Drakes Equation

The Space Science Board of the prestigious National Academy of Sciences responded positively to recent advances in the study of extraterrestrial life. It authorized a small conference on the subject at the National Radio Astronomy Observatory located at Green Bank, West Virginia. Notable scientists attended this meeting in November 1961. Attendees included Melvin Calvin, Giuseppe Cocconi, Frank Drake, John C. Lilly, Philip Morrison, Bernard Oliver, and Carl Sagan.

John Lilly, a popular researcher of dolphin intelligence, opened the Green Bank conference. He spoke about his research on communication with dolphins. Dolphins have brains slightly larger than humans and a density of brain nerve cells similar to a human brain. These facts convinced Lilly that dolphins possess intelligence comparable to humans. Lilly believed that dolphins had developed a complex language—he called it dolphinese—and that he would eventually decipher it. He predicted that by the 1980s, humans would establish communication with another species, if not extraterrestrial, then a marine organism on Earth.

Several of the participants drew parallels between dolphins and extraterrestrials. If dolphins are as intelligent as humans, then intelligence has emerged independently more than once on Earth. This was proofthat intelligence was not a rare commodity in the universe. Scientists who learned how to communicate with intelligent dolphins could develop techniques to communicate with intelligent aliens.

Lilly's fellow conferees realized that there were drawbacks to the comparisons he drew between dolphins and intelligent extraterrestrial life. Dolphins spend all of their time in water, they have no hands, and their superior intelligence did not lead them to develop technology. Similarly, extraterrestrials confined to an aquatic planet might be intelligent but incapable of using fire or building a radio transmitter to send messages to Earth.

Frank Drake, who was responsible for the content of the Green Bank meeting, looked for a general principle to focus the discussion. In the process, he produced an equation that included the key factors needed to determine the probable number of intelligent communicative civilizations present in the Galaxy. His pioneering effort is called the Drake or Green Bank equation.

Drake's equation was the first attempt to quantify the probability of communicating with an extraterrestrial civilization. It became the single most important formulation in the search for extraterrestrial intelligence and has remained popular for over forty years. Drake's equation was not entirely original. Several of his contemporaries had made similar calculations.

Drake's use of probability in his equation needs clarification. The determination of the probability of finding extraterrestrial life on an extrasolar planet should not be confused with the relative frequency approach to probability In the latter case, one determines the probability of a flipped coin showing heads or of a given card being picked from a deck of cards.

The approach used in Drake's equation falls under the rubric of personal or subjective probability Here the probability assigned to an outcome depends upon the subjective judgment of the investigator. Two persons with different knowledge, experiences, and feelings might assign different probabilities to the same event.

Drake incorporated subjective probability in a comprehensive equation he wrote for the determination of advanced life on other worlds. His equation was presented in a simple mathematical form. Its interpretation and solution, however, were never simple. They created problems and controversies that remain unresolved today. Drake's equation reads as follows:

N is the number of civilizations in our Galaxy with the technological competence to transmit and receive radio signals. If N is very small, then we are unlikely to detect any incoming signals. If it is large, a search that begins with nearby stars is a worthwhile strategy because of a reasonable probability of finding civilizations close to us.

The value of N is determined by multiplying the terms on the right side of the equation. These terms represent factors influencing the existence of intelligent communicative life in the universe.

R* mean rate of star formation in the Galaxy fp fraction of stars having planets.

ne number of planets per star with environments capable of supporting life. fl fraction of habitable planets that actually support life. fi fraction of life-bearing planets on which intelligent life appears.

fc fraction ofintelligent civilizations that might communicate with the rest of the Galaxy. L lifetime (in years) of technically advanced civilizations.

To summarize: We need to know the mean rate of star formation in our Galaxy when the solar system emerged, the fraction of those stars having planets, the fraction of the above planets that can support life that actually do, the fraction of life-supporting planets that have developed intelligent life, the fraction of planets that have the means and are willing to communicate using radio waves, and the average lifespan of extraterrestrial technological civilizations.

The first three factors are astronomical, the next two biological, and the last two social. When Drake wrote his equation on the blackboard for the Green Bank audience, no astronomer could state with certainty that any star, other than the Sun, had a planetary system.

