CHAPTER SIXTEEN

THE MATHEMATICS OF TALKING WITH ALIENS

16.1  THREE VIEWS OF ALIEN INTELLIGENCES

Apart from space travel, contact with alien races and civilizations is the theme of science fiction. In this chapter we will examine the issue of communication with alien races. There are, of course, many hurdles to overcome in any communication with intelligent aliens. The first is whether any exist at all. Science fiction writers tend to adopt one of three views:

1. Alien life is common across the galaxy.

2. Alien life is rare, but intelligent aliens exist.

3. Alien life is nonexistent.

Let’s discuss each of these views in turn.

16.1.1 Alien Life Is Common across the Galaxy

The view that alien life is common across the galaxy is perhaps the most typical view in science fiction stories written from the early 1900s to the 1980s. In popular culture, the TV show Star Trek in the 1960s exemplified this view. The show featured a new alien culture and civilization almost every week, with recurring examples of the Vulcans, Klingons, and Romulans. Each of the new series in the franchise introduced new intelligent alien species until there are probably now several hundred in the Star Trek canon. To some extent this is because many of the writers for the original series were also well-known science fiction novelists, including Norman Spinrad, Theodore Sturgeon, and David Gerrold, who got his start writing for the show. Larry Niven wrote an episode for the short-lived animated series in which he injected the Kzinti, an alien race from his Known Space stories.

TV science fiction has tended to follow the leader in this regard: the show Babylon 5, while different in tone and mood from Star Trek, was set on a space station crowded with representatives of dozens of other spacefaring races. This is also typical of science fiction movies as well, the premier example being the Star Wars saga. It is also true of the recent Avatar, at least implicitly, as humanity finds an example of an intelligent alien race living on an inhabitable moon of a gas giant planet in the nearest star system to our own.

From what I can tell, ideas in the movies and on TV tend to be about 20 years behind science fiction novels and stories. The idea of the inhabited universe seemed to peak in the early 1980s. Again, alien contact is a pervasive theme in science fiction. William Gibson’s novel Mona Lisa Overdrive marginally involves contact with aliens from Alpha Centauri, although it is completely unimportant to the plot; the novel could have been easily rewritten without it [96].¹ There are many stories in which the existence of alien races is present in the background, so to speak, but is unimportant to the plot: many of Asimov’s works fall into this category. The usage seems often to be more a way of signaling the work as science fiction rather than contributing anything of substance to it. However, this is verging on literary criticism, which I promised I wouldn’t do.

Among written works, Niven’s Known Space stories are among the best examples of this idea. Niven has invented many different and fascinating alien races, from the humanoid (the Kzinti and Pak) to the vaguely mammalian (Pierson’s Puppeteers) to the nonhumanoid (the sessile but telepathic Grogs and the very alien Outsiders). Again, the idea is quite common: Robert Heinlein’s juvenile novel Have Space Suit—Will Travel features two alien races at the beginning of the novel (the mother-thing’s race and the race of the aliens trying to invade Earth) but leads to the human race being put on trial before an assembly of literally thousands of other intelligent alien races by the end of the novel [114]. I cannot end this discussion without also mentioning Olaf Stapledon’s amazing Star Maker, a broad “history” of the universe and the quest of its many races to understand its maker [225]. The novel is a classic of science fiction by its best English-language author: descriptions of the alien races are many and varied, including crustacean-like creatures, creatures in the form of intelligent boats, intelligent vegetation, and so on. The science is outdated, but it is still one of the best science fiction works ever written.

The notion of a “crowded universe” stems from the principle of mediocrity, otherwise called the Copernican principle: the idea that our planet is a typical planet circling a typical star in a typical galaxy (in perhaps a typical universe. …) From everything we know about astronomy, physics and chemistry, this is true, especially now that we know of more than 700 planets circling other stars. However, the “Great Silence” has called this idea into question over the last 20 years or so. Enrico Fermi was perhaps the first person to express the problem: if many races have evolved in our galaxy, then they probably evolved over the course of billions of years. However, given a species capable of traveling among the stars, even at speeds of only a fraction of the speed of light, it would take only millions of years to explore the galaxy. So why aren’t they here yet? Or if star travel is impossible, if there are many races out there who want to talk to us via radio communications, why haven’t they contacted us yet [132]? SETI has been around in one form or another for fifty years, but the silence has been unbroken.

