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then you have to somehow dream up some force
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so that if you did this integral
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the answer does not depend on the path.
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You realize, that looks really miraculous
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because we just wrote down an arbitrary force
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that we all cooked up together with these exponents,
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and the answer depends on the path.
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And I guarantee you,
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if you just arbitrarily write down some force, it won't work.
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So, maybe there is no Law of Conservation of Energy
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in more than one dimension.
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So, how am I going to search for a force that will do the job?