Although there were physicists, astronomers, and biologists at the Green Bank meeting, no one represented the social sciences. There was no one competent to discuss the nature ofcivilizations, the character and relative proliferation of technological civilizations, and the longevity of technological civilizations.

The strength of Drake's equation is its simplicity and its combination of astronomical, biological, and social factors. At a critical time in the search for extraterrestrial life, the equation neatly summarized the outstanding issues for discussion. Drake's equation does not make a fundamental statement about the nature of the physical world. Graham Farmelo, who listed the Green Bank formulation among the greatest equations of science, said that Drake "put the subject into a truly scientific-looking format."8

Estimation of the first factor in Drake's equation, the mean rate of new star formation in our Galaxy, came from the astronomers who met at Green Bank. They guessed conservatively that one new star would form each year but were willing to consider as many as ten. The solution of the first factor was easier than judging the number of stars in our Galaxy with planetary systems (factor two). At that date, astronomers knew only one such star, our Sun. The Green Bank estimate was that 1/5 to 1/2 of all stars possessed planetary systems. When the discussants weighed the importance of the remaining factors, the estimates became more speculative.

Astronomers next estimated the third factor, the number of planets per star with life-supporting environments. Using our solar system as their guide, they estimated one to five planets. Factor four was the fraction of planets with environments suitable for life that supported life. Sagan and Calvin gave an optimistic response. They claimed that given enough time, life would eventually appear in a suitable environment.

Lilly and Morrison joined forces in assessing the fraction ofintelligent life that would appear on life-bearing planets (factor five). They argued that intelligence favored survival of organisms and that intelligence would inevitably arise along the path of organic evolution. Morrison reminded the group of the importance of convergence in evolution, the tendency for different species to adapt in similar ways to environmental demands. Morrison cited Lilly's recent work on dolphins to prove that two radically different organisms on Earth had converged on intelligence. The conferees concluded that wherever there was life in the universe, it would show signs of intelligence.

By this time the Green Bank group had reached the last two factors, numbers six and seven. The evaluation of these factors needed the help of historians, anthropologists, and sociologists, who were not at the meeting.

The sixth factor was the fraction of intelligent extraterrestrial societies to develop the technology and interest to communicate across deep space. The Green Bank participants scavenged their knowledge of world history seeking an answer to the questions posed here. How could one be certain that every alien civilization would develop communication technology? If an advanced civilization devised the appropriate communication technology, would they necessarily use it? After much inconclusive discussion, the participants decided that from one-tenth to one-fifth of intelligent extraterrestrial societies might attempt to signal other parts of the Galaxy.

Factor seven, the lifetime ofthe technologically advanced communicative societies, was the most important one. Some members ofthe Green Bank assembly, taking their cue from the ongoing Cold War, envisioned technological civilizations destroyed in nuclear holocausts. Others thought that advanced civilizations might exhaust their natural resources, as industrial societies were doing on Earth, and expire. Still others imagined epidemics or internal structural collapse ending an era of spectacular technological growth. The participants decided after much conflicting discussion that the lifetime of advanced technological civilizations ranged between one thousand years and more than one hundred million years. If a technological civilization managed to escape early destruction, then its chances of long-term survival were excellent.

Multiplying Drake's factors yielded an answer for the critical number N. The result was that between one thousand and one billion Galactic civilizations possessed the capability and interest to communicate with the Earth. Most of the attendees felt the higher number was more accurate.

The Green Bank conference accomplished much more than offering tentative answers to the questions posed by Drake's equation. It gave legitimacy to the search for extraterrestrial intelligence. Carl Sagan remembered the Green Bank meeting fondly as a time when a small group of reputable scientists gathered to discuss intelligent life on other worlds.

Historian of astronomy Steven J. Dick assessed the Green Bank results somewhat differently. He declared: "Perhaps never in the history of science has an equation been devised yielding values differing by eight orders of magnitude. . . . each scientist seems to bring his own prejudices and assumptions to the problem."9

A few scientists judged the Drake equation useless. At one point, Joshua Lederberg called it "Hocus-pocus,"10 and SETI researcher Christopher Chyba warned that it "is a shorthand for what we are trying to understand, rather than a tool for precise calculation."11 Others attempted to modify features of the original equation. Nevertheless, at the beginning of the twenty-first century, Drake's formulation continues to exert its influence on thinking about intelligent alien life. In 1998 science writer Amir D. Aczel devoted an entire book to the resolution of the equation. Using modern probability theory, Aczel concluded that life exists on at least one other planet somewhere in the universe.

