Why do objects appear to shrink as they approach the speed of light?

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Why, when nearing the speed of light, do objects appear to be shrinking to someone in a different frame of reference?

I understand time dilation, but not the horizontal distortion.
 
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If an object is traveling towards an observer at near light speed, by the time the light from the near end of the object reaches the observer, the far end is much closer and the light reaches from the far end reaches the observer relatively sooner. I'm not sure if this is more than just an "optical" illusion under general relativity.
 

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