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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

Gate  
  A opening through spacetime to other worlds.  

As far as I know, this is the first use of the word "gate" to describe this idea.

Gordon’s obvious bewilderment seemed to amuse the bluish-gray monstrosity. "May I introduce myself?" he asked with a mocking note in his metallic voice. 1 am Arlok of Xoran. I am an explorer of Space, and more particularly an Opener of Gates. My home is upon Xoran. which is one of the eleven major planets that circle about the giant blue-white sun that your astronomers call Rigel. I am here to open the Gate between your world and mine.”

"We of Xoran need your planet and intend to take possession of it," Arlok continued, "but the vast distance which separates Rigel from your solar system makes it impracticable to transport any considerable number of our people... it requires over five hundred and forty years for them to cross that great void. So I was sent as a lone pioneer to your Earth to do the work necessary here in order to open the Gate that will enable Xoran to cross the barrier in less than a minute of your time."

"That Gate is the one through the fourth dimension, for Xoran and your planet in a four-dimensional universe are almost touching each other in spite of the great distance separating them in a three-dimensional universe... by the use of apparatus to open a Gate, [we] pass through a thin sector of the fourth dimension..."

Technovelgy from The Gate to Xoran, by Hal K. Wells.
Published by Astounding Science Fiction in 1931
Additional resources -

Although this seems to have been the first, Jack Williamson used the same word and idea in his Through the Purple Cloud published just a few months later in Wonder Stories:

The purple circle that came in front of the plane looked just like that… We have seen the gate to our world opened again - I am sure of it.

This idea has been used many times; I was also thinking of how Robert Heinlein used the idea of the Ramsbotham Gate from his 1955 novel Tunnel in the Sky:

Ramsbotham's discoveries eliminated the basic cause of war and solved the problem of what to do with all those dimpled babies. A hundred thousand planets were no farther away than the other side of the street. Virgin continents, raw wildernesses, fecund jungles, killing deserts, frozen tundras, and implacable mountains lay just beyond the city gates, and the human race was again going out where the street lights do not shine...

Also, compare to the Invasion Gate for Aliens from Monsters of Mars (1931) by Edmond Hamilton, the gateway from Wanderer of Infinity (1933) by Harl Vincent, the Jiffy-Scuttler from Prominent Author (1954) by Philip K. Dick, Ramsbotham Gate from Tunnel in the Sky (1955) by Robert Heinlein, the farcaster from Hyperion (1989) by Dan Simmons.

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Additional resources:
  More Ideas and Technology from The Gate to Xoran
  More Ideas and Technology by Hal K. Wells
  Tech news articles related to The Gate to Xoran
  Tech news articles related to works by Hal K. Wells

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