Picture the surface of a balloon. The entire universe is that 2 dimensional surface. When you blow up the balloon it expands and the entire 2 dimensional surface gets bigger, but there is no “center” that everything is moving away from. Now imaging a 3 dimensional sphere in 4 dimensional space. It started as a single point and expanded in every direction, but there is no center everything is moving away from. Everything is getting further from everything else.
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