16.1.2 Alien Life Is Rare but “Out There” for Us to Find

Perhaps there aren’t thousands or millions of other races in the galaxy; perhaps there are only one or two other races. The best exemplar of this idea is the novel The Mote in God’s Eye, by Larry Niven and Jerry Pournelle, which involves the first contact between humans and “moties,” humanoid aliens whose runaway population problems cause them to exist in a state of almost perpetual warfare. The reason it takes humanity over a thousand years as a spacefaring civilization to discover the moties has to do with the features of the “hyperspace” drive (invented by Dan Alderson of Caltech to the authors’ specifications) [186].

There aren’t a lot of novels involving only one alien race out there simply because if you postulate one, you might as well postulate as many as you want.

16.1.3 We Are Alone

One of the earliest major works of science fiction from which aliens were noticeably absent was Asimov’s famous Foundation trilogy, centering on the decline and fall, then subsequent rebirth, of the “galactic empire.” Asimov felt that the absence of aliens was odd enough that in later books in which he combined his robot stories with the Foundation, he went through a lengthy explanation of why the galaxy was devoid of intelligent life apart from humanity.

However, the idea that humanity is the only intelligent race in the galaxy has become, if not the majority position, at least a position among a significant minority, perhaps even a plurality, of science fiction writers since the 1980s. Again, popular culture tends to reflect this. Until the final episode, the reimagined Battlestar Galactica featured a universe devoid of alien life. The show focused more on the interaction of the human race with the Cylons, who could be termed an alien species that humanity itself created.

The reason for this gradual change lies in a paradox. Even as scientists have accepted the Copernican principle and have learned that planets, the potential sites of life in the universe, are common, they have also learned that the planets themselves vary enormously from one another, and that the conditions leading to life on a planet are probably very restrictive. Beyond this is the question of the evolution of life on a planet into an intelligent, tool-making civilization capable of space travel, or at least of radio contact with similar civilizations. Most physicists and astronomers tend to feel that once life begins on a planet, the evolution of some species capable of interstellar communication is almost inevitable [239]. The idea is that because evolution proceeds by random changes favoring survival characteristics, and (from the human experience) intelligence and tool using are very much aids to survival, then the evolution of an intelligent species is almost inevitable, given time and the random selection of the fittest.

Evolutionary biologists feel differently. They point out that the evolution of the human race required the convergence of a number of unlikely events. For example, if the dinosaur-killing comet hadn’t smashed into the Yucután Peninsula 65 million years ago, mammals might not have become the dominant biological order on the planet.

16.2  MOTIVATION FOR ALIEN CONTACT

If the aliens exist, the second hurdle to overcome is devising a plausible reason for them to contact us. There are good reasons for noncontact: Star Trek’s Prime Directive is a good example from science fiction. Historical meetings between technologically advanced civilizations and less advanced ones in Earth’s own history underscore the dangers of such contacts. Perhaps the aliens are avoiding contact because they don’t want to harm us. Stanislaw Lem illustrated the dangers of such issues [149]. Cosmic timescales being what they are, an advanced civilization may be millions or billions of years older than our own. Any revelations they may choose to send us might be meaningless (like discussing quantum physics with the ancient Phoenicians) or, if practical, extraordinarily harmful (like sending plans for a nuclear bomb to 1939 Europe). However, if the aliens do choose to visit us or talk to us, why might they do so? Some reasons follow.

16.2.1 War with Us

The astronomers tacitly assume that we and the little green monsters would welcome each other and settle down to fascinating conversations. Here again, our own experience on Earth offers useful guidance. We’ve already discovered two species that are very intelligent but technically less advanced than we: the common chimpanzee and pygmy chimpanzee. Has our response been to communicate with them? Of course not. Instead, we shoot them, dissect them, cut off their hands for trophies, put them on display in cages, inject them with AIDS virus as a medical experiment and destroy or take over their habitats.… If there really are any radio civilizations within listening distance of us, then for heaven’s sake let’s turn off our own transmitters and try to escape detection, or we’re doomed.

