I would like to know if our vision bends with the earth or if the earth truly is round. If I look through a strong enough telescope to see around the world, would I be able to see the back of my head? And, if the farther out into space we look the further back in time we look, could it therefore be said that the reason we have found no life as of yet is because life has not had the chance to come into creation at the point in time we are looking at? I mean, maybe it hasn't evolved yet because we're seeing it as it was thousands of years ago. Whereas, if we could see at present time, maybe we would see humanoid settlements?
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$\begingroup$ Perhaps you could ask two separate questions. $\endgroup$– CommunistyCommented Oct 18, 2017 at 7:24
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1$\begingroup$ @TravisNorred If this is truly going to be your only time using the site, make sure you accept whichever answer you feel best answers your question before you abandon it. $\endgroup$– Kieran MoynihanCommented Oct 18, 2017 at 8:09
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$\begingroup$ My point wasn't to make your life harder. The point of this site is that when questions are asked and answered people with the same kind of question could easily see the answers about it. By making clear questions you are helping others wondering the same question in addition to yourself. You wouldn't search this site with the phrase: 'Have scientists thought about these two questions?'... $\endgroup$– CommunistyCommented Oct 18, 2017 at 8:31
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Yes, scientists have thought about those two questions.
The mass of the earth is not large enough to curve spacetime sufficiently that you would be able to see the back of your own head through a telescope. For you to be able to do this, you would need to be positioned just on the edge of the “photon sphere” of a black hole (as per Solenodon Paradoxus’ comment, positioning yourself on the event horizon would not allow you to see the back of your head).
Of course it is possible that you are right. The more pertinent point, however, is that we would have expected that life may have formed in other systems long before it emerged on our planet. Life has, on our planet, existed for (approximately) $\frac{1}{3}$ of the duration of the universe (since the big bang), while galaxies and solar systems of all types have existed for the vast majority of time. Even in our own galaxy, and that of our neighboring galaxies, there have been hundreds of billions of stars since the formation of the galaxy; yet, as far as we know, we are the only life forms to exist. So, in answer to your question: yes, life may exist outside of the range of our vision; however, we should expect it to exists within our range of vision, and look for it there—rather than trying to look where we cannot.
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1$\begingroup$ Good answer, but (1) is technically imprecise. Light-like orbits around a black hole lie completely outside of the event horizon. You don't need to cross or even come close to the horizon to be able to see the back of your head – resting at a safe distance of $2 r_s$ is already enough. $\endgroup$ Commented Oct 18, 2017 at 8:14
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$\begingroup$ @SolenodonParadoxus Thank you for pointing out my misunderstanding, correcting with reference to your comment. $\endgroup$ Commented Oct 18, 2017 at 8:22
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$\begingroup$ I would add to point 1. something along the lines of 'Yes, our vision bends imperceptibly around the earth and yes, the earth is truly round.'. $\endgroup$ Commented Oct 18, 2017 at 8:40