For years, scientists have tried to explain the Fermi paradox, which says simply that if the probability of intelligent life evolving on other planets is anything greater than 0, there is such a mind numbingly huge number of planets in the galaxy that we would expect the number of advanced civilizations in the galaxy to be astronomical. So, according to the Fermi paradox, where are they?

Another way to express this is the Drake equation. The Drake equation expresses the expected number of advanced civilizations in the galaxy as:

N = N* * fp * ne * fl * fi * fc * L / Tg

So, what is N? Obviously, it can't be a very small number, because if it were too small we ourselves would not exist. But, if the number were much larger than one, we would expect the galaxy to be positively overflowing with advanced civilizations. Considering the milky way galaxy is at least 8 billion years old, and it would take somewhere between 5 and 50 million years for an advanced civilization to fill the galaxy, any other advanced civilizations in the galaxy would likely have been around for a billion years or more and would have long since filled the galaxy. In fact, if that were true, we probably would not be here, because any adavanced civilization would have colonized earth hundreds of millions of years ago, and we would not be here.

The only plausible solution to the Drake equation is that N is approximately 1. Any smaller and we would not exist. Any larger and we also would not exist. So, the mere fact that the human race has evolved on this small blue planet orbiting an unremarkable yellow dwarf star in a quiet corner of the milky way galaxy probably means that the solution to the Drake equation is, 1!

http://hanson.gmu.edu/greatfilter.html

If it is one of our past steps, such as the development of single-cell life, then we shouldn't expect to see such independently evolved life anywhere within billions of light years from us. But if it is a step between here and a choice to explode that is very improbable, we should fear for our future. At the very least, our potential would have to be much less than it seems. Optimism (as defined here) regarding our future is directly pitted against optimism regarding the ease of previous evolutionary steps. To the extent those successes were easy, our future failure to explode is almost certain.

Essentially if you define the steps along the path to societal explosive growth towards galactic colonization to be something like:

1. The right star system (including organics)
2. Reproductive something (e.g. RNA)
3. Simple (prokaryotic) single-cell life
4. Complex (archaeatic & eukaryotic) single-cell life
5. Sexual reproduction
6. Multi-cell life
7. Tool-using animals with big brains
8. Where we are now
9. Colonization explosion

And you take into consideration the fact that we see no evidence in the Galaxy for an existing galactic civilization, then something along the path from 1-9 is a Great Filter.  Something is blocking the creation of galactic civilizations.

From this it follows that if the steps 1-7 are easy, then the jump to step 9 must be very very hard.  The reverse of course follows.  The Great Filter may already be behind us and now we have smooth sailing.

My bet is that the Great Filter is in front of us.

BBC: Galaxy has 'billions of Earths'

Extrapolation done by Dr. Alan Boss of the Carnegie Institution of Science.  Based upon the 300+ planets found so far he has estimated that there are perhaps billions of earthlike planets in the galaxy.

So using his number that places us halfway through the Drake equation.

N = R* × f_p × n_e × f_l × f_i × f_c × L

[link: Drake Equation]

Of course the numbers get harder to know (or estimate) the further towards the right side of that equation.  But just think we didn’t even have the data to make an educated guess five years ago.

Frank Drake is famous for his Drake equation which attempts to estimate the amount of intelligent life in the universe.  It is actually fairly simple.

N = R* × f_p × n_e × f_l × f_i × f_c × L

where:

• N is the number of civilizations in our galaxy with which we might hope to be able to communicate;

and

• R^* is the average rate of star formation in our galaxy
• f_p is the fraction of those stars that have planets
• n_e is the average number of planets that can potentially support life per star that has planets
• f_ℓ is the fraction of the above that actually go on to develop life at some point
• f_i is the fraction of the above that actually go on to develop intelligent life
• f_c is the fraction of civilizations that develop a technology that releases detectable signs of their existence into space
• L is the length of time such civilizations release detectable signals into space.

Stephen Hawking

Stephen Hawking comes along in this speech and essentially, from what I can gather, argues that the first four variables/functions hold potentially high values. 

The early appearance of life on Earth suggests that there's a good chance of the spontaneous generation of life, in suitable conditions.

He then lays out four reasons as to why we haven't been contacted yet.

He subscribes mostly to point 2.  Wherein the probability of life is reasonable but the probability of intelligence is low.  Which implies that the last three of Drakes functions/variables are quite low.

Seems somewhat probable due to the current lack of evidence to the contrary. So if you treat the Drake equation as merely a framework and plug in realistic numbers that reflect the likely rarity of intelligent life you get a very low chance of encountering an intelligent species out there.