I've come to reject the common "SETI" (search for extraterrestrial intelligence) wisdom that there must be millions of technology capable civilizations within our "light sphere" (the region of the Universe accessible to us by electromagnetic communication). The Drake formula provides a means to estimate the number of intelligent civilizations in a galaxy or in the universe. Essentially, the likelihood of a planet evolving biological life that has created sophisticated technology is tiny, but there are so many star systems, that there should still be many millions of such civilizations. Carl Sagan's analysis of the Drake formula concluded that there should be around a million civilizations with advanced technology in our galaxy, while Frank Drake estimated around 10,000. And there are many billions of galaxies. Yet we don't notice any of these intelligent civilizations, hence the paradox that Fermi described in his famous comment. So where is everyone?
We can readily explain why any one of these civilizations might be quiet. Perhaps it destroyed itself. Perhaps it is following the Star Trek ethical guideline to avoid interference with primitive civilizations (such as ours). These explanations make sense for any one civilization, but it is not credible, in my view, that every one of the billions of technology capable civilizations that should exist has destroyed itself or decided to remain quiet.
The SETI project is sometimes described as trying to find a needle (evidence of a technical civilization) in a haystack (all the natural signals in the universe). But actually, any technologically sophisticated civilization would be generating trillions of trillions of needles (noticeably intelligent signals). Even if they have switched away from electromagnetic transmissions as a primary form of communication, there would still be vast artifacts of electromagnetic phenomenon generated by all of the many computational and communication processes that such a civilization would need to engage in.
Now let's factor in what I call the "law of accelerating returns" (the inherent exponential growth of information technology). The common wisdom (based on what I call the intuitive linear perspective) is that it would take many thousands, if not millions of years, for an early technological civilization to become capable of technology that spanned a solar system. But because of the explosive nature of exponential growth, it will only take a quarter of a millennium (in our own case) to go from sending messages on horseback to saturating the matter and energy in our solar system with sublimely intelligent processes.
The price-performance of computation went from 10-5 to 108 cps per thousand dollars in the 20th century. We also went from about a million dollars to a trillion dollars in the amount of capital devoted to computation, so overall progress in nonbiological intelligence went from 10-2 to 1017 cps in the 20th century, which is still short of the human biological figure of 1026 cps. By my calculations, however, we will achieve around 1069 cps by the end of the 21st century, thereby greatly multiplying the intellectual capability of our human-machine civilization. Even if we find communication methods superior to electromagnetic transmissions we will nonetheless be generating an enormous number of intelligent electromagnetic signals.
According to most analyses of the Drake equation, there should be billions of civilizations, and a substantial fraction of these should be ahead of us by millions of years. That's enough time for many of them to be capable of vast galaxy-wide technologies. So how can it be that we haven't noticed any of the trillions of trillions of "needles" that each of these billions of advanced civilizations should be creating?
My own conclusion is that they don't exist. If it seems unlikely that we would be in the lead in the universe, here on the third planet of a humble star in an otherwise undistinguished galaxy, it's no more perplexing than the existence of our universe with its ever so precisely tuned formulas to allow life to evolve in the first place.