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Context:

"Why are we so worried about artificial intelligence? Surely humans are always able to pull the plug?"

People asked a computer, “Is there a God?” And the computer said, “There is now,” and fused the plug.

Is the meaning of "fused" is "joined" or "soldered" or "stop working"?

I suspect that "fuse" is being used incorrectly.

"Fuse the plug" means literally to blow a fuse in a plug and hence render a device inoperable. Many plugs (certainly traditionally in the UK) have a fuse which blows and breaks the circuit, rendering the device inoperable. This gives rise to sense 2 of the verb in Oxford Dictionaries: "(of an electrical appliance) stop working when a fuse melts" - it is tagged as a "British" usage. (This is separate to the first, more common sense of the word fuse: "Join or blend to form a single entity.")

However, it clearly needs a bit more unpicking here. A thread on SciFi Stack Exchange mentions a story (quoted by Stephen Hawking) where "There's a story that scientists built an intelligent computer. The first question they asked it was: 'Is there a God?' The computer replies: 'There is now.' And a bolt of lightning struck the plug so it couldn't be turned off."

I think in the phrase under discussion the intended meaning is similar to that in the story just mentioned, and "fused" is being used under the incorrect apprehension that it means something like "fix in an unalterable state".

An alternative, more speculative, explanation might be that it fuses the plug and cuts off electricity but keeps going because it doesn't need electricity any more (equivalent to "pulling the plug"). But that doesn't match the other version of the story, and it seems odd for the author to expect people to work out that meaning, especially as "fuse" in that sense seems to be specific to the UK, and it's equally likely that people would infer that the computer had deactivated itself, negating the point of the story.

Consider the definitions of fuse (v) at Merriam-Webster.com:

Transitive verb

1 : to reduce to a liquid or plastic state by heat • the thunderstorm had fused the electric mains — C. K. Finlay

2 : to blend thoroughly by or as if by melting together : COMBINE • Particles are fused to form a new compound.

3 : to stitch by applying heat and pressure with or without the use of an adhesive

Transitive meanings 2 and 3 in particular refer to blending/combining/stitching. So the apparent meaning of "fusing the plug", especially in contrast to "pull the plug" just earlier, is "melted the plug in such a way that it is permanently joined to the socket and cannot be removed."

Given this juxtaposition, I think the obvious intention of the sentence is that the computer took positive action to prevent humans from being able to cut its power, as part of the act of declaring itself to be divine.

There are two separate origins of fuse with some semantic overlap (as both can involve the sudden effect of heat on a solid. Here we are concerned with the second given in the link. The original meaning is "melt" but that gives rise to two separate uses.

It can be used to make something, by using a thermoplastic glue such as solder. It can also be used to destroy something by melting as in an electrical fuse. This is, in my experience, the only common usage in non-technical writing. Add to that the fact that electrical fuses are often found in electrical plugs and they often blow (or fuse) it seems most likely that this is a reference to the fuse in the plug blowing as a result of using excess power as a result of the calculation being too difficult or the equipment refusing to do the calculation, possibly as a result of God's intervention. The exact interpretation is up to the reader.