The C-Index is a way to think about the difficulty and likelihood of detecting other civilizations. It's a distance, in light years. The question is "What's the farthest away a twin Earth with the same technology could be so that we would hear each other, given how 'loud' we are and our detection technology?" Interestingly, we couldn't hear our own radio waves more than about a half light year away, and we're actually getting quieter, not louder.
A reader of XKCD's What-Ifs asks Randall Munro pretty much this exact question: "Let's assume there's life on the the nearest habitable exoplanet and that they have technology comparable to ours. If they looked at our star right now, what would they see?"
The Sad World of Uncited Papers
1 hour ago