The so-called Fermi paradox tells much more about humans than about the abundance of intelligent life in the universe. The paradox can be stated in this way:
The apparent size and age of the universe suggest that many technologically advanced extraterrestrial civilizations ought to exist.
However, this hypothesis seems inconsistent with the lack of observational evidence to support it. (wiki)
The paradox arises because we assume that technologically advanced civilizations should be observable. However this is very unlikely. Why? Well because any civilization that passes the threshold of mortality is unlikely to be dependent on solar energy (like most life on earth is, directly or through the assimilation of dead bodies of animals and plants). Most likely they will inhabit large structures in space that will not emit large quantities of light or radiation.
The problem for us, humans, is that we are on the very beginning of technological discovery. Only a few thousands years ago we were mastering arrows, iron. Only a few decades for computers and transistors. What is that in a scale of millions of years? Of course, to us, to me and you, the present seems the most important place in history, and we are so used to it that we imagine things will remain for this forever. But looking just a bit into the future we can imagine that we will increasingly be able to master the ability to modify our own bodies in order to increase our lifespan and capabilities, and, eventually, to design new bodies from scratch which we can inhabit. This will most likely take less than a million years which is nothing on a cosmic scale. So, the chance of finding civilizations that are on the same kind of technological stage as we are is close to zero. We are a curiosity in the cosmic journey of time. Our kind of technology or civilization can only last for a few thousand years, until either we destroy ourselves or create an entirely new way of life (with lifespans and minds much larger than our current ones).
So, even if technological advanced civilizations were everywhere, even in our planet, even with only a few million years ahead of us, they would probably be so different from us that we would not even be aware of their existence even if they were next to us.
How could this be? Well, would you attempt to talk to an ant, to a dolphin, to a gorilla? We are simply too different. Communication with such different species would demand that we first destroy them, we would have to change their brains, their minds in such ways that they would be not ants, dolphins or gorillas anymore. What would be the point of that?
As technological development continues it allows for living beings to create their own bodies and minds. In less than a million years beings with unlimited lifespans, memories, computational and observational power emerge. It is this kind of beings that we should expect to find throughout the galaxy. They would not need the energy of stars to survive, nor planets. To such beings we would be much more similar to animals than to intelligent life. Guided by instinct, fears and superstitions; irrational, limited, ugly. Can you imagine a being that can assume many different shapes. We would not need to get dressed, to hide its fat. He could connect its sensory organs into something as small as a dandelion seed, or even smaller perhaps, from which he cold observe the planet without being seen. In fact bodies for these intelligences should be discardable, optional, just as we were clothes they will were bodies at will and according to circumstance.
Imagine human beings a few thousand years from now, with bodies similar to those of the movie "Exterminator". We could go about into the wild forests without fear of being eaten or hurt. We would not have to kill for food, but it would be nice just to hang there, in all that diversity, just for the fun of it, sharing the lives of lions and trees and insects. The less we interfere the more we could see things in their extravagant originality, the more we could learn. In the same way, such beings from a more advanced civilization, with their infinite minds and powers, would probably not want to be noticed by us, for they would only be able to communicate with us by destroying who we were.
Even if they had an interest in discovering earth, they would probably have as much curiosity for us as for the lives of many fish and insects and mollusks, mammals and so on. And they would probably find it as hard to communicate with us as with them. An analogy can be established with computers. A general processing computer will be able to "speak" with any other general processing unit. But specific components, which have only limited functionality, will have trouble in processing whatever information that does not fit their original design. An ancient graphics card (not a GPGPU) will only be able to process specific information, regarding images, and nothing else. Humans have much more diversity in the kinds of thoughts they can have than most other animals we know of. But even life on earth can show us our severe limits:
Savants show us how even a primitive brain like ours can make vast computations, "see" immense numbers like Pi (search for Daniel Tammet) or store vast amounts of information. Many people have "absolute pitch", they can "see" the frequency of a note, identifying precisely which is which. Many animals are capable of orientation over large distances (they have a kind of built in gps). Other animals see more frequencies of light, or use eco-location (bats) or are able to use ultrasounds to see inside others (dolphins). Even rudimentary computers wich we are able to build just after a few decades from discovering the first ones, are able to store and treat some kinds of information on a much larger scale than we can. The culture that we have produced as a species can only be partially absorbed, even by our most talented individuals. A being from an advanced civilization would likely be able to understand every single part of our civilization better than any of us. What would he have to say to us? What could he learn from talking to us? The fact is, we cannot even imagine the mind of such a being, no more than a monkey can iagine the mind of a human.
