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xkcd #2867: DateTime
(imgs.xkcd.com)
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It might be more accurate to say that Unix time is the number of days since Jan 1st, 1970, scaled by 24×60×60. Though it gets a bit odd around the actual leap second since they aren't spread over the whole day. (In some ways that would be a more reasonable way to handle it; rather than repeating a second at midnight, just make all the seconds slightly longer that day.)