I don't believe this nonsense, but if ya do here's some thoughts.
Yes it is already the 21st in some parts of the world, but the Mayans built their calendar for their location and time zone. So it only matters if it is the 21st in Latin America.
Also, it isn't specified what time on the 21st, so it could be 11:59 pm on the 21st, or like previously stated it could be the 22nd because the calendar did include the 21st.

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