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Dima Kogan writes program to resolve lunar terminator paradox
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Illustration only Photo by Tobias Jelskov on Unsplash
Dima Kogan developed a simulation to explain why the moon appears to point up after sunset, a phenomenon he found confusing in existing online explanations.
The post demonstrates a specific failure mode in current AI models, which struggled to reason through the geometric logic despite having access to incomplete internet explanations. It highlights the gap between pattern matching and genuine spatial reasoning in LLMs.
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The paradox arises because observers look up at the moon from below, causing the dark side to appear on the bottom edge even when the sun is below the horizon.
Kogan's program visualizes how the visible illuminated portion changes as the moon's elevation increases from the horizon to the zenith.
The author notes that Claude and Gemini failed to comprehend the geometry, engaging in circular arguments rather than deriving the correct spatial relationship.
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Dima Kogan addressed a common optical illusion where the moon appears to point upward after sunset, contrary to the expectation that the illuminated side should face the sun's position below the horizon. He found existing online descriptions insufficient for his understanding and built a custom program to simulate the geometry. The core issue is the observer's perspective: looking up at the moon from below shifts the visible dark portion to the bottom edge of the disc.
The simulation clarifies that the effect is most pronounced with a full or nearly full moon. When the moon is low on the horizon, the sun is directly behind the observer, illuminating the entire visible face. As the moon rises higher in the sky, the observer sees more of the moon's underside, which is in shadow, creating a dark slice at the bottom that makes the lit portion appear to point up.
Kogan also used the project to evaluate the reasoning capabilities of current AI tools, specifically Claude and Gemini. He reported that both models were unable to comprehend the spatial logic, instead producing circular arguments based on incomplete internet sources. This suggests that these models lack the necessary reasoning capability to distill complex geometric relationships into a coherent understanding.
The post serves as a case study in the limitations of large language models when faced with problems requiring first-principles spatial reasoning rather than pattern recognition. While the models could access relevant text, they failed to synthesize it into a correct explanation of the physical phenomenon. The author concludes that this specific type of reasoning gap indicates that AGI is not yet achieved.
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