The Green Bank Formula Help (page 4)
Introduction to the Green Bank Formula
Suppose that the evolution of intelligent life on our planet Earth is not a miracle. Then extraterrestrial life exists! This part of the problem being solved by faith, let’s play a mind game that involves an attempt to calculate the number of other intelligent civilizations we would find if we could travel freely among the stars, galaxies, and clusters of galaxies throughout the known Universe. This mind game involves cheating on the “probability fallacy.”
We are going to talk about the likelihood , as a proportion, that certain things have happened, are happening, or will happen in our Cosmos. When we say that the chances of some event taking place on a planet are 1 in 100, we really mean that if we could visit a large number of planets, say, 1 million of them, then that event would be discovered on 1/100, or 10,000, of them.
In 1961, a conference was held at the Green Bank radio telescope observatory, the same place where Project Ozma was conducted. The object of the meeting was to make an estimate of the number of technologically advanced civilizations (defined as capable of communicating by electromagnetic means such as radio) that exist in the Milky Way galaxy. We know this number is at least equal to 1 because we are here and we have radio. Is the number greater than 1? If so, how much greater?
At this conference, the astronomers, led by Frank Drake and Carl Sagan, developed a formula to determine the number of technologically advanced civilizations in our galaxy. It has been called the Green Bank formula , the Drake formula , or the Drake-Sagan formula . Several factors are involved in this mathematical equation; some of them are probabilities . The complete formula consists of the product of all these factors. Let’s look at the factors one at a time, and then we’ll evaluate the entire formula by “plugging in” some educated guesses.
Star Formation: R
Let R be the average number of new stars that are born in our galaxy each year. There are about 200 billion (2 × 10 11 ) stars in the Milky Way, and the galaxy is thought to be about 10 billion (10 10 ) years old. This might lead one to suppose that an average of 20 new stars are born every year, that is, that R = 20. Let’s be a little bit conservative because we can’t be certain that stars have always formed at the same rate during the lifetime of the galaxy. For our calculations here, let’s use R = 10. This value has been suggested as reasonable by many scientists.
Planetary Systems: F P
Let f p be the fraction, or proportion, of stars in our galaxy that have planets orbiting around them. Until recently, astronomers had almost no idea of what f p might be. However, observations with the Hubble Space Telescope and other instruments have shown that planetary formation is not a fluke. It happens with other stars besides our own Sun. Some estimates of f p range up to 0.5; that is, half of all new star systems include planets. Let’s be more conservative and estimate that only 1 in 5 stars have planets. Thus f p = 0.2.
Planets Suitable For Life: N E
Suppose that we look at a large number of star systems with planets. Some of these planets will have environments suitable for the evolution of life as we know it; others (probably most) will not. If we are able to look at a large enough sampling of star systems with planets, we will come up with a number n e , the average number of life-supporting planets per planetary system. The fact that a planet can support life does not necessarily mean that life exists but only that the environment is such that life could exist there. We have seen only one planetary system thus far in enough detail to get any idea of the value of n e , and statistically, it is nowhere near enough. We might guess that n e = 1 if our Solar System is an average one. However, the more we get to know our planet Earth, the more we realize what a special place it is. Again, let’s be conservative and suppose that there exists a planet suitable for life on only 1 out of every 2 star systems that have planets. Then n e = 0.5.
Development Of Life: F L
If a planet is ideal for the development of life, there is no guarantee that life arises and evolves. A large asteroid or comet impact would cut evolution short if it were violent enough. An unfavorable change in the behavior of the parent star also would snuff out life. A close call with a passing celestial object, such as a neutron star or a black hole, would disrupt the orderly nature of the planetary orbits of the star system. The big question is this: Was life created, and did it get going on its evolutionary way on Earth because of a series of flukes so rare as to have a “combined probability” of almost zero? Scientists have created complex molecules thought to be the precursors of living matter in a laboratory, but this is not the same thing as synthesizing life and demonstrating that its formation is a common thing.
The best we can do with respect to f 1 , the proportion of planets suitable for life on which life actually develops, is make a wild guess. Let’s call it 0.1, that is, only 1 out of every 10 planets with a good climate can support life.
Evolution Of Intelligence: F i
On Earth, life evolved to near perfection in the form of the dinosaurs. However, none of them had brain power approaching that of primates such as monkeys, let alone human beings. If it were not for a supposed small asteroid or comet splashdown around 65 million years ago, the dinosaurs would still be here, and the Earth would be a vastly different place. Many evolutionary scientists think that Homo sapiens wouldn’t exist. Evolution would never have produced our forebears. Dinosaurs would have eaten them!
