ON a Tuesday evening this spring, Sergey Brin, the co-founder of Google, became part man and part machine. About 40 people, all gathered here at a NASA campus for a nine-day, $15,000 course at Singularity University, saw it happen. While the flesh-and-blood version of Mr. Brin sat miles away at a computer capable of remotely steering a robot, the gizmo rolling around here consisted of a printer-size base with wheels attached to a boxy, head-height screen glowing with an image of Mr. Brin’s face. The BrinBot obeyed its human commander and sputtered around from group to group, talking to attendees...