Their radio transmissions may well have reached us when we were banging rocks together for communication and now they're using something bigger and better. I mean, it's a big timeframe we've got to deal with, not to mention a big universe. After all, you say the galaxy is only 100,000 light years across...and radio waves travel at the speed of light (or thereabout), that means that it'd take 100,000 years to get here from the other side of the galaxy. So, it's still a big ballpark.
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