Does anyone remember a short story in an anthology where hyperspace travel was possible only if the passengers were asleep in the vessel? One fellow decided that he would remain awake during the journey. Since they were traveling infinite distances through infinite time he got from jump point to destination in a short period of time but since he was awake he experienced all of eternity and it wiped his mind. The title Faraway Stare comes to mind after years of thinking about it but I can't find any material that matches.
This is possibly the Stephen King short, The Jaunt
Teleportation is possible, but people are put to sleep before being sent, because time in the jump passes differently, and conscious minds go insane. A father and his family are preparing to travel to Mars, and his overly-curious son holds his breath when the sleeping gas is administered, and goes through the jump conscious.
As you might guess, it doesn't end well....