Xenology: An Introduction to the Scientific Study of Extraterrestrial Life, Intelligence, and Civilization

First Edition

© 1975-1979, 2008 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Xenology: An Introduction to the Scientific Study of Extraterrestrial Life, Intelligence, and Civilization, First Edition, Xenology Research Institute, Sacramento, CA, 1979; http://www.xenology.info/Xeno.htm


 

23.1.1  The Drake Equation

The Drake equation was developed to answer a specific and pragmatic question: How many advanced technical civilizations exist in our Galaxy, having both the interest and the ability to engage in interstellar communications of some kind? The earliest form of the Drake equation, much like the Shapley calculation, consists essentially of a string of probabilities that are multiplied together to achieve the final result.* If N is the total number of communicative extraterrestrial civilizations, then, according to Drake:

N = Nstar fp ne fl fi fc

where Nstar is the number of stars in the Milky Way Galaxy which would be suitable suns for life-bearing planets; fp is the fraction of these "good suns" actually having planetary systems; ne is the number of planets with an environment suitable for life, per solar system; fl is the fraction of suitable planets on which life finally does arise; f1 is the fraction of life-bearing worlds upon which intelligence appears; and is the fraction of planets harboring intelligent creatures who go on to develop the complex technology of interstellar communication.

What values should we assign to these variables?

At the end of Chapter 4, we concluded that about 5% of all stars in the Galaxy -- roughly ten billion suns -- should have characteristics suitable for the emergence of life. Most of these will lie in the Disk and the outer Core regions of the Milky Way. Hence we choose Nstar = 1010 "good suns."

What about fp? Astronomers now know that most stars are double or multiple.3260 Many "dark companions" have been confirmed, circling quite a few of the nearest stars, during the past century. There are numerous reports of possible planetary bodies (jovian-sized and larger) in orbit around a dozen or so of Sol’s stellar neighbors. In light of all the evidence, fp = 1 is probably reasonable.

How about ne? Based on the work of Dole and others, many astronomers believe that most single-star solar systems are likely to have from 7-13 major planetary bodies orbiting at various distances.1258,2714 Further, if we use our own system as an example of the typically exotic, we see that one out of nine planets has an environment suitable at least for our kind of life (carbon aqueous). So ne = 1 is certainly a plausible estimate. (Note that the possibility of lifeforms with alternative biochemistries merely serves to increase ne.) And recent studies of the origin of life on this planet seem to suggest that abiogenesis is virtually inevitable wherever a suitable environment exists, given enough time. There is wide spread agreement that setting fl = 1 cannot be too wide of the mark.

What about the two remaining factors, fi and fc? Optimists generally assert that the development of intelligence is evolutionarily inevitable, since brains must serve the same negentropic master as the life process itself. In addition, they argue, intelligence begets society and society begets technology as population pressures mount and per capita resources dwindle. Under this view, fi = fc = 1. Other scientists are not so sanguine about the inevitability of intelligence and culture. Human intellect has risen only in the last ~106 years, and culture in only perhaps ~105 years. This represents a mere 0.02% and 0.002%, respectively, of the total time life has existed on Earth. Maybe we’ve just been extraordinarily lucky, and conscious intelligence normally requires much more time to emerge. Or per haps sentience usually fails to evolve at all before the local sun reaches the end of its life. And there are too many examples of technologically static and socially "arrested" cultures on Earth to ignore. Scientists who have attempted to balance these conflicting "optimistic" and "pessimistic" viewpoints generally conclude that fi = 0.1 and = fc = 0.1 are not unreasonable numbers.3241

Multiplying all six factors together gives N = 1010 x 1 x 1 x 1 x 0.1 x 0.1 = 100,000,000 communicative technical civilizations in the Milky Way alone. Or, omitting the factor we conclude that there may be as many as one billion intelligent alien races scattered throughout the Galaxy, each separated from the next by an average distance of 34 light-years. Table 23.1 gives the estimated number of sentient extraterrestrial species expected to lie within a radius R of Earth.

 


Table 23.1 Number of Stars, "Good Suns," and Intelligent Alien Races Within Radius R of Earth, using the Early Drake Equation Formulation

Radius R
Est. Number of Stars in Disk, 
Within Radius R of Earth
Est. Number of 
"Good Suns" 
Within Radius 
R of Earth
Intelligent 
Alien Races 
Within Radius 
R of Earth
(light-years)
     
10
10
(1)
(1)
20
100
5
(1)
50
1000
50
5
100
10,000
500
50
200
100,000
5000
500
500
1,000,000
50,000
5000
1000
8,000,000
400,000
40,000
2000
40,000,000
2,000,000
200,000
5000
300,000,000
15,000,000
1,500,000
10,000
900,000,000
45,000,000
4,500,000


 

This simple form of the Drake Equation is static, however. It assumes that a communicative civilization, once formed, survives indefinitely. But all species eventually become extinct; even stars and galaxies eventually must die. Xenologists who work with the Drake Equation methodology prefer to include a dynamic component which takes account of the possible destruction of civilizations. This results in the "traditional" version of the Drake Equation, as follows:

N = Rstar fp ne fl fi fc L

where Rstar is the mean rate of "good star" formation in the Galaxy (1010 stars / 1010 years = 1.0 "good suns"/year) and L is the average lifespan of a typical alien technical civilization. Plugging in numbers as before, we find that N = 1.0 x 1 x 1 x 1 x 0.1 x 0.1 x L = L/100. The mean lifetime of a civilization appears to be of critical significance in the calculation. What do we do with L? Optimists may insist that technical cultures should be able to survive for 108 years. This corresponds roughly to the reign of the dinosaurs on Earth, and to the time ant society has persisted. There is no reason, argue the optimists, why humans and smart ETs could not do at least as well using the benefits of high technology. Accepting L = 108 years, then N = 1,000,000 sapient cultures in the Milky Way at the present time.

