I remember in the early 2000s reading a short story collection, a sci-fi book in the nanotech subgenre. One of the stories had something to do with organisms that would search for newer axiom systems in which they could thrive, somehow the more interesting, or rich, axiom systems being the ones that would give better survival odds. Does anyone remember the particulars of this story? I've been wanting to reread it for some time, but haven't been able to locate it.
Sounds like Greg Egan, but I don't recognise that particular story. If you don't get a result here, try a story identification question on Stack Exchange, the residents there are amazing at this:
YES! That's the one :-)
Thanks for identifying it. And it was in that anthology "Nanotech" having editors Jack Dann and Gardner Dozois. I found this interesting article about the story, with links to other similar stories:
"Marsden's data stores contain a fragmented catalogue of mathematical variants. All founded on the postulates of arithmetic, but differing in their resolution of undecidable hypothesis."
"Undecidability. You're talking about the incompleteness theorems,"
"Right. No logical system rich enough to contain the axioms of simple arithmetic can ever be made complete. It is always possible to construct statements that can be neither disproved nor proved by deduction from the axioms; instead the logical system must be enriched by incorporating the truth or falsehood of such statements as additional axioms..."
The Continuum Hypothesis was an example.
There were several orders of infinity. There were 'more' real numbers, scattered like dust in the interval between zero and one, that there were integers. Was there an order of infinity between the reals and the integers. This was undecidable, within logically simpler systems like set theory; additional assumptions had to be made.
"So one can generate many versions of mathematics, by adding these true-false axioms."
"And then searching on, seeking out statements which are undecidable in the new system. Yes. Because of incompleteness, there is an infinite number of such mathematical variants, spreading like the branches of a tree...."
This time he would reach the Sky. This time, before the Culling cut him away...
The tree of axiomatic systems beneath him was broad, deep, strong. He looked around him, at sibling-twins who had branched at choice-points, most of them thin, insipid structures. They spread into the distance, infiltrating the Pool with their webs of logic. He almost pitied their attenuated forms as he reached upwards, his own rich growth path assured...
Almost pitied. But when the Sky was so close there was no time for pity, no time for awareness of anything but growth, extension.
Little consciousness persisted between Cullings. But he could remember a little of his last birthing; and surely he had never risen so high, never felt the logical richness of the tree beneath him surge upwards through him like this, empowering him.
Now there was something ahead of him: a new postulate, hanging above him like some immense fruit. He approached it warily, savoring its compact, elegant form.
The fibers of his being pulsed as the few, strong axioms at the core of his structure sought to envelop this new statement. But they could not. They could not. The new statement was undecidable, not deducible from the set within him.
His excitement grew. The new hypothesis was simple of expression, yet ....
Interesting that they included Cryptonomicon, which is arguably more about IT than mathematics, but they failed to include Stephenson's Anathem [1]: a book about people who live in monasteries called "maths" [2], who spend their whole lives doing mathematics (including at least one scene where the monks demonstrate a basic proof to a novice), in a book which is at its core an apology for mathematical realism, and approaches Platonic metaphysics through a mathematical lens.
Me too! I have a feeling that maybe Anathem appeals to the kind of people who themselves would be pushed into a math at a young age, like Barb. If I was on Arbre, there is no way I would have been tolerated in Sæcular society beyond my 11th birthday, and a.s. I'd be in a centenarian by now.
Definitely not the best, but the most mathematical fiction book might go to Surreal Numbers: How Two Ex-Students Turned On to Pure Mathematics and Found Total Happiness by of course no other than Donald Knuth.
And you could put The Part-Time Parliament by Leslie Lamport near that if you stretch it.
math as a plot device is difficult as anything other than a macguffin, and then even if you did manage to create a popularized understanding of a concept, the backlash about calling it misleading, and to discourage people from reading it, would overpower it.
its why you dont write music for people who make music, there are too few of them to bother pleasing and most will just talk about how you dont know what youre doing and their own basement project is superior. the dearth of mathematical fiction could also be attributed to successful writers knowing better than to write for insufferable readers.
If the point is to list SF stories where a mathematical idea (broadly construed) or a mathematician plays a central role, the following immediately come to mind (for me): Asimov's Foundation, Ted Chiang's "Story of Your Life," and HG Wells's "The Star." (Latter two are not exactly book-length, but I really liked them...)
