1 in 10 billion trillion is some pretty serious odds.
It does get more complicated if we factor in life happening quickly enough without an extinction event.
But after looking at images like this there is just NO WAY we are the only ones.
What I'm more pessimistic about is how long such intelligence might live. How many civilizations reached a point of harnessing nuclear power and then wiped themselves out with nuclear war?
Suddenly 1 in 10 billion trillion odds doesn't seem so (and I apologise in advance for this) astronomical...
Think about other earth-centric scenarios, and try and imagine if dolphins or octopuses or fungus or maybe even insect colonies or plant ecosystems had "won" and become the apex lifeforms on earth instead of humans. I wonder just how different concerns like "civilisations" and "war" and "nuclear power" would have played out in those cases? I wonder if assumptions like "industrial revolutions" and the inevitability of scientific discovery being used in detrimental ways like we have done with nuclear science actually correlate with "intelligence"?
That’s about 100^5, so one way to think of this is that if you categories these by any four properties (temperature, stability, hydration, day length) then you’d expect about 100 samples for any point in that 4D space.
So even if you believe Earth is unique along four critical metrics, there are about a hundred planets per galaxy that also have those attributes within a percentage point. If you allow some wiggle room then you have tens of thousands or even millions.
We know conditions here on Earth varied significantly more than 1% over billions of years and life survived and even thrived.
It's just too arrogant to think we currently can place odds on all the important events necessary for us or something like us to come into being. At the time this equation was devised, I'm not even sure they understood how crazy lucky the development of mitochondria was.
In reality, we just don't know the many factors that might've affected our outcome. Also, it's just pure lottery falacy to reason about the statics that specifically "we" exist. If the odds for some strange reason settled out around about 1 of there being a single sentient species in our universe, that species would come to reason about itself and produce the same long odds of their existence. It's a longshot that a specific someone wins the lottery twice. It is a statistical inevitability that someone will win twice.
Whoever they are, they can't alienate themselves from being the one despite all the statistical huffing and puffing they can conjure. We will only know how special we are when we find another or once we have surveyed enough planets in depth.