

O yeah, there’s also a very nice site abt math in fiction:

http://kasmana.people.cofc.edu/MATHFICT/

Which Graham had already mentioned. Sorry.

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I would also add

The Planiverse: Computer Contact with a Two-Dimensional World by A. K. Dewdney

The Atrocity Archives by Charles Stross

The Time Ships by Stephen Baxter (containing a lot of interesting mathematics)

The Difference Engine by William Gibson

Eon by Greg Bear The Peace War by Vernor Vinge