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We do not yet have a way to show without any doubt
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that the underlying equations imply the phenomenon that we see
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when we apply it to the problem of quarks.
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By putting it on a big computer
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we are fairly certain that's correct.
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That will be like solving Newton's laws on a computer;
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but what Newton did was didn't solve it on a computer
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but solved it analytically.
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So quite often, in the past,
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whenever a theory is accepted,
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it's because the consequences can be worked out
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and compared to the experiment.