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                    "There's an optical illusion known by names like the \"lunar terminator paradox\".\nThis has much discussion and descriptions online, but none made sense in my\nhead, so I wrote this program to figure out what was going on. The paradox:\n\n\n\nThe moon is illuminated by the sun\n\nAfter sunset, the sun is below, so we would expect the illuminated portion of\nthe moon to point down, towards where the sun is\n\nThis isn't what always happens!\n\n\n\n\nI was camping in the mountains with a friend recently. We were looking up at the\nsky, just after the sun has set. The moon was clearly pointing up.\n\n\n\nAfter playing with this program, I have clarity: we're looking up at the moon\nfrom below. The most pathological case is a full moon. Let's say the moon is on\nthe horizon: elevation=0. If we're looking at this low moon, and the moon is\nfull, the sun is directly behind us. The moon is fully illuminated, and we see\n100% of the moon disc lit up.\n\n\n\nNow, what happens if the moon is not at the horizon, but higher up at the sky?\nEffectively, the sun is infinitely far away, so the same part of the moon is lit\nup. But we're now looking at the moon from below, and we would see some of the\ndark side on the bottom edge. I.e. the moon appears bright at the top, but has a\ndark slice missing at the bottom: it points up! Even at sunset.\n\n\n\nThis is the most clearly weird case. A half-moon has no paradoxical behavior,\nand the more full the moon, the more clearly we can observe the bright moon\npointing up despite the sun being down.\n\n\n\nI produce two plots. At 3/4-full moon at sunset we look at the moon as it rises\nfrom the horizon all the way up to the zenith:\n\n\n\n\n\n\n\nIf the moon is at the horizon (elevation = 0), we see the expected 3/4-lit disc.\nAs the moon rises, we see more and more of its bottom, and thus more and more\ndark areas show up: It clearly points up at sunset!\n\n\n\nWe can also move the sun around. Let's say the moon is 60deg up; let's move the\nsun from new-moon to a full-moon:\n\n\n\n\n\n\n\nIn the darkest configuration, we can still see a lit crescent on the bottom: the\nillumination is all on the opposite side, but we can see a slice of the\nilluminated back side. As the sun swings around, we see more and more of the\nmoon. At azimuth = 90deg, we have a half-lit moon. Past that, more and more of\nthe moon is visible, always pointing up.\n\n\n\nThis was also a super interesting study of the current state of AI tools. As I\nwas writing this and debugging, I would talk to Claude and Gemini about how this\nworked and what I should be seeing. They were both completely unable to\ncomprehend this, and would make infinite circular arguments. Clearly they read\nsome incomplete explanations on the internet (as I have), and lack the reasoning\ncapability necessary to distill it into something resembling \"understanding\".\nAGI is not here yet."
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