Pessimists point out that human technology is highly militaristic (and even that militarism may be necessary for the evolution of intelligence and technology3241). They note that the accumulated global destructive power today exceeds 10 tons of TNT (or its equivalent) per person. This may be viewed as a round ball of dynamite two meters in diameter hanging over the heads of every man, woman and child on Earth.22 Initiation of global destruction rests in the hands of only a few dozen people, and the world military balance becomes more precarious with each passing decade. In the opinion of the pessimists, L may be on the order of decades, not eons. (Compare Berry77 and Viewing and Horswell3088 with Brown3272 and Hoyle.2998) Choosing the "generous" value of L = 102, the number of communicative civilizations extant in the Galaxy today falls to N = 1 (that is, us).85

The traditional Drake Equation may be written in the reduced form N = Lo L, where Lo is the mean birth rate of new technical civilizations per annum in the Milky Way. Since deaths should equal births in a stable population, L may also be interpreted as the mean death rate of advanced societies. (Mathematically, Lo = Rstar fp ne fl fi fc.) In the analysis above we found that N = L/100, or Lo = 10-2. An optimist, however, might choose Lo = 1 society/year, in which case N = L. A pessimist, on the other hand, might select Lo = 10-4 societies/year, which gives N = L/10,000. (The results of choosing various ET community "turnover" rates are displayed on the graphs in Figure 23.1.) Once the xenologist has selected the cultural birth rate with which he feels most comfortable, both the number of extant technical communities and the average distance between them may be exactly determined. It is interesting to observe that only by making the most optimistic assumptions possible can we place the nearest advanced extraterrestrial civilization within 100 light-years of Earth.

 


Figure 23.1 Number of and Distance to Extraterrestrial Civlizations as a Function of Cultural Longevity

 


 

Modern xenologists have made still further improvements on the methodology of galactic demography.57 The traditional version of the Drake Equation uses a mean value for Rstar -- the rate of formation of "good suns" in the Galaxy -- which is averaged over the estimated 10 eon lifetime of the Milky Way. Yet astrophysicists recognize that the rate of star production from interstellar gases and dust has not held constant over time. Ten eons ago, the rate was perhaps two or three orders of magnitude higher than the mean; today, it is an order or two below. By taking this fact into account xenologists are more accurately able to calculate the number of alien civilizations which coexist (or have coexisted) in the Galaxy at any time t. In mathematical terms, the number N becomes the time-function N(t).

Consider the graph in Figure 23.2 below. The leftmost curve, marked R*(t), represents the total number of solar systems suitable for the emergence of life as a function of galactic time. At each of these useful sites, xenobiologists tell us, life should originate within a few hundred million years. This event is then followed by a gestation time during which life and intelligence evolve, eventually resulting in the rise of a technical culture. For reasons that will become clear presently, we choose to set fi = fc = 1 (that is, Lo = 1) for the purposes of this calculation. In other words, we optimistically assume that every "good sun" eventually spawns an advanced alien civilization.

 


Figure 23.2 Population of Extraterrestrial Civlizations as a Function of Galactic Time (modified from Oliver1305)


 

Applying the Hypothesis of Mediocrity and the example of Earth, xenologists believe that a good average value for the gestation time C should be on the order of that for human culture, about 4.5 x 109 years. Depending on local environmental conditions this quantity undoubtedly will vary considerably, but it seems that 4.5 eons is a reasonable mean or "expected" value.

After the gestation period has elapsed, the number of sites in the Milky Way having communicative civilizations rapidly increases, following roughly the shape of the R*(t) curve. Later, when the average lifetime L of the typical technical culture has expired, extraterrestrial civilizations begin to die off along a curve parallel to the growth. (These two curves are labeled "BIRTH" and "DEATH" on the graph.) For reasons that will become apparent, we choose a very optimistic value for L of 109 years.

To obtain the Galactic population (the number of coexisting civilizations) at any given time t, galactic demographers simply subtract the death curve from the birth curve. The difference is the number of alien technical cultures which have been born but have not yet died at time t. On the graph this population curve is designated N(t).1305

Perhaps the most fascinating result of this analysis is the size, shape and position of N(t). Apparently the population of coexistent technical civilizations peaked out about four billion years ago, when primeval ooze still slopped the rocky shores of ancient Earth. Humanity thus appears to be a latecomer on the cosmic stage -- the majority of Galactic history has come and gone without us.442 Seemingly, advanced life was more common in the past than it is now.57 While there still exist a billion sites of life extant in the Milky Way today (50% of the peak reached 4 eons ago) there are some seven billion sites of extinct alien civilizations for starfaring archaeologists of the future to pore over. In other words, about 7 of every 8 technological alien cultures that have ever existed are extinct today.

It now becomes clear why we chose such optimistic values for fi, fc, and L.

Changing these numerical assumptions to more pessimistic values does not alter the sobering conclusion that humanity may have missed most of the Galactic action. For L, we’ve already selected as optimistic a figure as common sense will permit; smaller values merely serve to decrease the galactic population overall and to shift the peak of N(t) further back in time. Choosing more conservative numbers for and in the Drake Equation has a similar effect. In fact, only by positing an unreasonably lengthy mean gestation time plus mean lifetime (G + L) greater than 12 billion years can demographers arrange for humanity to sit on the rising side of the curve representing the civilized population of the Galactic community.

 


* Skeptics have wryly asserted that the Drake Equation is nothing more than a clever way to compress a large amount of ignorance into a very small space.

 


Last updated on 6 December 2008