Has anyone written a story with this idea in it?

The idea being: The society depicted in the story uses technologies similar to computing devices–but the computations are actually done by rational agents hand-calculating at a very rapid pace. What I really have in mind is a bunch of actual human beings residing in a kind of parallel world where time goes much faster than it does here.

Any published works I’ve never read that have that idea as part of their background?

Like the mentats in Dune?

Not human beings but there’s a book where the protagonists are (IIRC) sort of super-slugs living on the surface of a neutron star… off to Google

Oo, here it is Dragon’s Egg

I thought of Dune immediately as well.

Souls in the Great Machine (and it’s two sequels) by Sean McMullen uses a fairly similar idea.
In a non-technological future, a monastery-like facility has hundreds of people all drafted into doing tiny bits of calculations which all add up to some serious computing power (well, serious compared to none at all, that is!)
There’s no parallel world stuff, though, and it’s all takes time to generate answers…

There was a story by (I think) Arthur C. Clarke. The central computer on a spaceship breaks down, leaving the crew unable to pilot it, but they all work together performing the calculations manually, with hastily improvised abacuses (or is it abaci).

An Isaac Asimov story, *The Feeling Of Power*tells of a scientist of the far future who dicovers the previously unkown art of calculations with pencil and paper, instead a computer. The military quickly realizes that the discovery can lead to a new generation of weapons, piloted by cheap expendable humans, instead of valuable computers.

Vernor Vinge’s “Cookie Monster” http://www.analogsf.com/0310/cookie.shtml (and to some extent his novel Deepness in the Sky) have that gimmick.

I have another “is there…” question, and I hope the OP doesn’t mind me asking here.

Is there a story about someone being a Day Trader, one that literally trades days for people? You know, though the day trader Joe Blow trades his Monday for John Doe’s Wednesday.

They didn’t do it super quickly, but the computers which Feynman supervised at Los Alamos were people (mostly women) who would compute parts of a mathematical problem that needed to be solved for the bomb work.

This premise (albeit vaguely) was a minor element in The Diamond Age, in which a society known as The Drummers collectively solve intractable math problems in a manner I can only liken to the climax of a drugged-out orgy in New Orleans during Spring Break.

Logopolis - The residents preform manual calculations on abacus and speak a mathematical language. The people in the buildings send the results back to a the central register, which are people in a room. The computations affect the material world so all calculations must be done by the mind of a living person. They are keeping the universe from ending by entropy, with their mathematical calculations. The universe should have already ended and quickly will if they stop the calculations.

Castrovalva - A single person from the Logopolis story is sustaining a totally made up universe that consists of a town.

Pratchett’s Discworld has “personal disorganizers”, among other technology, that’s run by little demons. Though it’s debatable whether Discworld demons count as sentient, since they’re completely without creativity.

And my mom’s always maintained that the real way that computers work is that there’s a Japanese leprechaun living inside the box, and when the repairman comes, all he’s really doing is slipping the little fellow some sushi and soda bread.

I immediately thought of this story when I read the OP…TRM