I stand by the belief that it’s really not that astounding. While it’s a fun thought experiment, and the math is fine, there are a couple of fundamental logical flaws with the conclusion that there’s a surprising lack of aliens. Both of them are surprisingly anthropocentric with a bit of hubris.
First is the idea that if we don’t know something to be true, it must be false (it can’t just be unknown). That assumes that we know everything. We don’t even know if we would be able to recognize signs of alien civilizations to be such even if there were a pile of them on our desks right now.
The second is that the idea that we’ve even really been looking for the right things and in the right places (when we don’t know what either of those are) is a big assumption. Mostly we’ve pointed some radio telescopes at a small fraction of the stars out there and listened to a specific frequency for a few minutes to try to detect a pattern like what we think we would send. That’s all under the assumption that any intelligent alien would make a massively-powerful radio transmitter, tune it to just that frequency, and continuously transmit something that we could recognize in our direction. Because that’s what we thought we would do. But why would they? We don’t even do that and it was our idea!
The logic is sort of like: we’re animals and we wear shoes, so if there are kangaroos and they’re real animals, they must wear shoes too. We’ve been looking in our closet for years (because that’s where we keep our shoes, so naturally they’d put their shoes in our closet too) and we haven’t seen any kangaroo-foot-shaped shoes, so therefore kangaroos must not really exist.
