Let's see: We've been okay with radio for less than 200 years so far. The earth was formed ballpark 4.5 billion years ago. The big bang was about 13.7 billion years ago.
Assume that to get a civilization need a planet and, thus, elements heavier than hydrogen and helium. Those heavier elements are created in big stars that supernova, that is, have their cores collapse under gravity and blow off their outer layers where during the explosion all the heavier elements in the periodic table are created by fusing together lighter elements. So to get a planet, have to have a star form, burn out, and supernova. So, assume that are getting candidate planets 3.7 billion years after the big bang. Then have been forming candidate planets for 10 billion years.
Now take the planets that have achieved mastry of radio (i.e., working with photons from 60 Hz up to gamma rays). Take the date when they first made this progress with radio. Take the distribution of those dates over the planets. That distribution is 'concentrated' on the last 10 billion years. Now in that distribution spread out over 10 billion years, what is the probability mass of the last million years? It's TINY. Maybe it's 0.01%. Then 99.99% of the civilizations that mastered radio did it over one million years ago and, thus, are a million years or more ahead of us. Done.
Assume that to get a civilization need a planet and, thus, elements heavier than hydrogen and helium. Those heavier elements are created in big stars that supernova, that is, have their cores collapse under gravity and blow off their outer layers where during the explosion all the heavier elements in the periodic table are created by fusing together lighter elements. So to get a planet, have to have a star form, burn out, and supernova. So, assume that are getting candidate planets 3.7 billion years after the big bang. Then have been forming candidate planets for 10 billion years.
Now take the planets that have achieved mastry of radio (i.e., working with photons from 60 Hz up to gamma rays). Take the date when they first made this progress with radio. Take the distribution of those dates over the planets. That distribution is 'concentrated' on the last 10 billion years. Now in that distribution spread out over 10 billion years, what is the probability mass of the last million years? It's TINY. Maybe it's 0.01%. Then 99.99% of the civilizations that mastered radio did it over one million years ago and, thus, are a million years or more ahead of us. Done.
Okay?