Flatland was highly recommended in homeschooling circles I ran in back in the day.
A book that notably does not belong on this list but I read it because I thought it would be mathy has the title The Man Who Counts which I completely misinterpreted and continued to be befuddled by even after I finished reading it, having spent the entire book waiting for the math part of the story that never came.
Carl Sagan’s novel Contact is ultimately about a surprising fictional mathematical result, although this is only revealed IIRC toward the end.
The movie adaptation with Jody Foster changes the plot and leaves out much that the 90s movie studios thought general audiences wouldn’t be interested in.
Without giving away too much, the fictional result is a really clever thought experiment by Sagan about the nature of god, if he exists. (Although Sagan wasn’t the first to think of it, he was the first to put it in such an accessible way.)
It’s a fantastic novel, which for some reason isn’t much read these days.
Agreed about being in for a treat! Aww, book three is absurd but one of the most impactful books I have read. I was angry/frustrated with the ending for weeks but that just made the ideas stick better and hold more weight.
Suspension of mathematical disbelief is hard to sustain seriously or at length.
Accordingly, the best mathematical SF/fantasy I can think of is in short stories or novellas which are meant to be humorous. In particular, those criteria characterize:
-- Most of the stories in Fantasia Mathematica and its quasi-sequel anthology Mathematical Magpie.
-- Flatland, which is novella length.
-- The Dragons of Probability, or anything else in Lem's Cyberiad.
Don't be presumptuous; of course i read the article (such as it is).
Other than "Flatland", the other two are not that well-known and the Wikipedia pages for the books are far more informative than this "article"; hence my comment.
PS: One of the comments on the above article's webpage points to this site which seems to be an exhaustive list of "Math Fiction" books - https://kasmana.people.cofc.edu/MATHFICT/
Someone already mentioned Permutation City by Egan, but look at his website for other math ones; he is considered one of the hardest sci-fi authors out there (?).
I second "The Three Body Problem" series (writing is meh but I think the ideas are excellent. Disclaimer: first half of book one is a slog to get through but the second half onwards is fantastic, in my opinion. I keep thinking about the book many years later on a near biweekly basis).
"The Gods Themselves" by Asimov isn't a book mentioned here yet—it has nice math-physics energy ideas.
This list should also include Charles Stross Laundry Files series.
The concept of high math being a gate to higher dimensions and effectively magic powers provides great setting to a witty and humorous sci-fi prose placed in modern England
Greg Egan's diaspora is in this list of 12 books. They chose the novel Diaspora, but many of his short stories and novels are very mathematical. I remember stories about a toric universe, or playing football on a relativistic field (with a pseudo-Riemannian geometry)…
A big miss in this list is Christopher Priest's "Inverted world", about living in a non-Euclidean world.
I've other SF books with a of focus on math, from the "The stochastic man" to "Ninefox gambit", but they were either not enjoyable or with ridiculous mathematical contents.
I enjoyed Heinlein's "And He Built a Crooked House" which is a short story involving tesseracts and 4th dimensional geometry. It was published in the short stories collection "The Unpleasant Profession of Jonathan Hoag".
38 comments
[ 2.4 ms ] story [ 80.9 ms ] threadhttps://scifi.stackexchange.com/questions/tagged/story-ident...
The story is almost certainly Stephen Baxter's The Logic Pool.
https://kasmana.people.cofc.edu/MATHFICT/mfview.php?callnumb...
And this quote:
"Marsden's data stores contain a fragmented catalogue of mathematical variants. All founded on the postulates of arithmetic, but differing in their resolution of undecidable hypothesis." "Undecidability. You're talking about the incompleteness theorems," "Right. No logical system rich enough to contain the axioms of simple arithmetic can ever be made complete. It is always possible to construct statements that can be neither disproved nor proved by deduction from the axioms; instead the logical system must be enriched by incorporating the truth or falsehood of such statements as additional axioms..." The Continuum Hypothesis was an example. There were several orders of infinity. There were 'more' real numbers, scattered like dust in the interval between zero and one, that there were integers. Was there an order of infinity between the reals and the integers. This was undecidable, within logically simpler systems like set theory; additional assumptions had to be made. "So one can generate many versions of mathematics, by adding these true-false axioms." "And then searching on, seeking out statements which are undecidable in the new system. Yes. Because of incompleteness, there is an infinite number of such mathematical variants, spreading like the branches of a tree...."
