 We can also imagine that the means of turning the lamp off and on does not involve any spacetime location at which at least one physical quantity is infinite; Grünbaum (1968) describes a scenario that fits this specification. In that case, the means of turning the lamp off and on converges to a specified state at the end of the two minutes, and there is an answer to the question that lies in the details of the specified state. But that answer is underdetermined by the brief description that we were initially given, as Benacerraf (1962) argues: we can have the lamp on at the end of the two minutes, or off at the end of the two minutes, depending upon the details of the implementation of Grünbaum’s proposal. Huemer (2016: 198–201) points out that if we hold fixed enough physics, then, before the end of the two minutes, the activation of the mechanism will stop changing the state of the lamp. So, depending upon your views about the range of what is possible, you may regard as impossible even cases in which there is no spacetime location at which at least one physical quantity is infinite.