More funny things happen at singularities as the poles.

If you are standing at the North pole all possible directions are south (and the sun rises and sets in the south though not very often).

If two people stand at opposite sides of a pole facing each other and discussing where East might be they both can point in completely opposite directions to indicate East and both of them are correct. The same holds true for all other directions. Both have to point to opposite directions to be correct.

If you are at roughly 16 cm from any Pole and walk 1 m exactly to the East (or West) you are again at the point from where you started your journey. Yes, and you have crossed all time zones and the date line.

Wolfgang