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"You have to budget the number of fuzzy rules you use to control a system. It turns out, you can state the optimality principle in three words: 'patch the bumps.'"
- Bart Kosko

Multi-Generation Space Vessel (Generation Ship)  
  A space ship and voyage intended to last across multiple human generations.  

Very early science fiction story about this idea.

THE SPACE VESSEL was traveling swiftly. Behind it stretched the vast, frightening reaches of interstellar space...

For over five thousand years they had Voyaged on and on, steadily, ceaselessly, two hundred and fifty miles a second, eighty billion miles a year. Time had ceased to hold any meaning; space itself was. an interminable nothingness in which they seemed suspended forever and ever...

This was their world, their planet — this swift-traveling, yet seemingly moveless vessel. They knew no other, knew nothing of the wilder, freer life, except for tales distorted by the mists of time and many tellings, legends that smacked, perchance, of wish fulfillments for that earlier Golden Age of their ancestors.

Warlo, his tawny beard and high forehead granting him a nobility his slighter frame could not, turned wearily back to his instruments. On him devolved the management of the space ship, the government of its thousand-odd inhabitants.

Their strangely remote ancestors had builded well. The long ellipsoid of still unrusted, still unpitted metal was almost a mile from stem to stern, and half a mile in diameter at its widest point. It was a world in miniature, a closed cycle in which nothing was wasted, nothing dissipated.

The radiant walls still glowed as of old, though somewhat dimmer, and furnished light and the stimulating rays without which life cannot exist. One half of the ship — toward the stern — held earth and loam — in which strange plants — succulent, nourishing — grew and flourished. Stranger animals, small but fat and tender, grew to maturity in crystal-inclosed runs, bred their young, and paid the eventual penalty for all toothsome, subordinate forms of life.

By careful, exact measuring a delicate balance was established between plant and animal, between carbon dioxide and oxygen, between warmth and cold. A delicate balance, that called for unceasing, unremitting attention on the part of the leader and his corps of scientists ; a balance, that, once broken, would lead to irremediable disaster.


(The landing 'The Return of the Murians' by Nat Schachner)

Technovelgy from The Return of the Murians, by Nat Schachner.
Published by Astounding Stories in 1936
Additional resources -

Don Wilcox described this idea in his 1940 story The Voyage That Lasted 600 Years:

“This is Captain Sperry telling you good-by,” the amplified voice boomed. “In behalf of the thirty-three, I thank you for your grand farewell. We’ll remember this hour as our last contact with our beloved Earth.”

The crowd held its breath. The mighty import of our mission struck through every heart.

“We go forth into space to live—and to die,” the captain said gravely. “But our children’s children, born in space and reared in the light of our vision, will carry on our great purpose. And in centuries to come, your children’s children may set forth for the Robinello planets, knowing that you will find an American colony already planted there.”

The captain gestured good-by and the multitude responded with a thunderous cheer. Nothing so daring as a six-century nonstop flight had ever been undertaken before.

Robert H. Goddard was perhaps the first to write about multi-generational interstellar voyages in his 1918 essay "The Last Migration". He described the death of the Sun and the need for an interstellar ark. The crew would face the centuries of travel by sleeping and would be awakened when they reach another star system.

Take a look at the article for the first use of the sf phrase "generation ship" from Star Ship (1955), by E.C. Tubb, which has additional references.

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Additional resources:
  More Ideas and Technology from The Return of the Murians
  More Ideas and Technology by Nat Schachner
  Tech news articles related to The Return of the Murians
  Tech news articles related to works by Nat Schachner

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