mike3 wrote:

I was wondering: How do we know it would even be possible to receive
the signals from aliens even if they did exist and did send out radio?
Considering we have a galaxy full of stars blasting out far more
intense radio signals than any ground-based transmitter could.
Wouldn't it be like trying to listen for a fly buzzing on the other
end of a stadium, with 50,000 screaming fans in between you and it?

How do sonars hear a submarine miles away in the midst of all the noise in
the ocean?

You listen for a particular frequency while filtering out _all_ the other
frequencies. If the signal is greater than the noise in that very narrow band
you hear it. Further, you can integrate that frequency over time. Noise in
that band will average out to zero while the frequency will increase with time.

Using your example how do you hear your friend sitting next to you in a
stadium in the midst of all the noise in a stadium? You can also talk in a
loud factory and there the trick is not to shout but to speak normally and
distinctly. The ear is very good at picking out the frequencies of interest.

The only requirement is to have frequencies of interest louder than the noise
at those same frequencies. The broadband noise level (stadium noise) is not
important. The entire radio/TV spectrum has a huge noise level broadband. But
by tuning to just a narrow range of frequencies you can pick one station out
of all the stations and all the noise.

In practice, SETI is looking at the "water hole" frequency which is
particularly quiet over very long distances. It is assumed anyone sending
knows that also and chooses that frequency so as to be heard. That assumption
does not apply unless there is a deliberate attempt to communicate. I am not
aware of any reasoning which can lead to a second frequency to monitor so
after that one frequency it is a crap shoot.