—JARED DIAMOND, THE THIRD CHIMPANZEE [61, PP. 214–215]

The idea of war with alien races dates back to H. G. Wells’s War of the Worlds, published in 1898 [248]. The excerpt from Jared Diamond tells you pretty much all you need to know about the conception of the aliens: they are space vampires who survive by exsanguinating human blood and injecting it directly into their veins. They are bent on conquering Earth because Mars, in the novel an older world than Earth, is gradually becoming unfit for life (à la Percival Lowell’s ideas). Wells, a passionate socialist, extrapolated the motives and actions of European colonialists in the Americas and Africa for his Martians. The book spawned imitators, especially in movies and TV, where several film adaptations of the novel were made, plus Orson Welles’s famous 1938 radio broadcast and movies ranging from Plan 9 from Outer Space to Independence Day. It’s not as popular a theme in science fiction literature as in the movies because of the fundamental difficulties of space travel and the perhaps mistaken idea that advanced civilizations would have moved beyond the need for warfare.

The complementary idea of humans as interplanetary or interstellar aggressors is less common; the recent movie Avatar is almost a lone example among science fiction movies. Olaf Stapledon explored this idea in some of his novels published in the 1930s. In particular, Last and First Men involves the human race exterminating a race of sentient underwater creatures on Venus. This was because the decay of the Moon’s orbit and its ultimate impact on Earth were making Earth unlivable [225]. Despite the scientific inaccuracies, the story provides an interesting psychological study of the Fifth Men, the branch of the human race responsible for the genocide. Stapledon discusses the psychological swings between elation and despair this race faced as it debated the morality of destroying another sentient race to ensure its own survival. His consideration of these moral issues makes Stapledon all but unique among science fiction writers past or present, and his novels are worth reading today. The same idea in a different guise crops up in his novel Odd John, about a race of supermen living among ordinary humans. There the debate is over the morality of exterminating the normal human race to ensure the survival of the more evolved species.

This begs the question of whether interstellar warfare is possible. Here the answer is easy: if interstellar travel is possible, then interstellar warfare is possible. The issue has to do with energetics. Let’s say that an alien civilization has the capability of creating a starship capable of traveling at 86% the speed of light. The reason for this particular velocity is that the relativistic gamma factor at this speed is 2, meaning that the kinetic energy at this speed is equal to the rest mass energy, Mc². Our canonical 10,000 kg starship has a kinetic energy of 9×10²⁰ J, the equivalent enegy of 200,000 H-bombs. A few other ways of visualizing this are:

1. The United States uses about 9×10¹⁹ J of energy in a year, so this is about the total energy use of the United States over a 10-year period.

2. Most asteroids impact the Earth at speeds of about 30 km/s, so if the spaceship impacted Earth, it would have the same effect as an asteroid of mass 200,000,000 kg hitting Earth. This isn’t quite in the dinosaur-killer league but it is substantially larger than the comet that impacted Tunguska, Siberia, in 1908.

3. In a prior chapter we saw that turning on the engines for a spaceship of such size would irradiate the Earth with gamma rays equivalent in power to the total energy the Earth receives from the Sun, potentially sterilizing the planet.

The last item is interesting, in that the drive for an interstellar spaceship makes a good weapon all by itself. The first time I encountered this idea was in the story “The Warriors” in Larry Niven’s collection Tales of Known Space, in which a human spacecraft destroys a Kzinti using its engine, which uses a laser for propulsive power (this is essentially the idea of the photon rocket of chapter 9) [181]. You don’t need the drive to be a laser; the propulsion system for any macroscopic spacecraft capable of star travel must be capable of inflicting a lot of damage on a planetary civilization simply by the laws of physics. This make one part of the movie Avatar ridiculous. At the end of the movie, the triumphant Na’avi send the humans back to Earth on the spacecraft they arrived in. However, there is no way in which they could have “deweaponized” the starship, which was capable of traveling at two-thirds light speed and was considerably larger than 10,000 kg. The humans could render Pandora uninhabitable simply by turning on its engines. Better for the Na’avi just to kill them all. Jake Sully, of all people, should have spotted this flaw in the plan.

