Yesterday I posted a modification of the Drake equation that was intended as a speculative tool – no, rather a speculative toy – to assess the probability that Earth and its biosphere have been detected by at least one alien civilization during the last three billion years. I presented an example according to which there was a 99 percent chance that our planet has been detected.

Let’s now take another try with the equation: If we change just the value of the fraction of extraterrestrial civilizations which conduct exoplanet searches (f_{s} in the equation) from 0.1 to 0.01, the probability that our planet has been detected lowers from 99 to 35 percent. If we further lower the average number of habitable planets per star that has planets (n_{e}) from 2 to 0.5 and the fraction of life-harbouring planets on which intelligence evolves (f_{i}) from 0.01 to 0.001, the probability of detection swings to 1 percent. So according to this example it is virtually certain that Earth has not been noticed.

The point is that both this and the Drake equation are speculative – they can be nice toys to play around with and maybe sometimes even good tools to clear up muddy thinking, but they offer no firm answers to anything.