Regarding extra-terrestrial civilizations, we are certainly as primitive to them as other species are primitive to us. It is only a matter of how many millions of years separate us. In any case, it isn't strange at all that beings that do not feed on solar power should be invisible to our present rudimentary technology.
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This might make sense to a very obscured mind, but if e think about it for a minute we will see it makes no sense: civilizations similar to our own in terms of technological development would never be observable to us in the region of the galaxy we inhabit (only in dense clusters of stars would such civilizations be able to make themselves visible to one another). On the other hand, overcoming our present technological limits is also to give rise technologies that will bring about beings that do not have the same kind of biological constraints that we know. They will not have a limited time to live (they will be almost immortal compared with our lifespans), they will have minds that are so vast that they cannot be compared with our own, they will likely not feed on solar power (as we do, through the assimilation of dead bodies of animals and plants) but will lead an existence independent of planets and solar systems.
Why should such beings want to contact us? How could they? Their vision of the universe would be at least as different as ours is regarding a gorilla.
So the Fermi paradox would only make sense if we attribute to mankind a special place in the evolution of life, as if our particular state in the last hundred years or so was particularly dominant in a universe billions of years old. Certainly we do have a special place now, in our planet. We are the dominant species and we intend to colonize beyond our planet. But in the greater scheme of things man is only another small step in the multifarious story of the universe. Like innumerable other species of the past we shall give rise to other forms of life, and the survival of descents similar to us through the next fifty million years, for instance, is not clear at all.
So, when we ask why don't other civilizations appear to us all over the place, we should point out that such beings are inevitable different from us. As we are different from ants, sparrows, alligators, etc, so they will be different from us. Now, would we travel to a different planet to be with a sparrow or an alligator? What would we learn from it? We could certainly teach them a few tricks, but it would be much more fun to watch them to interact with each other, for these beings are physically and mentally so different from us, that any full communication with them would demand that we would change their physical and psychological outlook to the point of destroying what or who they were. So, it would perhaps be more interesting to watch them interact with each other in their own peculiar ways than to interfere or make ourselves known (which, even if we did, would have little meaning to them, an alligator would just see us as "meet he cannot eat").
So, when we ask: "why don't we see such extraterrestrial advanced civilizations", the answer is: because they are very different from us.
How will such civilizations look like? Well for someone like me, who has the brain of a primate and has only seen life on earth, it is very difficult to imagine. But we can at least imagine how some of our descents will look like if they are successful in breaking the current limits of humanity in the next half million years or so.
First they will not be mortal, probably they will also not feed on living organisms (animals nor plants) because they will have other, more efficient, sources of energy (like a derivative of nuclear power). They will not need planets or stars, leaving them for safer environments. Although they might retain an interest in maintaining contact with such places.
The minds of our descendants (if successful) will be much more vast than ours. Their brains (or computers) will be able to have almost instant access to all the information available to that civilization, and personal and communal memory may be less defined that ours. Their ability to process information will also be much more developed and their senses should also evolve.
Of course, we will have (as a civilization) many kinds of descendants. Some will be dogmatic, others will seek pleasure, others will live in constant fear, others will search for weapons, etc. But once even a small community of trans-humans arise, they will mos likely survive, for their ability to deal with the world successfully is greater than what can be achieved with only our natural abilities alone.
This means that intelligent life arising in other planets will rapidly evolve from the stage of primates to the stage of immortality. Intelligent life in general should not depend on the energy of stars, they will also not be very conspicuous because they will not have the need to emit great quantities of light, etc. So, if they are here, they would probably would have no use for us or our planet, and they would not want to interact with us, at most simply observe. Although probably a few minutes would suffice for the human species, and, probably, they would be as interested, or even more interested, in studying many other species in our planet.