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"Poised between intransigent scepticism and uncritical credulity, it [science fiction] is par excellence the literature of the open mind."
- John Brunner

Ultra-microrobot  
  A nanomachine; a machine whose parts are no bigger than atoms.  

In the story, the last two survivors of an expedition are the victims of a peril too small to see. Pilot Al Kerny had an idea:

"...it's almost certain that what made those tiny wounds in MacDowd and the rest of the men were some kind of solid objects - poisoned projectiles that are so small that they're out of sight. The thing to do is to get down to their level of smallness, magnify them so we can fight them in their own size plane..."

He gets out a Scarab - a "microrobot" - about a quarter of an inch long. Scientist Dr. Kurt Rolf was sceptical; even at a quarter of an inch in length, it was hopelessly too big.

"...you haven't got all of my idea yet, Doc. I don't mean that you should construct this ultra-microrobot with your own fingers, of course - at least, not directly. I mean that you should manipulate the robot control, making our Scarab do the work.

Rolf was silent for a moment. Then fierce eagerness seized him...

"With the Scarab as big as a beetle, I could make a Scarab as big as a sand grain. This second Scarab could build a miniature of itself, as big as a dust grain. The third Scarab could construct a fourth, bearing the same proportions as the first to the second, or the second to the third. And so on, down, to the limit imposed by the ultimate indivisibility of the atoms themselves."

From A Menace in Miniature, by Raymond Z. Gallun.
Published by Astounding Stories in 1937
Additional resources -

This story clearly anticipates the idea of a nanomachine, and provides a method for constructing such a device. Other parts of the story contain speculations on whether or not materials would have the necessary properties in extremely small sizes.

Nobel prize-winning physicist Richard Feynman made quite a stir in his famous 1959 speech on nanotechnology by essentially reiterating what Gallun suggested more than twenty years earlier.

Now comes the interesting question: How do we make such a tiny mechanism? I leave that to you. However, let me suggest one weird possibility. You know, in the atomic energy plants they have materials and machines that they can’t handle directly because they have become radioactive. To unscrew nuts and put on bolts and so on, they have a set of master and slave hands, so that by operating a set of levers here, you control the “hands” there, and can turn them this way and that so you can handle things quite nicely.

… Now, I want to build much the same device—a master-slave system which operates electrically. But I want the slaves to be made especially carefully by modern large-scale machinists so that they are one-fourth the scale of the “hands” that you ordinarily maneuver. So you have a scheme by which you can do things at one- quarter scale anyway—the little servo motors with little hands play with little nuts and bolts; they drill little holes; they are four times smaller. Aha! So I manufacture a quarter-size lathe; I manufacture quarter-size tools; and I make, at the one-quarter scale, still another set of hands again relatively one-quarter size! This is one-sixteenth size, from my point of view. And after I finish doing this I wire directly from my large-scale system, through transformers perhaps, to the one-sixteenth-size servo motors. Thus I can now manipulate the one-sixteenth size hands.

Well, you get the principle from there on. It is rather a difficult program, but it is a possibility.

Science fiction fans of course know that when Feyman is taking about "set of master and slave hands" he is referring to waldoes, which were invented by Robert Heinlein. So, I think sf writers anticipated this idea no matter how you slice it.

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Additional resources:
  More Ideas and Technology from A Menace in Miniature
  More Ideas and Technology by Raymond Z. Gallun
  Tech news articles related to A Menace in Miniature
  Tech news articles related to works by Raymond Z. Gallun

Ultra-microrobot-related news articles:
  - Robots Making Smaller Robots Making Smaller Robots
  - 3D DNA-Directed Nanoassembly
  - Robotic Insect Pop-Up Origami Fabrication
  - World's First Rapid 3D Nanoscale Printer
  - UR3 Robot At Work On Copies Of Itself

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