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A chronometric singularity (also called a temporal or horological singularity) is a point at which time cannot be measured or described.
An example involves a time at a coordinate singularity, e.g. a geographical pole. Since time on Earth is measured through longitudes, and no unique longitude exists at a pole, time is not defined uniquely at this point. There is a clear connection with coordinate singularities, as can be seen from this example. In relativity, similar singularities can be found in the case of Schwarzschild coordinates.
Stephen Hawking once compared by a talk-show guest's question about "before the beginning of time" to asking "what's north of the north pole".