Shortly after the Green Bank meeting, Frank Drake sent the participants a hypothetical interstellar message. Drake intended to show the form such a message might take and the information it might convey. He invited his Green Bank colleagues to try their hand at deciphering his contrived message from the stars.

Drake's message consisted of 551 ones and zeros arranged consecutively as they might appear on a continuous piece of tape. No single recipient deciphered the entire message, but different individuals solved various portions of it. Drake translated his message into the purported universal language of mathematics. Mathematicians know that 551 factors into two prime numbers, 19 and 29. This suggests arraying the ones and zeros into 29 groups of 19 characters each, or vice versa. Neither of these choices makes any sense until the recipient of the message converts the ones and zeros into squares of two colors, say black and white. When correctly assembled, the result resembles an unsolved crossword puzzle.

Crude, but recognizable, pictures emerge when the recipient arranges the contrasting squares into twenty-nine groups of nineteen squares each. In the bottom center of the array of squares is a primate-looking figure that, according to the coded information, stands about ten feet tall. The figure's two legs are planted on the ground, his head is in the air, and his arms are stretched out along his torso. Along the left margin, Drake displayed a sketch of the alien's solar system with its nine planets. The schematic drawings of the oxygen and carbon molecules at the top right of the array indicate the messenger's life chemistry.

Planet 4, the home planet of the message transmitter, has a population of 7 billion inhabitants, a number provided in binary notation. Since planet 3 has a small population of 3,000, it must be a colony of planet 4. The eleven inhabitants of planet 2 represent a team ofscientists exploring the body. Obviously, Drake added these fictional details to make the message more interesting and challenging.

Like Drake's equation, his interstellar message appeared in books and articles written by scientists and popularizers of science. Melvin Calvin included it at the end of an article he wrote for Science Digest (1963) and promised a solution in a later issue of the magazine. Science journalist Walter Sullivan reprinted it in his very influential book We Are Not Alone: The Search for Intelligent Life on Other Worlds (1964). Sagan and Shklovskii discussed it at length in Intelligent Life in the Universe (1966).

Drake's squat little figure, fashioned from black squares, became as popular as his equation. The reproduction of Drake's message in books written by well-known scientists has given it an aura ofauthenticity approaching that ofan actual communication from the stars.

Drake's interstellar message has attained a longevity and authenticity that its author probably never intended. It gained special appeal from its association with the binary code used in electronic computing. However, the form of Drake's message was not new.

Forty years earlier, two contributors to Scientific American (March 20, 1920) proposed a similar system for communicating with intelligent aliens. In an article entitled "What Shall We Say to Mars?" H. W Nieman and C. W Nieman proposed using Morse code to establish contact with Martians (Fig. 8.2).

The Niemans did not intend to teach Martians the basics of Morse code. They recommended sending dots and dashes, as flashes oflight, with a long pause

Telegraph System Using Dots And Dashes

fig. 8.2. In 1920 the Nieman brothers proposed sending a coded wireless message to Mars. They used dots and dashes to create images. (H. W. and C. Wells Nieman, "What Shall We Say to Mars?" Scientific American, March 20, 1920. Copyright 1920 by Scientific American, Inc. All rights reserved.)

fig. 8.2. In 1920 the Nieman brothers proposed sending a coded wireless message to Mars. They used dots and dashes to create images. (H. W. and C. Wells Nieman, "What Shall We Say to Mars?" Scientific American, March 20, 1920. Copyright 1920 by Scientific American, Inc. All rights reserved.)

to indicate the end of a block of signals. Martians were expected to convert the flashes into black and white squares. Different sequences of dots and dashes yielded different visual messages.

The Nieman technique of communication enabled senders to transmit simple mathematical figures or more complex pictures. The authors illustrated their article with an arrangement of squares depicting a human figure. The figure is shown in frontal and side views. In the frontal view, the figure's left hand is raised, perhaps to show it bends at the elbow.

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