Re: Are we really alone?
On the face of it, 800 million to 800 trillion possiblities seem like such a large number that we surely would have had visitations by now. Though all the evidence I have seen supports the idea that we have and still are having such visitations, there has been no official public contact that provides an inescapable smoking gun for one and all to see.
So let' suppose that may we haven't yet had visitors. I don't think that would necessarily fly in the face of the odds being tremendously in favor of extra-terrestrial intelligent life at all. Consider first of all, the vastness of space. If the universe is figured to be over 14 billion light years across and light travels 6 trillion miles in a year, then the universe would be 84,000,000,000,000,000,000 miles across. If the planets with extra-terrestrial intelligent life were scattered fairly evenly throughout the universe, they could easily be hundreds of trillions of miles apart. Of course, the likelihood is that some are much closer to one another and some are much further apart. We might simply be one of the ones that are quite far apart from any other planets with intelligent life.
Then again, it also could be that any space faring race capable of travel at faster than light speeds that could reach us fairly quickly a la Star Trek or Stargate Universe or whatever, might be so far advanced that we are nothing more than something out of phylum protozoa to them.