http://www.vavatch.co.uk/books/baxter/index.htm
Quoting from the beginning of the story:
This time he would reach the Sky. This time, before the Culling cut him away... The tree of axiomatic systems beneath him was broad, deep, strong. He looked around him, at sibling-twins who had branched at choice-points, most of them thin, insipid structures. They spread into the distance, infiltrating the Pool with their webs of logic. He almost pitied their attenuated forms as he reached upwards, his own rich growth path assured... Almost pitied. But when the Sky was so close there was no time for pity, no time for awareness of anything but growth, extension. Little consciousness persisted between Cullings. But he could remember a little of his last birthing; and surely he had never risen so high, never felt the logical richness of the tree beneath him surge upwards through him like this, empowering him. Now there was something ahead of him: a new postulate, hanging above him like some immense fruit. He approached it warily, savoring its compact, elegant form. The fibers of his being pulsed as the few, strong axioms at the core of his structure sought to envelop this new statement. But they could not. They could not. The new statement was undecidable, not deducible from the set within him. His excitement grew. The new hypothesis was simple of expression, yet ....
[1] https://en.wikipedia.org/wiki/Anathem
[2] https://en.wikipedia.org/wiki/Matha
(The war of the flowers was brilliant...)
And you could put The Part-Time Parliament by Leslie Lamport near that if you stretch it.
its why you dont write music for people who make music, there are too few of them to bother pleasing and most will just talk about how you dont know what youre doing and their own basement project is superior. the dearth of mathematical fiction could also be attributed to successful writers knowing better than to write for insufferable readers.
A book that notably does not belong on this list but I read it because I thought it would be mathy has the title The Man Who Counts which I completely misinterpreted and continued to be befuddled by even after I finished reading it, having spent the entire book waiting for the math part of the story that never came.
The movie adaptation with Jody Foster changes the plot and leaves out much that the 90s movie studios thought general audiences wouldn’t be interested in.
Without giving away too much, the fictional result is a really clever thought experiment by Sagan about the nature of god, if he exists. (Although Sagan wasn’t the first to think of it, he was the first to put it in such an accessible way.)
It’s a fantastic novel, which for some reason isn’t much read these days.
https://homepages.inf.ed.ac.uk/rmayr/cyberiad.html
Accordingly, the best mathematical SF/fantasy I can think of is in short stories or novellas which are meant to be humorous. In particular, those criteria characterize:
-- Most of the stories in Fantasia Mathematica and its quasi-sequel anthology Mathematical Magpie. -- Flatland, which is novella length. -- The Dragons of Probability, or anything else in Lem's Cyberiad.
1) Flatland - https://en.wikipedia.org/wiki/Flatland
2) Sphereland - https://en.wikipedia.org/wiki/Sphereland
3) Flatterland - https://en.wikipedia.org/wiki/Flatterland
Always RTFA before commenting. That's what we're all here for: discussion of TFA.
Other than "Flatland", the other two are not that well-known and the Wikipedia pages for the books are far more informative than this "article"; hence my comment.
PS: One of the comments on the above article's webpage points to this site which seems to be an exhaustive list of "Math Fiction" books - https://kasmana.people.cofc.edu/MATHFICT/
I second "The Three Body Problem" series (writing is meh but I think the ideas are excellent. Disclaimer: first half of book one is a slog to get through but the second half onwards is fantastic, in my opinion. I keep thinking about the book many years later on a near biweekly basis).
"The Gods Themselves" by Asimov isn't a book mentioned here yet—it has nice math-physics energy ideas.
https://en.m.wikipedia.org/wiki/The_Laundry_Files
A big miss in this list is Christopher Priest's "Inverted world", about living in a non-Euclidean world.
I've other SF books with a of focus on math, from the "The stochastic man" to "Ninefox gambit", but they were either not enjoyable or with ridiculous mathematical contents.