Is There Anybody Out There?

In the 1960's an astronomer named Frank Drake developed a statistical equation that can be used to estimate the number of civilizations that presently exist in the Galaxy and are capable of communication using electromagnetic radiation (e.g. radio waves). This equation, known as the Drake equation, is:

N_c = R^*f_pn_ef_l f_if_tL

The terms in this equation are the following:

N_c is the number of civilizations that presently exist and are capable of communication. Since we exist, we know that N_c is at least 1.
R^* This is the number of stars that form per year in our Galaxy
f_p is the probability of planetary formation per star. A probability is a number between 0 and 1.
n_e is the number of "Earth-like" planets per planetary system. Earth-like in this respect means a planet with a liquid surface.
f_l is the probability that primitive life forms on a planet with a liquid surface.
f_i is the probability that on a planet with primitive life, intelligence emerges
f_t is the probability that the intelligent civilization becomes technological and develops the means to communicate
L is the lifetime of the civilization in its communicating phase. Note that L for the Earth would be about 100 years, even though civilization has been around for at least 10,000 years.

To get a value for N_c requires finding values for each of the parameters and multiplying the whole string out. Certainly this is guesswork, but we can make some intelligent decisions. Below is one way this equation can be solved.

The Drake equation can be broken up into three parts, an astronomical part involving the terms R^*, f_p, n_e , a biological part involving the terms f_l,f_i , and a socio-economic part involving the terms f_t, L. The most certain part of this equation is the astronomical part. The biological part is fairly unknown although it can be done with a set of reasonable assumptions. The socio-economic part is an exercise in complete speculation. With these caveats in mind, we now offer our preferred solution to the Drake Equation:

The Astronomical Factors:

R^* = 10. This we know, on average 10 stars per year form in the Galaxy.
f_p = 1. This is a statement that planetary formation is a necessary consequence of star formation and therefore that other solar systems are ubiquitous. The recent discovery that many nearby stars have Jupiter mass planets in orbit about them is an important confirmation of this hypothesis. It has also been long known (since the IRAS mission in 1984) that some nearby stars have dusty disks of material around them. Finally, low mass stars like the Sun are observed to rotate very slowly compared to what you would expect based on angular momentum conservation. In the case of our Sun, the initial angular momentum in the interstellar cloud out of which it formed, was converted to orbital angular momentum instead of the rotational angular momentum of the actual star. The formation of a binary star system would also accomplish this.
n_e = 1. This statement says that in all solar systems there is 1 object that is the right distance from the host star such that the temperature is conducive for the condensation of water vapor. The accretion process for planetary formation, briefly described earlier in this Chapter, suggests that planets sweep up zones of debris in more or less random places. In this case, the odds of a planet forming in the habitable zone around a given star are high.

The Biological Part:

f_l = 1. This is a statement that the formation of amino acids on a planet with a liquid surface has a very high probability. This statement seems fairly safe as it's been known ever since the famous Miller-Urey experiment in the 1950's that the synthesis of organic molecules (principally amino acids) from atmospheric chemistry is relatively easy.
At this point our statistical statement is that the Galaxy is teeming with primitive life on planetary surfaces.
f_i = 0.1. This value means that on only 10% of those planets with simple organic molecules does intelligent life arise. Since we know very little about this process, this term could be considerably less than 0.1 and therefore our own existence is improbable. For instance, we know that the Earth periodically suffers mass extinctions of species (most likely due to large asteroid impacts). Perhaps its improbable for a planet to recover from such an event to keep the evolutionary machine moving forward. The one thing that we think we do know about the transformation from primitive to intelligent life is that it takes billions of years. So perhaps all that is required is billions of years of trial-and-error processes in some distant ocean to eventually produce intelligence. If that is the case, intelligence on a planetary surface with a liquid ocean is highly probable.

The Socio-Economic Part:

f_t = 0.1. This states that on only 10% of those worlds in which intelligence has arisen does technology also arise. This might seem to be an odd statement as many believe that technology is a manifestation of intelligence and is therefore a natural consequence of it. In that case f_t would be 1. However, technology has a definite downside with respect to planetary management in that it creates (and perhaps even demands) non-equilibrium growth and hence threatens the long term sustainability of the intelligent species itself, which is not a very intelligent thing to do. Hence, perhaps it's possible that some intelligent species consciously choose not to develop technology because they are able to look thousands of years in advance and see the consequences. Just because that didn't happen on this planet does not mean that such an outlook is impossible. Note if we combine our estimates of f_t and f_i then we get that only 1% of all planets which host primitive life evolve a civilization that is capable of communication. Again, the number could be much lower than this.
L = 10⁷ (10 million years). How does one arrive at this estimate? Well, we can make the following assumption: 99% of all intelligent civilizations that ever evolve from some primordial ooze are incapable of solving their growth problem and have a technical lifetime of only 1000 years before disappearing. Hence, at any given time in the Galaxy, these civilizations are extremely rare. We then assume that the remaining 1% either solves their growth problem or never has one in the first place and has a lifetime of 1 billion years. One percent of 1 billion is 10 million and that's how we arrive at our value for L . Now, of course, its possible that these "equilibrium" societies never choose to develop technology which is why that can live so long. At the same time, it may will be that out of sheer curiosity these same civilizations develop technology on a small scale in order to achieve communication. Our current use of the Internet is an example of a global communication system that is not particularly resource intensive.

