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"The immediate problem with our meat brains is that they have no back-up. We can lose the most precious information we have from one bump on the head or stroke. You want a mind system with back-up that can access other databases."
- Bart Kosko

Metal Calculator Planet  
  A planet covered entirely with machinery to a height of twenty miles and covered with a metal roof.  

In this great story by Simak, explorers land on a mysterious, dead planet that appears to consist entirely of burnished metal.

...there was a metal planet, third outward from the sun. Not a lump of metallic ore, but a planet with a surface - or a roof - of fabricated metal burnished to the polish of a bright steel mirror.

And what happens when they find the door to the inside?

It was machinery, of course. It could be nothing else...

There were shafts and pools and disks and banks of shining crystal cubes that might have been tubes, although one couldn't be sure.

There were cubic miles of it, and it glistened like a silvery Christmas tree in the fanning of the helmet lights, as if it had been polished no more than an hour before...

They found the planetary surface - twenty miles below.

From Limiting Factor, by Clifford Simak.
Published by Startling Stories in 1949
Additional resources -

What was the purpose of the machinery?

"An analytical machine is a matter of size," said Buckley. "Each integrator corresponds to a cell in the human brain. It has a limited function and capability. And what one cell does must be checked by two other cells. The 'tell me thrice' method of making sure there is no error.'"

The explorers theorize that the planet was an enormous calculator that was abandoned when it was no longer possible to build any additional elements.

This notion anticipates the idea that the Earth is really an enormous computer built to discover the ultimate question; this idea appears in the work of Douglas Adams.

The stories that later became the Foundation trilogy were published starting in 1942 (and throughout that decade), so the idea of a planet that has been entirely built over is probably Asimov's.

If you enjoy computers on a planetary scale, check out the Gigagnostotron from Stanislaw Lem's 1965 novel The Cyberiad: Fables for the Cybernetic Age.

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Additional resources:
  More Ideas and Technology from Limiting Factor
  More Ideas and Technology by Clifford Simak
  Tech news articles related to Limiting Factor
  Tech news articles related to works by Clifford Simak

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