Drake Equation

The annual rate of stellar formation within the Galaxy. We can place this figure fairly safely in the range 10 to 20, with observational evidence favouring the higher figure.

The fraction of these stars that form planetary systems. Less than a decade ago, we could do no more than guess at this figure. Since 1995, a wealth of data has become available showing that extrasolar planets not only exist, but are a fairly common phenomenon. A widely accepted value for f_p is 0.2.

The expression R f_p, then, is calculable with at least a fair degree of accuracy: 20 x 0.2, which gives a value of four planetary systems coming into existence each year in our Galaxy. The next four factors attempt to calculate how many technological civilizations will develop within these systems. In each case, a highly optimistic and pessimistic figure is suggested, with the aim of at least defining a likely range of values for N.

The average number of planets in a system that are suitable for the development of life. This is a particularly difficult figure to estimate, since the conditions needed for life to start are not known with any certainty. We might perhaps base the value on locations where amino acids are likely to have emerged spontaneously. For our Solar System, at least, this results in a surprisingly large number. Earth is a certainty, of course, but an argument could be made for at least two of Jupiter's moons, and even Jupiter's own atmosphere. Saturn's moon Titan seems to have all the necessary ingredients, and in the distant past Mars supported an ocean environment, making it a candidate too. For our own Solar System, this gives an estimate of six candidates. Note that we aren't concerned with whether life actually does exist in all these locations - it almost certainly does not - the value describes locations where life could appear.

The value of six seems intuitively to be more than a trifle optimisitic: it may very well be that a far more complex array of factors is needed for life to be possible, though it's almost impossible to define what these factors might be. As a pessimistic offset to the high value of six, a figure such a 0.1 seems at least plausible (that is, a planet where conditions are right for life to emerge appears only once in every ten planetary systems).

The fraction of planets where life might appear on which it actually does. Again, there is very little basis for a calculation here. Using the possibility of amino acid formation to calculate n_e, though, at least gives us some basis for estimating f_l. We know that, under the right conditions, amino acids will form spontaneously from common chemicals, and will proceed to organise themselves into molecular chains known as peptides. Depending on the particular amino acids in the chain, even relatively simple peptides will demonstrate interesting properties, including - highly relevant to the question of life - the ability to replicate themselves. The available evidence seems to point quite strongly towards this kind of process taking place on the early Earth, but what is far less clearly understood at present is how these self-replicating molecules advanced to the point where they could realistically be referred to as 'life'.

It may be that the development of self-replicating chains of amino acids leads almost inevitably to more and more complex systems, and that once the process has started life will emerge all but automatically. If this is true, then f_l is close to 1 - we'll use a figure of 0.95 as an optimistic estimate.

For all we know, though, the next step in the process is very far from automatic. It may be that the young Earth with its cargo of self-replicators experienced some highly unusual event (the arrival of a meteorite carrying just the right chemicals, for example) that triggered its development into true life. If this pessimistic view is correct, then the appearance of life might be extremely rare, though it's impossible to guess how rare without knowing the nature of the 'trigger'. We might estimate a pessimistic f_l at 0.001 - one chance in a thousand.

It should be noted that these guesses can only take into account what little we know of the development of life on Earth. For all we know, the amino acid route might be unusual in the Galaxy as a whole, with most life emerging by some process entirely unknown to us.

The fraction of those planets on which life appears where it evolves into an intelligent form. This seems to be a fairly simple question at first sight, but the more closely we look at the idea, the more difficult 'intelligence' is to define. Intuitively, we tend to define humans as the only life on Earth that can claim intelligence, but to imagine intelligence beyond the Earth we need to consider the matter from a non-human perspective, and that's very difficult to achieve.

A hypothetical non-human observer might consider for example the ventilated, air-conditied cities of termites, the agricultural activities of certain ants, the immensely complex communication patterns of cuttlefish, the social structures of dolphin communities, or the inventive tool-making and cultural diversity of chimpanzees. The value of f_i depends on how broadly we define 'intelligence'. If we allow some or all of these examples of non-human intelligence, then we can say that it has evolved independently on several occasions, and therefore f_i must be high, at say 0.75.

Alternatively, if we take humanity as the benchmark, then intelligence has appeared just once in the history of life on Earth, and must be a rare commodity. Perhaps the path of evolution of life on Earth is somehow unusual in the Galaxy as a whole. For example, the existence and sudden disappearance of the dinosaurs certainly had a significant impact on the development of mammals and ultimately humans. If evolutionary 'U-turns' like this are fairly rare events, then it may be that f_i is quite low: 0.1, for example.

The fraction of intelligent lifeforms that develop the capacity for interstellar communication. This figure is extremely difficult to estimate, but even on the most optimistic assessment it would seem to be quite low. Even if we admit all the candidates for intelligence listed above, very little potential emerges. The 'technologies' of termites and ants are instinctive in nature, and driven by evolutionary necessity: it's hard to see how this could lead to radio telescopy. Dolphins, however intelligent they may be, have no means of manipulating their environment, and so any kind of dolphin technology is out of the question.

To have any hope of developing to this level requires a capacity for tool use and an adaptive, inventive intelligence. Among all of Earth's life, this is restricted to one particular group of animals, the apes, and of these only humans have come close to the level of technology required to contact other civilizations. On this basis, even an optimistic estimate would for f_c would be low - say 0.1 or one-in-ten. A pessimistic estimate would be much lower still, at about 0.001 or one-in-one-hundred.

We're now at the point where some calculations are possible. Taking the optimistic estimates throughout the above, we can compute that life will emerge somewhere in our Galaxy 22.8 times a year (about once every sixteen days), and that 1.71 communicating civilizations will develop in the same period. These are remarkable figures - they suggest that a civilization comparable to our own will appear, somewhere among the stars of the Milky Way Galaxy, every seven months. These figures represent an upper limit - the best possible scenario.

The pessimistic calculation, as expected, results in much reduced expectations. According to these estimates, the Galaxy will see life appear just once every 2,500 years. The annual rate for the appearance of intelligent technological civilizations is even lower: 0.0000004. On this basis, such civilizations will appear at intervals of about 2½ million years. This represents something like a minimum figure, and although 2½ million years might seem like a long time, it is still an extraordinary result. That's especially true when we consider the final factor in the Drake Equation, L.

The L term refers to the lifetime of a communicating civilisation or, more precisely, the lifetime over which that civilisation might attempt, or be capable of, communication. We have very little basis to even estimate what this number might be (and indeed we might expect it to vary very considerably). In some cases it might be a matter of decades, in others a civilisation might continue to communicate indefinitely, up to the lifetime of the Galaxy itself (L_G).

The value of L_G can be estimated with some confidence. We might assign a conservative estimate of about 10,000,000,000 years (though in fact the true figure might be somewhat higher than this). We can apply this value to the rates of civilization development to see how many technologically sophisticated we would expect to find within our Galaxy.

The optimistic rate was 1.71 per year, and multiplying this over L_G years gives a total of 17,100,000,000 civilizations. This seems far too high - the Galaxy would be crammed with intelligent life, with civilizations emerging around some 9% of the Galaxy's stars. This figure is surely too extreme be correct.

The pessimistic estimates give a figure that seems more likely, but still a remarkably high one. According to these values, our Galaxy is host to about 4,000 technological species. If we presume that these are spread fairly evenly through the spiral, these would develop very roughly 1,000 light years from one another. These figures are by no means certain, of course, and as minimal values may be rather too pessimistic. Nonetheless, they seem realistic, and go some way to explaining why these beings are so difficult to locate: just one star in fifty million would be host to an advanced civilization.