The Paradox was so named after an informal discussion in 1950 where physicist Enrico Fermi brought up the subject. His conjecture was based on a mathematical probability model called the Drake Equation, which, when feed the proper data, will produce a rough estimate of the number of space-faring civilizations in our galaxy at this point in time. The exact values of certain points of data in the equation are constantly changing, such as the estimate of the average number of planets a star system might have or the type of star system, as certain types of binary systems are much less capable of sustaining planets in a stable orbit. The Drake Equation's results can come out to anywhere from 1,000 to 100,000,000 depending on the exact data used, but even using the smaller part of this range, a thousand space-faring civilizations should make noise, lots of it.
Look at humans. We've been space-capable for just the last half-century, and yet even before that we were blasting radio and TV signals into space for the entire universe to hear. Hitler's opening speech at the 1936 Olympics, the first broadcast strong enough to leak into space, has already travelled outwards 76 lightyears. That's right, Hitler will be the first human any alien who's watching gets to see. The thought is, we're a young people, imagine what a far older civilization would send out, especially if they covered a few stars. An empire of that size should look like a bright "Right Here" neon sign, and yet our radio telescopes pick up nada.
There are possible solutions though. What if the aliens didn't want to be found? Think Columbus and the Indians, hostile takeover of a less advanced people. If an advanced race were to show up in orbit they could easily wipe us out in one of many ways, then have our planet for themselves. So a species might be wise to stop broadcasting and keep all future communications on tight channels, make sure nobody could hear them. If that's the dominant mentality in this area of the Galaxy, we shouldn't expect to hear much.
And then there's the Zoo Hypothesis, that a race of Superintelligent Galactic Police make sure nobody stops in and says "Hello" to us while we're still developing; like the Prime Directive from Star Trek. It might seem cruel to do such a thing, just leave us here to bomb ourselves into extinction, but maybe that's the point. If a species isn't capable of maintaining and prospering itself, or chooses the path of violence and conquer, what use would it be to a galactic community? Better to let the good ones fight there way up the ladder and sit back as the bad ones blow themselves to pieces.That's another idea to, they're all gone because they've manage to destroy themselves. Any species that develops nuclear power could destroy itself with relative ease, never to be heard again. Hell, we almost did it a few times. Wouldn't that be a nightmare, we finally get to space to find out we're the only ones who've managed to get that far, humans as the smartest beings in the Universe. Pray to whatever god you have that never happens, imagine the size of our egos.
A final, less dismal idea is that we've simply come to our prime in a "Dead Zone", meaning we've just missed everybody. Empires might have risen and fallen while we drew pictures in caves, but we missed their phone calls, and now everybody's either dead, in a Dyson Sphere, or transcended. Next week I'll actually try to talk about what transcend means, it's not what you might think.
All in all, that's a lot of text, if you got this far, congrats.

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