Any star drive is a weapon capable of inflicting horrific, potentially world-sterilizing damage. Any civilization capable of star travel is capable of interstellar warfare. Greg Bear explored this potential in his novels The Forge of God and Anvil of Stars; in the first, Earth is destroyed by an alien race, and the children of the survivors set out to destroy the aliens responsible in the second [32][34]. The reason the aliens have for destroying the world is a little puzzling; it seems essentially to be a preemptive strike on their part, a pervasive racial paranoia that if they don’t destroy us, we will eventually come out and destroy them. I guess this is a possible motivation, the flip side of the worry shown in Diamond’s quotation at the opening of this chapter, but it seems over the top. In Niven and Pournelle’s Footfall, the motivation is that the invading aliens represent a faction that lost a war on their home planet and need Earth as a new home. We see Niven’s use of problem limitation here, as any race of beings capable of traveling across the cosmos should be able to pummel twentieth-century Earthlings into submission in a matter of seconds, but the aliens portrayed are not very bright beings created as servants of a highly advanced alien race that killed itself off long before the story begins. The elephant-like aliens are using borrowed technology and have a psychology appropriate to herd animals, allowing humans to dominate them (after a hard fight) despite their initially dropping an asteroid on Earth [187].

Alien invasion doesn’t need to be particularly energy expensive; various writers have posited invasion by alien microbes carried across interstellar distances by stellar winds or virtual invasions when alien broadcasts effectively invade our computer systems or give us bad information, as in the movie Species. The motive for these attacks is a little hard to judge except for the general rule, “all inhuman aliens are bastards,” which seems to be the base assumption of most TV or movies. Humans, of course, broadcast computer viruses essentially for the fun of it, so assuming that alien races would be too evolved to broadcast the interstellar equivalent of ILOVEYOU is probably unwise.

The origin of the idea of the spread of alien life through microbes is probably the “panspermia” theory of Fred Hoyle and Chandra Wickramasinghe, which postulated that life on Earth was seeded by comets carrying the basic building blocks of life. Bacteria and viruses were carried by radiation pressure from one star to another over cosmic timescales, ultimately landing by accident or design (as in the directed panspermia theory of Francis Crick) on a random world, beginning life there if the conditions were right. It’s worth taking a little time to evaluate the idea scientifically.

As mentioned in previous chapters, light exerts a force on objects it falls onto. This is the basis of the matter-antimatter (or photon) rocket: the force exerted is given by the formula

where I is the total intensity (power per unit area) of the light incident on the object, c is the speed of light, A is the surface area of the object, and k is a dimensionless parameter that describes how effective the object is in scattering light: k depends on the wavelength of the light and the exact shape of the object. If the object is large compared to the wavelength, k will be somewhere between about 1/2 to 2. We’ll simply assume it is 1 for now.

If we assume that the microbe being sent through space is spherical, then its area is given by the formula

where r is its radius. Its mass is its volume times its average density (ρ):

The acceleration of the microbe will be the force exerted on it divided by its mass:

The smaller the object, the greater the acceleration. In Earth’s orbit the solar constant (intensity of light from the Sun) is 1,360 W/m²; if we assume that our microbes have a density the same as water (1,000 kg/m³) and a radius of 1 µm (=10⁻⁶ m), we get an acceleration of about 0.01 m/s². This doesn’t sound so high, and of course, the acceleration drops as it gets farther from the Sun, but with this acceleration over a distance of 1 AU, the speed of the bacterium will be 64 km/s—greater than the escape speed from the Solar System. It isn’t going anywhere fast, but it could make it to the Alpha Centauri system in about 20,000 years. One plausible invasion scenario would be genetically engineered bacteria or viruses, or even the basic genetic material needed to seed other planets with higher-order life, sent out by an alien race to colonize other worlds. This could be done at a tiny fraction of the cost of sending starships containing fully sized aliens: a bacterium moving at 86% of the speed of light has a kinetic energy of only about 400 J. Now, there isn’t any way I know to slow it down once it reaches its destination (though there might be). This might be the means by which the unseen alien intelligences managed the Chtorr invasion of the Earth in Gerrold’s series, although it hasn’t been revealed yet. Fast or slow, this invasion strategy is much more plausible than almost any other scenario because of the small amount of energy needed.

16.2.2 Trade or “Enlightenment”

When you trade among the stars, there is no repeat business.

