Yes, probably, but then on the other hand, if panspermia (https://en.wikipedia.org/wiki/Panspermia) was the cause of life here, whatever mechanism was at work (e.g. interstellar objects, fragments from an exploded system) then it would make sense to have seeded clusters of stars. Fun to think about, obviously, who knows.

No, because the volume of the ball around earth grows with distance cubed. Assuming of course that searching in a bigger space is likely to find more non-earth life.

For each given distance, yes, but the property that's interesting to humans is binary: "near" vs "far". It's also subjective, but almost any definition would put most of the galaxy in the "far" category, thereby making it more likely that a random location is "far".

I’m actually not sure that’s what he meant. I think he meant that if you picked two planets to have life on them at random, and the pairwise distances between planets forms a uniform distribution, then the distance between the two planets randomly chosen is equally likely to be any distance.

This is not true even in an extremely idealized model. For example, if you pick two random points in a unit cube, they are much more likely to be a moderate distance apart (on average, about 0.66 units) than they are to be very close together.

https://people.kth.se/~johanph/habc.pdf

> The chances of the only two civilisations in the entire galaxy happening to be neighbours, among 400bn stars, absolutely stretches the bounds of rationality.

I think this is dependent on the conditions by which one or more related lifeforms emerged. It's entirely possible life here came from there or from there to here and the reason it's here and there is because it's close. Chances assuming no travel between the two places is just silly.

But isn't it easier to detect nearby signals from ones of equal power from further away?

If so, why should we be surprised that we detect those signals which are easier to detect before those which are more difficult to detect?