There are approximately 100,000,000,000 stars in our galaxy (easy way to remember this order of magnitude is it's one hundred, thousand, million). Usefully there are also approximately the same number of galaxies in the universe. And assuming every star has about the same number of planets orbiting it as our Sun, and that the Milky Way is an average size of galaxy, that means there are around 100,000,000,000,000,000,000,000 planets in the universe. A lot.
Scientists have long debated the probability of life, as we would recognise it - reproducing, eating, etc - existing outside Earth. Most agree mathematically that it's a certainty. What they did was take all the components they believed were required for life to have evolved on Earth and then extrapolate what they know about the existence of these components on other worlds. This therefore excludes all possibilities of other life systems requiring, for example, very high temperatures, toxicity (for us), lack of solid land or water, no carbon or oxygen etc. The number they arrived at was still enormous. They then reduced it extensively to allow for evolutionary processes to have become established (it's generally believed that the simple carbohydrate molecule of formaldehyde needed to have existed before DNA could form) and for the planet (presumably, rather than its star) to have reached a sufficiently stable and benign (whatever that might mean) state for long-term evolution of systems like biological cells to appear.
That's all well and good. So given there are definitely aliens wandering around other planets somewhere else, why do I think we'll have evidence of this soon? Because we are living in an age of technology unlike anything your parents or any previous generation of our species could possibly fathom or even recognise. Today we can detect incredibly feint radio waves coming from the outer edges of the universe 46,000,000,000 light years away (and a light year is about 10,000,000,000,000 km - so multiply one number by the other to give how many kilometres we can now detect signals being emitted). 100 years ago our natural audible range was a couple of hundreds yards and our visual range was a mile or so. We didn't even know radio waves existed. So us detecting them, and them detecting us were virtually impossible until very very recently.
So homo sapiens has been around about 800,000 years. And we've no reliable evidence yet that any of our ancestors have ever encountered aliens. But maybe that's because aliens didn't know we were here combined with the fact that we couldn't detect very distant aliens until only a year or so ago. Our technology is therefore now, and uniquely in our history, capable of delivering and receiving communications from whatever aliens might exist who have also developed similar or better communications technologies (including inter-galactic travel).
We're the only species on our planet to have evolved technical expertise. So even if you reduce the odds of homo sapiens' communications skills being developed by a single species on another world, there is still a near certainty that:
- Extra-terrestrial life exists
- At least half of all extra-terrestrial species are smarter than us
- They can now detect us because we've only recently been transmitting coherent signals that might reach them
- We have within the past year or so developed the sensitivities (and continue to improve on them) to be capable of detecting them
- They've already discovered us and are waiting for the most appropriate time to communicate with us. As our technology advances day by day, that time must be approaching fast.
- We might still discover them - albeit thousands, perhaps millions of years in their past. Why not hook up your PC to the SETI (Search for ExtraTerrestrial Intelligence) processing network? I'll let you know if mine discovers anything!
- There are possibilities that certain future communication technologies will not experience any time delay between transmission and reception irrespective of distance. It's all part of quantum entanglement. We're not there yet, but within our lifetime it may become a reality. And if aliens have also developed it...