—LARRY NIVEN, “THE FOURTH PROFESSION,” IN ALL THE MYRIAD WAYS

The issue of commerce between the stars is pretty simple: energetics and time effectively prevent it, or at least prevent physical trade. Consider the following: even traveling at 86% of the speed of light, travel to Alpha Centauri will have a round-trip time of 10 years. And that’s the nearest system. The cost is also horrific: the kinetic energy of anything with a mass of 1 kg moving at that speed is 9×10¹⁶ J. At current energy costs of about 10 cents per kW-hr this corresponds to about $300 million per kilogram. This isn’t the entire cost, however, as the relativistic rocket equation tells us that we need 1.4 kg of antimatter (combined with an equal amount of matter) to give 1 kg of payload this velocity. Plus more to slow down to a stop, reverse course with the goods, and slow to a stop again on return. It is hard to imagine anything that could be traded at a profit given the fundamental problems. This is where the fundamental premise of the movie Avatar breaks down: the cost of unobtainium, available only on Pandora, will probably be at least an order of magnitude higher than the quoted value of $20 million per kilogram.

The exchange of information is orders of magnitude cheaper. Communication between alien civilizations via radio waves is faster and cheaper than any exchange of material goods: radio travels at the speed of light, faster than any material object can travel. Cocconi and Morrison showed in the 1950s that it would be possible to detect Earth’s radio transmissions, using then current radio telescope technology, from a distance of more than 10 light-years [60]. So communications between alien civilizations is possible, but is there anything we would want to say to them? I discussed this above: it is possible that aliens wouldn’t want to talk simply because they wouldn’t have much to say to us. However, merely saying “hi” and nothing more would immediately become the most important radio message ever received.

16.2.3 Mars Needs Women!

The successful cross between a human and a Vulcan … is about as likely as the successful mating of a Vulcan and a petunia.

—CARL SAGAN, 1968 NEW YORK TIMES ARTICLE

This is more of a joke than anything else: any competent science fiction writer understands the issue that interspecies “relations” are unlikely. The genetic information for most species on Earth is stored in deoxyribonucleic acid (DNA); it is unlikely that this is the only possible genetic molecule, so there is almost no chance that life evolved on another world would be “compatible” with ours. Even if it was DNA based, aliens would represent different species from humans. As Larry Niven put it in his essay “Man of Steel, Woman of Kleenex,” sexual relations between a human and an alien is what Tom Lehrer once called “animal husbandry” [178].

There is also no reason for them to look much like us. TV shows feature humanoid aliens because it is easier to make human actors look like humanoid aliens than protoplasmic blobs. Perhaps the Anna Karenina principle comes into play here, too: there may be issues that force intelligent, tool-wielding aliens to look more or less humanoid. Until we find examples, of course, we can’t know.

16.2.4 Utterly Alien Motives

A large genre of science fiction concerns alien contact in which the motives for contact are unknown and to a large extent unguessable. The authors of these stories tend to be non-U.S. or non-UK writers, many of them from the former Soviet bloc countries. In the Russian novel Roadside Picnic, by Arkady and Boris Strugatsky, the alien contact is invisible in addition to being inscrutable [230]. In this novel, the “Visitation” has altered several areas of Earth: in them, the laws of physics break down, miracles happen (usually deadly ones), and there are treasures for intrepid explorers to find. The aliens are entirely offstage (if they were ever there in the first place). The only evidence that they ever came is the “Pillman radiant,” an imaginary line in space along which the Visitation seems to have come. Dr. Pillman, the discoverer of the radiant, likens the Visitation to a roadside picnic in which visitors to a picnic site leave their trash without bothering to pick it up, but it isn’t clear that this is the motivation for the Visitation. Stanislaw Lem in Microworlds gives a more honorable motive for the Visitation, but it isn’t clear that his explanation is correct, either [150]. I suspect that Roadside Picnic was a primary motivation for the excellent TV miniseries The Lost Room, but cannot prove it; the “Event” of that series is very similar to the Visitation of the novel.

