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I am looking for a short story were there is an alien civilization that has been living underground for millenia since the surface froze. A minor but very specific detail I remember is they point out the number of milliseconds it takes for light to travel across their cavern, making it hundreds of kilometers wide, compared to the years to cross interstellar space. They decide to invade Earth by first sending a small cube, and then beaming a mind to Earth to possess a human an activate the cube. I don't remember what the cube does or why it doesn't just activate by itself. They specify that the cube can be activated by twisting knobs on it if it turns out humans are a weak species, or exerting force on its sides if humans are strong, or telekinetically in case the receiving human is paralyzed.. However, the mind ends up in a human baby, who lacks the physical or mental strength to activate the cube. The aliens don't know about babies because they've grown their offspring artificially since they moved underground.

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    I'm sure I read this as a boy, so it's a golden age story. Commented Feb 3, 2023 at 9:38
  • BOOM! It's Asimov! Commented Feb 3, 2023 at 10:33

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The Deep by Isaac Asimov. I read it in the 1973 anthology The Best of Isaac Asimov but it's been published all over the place.

The description of the cube is:

He went on, "This does not mean that the body you find yourself in, its mind and its emotions, may not be completely alien. So we have arranged for three methods of activating the Receiving Station. If you are strong-limbed, you need only exert five hundred pounds of pressure on any face of the cube. If you are delicate-limbed, you need only press a knob, which you can reach through this single opening in the cube. If you are no-limbed, if your host body is paralyzed or in any other way helpless, you Can activate the Station by mental energy alone. Once the Station is activated, we will have two points of reference, not one, and the Race can be transferred to Planet X by ordinary teleportation."

The reference to the cavern size is:

Roi said, "You know the speed of light, I suppose."

"Of course," she replied readily. It was a universal constant. Infants knew it. "One thousand nine hundred and fifty-four times the length of the cavern and back in one second."

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    Wow, I thought I knew every Asimov short story, but this is completely unknown to me somehow, even though I own books it's in. Well done. Commented Feb 3, 2023 at 14:04

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