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At least go with automagically, which I take to mean that the mechanism is programmed, but it took some arcane steps to get the damn thing working

In the wise words of Strong Bad...

"The word 'technology' means 'magic'! It's basically anything that's really cool that you don't know how it works."

We know how it works, it changes the brightness based on screen contents.

That's what it does, not how it works.

I.e., 'What' is just the top-level abstraction. 'How' is the functional composition underneath.

No the guy released the source code so you do know how it works as well

It's the influence of Apple marketing.

It was always my understanding that in programming "magic" is just a shorthand for "I don't feel like explaining the implementation in that much detail right now".

The Jargon File defines it similarly: http://catb.org/jargon/html/M/magic.html