Stanislaw Lem has two novels premised on alien contact with unknowable motives, Solaris and His Master’s Voice, and a third, Fiasco, in which the tables are turned: humanity attempts to contact an alien race but our motives are completely misunderstood [151]. In Solaris an intelligent planet attempts experiments on astronauts investigating it, for completely unknown reasons. [148]. In His Master’s Voice, scientists intercept an alien message and are completely unable to decipher it; various attempts lead to interesting discoveries, but the content of the message remains completely unknown [147].

Philip K. Dick is one of relatively few American writers who have attempted stories constructed on unknowable alien motives. In Galactic Pot-Healer the protagonist (a “pot-healer,” or ceramics mender) is dragged into a conflict on a distant planet where he understands only the vaguest of the motives or powers of the beings fighting one another to raise a sunken cathedral [68], I find stories like this plausible, in that it is very difficult to communicate with members of species as close to humans as chimpanzees. What luck would we have with aliens? But putting all this aside, let’s get down to Earth and think about how likely it is for us to be able to make contact, whether we can understand them or not.

16.3  DRAKE-EQUATION MODELS AND THE MATHEMATICS OF ALIEN CONTACT

If we were to receive a greeting from an alien civilization tomorrow, we could be pretty confident it was within 50 light-years of us. Our world has been broadcasting radio signals for only about a century, so to receive a signal from aliens would indicate they found our signal and sent us back a reply within that time. This implies a certain density of alien civilizations in our galaxy of roughly one per every (50 LY)³, or 8×10⁻⁶ LY⁻³. The Milky Way Galaxy is a spiral galaxy composed of 3×10¹¹ stars, some 1×10⁵ light-years across and 1,000 light-years thick, so the total volume is approximately that of a cylinder with radius R = 5×10⁴ light-years and thickness 1,000 light-years; this implies that the total volume is ≈ 8×10¹² LY³. If such civilizations are distributed uniformly throughout the galaxy (which is not necessarily a good assumption), then the reception of such a message would imply about 64 million advanced civilizations currently in the galaxy. This seems like an incredibly large number. Of course, the fewer civilizations there are, the longer it will take to talk to them.

Let’s make a simple model for this. Let’s hypothesize that the average number of alien civilizations currently in our galaxy can be expressed as

Here, g is a “generation rate,” which indicates the number of galactic civilizations that achieve a technological level suitable for interstellar communication; this is a certain number per year being “born.” N is the number of such civilizations in the galaxy at any given time, and L is the lifetime of the civilization. Let me give an analogy for what is going on here: Imagine standing in a dark meadow in the middle of the countryside in summer. All around you, you see fireflies flicker on and off. How often do you see more than one firefly lit up? That depends: if a lot of fireflies on average “light up” every second, or if they stay lit for long periods of time, then your odds are good that you will see more than one. If, on the other hand, very few light up every second and they stay lit up only briefly, then the odds aren’t good. The number of fireflies lighting up every second corresponds to g; the amount of time they stay lit up corresponds to L. Intelligent life in the cosmos may be akin to those fireflies—brief flashes lighting the darkness.

All three quantities, N, g, and L, are unknown. The astute reader will recognize this as a version of the Drake equation. In 1960 Frank Drake proposed a statistical model to estimate the number of alien civilizations in the galaxy. In his original version of the equation,

It’s worthwhile considering the variables here:

•  G: the rate at which stars form. This is the only variable that is known with any precision: G ≈ 7 per year.

•  f_p: the fraction of all stars in the galaxy with planets. In 1960 there were no known exoplanets; now there are more than 700 known ones. The value of f_p is probably somewhere between 0.05 and 0.2 (5% and 20%) based on the statistics of stars with planets. As discussed in previous chapters, the probability of a given star having detectable planets increases with increasing metallicity, and is also a function of stellar class.

•  n_e: the average number of Earth-like planets circling the star. This figure is highly problematic. As discussed earlier, a planet being “Earth-like” depends on a number of factors, some of which are interrelated. Depending on how you define it, there are between one and three Earth-like planets in our own Solar System, but the average number per solar system is likely to be much lower.

•  f_l: the fraction of Earth-like planets that develop life. This and the next two variables are completely unknown. It might be high, as Earth developed life only about 700 million years after it formed.

•  f_i: the fraction of planets developing intelligent life.

