Do the math? I'd like to see some calculations then, because I'm curious to see what sample size and what distributions we're using to extrapolate to all 20,000,000,000,000,000,000,000 of those stars. That ought to be one bizarre confidence interval when constructed by anyone who isn't Stephen Hawking.
I get that it's ridiculous to assume that not one of those other stars has life somewhere surrounding it. But someone I used to know would say things like "do the math" when he actually didn't understand anything about probability or statistics, and lord knows I'm too lazy to crack out my own prob & stats textbooks from many moons ago. I'm genuinely curious (not as a challenge, but more for my own interest) to see if anyone has attempted any calculations on this matter.
Actually, the numbers I used to calculate that were actually the lowest numbers I could find. The values that I've found actually range anywhere between 200-500 billion stars in our galaxy, other galaxies range anywhere between a few million to a few hundred trillion, and there are anywhere between 100 billion to 170 billion galaxies in the observable universe. The numbers I used were the ones that made the most sense to me, as they were the easist for me to use. I can't use something as radical as the variance in the number of stars in a galaxy. So I simply used ours as a baseline and used the lowest number I found for how many stars there were in our galaxy and the lowest number I found for how many galaxies there are in the known universe.
So, to say that we're truly the only life in our universe is to simultaneously say that our galaxy is the only galaxy that has life, and that our star is the only star that has life. In other words, it's 1 in 200 billion in 100 billion. Which is 1 in (2 * 10^11) * (1 * 10^11); or 1 in (2 * 10^22). That's a 1 in 20,000,000,000,000,000,000,000 chance that our star is the only star that has life in it's solar system; given the figures that I used. It COULD be radically different, but there's simply no agreeable number, and if it were different, chances are it would be significantly higher.
Of course, that's not taking into account the very strict conditions in which life as we know it is able to flourish. However, most stars have a habitable zone where water is capable of existing as a liquid. Cooler stars tend to have their HZ closer, while hotter ones tend to have theirs further out. It's simply a balancing act between their gravitational pull, the amount of heat they generate, and the proximity to their planets, that determines whether or not their surrounding planets are capable of supporting life. I'll admit that right here and now, I have no knowledge about those figures, but they'll massively skew the figures I listed. I'm simply looking at things on a stellar level, not a planetary one.
I do want to make one thing perfectly clear. I don't, in any regard, believe it to be "ridiculous" (as you put it) that we're alone. I'm very mathematical, and even the smallest chance is still not zero. Even if it's a one in (2 * 10^22) chance of happening, that's means there's still a possibility, however unlikely, of it happening. Highly unlikely, yes. Ridiculous, not to me.
But, that still doesn't answer my question. Are we alone because we're literally the only life in the universe, or are we alone because we will probably never discover alien life if it did exist? I mean, even if Andromeda is simply teeming with life, we simply don't possess the technology to ever visit it, so would we still be "alone"?