There's another requirement there; there have to be no false positives either. Charlie, who lives halfway around the world, can't be falsely reported to be near

There's another requirement there; there have to be no false positives either. Charlie, who lives halfway around the world, can't be falsely reported to be nearby. I don't get what pixcavator is driving at with the x sin(10x) notion but it seems to fail the Charlie test to me. If this function has to preserve both proportionate nearness and farness, without false positives, it to seems me that it's just an ordinary geometric transform and therefore easy to reverse. IANAM (I am not a mathematician).