•  f_c: the fraction of intelligent life that develops technology able to communicate over interstellar distances (i.e., radio).

Needless to say, the equation and its interpretation have engendered much controversy. In response to criticism, Drake has called it a way to “organize our ignorance.” The formula is valid for estimating the number of intelligent alien races only if the variables are statistically independent of one another. This is unlikely to be true. In particular, when we look at n_e, what exactly do we mean by an Earth-like planet? That number, n_e, could be estimated by a mini-Drake equation of its own: we could estimate the average number of planets in the habitable zone times the number whose orbital eccentricities are small enough times the number that are the right size times.…

In any event, we don’t know most of the factors that go into g. We also don’t know L. Remember, L is the lifetime of the “typical” advanced civilization. However, “advanced” means “being able to receive and transmit communications over interstellar distances”—otherwise we couldn’t communicate with them. On Earth we have had this capability for less than 110 years, depending on how you define it. We’ve been listening for alien signals for only about 50 years. This probably represents a lower bound on L, but it isn’t clear what an upper bound should be.

Michael Shermer in an article in Scientific American estimated the average life span of a human civilization as 420 years; these civilizations were all preindustrial, but if this is a reasonable estimate for the life span of a technological civilization, there is no hope of contacting aliens [218]. There has been heated debate over this article on the web, but Shermer’s reasoning isn’t stupid. For one thing, any advanced technological society implies a wealth of energy. The generation of energy in our society rests almost entirely on nonrenewable resources, which will probably be depleted in less than a century if their use continues at the same rate as today. We’ll take up the issue of how long human civilization can last in later chapters. For now, is there anything at all we can say about the possibility of alien contact, given our lack of knowledge of all of the variables above?

Well, first of all, we want the product g L>2, so that there is someone else to talk to. This is not a hard-and-fast rule, as these numbers represent averages, but it seems like a reasonable criterion. Unfortunately, this is a necessary but not sufficient condition. We also need to be able to communicate, which will be impossible to do within the lifetime of our civilization if the alien worlds are spread too far apart.

If galactic civilizations are uniformly distributed, then we can imagine them as being spread over the volume of a cylinder with a very high aspect ratio (i.e., 100:1) between radius and height. Therefore, if these civilizations are separated by distances larger than about 1,000 light-years, it makes more sense to discuss them in terms of the number per unit area spread over a disk representing the galaxy with radius R = 50,000 light-years. If we send a radio signal from Earth and expect it to be intercepted by aliens after a time t, then we can relate N to t as follows:

This is a straightforward probability argument: the expected number of civilizations that receive the signal is equal to the area the signal spreads over (ignoring the thickness of the galactic disk) multiplied by the area density of such civilizations. (From here on, I’ll work in units in which c = 1, to make life easier).

If we want to receive a signal in return, then t ≤ L/2. That is, if our advanced technological civilization has a finite life, the aliens had better be close enough to signal us back before it ends. From this, we can put a lower bound on the lifetime required for us to be able to talk to the aliens. Using N = g L, we can derive

So we have two criteria:

and

Both criteria must be satisfied in order to be able to talk with the aliens. Figure 16.1 shows what this implies. Note that g decreases to the right.

The graph is separated into two regions. Above the line, contact is possible. There are enough aliens out there to talk to and our civilizations will endure for a long enough time to make contact. Below the line, contact is unlikely, as either there are no other civilizations in the galaxy or they are separated by such a large distance that contact will not be made within the lifetime of the civilization.

For low values of g, the harder criterion to satisfy is the first one; the odds of having any other civilizations in the galaxy at a given time are low no matter what you do. However, as g gets larger, for a value of g around 3×10⁻⁵ per year, it is now harder to satisfy the criterion that the civilization must last long enough for a conversation to happen. It is very likely that g < 10 per year, as the stellar generation rate is less than this, and all the other factors going into g tend to decrease it. The implication is that no matter what, the minimum lifetime for advanced civilizations is about 1,000 years if we want contact to be even a bare possibility. This leads us into the final section of the book: how long can an intelligent species hope to last?

Note

1. Gibson is an interesting example of an author who has gradually removed many of what people think of as science fiction trappings (alien contact and space travel, to name two things) from his novels while still keeping a very science fiction feel to his writing.