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Illano comments on Harry Potter and the Methods of Rationality discussion thread, March 2015, chapter 119 - Less Wrong Discussion
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Using the time it takes Earth to rotate one degree gives you 86400 seconds in a day /360 degrees = 240 seconds. But the length of the day has been getting larger as the Earth slows at a rate of about 1.7 ms/century wiki
To find when one degree was equal to 234 seconds, we can find when a day was approximately 234*360 degrees = 84240 seconds, or approximately 127 million years ago. Putting the creation of the stone right in the middle of the Cretaceous Period.
Coincidentally, this also solves the issue of how the T Rex got away with such tiny arms. They had wands!