Are we alone in the universe? Where IS everybody?

The Fermi paradox is something that I've always liked thinking about. The Fermi paradox, named after the renowned physicist who asked, “Where is everybody?”, is the contradiction between the lack of evidence and the simultaneously high probability of the existence of extraterrestrial civilizations. It is a conflict of scale and probability.

The equation used to derive the probability of the existence of extraterrestrial civilization is the Drake Equation, written by Dr. Frank Drake in 1961.

The equation states that N, the number of civilizations, is assumed to be equal to the mathematical product of (i) R, the average rate of star formation, (ii) fp, the fraction of formed stars that have planets, (iii) ne, the average number of planets per star that can potentially support life, (iv) fl, the fraction of those planets that actually develop life, (v) fi, the fraction of planets bearing life on which intelligent, civilized life has developed, (vi) fc, the fraction of these civilizations that have developed communications that can release detectable signals into space and (vii) L, the length of time:

Calculations suggest that there are an estimated 100 million worlds were “life has beenforged by evolution” and that statistics say that the probability of intelligent life elsewhere in the universe is pretty high.

The equation was originally written as a way to stimulate scientific discussion at a meeting on the search for extraterrestrial intelligence (SETI). Much of the criticism towards the Drake equation comes from the fact that many of the terms of the Drake Equation are conjectural, and the net result is that the error associated with any derived value is so large that the equation cannot be used to draw any firm conclusions. Since then, however, astrophysicists have refined the Drake Equation, as more knowledge and information about space and planetary formation has been disseminated.

There are some interesting and logical hypotheses as to why we have yet to find intelligent life anywhere else in the universe (and you can find the equations and probabilities here if you're interested in the numbers), summarized here:

1. Rare Earth hypothesis and The Great Filter
   Rejects the mediocrity principle; states that extraterrestrial life is rare or nonexistent
2. Algae vs alumnae problem
   No other intelligent species have arisen/complex life may be common, intelligence is not. Therefore, it would be hard for humans to detect.
3. Intelligent alien species lack advanced technology
   Such civilizations would also be hard to detect by humans.
4. It in the nature of intelligent life to destroy itself
   Sagan and Shklovskii speculate that technological civilizations will either tend to destroy themselves within a century of developing interstellar communication capability or master their self-destructive tendencies and survive. There are many ways a civilization can destroy itself, including accidental environmental contamination or poorly designed artificial intelligence.
5. It in the nature of intelligent life to destroy othersIt has been suggested that a successful alien species would be a superpredator to the human race.
6. Periodic extinction by natural eventsExtinction events cause new life to die out and periodically destroy intelligent life before a species is able to develop the technology to communicate with other civilizations.
7. Intelligent civilizations are too far apart in space or timeIt is possible that non-colonizing but technologically advanced civilizations exist, but may be separated by several thousand light years, and one or both cultures will become extinct before meaningful dialogue can be established. It is possible that if other civilizations exist and are transmitting and exploring, their signals have not arrived to Earth yet (low probability).
8. It is too expensive to spread physically throughout the galaxyCosts may be too high for it to be feasible to attempt interstellar colonization.
9. Human beings have not existed long enoughThe period of human existence is a very brief period on a cosmological scale and may have not existed long enough to be detected by extraterrestrial intelligence.
10. Human beings are not listening properlyExtraterrestrials may transmit signals that employ unconventional data compression, frequencies, or modulations, that with our current technologies, we cannot detect.
11. Civilizations broadcast detectable signal but only for a brief period of timeCivilizations may have evolved beyond radio transmission and are communicating by principles of physics not yet understood by humans.
12. Civilizations tend to isolate themselvesSome advanced beings may divest themselves in the physical form, create massive artificial virtual environments, transfer themselves through mind uploading, and exist in totally virtual worlds; or they have developed increasing disinterest in the outside world.
13. Civilizations are too alienAliens may be too psychologically different to communicate with humans and a message broadcast by that species might seem like background noise to humans, and therefore go undetected.
14. SETI paradoxEveryone is listening, no one is transmitting.
15. Zoo hypothesisIntelligent extraterrestrial life does not contact Earth to allow for its natural evolution and development.
16. Planetarium hypothesisWe are living in an artificial universe, perhaps a form of virtual-reality “planetarium,” designed to give us the illusion that the universe is empty.
17. It is dangerous to contact other civilizationsPerhaps prudent civilizations actively hide away from everyone else in fear of fatal problems.
18. They are here undetectedA civilization advanced enough to travel between stars could visit or observe without us knowing.
19. UFO conspiracy theoryIt is possible that SETI or the government are not reporting positive detections, have been blocking signals, or suppressing publication.

Interesting hypotheses and concepts aside, broadly speaking, I think the Fermi paradox illustrates a side of science that scientists tend to dismiss when given "definitive" numbers in the form of statistics: While statistics and mathematical probability would dictate that there is a high chance of intelligent life existing elsewhere and that we should have found them by now, there is no evidence of extraterrestrial life. Likewise in science, while a statistical model or equation may be able to tell us how likely we are to get a result, that doesn't necessarily mean that not seeing those results means that an effect is not there or not possible, and that there are likely alternative explanations for why those results are not seen (i.e. statistical significance vs. scientific significance). Hopefully, though, the list of reasons why a results contradicts the statistics isn't as extensive or exhaustive as that for the Fermi paradox.