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I see something happening,
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I give it a pair of numbers, (x,t),
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you give the same event,
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another pair of numbers, (x',t'),
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and this is how they are related.
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So, I gave you an analogy, but let me repeat the analogy.
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If you're now talking about the xy plane
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rather than the xt plane,
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that dot is not an event.
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That dot is a coordinate of a point,
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maybe where something is sitting.
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I give to it a pair of numbers, x and y.