- To get to the wall I need to walk 1/2 the distance, then 1/2 the remaining distance, and so on ad infinitum
I'll have to disagree. To get to the wall, you don't need to walk 1/2 the distance. Just walk the whole distance and be done with it. If you walk half the distance, then you know how long the other half is.

Tim loves Meg so Tim dances with Meg. Why waste time taking half-steps when he knows how far he needs to go to dance!?