We argue that a global time index may not be computable. Time and simultaneity can be computable only locally.

Measurement of time is a process that takes time. This creates a lag between the measurement and the flow of time. The lag emerges from the definition of time and is not due to any physical limitation. Perfect measurement of time, therefore, may not be logically possible.

A Perfect Clock is an algorithm that can perfectly identify programs with a regular output from those with an irregular one. We argue that such an algorithm may not logically exist.