If we now multiply out all of our terms we get:

N_c = (10)(1)(1)(1)(.1)(.1)(10⁷) = 10⁶

One Million Civilizations or Just One

We conclude this Chapter by considering the implication of N_c = one million and give an argument as to why N_c might be just one. To most, one million civilizations capable of communication that exist right now would seem like a very large number. In reality, however, it is a very small number which indicates that intelligent life is rare, very rare, but not necessarily unique to this planet. There are approximately 10¹¹ stars in our galaxy which means, in perspective, that there is only 1 civilization per 100,000 stars. That's rare. When you observe the night sky on a moonless night in a dark location, the number of stars that you can observe with your naked eye is 3-4,000 depending on the quality of your eyesight. Thus, within our naked eye horizon we may well be the only civilization present. But beyond our naked eye horizon is the vastness of the Galaxy, a fact that we can not emotionally appreciate and which biases us towards uniqueness. We are not readily cognizant that we can only interact, in a sensory manner, with an extremely limited volume of the Galaxy and the enormity of what lies beyond our sensory horizon is not something easily grasped.

If we imagine that these 100,000 civilizations are randomly spread throughout the disk of our Galaxy, then the average distance to the nearest civilization is about 300 light years away from us. Even if we could develop a propulsion system that achieves a velocity of 0.1 c, it would take 3000 years to reach the nearest other civilization, presuming we know where it was in the first place. Moreover, although the civilization on the Earth does manifest itself by escaping Television and Military Radar (an ominous combination - perhaps this explains why no one has dropped in to say hello), it has only been doing this for 50 years so we would not expect any civilizations to have accidentally picked up our stray radio wave emissions.

More to the point, however, is that our estimate of N_c = one million is based on a very long average lifetime per civilization. In fact, for reasonable probability values, N_c is more strongly dependent on L than any other term. This means that each one of these civilizations are considerably more advanced than us and have already gone down the pathway to be included in the Galactic Club. This perhaps is the most significant conclusion that one can draw from this statistical argument: civilizations with short lifetimes do not matter and have only a very small window of detection in the Galaxy. To claim our place among other intelligent civilizations in the Galaxy requires that we adopt a different system of planetary management such that we achieve sustainability. Perhaps then, we will even be invited to apply for membership in the Club.

So far we have considered this hypothetical collection of one million civilizations to be static in nature. That is, they occupy their planet in an equilibrium state. However, perhaps curiosity causes them to develop space travel. Would it be possible for one of these civilizations to essentially colonize the entire Galaxy. Let's consider the following scheme:

One day, some civilization decides to use its resources to launch 1000 inhabited space ships in random directions.
Each spaceship is capable of a propulsion velocity of 0.1 c.
99% of all spaceships are destroyed before reaching another planet
Upon arriving at another planet, on average 10,000 years later, the surviving members of the civilization spend 10,000 more years on that planet converting its resources into 1000 more spaceships to repeat this exercise.

How long would it take to reach all 10¹¹ stars in our Galaxy if this scheme were rigorously followed. For instance, in the first step, one civilization eventually reaches 10 new planets. Twenty thousand years later, the resources of those 10 planets have been converted into 1000 more space ships per planet and now there are 10,000 exploratory space craft randomly cruising the Galaxy for new planets. The later timesteps in this sequence are summarized in the following table:

Year	Number of Planets Colonized	Number of Spaceships launched
1	1	1000
10⁴	10
2 x 10⁴	10	10⁴
3 x 10⁴	100	10
4 x 10⁴	100	10⁵
6 x 10⁴	1000	10⁶
10⁵	10⁵	10⁸
4 x 10⁵	10⁷	10¹⁰
10⁶	10¹⁰	10¹³
2 x 10⁶	10¹¹	10¹⁴

From which we find that the entire Galaxy can be colonized in just twenty million years via this scheme.

So, where are they?

The colonization argument presented above has been used to suggest that, in fact, N_c = 1 and that we are it. Earth. That's it, the sole keeper of the question marks in the Galaxy and perhaps the Universe. This is a disturbing thought as it implies an awesome responsibility on us earthlings. If we extinct ourselves we extinguish the very questions that the Universe has used to become self-aware. One resolution to this dilemma is simply that interstellar travel may be a lot more difficult than the above scheme suggests. Clearly, the average time of 10,000 years to reach another planet requires a multi-generation committment. The individuals that get on the spacecraft are not the same ones that get off 10,000 years later. Perhaps this is impossible. Then again, perhaps advanced cryogenics would make interstellar travel feasible. It's difficult to know.

What we do know is that we are unmistakably here and we are observers of the Universe. Our knowledge of the Universe may be primitive, but if so, this is a reflection of the primitive nature of the questions that we ask. But we have been investigating the nature of the Universe for only about 10,000 years. In this flyspeck of time we can't hope to have gained fundamental knowledge. The challenge for us, which stems from the study of Cosmology, is to preserve our civilization and our species so that we will be able to make inquires about the nature of the Universe for millions of more years. Only then can we acquire wisdom and truly understand our connection to the Cosmos and whether or not we are alone