Why the moon points the wrong way at sunset
There is an old astronomical puzzle that most people meet while camping: after the sun sets, the lit part of the moon sometimes seems to point up, toward empty sky, instead of down toward where the sun just went. It is called the lunar terminator paradox, and Dima Kogan wrote up a clean resolution of it this week, along with the simulation program he built to convince himself.
The paradox sounds simple. The sun lights the moon. After sunset the sun is below the horizon, so the illuminated face of the moon should tilt downward toward it. Often it does not. Kogan’s answer is that the paradox comes from a geometry error almost everyone makes, including the online explanations that try to wave it away with “perspective.”
The perspective explanation is real, but the standard accounts get it backwards in a subtle way. The sun’s rays are parallel, so moving the moon higher in the sky does not change which side is lit. What changes is the observer. When you look at a moon high in the sky, you are looking up at it from below, which reveals the bottom edge of the disc. On a full or nearly full moon, that bottom slice of the sphere is the far side, the part facing away from us and away from the sun’s apparent direction. It shows up dark. The disc reads as lit at the top and dark at the bottom: pointing up, at sunset, exactly when it “shouldn’t.”
The pathological case
Run the extremes. A full moon sitting on the horizon at sunset is lit face-on, because the sun is directly behind you. No paradox. Raise that same full moon toward the zenith without moving the sun, and you start seeing a dark sliver at its bottom edge. The more full the moon and the higher it sits, the more obviously it points the wrong way. A half-moon, by contrast, never misbehaves, because its terminator runs vertically through the disc and the geometry has no room for the illusion.
The plots make this concrete. At 3/4 full with the sun just set, a moon at the horizon shows the expected three-quarter disc. As it climbs, the dark bottom slice widens steadily, until near the zenith most of the bottom half reads dark despite the sun having set only minutes earlier. Nothing about the lighting changed. Only your viewing angle did. That separation between what is lit and what you see is the entire paradox in one sentence, and it explains why the moon “points up” most convincingly when it is fullest and highest, the exact conditions under which people notice it.
Kogan’s writeup includes two plots from his simulator: one scanning the moon from horizon to zenith at 3/4 full, where the dark bottom slice grows steadily as it rises, and one sweeping the sun’s azimuth around a fixed moon. Both plots make the effect mechanical rather than mysterious. The code is on GitHub if you want to poke at it yourself.
The AI angle
The most interesting part of the post may not be the astronomy. Kogan used the exercise to probe current AI assistants, walking Claude and Gemini through the geometry while debugging. Both models, he reports, could not internalize the explanation and looped through circular arguments instead. They had absorbed the internet’s incomplete explanations and could not reason from first principles to the correct one.
That is a useful data point for anyone evaluating these tools. Paradoxes like this one are cheap to verify: go outside, look up. The fact that frontier chatbots confidently misexplain a solvable geometry problem, one a hobbyist resolved with a weekend of code, says something about the gap between fluent recall and actual spatial reasoning. AGI is not here yet, as Kogan puts it, and the moon is happy to keep proving it.
Try it yourself
The simulator is a small open source project, and it doubles as a decent exercise in thinking about 3D orientation. The core insight generalizes: whenever you judge an object’s orientation, you are silently folding in your own position relative to it, and “which way is up” is a question about the observer as much as the object. Next clear evening with a moon near full, look up shortly after sunset and check for yourself. If the lit face seems to point the wrong way, you are seeing the same geometry error that fooled both you and the chatbots.
It is also a good reminder that writing code to test an intuition beats arguing about it. Kogan did not settle the question by reading more explanations; he wrote a renderer, scanned the parameter space, and looked at the plots. Two hours of work retired a puzzle that internet comment sections have chased for years.