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mushroom comments on What false beliefs have you held and why were you wrong? - Less Wrong Discussion
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I once believed that most people have a basic understanding of how Solar system works. My belief in humanity shattered when during a discussion with with several graduates of physics (!) I discovered that most of them do not know what is the orbital period of Moon. An impromptu survey revealed that about 8 people from 10 thought it was one day or one week. One knew, one even asked if I want to know sideric or synodic period.
I love the example of what causes the phases of the moon, because it's not knowledge that most (modern) people have cached, but figuring it out only requires drawing a bunch of picture and asking questions about them like "What would I see in this configuration?".
For my part, I never realized (or probaly just forgot) there was a pattern between the phases of the moon and the time of the moon's visibility until I did this exercise a few years ago.