Two theories that are identical in their predictions can have wildly different pictures of the world—like putting the Earth at the center of the universe rather than the Sun—and those pictures, in turn, determine a lot about the daily practice of science. If you think that the Sun is at the center of the solar system, rather than the Earth, you’re likely to conclude that there’s nothing special about Earth, or our solar system, and that there could easily be planets around other stars, even though both astronomical theories give the same predictions about how different lights will move across
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