Re: Physics and Mathematics
10 LY is 4,380x the distance of 20 light hours. So if everything else was equal that would need 19184400x the power. However even 100 LY might be a 1/10th of the distance of a neighbouring civilisation. And they'd have to be at the right stage of development and motivated to point a dish etc at us. Not likely.
So is someone 10 LY away going to point a giant dish (about 25m) at us just when we point a giant dish at them?
Then if the nearest tech civilisation was operating 100 LY away, 100 years ago, pointing a 25m dish at us they'd need 2500 MW!
No, in terms of any likely density of tech civilisations at the right time, the probability that they are near enough and pointing the big dishes at us is very close to zero. Physics and mathematics say it's not likely.
Any advanced civilisation looking for life elsewhere will use a big optical telescope in space and use spectroscopic analysis. The sending a radio signal idea is simply too expensive, short range and time consuming. You'd wait a long time for a reply even if it was plausible. In comparison the spectroscopic analysis is dramatically "cheaper", nearly instant and allows a survey of a huge portion of the sky in a few years.
Then what do you do if you find life? Unless someone has discovered that stargates / jump drive / hyperspace / synthetic wormholes / <insert fictional physics> is possible and can make them, a visit isn't possible. Laser / Radio communications only plausible for 100% likely already identified target planet some 10s of LY distance. That's barely the doorstep. Our galaxy's disc diameter is about 150,000 to 200,000 LY across. Even if technically advanced civilisations are 1% of stars (which seems a madly high figure) there might not be any other current tech civilisation within a 1000 LY. That needs 10,000x the laser or radio power of a 10 LY away "neighbour". Also 1000 years ago.
As Douglas Adams pointed out, Space is really big.