More tl;dr: the clock outside Edinburgh Waverley station only displays the correct time on New Years Eve, and no one wants it to read the correct time because it's a Scottish tradition now.
I was really hoping it would be something more like, because there's a mechanical flaw that causes the clock to run slow, and it takes three minutes reach the belfry of the clock tower from, the street. This means that when the clock master notices that the clock is running on time, he has three minutes to reach the belfry, and set the clock forward three minutes, so that it never runs slow enough to make people late.
I don't know. I use the same technique at home. I keep the clocks a few minutes fast, and even though I know that they are fast I find that it does help getting out of the house on time for the morning school run, etc.
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Or something like that.
What if they make it off by 3 minutes a random 50% of the time? Then people can't adapt and half the time they'll be "helped" with extra time.
Kind of useless in modern times but an interesting problem to think about.