I investigate whether there are general relativistic spacetimes that allow an observerµ to collect in a finite time all the data from the worldline of another observerλ, where the proper length ofλ's worldline is infinite. The existence of these spacetimes has a bearing on certain problems in computation theory. A theorem shows that most standard spacetimes cannot accommodate this scenario. There are however spacetimes which can: anti-de Sitter spacetime is one example.