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Bugmaster comments on Harry Potter and the Methods of Rationality discussion thread, part 15, chapter 84 - Less Wrong Discussion
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Fortunately, magic is widely available. That said, it should be possible to build such a clock using perfectly mundane means; after all, Discworld denizens do have perfectly ordinary mechanical clocks, AFAIK.
It would have to have its own tick completely muffled while just producing the fake tick. Perhaps the accurate time is produced by a clock on the other side of the wall.
Assuming, of course, that the clock does keep accurate time :-)
Pratchett quote a few posts upstream.