A mighty host descended on my email bag to explain the New Yorker cartoon about which I expressed bafflement in the April 22nd Radio Derb podcast.
Apparently it refers to a game that kids play in swimming pools. The name of the game is Marco Polo; and the bearded figure in the cartoon is Marco Polo himself (although the original seems to have been way beardier).
Got it. Thanks again to all. The only swimming pools around in my 1950s provincial English childhood were public ones, and they were declared off-limits by a lot of parents, including mine, because of the polio panic. I'm still a lousy swimmer, thanks to that damn virus.