I’m not sure it really does. Finely tuned small numbers, sure, but small numbers, there’s no problem with that.
We only know the numerator on the odds, the “one in” part. The denominator, “in x”, we do not know. That denominator may be huge. If it’s Grahams’s Number, then we should expect to be the only technological civilization within the observable universe, and pretty substantially beyond. If the chances of looking at any bubble the size of our observable universe, and finding technological life in it is tremendously small, then the only ones that would have any chance of finding it would be that technological life itself.
The fallacy involved in the Law of Small Numbers is seeing a sample size, and determining the denominator there to be small enough to account for the result, but no smaller.
And that’s where the fine tuning fallacy of the Law of Small numbers comes into play. It requires fine tuning to say that the chances of technological civilizations are high enough that there are a bunch out there, but small enough that we cannot come into contact with them.
The Fermi Paradox is not about communicating, it is about detecting their presence at all. Why is the Solar system not littered with Von Neuman probes, why has it not been mined out? Why are there stars in the sky, rather than blobs that only radiate in the infrared as they are encased in Dyson swarms?
A solution to the Fermi Paradox needs to explain why we will not ever do these things, or explain why we are unique in that we would.
It may be that we die out before we accomplish any of this. Sad, but possible. It may be that we find new laws of physics that allow us to create matter and energy from nothing, and not need to exploit the resources of the galaxy to fuel our every growing desire for more expansion. This would be awesome, but I find it unlikely.
The idea that we would have the capability of expanding into and exploiting the resources of the galaxy, but choose not to, I find the least likely of all. There are no known laws of physics that would stop us from doing so, and we are already taking the first tiny steps in a journey that will have us populating the entire galaxy within a few dozen million years, at most.
To counter this means that one has to explain why not some, not most, but all other alien civilizations would not take this route.
I agree, and that’s more or less my point. In these discussions, I usually preface that with “at least” a few billion light years, as I think that it’s probably much, much higher than that. The point is, though, that a few billion light years is the minimum, IMHO. Otherwise, we would see galaxies dimming out into the infrared, as they get colonized by their inhabitants.
A hundred million years is nothing on universal timescales, and there are around 150 galaxies and a thousand dwarf galaxies within a hundred million light years, even a billion years isn’t that long, and that gets us tens of thousands of galaxies. If any of them had life with the capabilities and motivations of mankind, then we would see at least some of them being “terraformed*” by now.
That’s why I put a lower limit as a few billion light years to the next technological civilization. I actually think it is much higher than that.
It is also worth noting that the universe is actually pretty young. It seems old to us, and relative to human timescales, it is. But to the projected lifespan of the universe, it’s barely an infant. The majority of those 200 billion stars you mention will be burning for a few hundred billion years. Most of them will become more habitable over time, as their stars settle down. The Earth only really has less than another billion years of being in the habitable zone of our Sun, as it heats up. Red dwarfs are also slowly heating up, but at a much slower rate, where a planet may spend tens of billions of years in the habitable zone. A planet around a red dwarf may be frozen solid right now, but in fifty billion years, find itself in a more comfortable climate, a climate that will be sustained for several times longer than the entire lifetime of the Sun. Give it a bit of time, and I think that that is where the vast majority of life, along with technological life, will arise.
In any case, someone has got to be first. And whoever that is will look out into a seemingly empty universe, and wonder where everyone else is.
*terraformed is not a great word for shaping a galaxy into a more useful and efficient form, but I’m not sure what word would apply there.