[thesteamboat]

From a previous discussion of this paper I took away the following clarifying insight:

The Drake equation is usually turned into the Fermi paradox via some estimations that show the average (mean) number of alien civilizations we expect to see is large (>1).

However, just because the mean is large does not imply that seeing 0 is low probability.

More concretely, suppose there were 10 possible 'parallel' universes. In 9 of them humanity is alone and in the tenth there are tens of millions of alien civilizations. The probability of appearing to be alone is 90% even though the number of alien civilizations we'd expect to see is in the millions.

[krapp]

You don't even need to invoke parallel universes. Look at the Hubble Deep Field photo[0]. Our observable universe has hundreds of millions of galaxies. It's entirely feasible for tens of millions of alien civilizations to be spread about and not visible to us in the narrow window of space and time in which we've been looking.

[0]https://en.wikipedia.org/wiki/Hubble_Deep_Field

[thesteamboat]

Invoking parallel universes was solely for ease of explaining/emphasizing the math, not because I think it's a realistic model.

Talking about the Hubble Deep Field kind of misses the point. The original Drake equation[0] estimates the number of alien civilizations in our galaxy. I probably should have used galaxies in my example, but left it with parallel universes as that is the common phrase.

[0]: https://en.wikipedia.org/wiki/Drake_equation