Intelligent Responses to Our Technological Signals Will Not Arrive In Fewer Than Three Millennia

What is the chance we start a conversation with another civilization like our own? Our technological society produced signals that could be received by other extraterrestrial civilizations, within a sphere around us with a radius of $\sim 10^2$ light years. Given that, the Copernican principle provides a lower limit on the response time that we should expect from transmitters on Earth-like planets around Sun-like stars. If our civilization lives longer, the expected number of responses could increase. We explore the chance of detecting a response in the future, and show that a response should only be expected to arrive after a few millennia.