How much of space has humanity observed?

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I vaguely remember reading somewhere something that, in its entirety, human civilization, with all its telescopes and radio dishes and cameras, has only "mapped" (seen and documented) about 3% of the (observable) universe. Can anybody make any comments on the reality of this? Is it even possible to make such estimates?
 
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I think we can make this estimate and your number is about right. Basically, of the observable universe, we see a distant shell represented by the CMB (Cosmic Microwave Background) at a redshift of z~1000, and we begin to see galaxies at ~z=6. In between these two, there is a large region where we have few observations, which is often referred to as the "dark ages". What fraction of the total volume this is depends on how you take the expansion of the universe into account, but if you use comoving coordinates (which is what most astronomers do), then your 3% number is about right. There are people actively working on trying to learn more about this region, mainly by studying the 21cm radiation emitted and/or absorbed during that time. I don't know your background, but the following paper helped me a great deal:

http://arxiv.org/abs/astro-ph/0310808
 

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