We have little to guide us on the question of the existence intelligent life elsewhere in the universe. But the physicist Enrico Fermi came up with the most obvious question: if the universe is teeming with advanced civilizations, where are they?

The so-called Fermi Paradox has haunted SETI researchers ever since. Not least because the famous Drake equation, which attempts put a figure on the number intelligent civilisations out there now, implies that if the number of intelligent civilisations capable of communication in our galaxy is greater than 1, then we should eventually hear from them.

That overlooks one small factor, says Reginald Smith from the Bouchet-Franklin Institute in Rochester, New York state. He says that there is a limit to how far a signal from ET can travel before it becomes too faint to hear. And when you factor that in, everything changes.

Smith uses this idea to derive a minimum density of civilizations below which contact is improbable within a given volume of space. The calculation depends on factors such as the lifetime of a civilization and the distance that it might be possible to communicate over and it produces some interesting scenarios:

“Assuming the average communicating civilization has a lifetime of 1,000 years, ten times longer than Earth has been broadcasting, and has a signal horizon of 1,000 light-years, you need a minimum of over 300 communicating civilization in the galactic neighborhood to reach a minimum density.”

So if there are only 200 advanced civilizations in our galaxy, the chances are that they’ll never notice each other.

Of course, we’ve no way of knowing how many advanced civilizations are out there. But this kind of thinking could, for the first time, put a limit on the number that could be out there: less than 200 perhaps?

It also has significant implications for Fermi’s line of thinking.

Would it be too early to say the paradox has been solved?

Ref: arxiv.org/abs/0901.3863: Broadcasting But Not Receiving: Density Dependence Considerations for SETI Signals