If an extraterrestrial person looked through a super telescope towards the Earth, being thousands of light years away, and could increase it to see living beings, would he see, for example, dinosaurs instead of us?

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This is a bit tricky question. You stated that if could increase the magnification of the said telescope, what images will be on its lenses? My answer would a real-time images of the earth and happenings around it. There is a big difference in seeing exactly the same image given that you could see the tiny details about it regardless of how much would the distance be between seeing a fraction of what is happening on to something(the earth alone) or inside it. If you could see something directly, distance will be an absurd factor. Also, I guess, what's best subject that I could relate your question to is about waves travelling around space with light years in distances or something like sound.