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The galactic habitable zone is sometimes defined as a torus around the galactic center with an outer radius of 10 kpc and an inner radius of 4 kpc. The volume of such a torus is roughly 5600 (kly) 3. Adopting the text's value of N = 100 technologically advanced civilizations in the Galaxy, then, on the average, each volume of 56 (kly) 3 within the galactic habitable zone is occupied by one such civilization. Also adopting the value L = 500 years as the technological lifetime of such a civilization (the time over which they have been sending out radio signals at the speed of light) , then through what volume of space would these signals have spread? What are the chances of two civilizations being within the same signal volume?
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