Lunar Terminator Paradox
3 hours ago
- The lunar terminator paradox is the surprising observation that after sunset, when the sun is below the horizon, the illuminated part of the moon often appears to point upward instead of downward toward the sun.
- The author wrote a program to understand the paradox because existing online explanations did not make sense to them.
- The key insight is that we look up at the moon from below: for a full moon near the horizon the sun is directly behind us, so the whole disc appears lit, but as the moon rises higher, we start seeing a dark slice along its bottom edge, making the lit part point upward.
- The effect is strongest for fuller moons; a half moon shows no paradoxical behavior, and the fuller the moon, the more clearly the lit portion points up even though the sun is down.
- Simulations show the same effect when sweeping the moon from horizon to zenith at 3/4 full, and when moving the sun from new-moon to full-moon with the moon elevated: the lit crescent or lit portion always appears on the upper side, pointing up.
- The author found that current AI tools like Claude and Gemini could not reason about this problem, instead making circular arguments, suggesting AGI is not yet achieved.