NavList:

Bill, you wrote:

"[he] spotted an analemma on--if I recall--a cave wall.  He said he was disappointed it was never referred to."

 

Just as well perhaps. Think about it: how could you get an analemma on a cave wall. If there's some little notch that admits light for only some brief period of the day, it will catch the Sun's light at the same Local Apparent Time every day. To get an analemma, you need to mark the Sun's position at the same Mean Time --clock time-- every day. You could get the up-down component, which comes from the Sun's changing declination, and that's enough to make a calendar, but the left-right component, which generates the classic "figure-eight" shape of the analemma, would seem to require a functioning clock.

 

There is one way to rescue the movie scene. Suppose the time-obsessed character in "Castaway" is so obsessed with time that he has studied, academically, the concept of LAT vs LMT (for those who haven't seen it, the ironic twist in the film is that the character is some sort of executive shipping manager for FedEx and he is literally obsessed with punctuality). Perhaps he understands the meaning of the analemma on the globe and has 'waxed philosophic' about its implications. Maybe there's a scene that ended up on the cutting room floor that shows the castaway back in civilization before the plane crash lecturing some fellow employee and pontificating that "even the Sun is late six months out of the year, but we at FedEx will be better than the Sun itself". If he had this information in advance, then by drawing out the analemma (roughly) on the wall of his cave from memory, the time-obsessed castaway would have a shred of civilization under his control in the form of knowing the approximate mean time every day at local apparent noon even when his watch had stopped running. This might have been too cerebral for a movie that was already slow-moving, but it's not outside the realm of possibility.