Tyson talks about the issue at the 15m 20s mark.
Most Android devices set the time based on the data they receive from GPS signals. While the clocks on the GPS satellites are incredibly accurate atomic clocks, the timekeeping system used by them was defined up to 1982.
A total of 15 'leap seconds' have been added to the Coordinated Universal Time (UTC) time scale since then, which Android handsets don't compensate for, so these handsets are running exactly 15 seconds too fast.
The GPS signal does include the offset difference between GPS time and UTC in the message it sends to receivers, but it seems that this information isn't being used by Android to correct for the leap seconds.
Interestingly enough, this has been listed as an Android bug since December 2009. It seems like an easy bug to fix, so I'm surprised it's been ignored for so long.
The iPhone also sets the time based on GPS data, but according to Tyson, iOS adds the 15 seconds into the equation, so Apple handsets show the correct time.
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