Episode 12 Encyclopaedia Galactica
Some topics seem like they haven't changed much over the last 33 years. Whether we have been visited by extraterrestials is one of those topics. I agree with Carl that extraordinary claims require extraordinary evidence. So far, there doesn't seem to be any credible evidence that contact has been made.
The Drake equation that estimates the number of civilizations within the Milky Way galaxy has also stood the test of time.The fact that we have found over 1000 exoplanets has increased the validity of the estimates for the leftmost factors in the equation. I've seen estimates that there are 33 billion Earth-sized planets in the habitable zones of their stars. Carl calculated that there were 100 billion planets with life.
The moon systems of Jupiter and Saturn have also proved that planets are not necessarily the only places to look for life. The chance that Mars had or has simple life has increased with the rovers discovering rocks that could have formed only in liquid water. The moons Europa, Enceladus and Titan all have their proponents for current life because they have liquid lakes and oceans.
The more uncertain factors are on the right side of the equation. The most uncertain one is "how long do civilizations last?" and that is a political question rather than scientific one. Carl calculated that there has been 1 billion planets with civilizations with radio communication. But when you use the fact that mankind has had radio communication capability for only a few decades of the Earth's 4.5 billion years, you have to multiply those 1 billion civilizations by (45 years / 4.5 billion years) 1/100,000,000 with a result of 10 civilizations currently in existence.
The observation that there should be aliens all over the place but we haven't seen them yet, is called the Fermi paradox. Carl proposes a couple of reasons for their absence. Possibly were the first ones on the block and the others are still in development. Another possibility are that they are here already. Observing us discretely without letting their presence be known. A third possibility is that civilizations become complacent and lose their drive to explore. Sometimes with the reduced support for science in the US, I'm worried that could be the direction we are headed in. A future with people so preoccupied texting what they had for breakfast with their smart phones they don't have any interest in looking at the stars in the sky anymore.
One of the recent topics up for debate is whether we should attempt to communicate by sending signals from Earth. Stephen Hawking thinks it is a bad idea. The odds are that any civilization we contact would be far more advanced than we are. Historically things haven't gone well when a backward civilization meets a much more advanced one, Aztecs vs the Spanish for example. I still remember the Twilight episode entitled "To Serve Man". The Earth thought it was a book on how the aliens would teach Mankind about all their great scientific discoveries but it turned out to be a cookbook. Maybe we can intercept that signal we sent to the globular cluster M13.