Major cosmic collisions, once life has started to evolve on a planet, are not too likely. According to the model of Solar System evolution currently accepted, by the time life was underway on Earth, most of the debris from the primordial solar disk had been swept up into the planets and their moons. But minor collisions are common; we can expect that there will be more of these on Earth yet to come. Interestingly, these minor collisions can serve as a catalyst for evolution, not a fatal blow, as would be the case with a major collision.
What proportion f i of planets where life has gotten started undergo evolution to the point where intelligence arises? The answer to this question dictates the range of values we can realistically assign to f i . Evolution and natural selection seem to be relentless processes; we have seen adaptation of species all the way down from ourselves (if we consider Homo sapiens a species of animal) to bacteria that develop immunity to antibiotics and viruses that evolve new forms, evading extermination. Given the relentlessness of the evolutionary process and the relative likelihood of changes in the environment that spur the emergence of new evolutionary pathways, we might assign f i a value of about 0.1. This is a conservative estimate.
Technological Advancement: F C
Even if a life form develops intelligence, it might not reach the level where it communicates by radio. On Earth, dolphins (porpoises) and whales can be considered intelligent to a degree. However, they lack hands with which to construct machines. Some porpoises have brains large enough to suggest that their intelligence surpasses that of Homo sapiens in some ways, but even if that is true, “dolphin smarts” are qualitatively different from “human smarts.”
Suppose that there exist planets covered by oceans teeming with marine animals having intelligence greater than our own. These animals would not have the physical ability to develop radio transmitters and receivers, cars, boats, and airplanes. They would have no need of these devices (as some people argue humanity has no need of radios, cars, boats, and airplanes). What proportion f c of intelligent species goes on to manufacture the means to communicate among the stars and to conduct their own SETI programs? It is hard to say. Let us suppose that 1 out of 10 planets with intelligent life harbors civilizations capable of communicating by radio; then that proportion f c is equal to 0.1.
Some scientists lump f i and f c together as a product because there is disagreement on exactly what level of brain power constitutes intelligence. Let’s get around this problem by estimating that f i f c = 0.01.
Average Lifespan Of Technological Civilizations: L
Once a civilization has become intelligent and has developed radio, and once it has turned its electromagnetic “ears” and “voice” to the heavens, how long will such beings remain capable of communicating? It is tempting to suppose that curiosity would drive any intelligent species, anywhere in the universe, to seek out life in other star systems, but we do not know this.
There is a dark point here: As part of our technological “progress,” we humans have created weapons of destruction that could annihilate our whole population or at least throw us back to near stone-age conditions. How likely is this? How long can we expect our society to exist as we know it, with radio telescopes and SETI programs? Let’s say that a civilization lasts for L years before evolving out of existence. What is the value of L ? Again, the best we can do is make a guess. During the 1960s and 1970s, at the height of the Cold War, many people became convinced that human civilization on Earth was doomed to bomb itself out of existence, and soon. Today this view is not as widespread, but unless and until Homo sapiens gets rid of its “war gene,” the danger remains.
Suppose that a planetary population, at least some of whom can communicate by radio, maintains this level of sophistication for at least 10,000 years before something—war, famine, disease, or asteroid impact—puts an end to it. Then L = 10,000. However, even in this case, after the disaster has passed, evolution would continue along its way, and in some cases this would lead to another technologically advanced civilization. This would multiply the value of L . Nevertheless, let’s be conservative and set L = 10,000.
The Complete Formula
The Drake formula in its entirety consists of the product of all the preceding factors and generates a number N . This is the number of technologically advanced civilizations that we should expect to find in the Milky Way galaxy:
N = R f p n e f l f i f c L
Let’s calculate N . Here are the values we have suggested for the variables in the Drake formula:
R = 10
f p = 0.2
n e = 0.5
f l = 0.1
f i f c = 0.01
L = 10,000
This yields a final estimate of N = 10. That is, based on the guesses made here as to the values of the variables, we can imagine that there are 9 technologically advanced civilizations in the Milky Way besides our own.
If these worlds are more or less evenly spaced in the spiral arms of the galaxy, it is unlikely that we will ever communicate with them by radio because the latency will be too great (unless, by coincidence, one of the other civilizations is within a few light-years of us). However, we have the capacity to hear signals from one of these societies even if we can never send a reply and expect it to be heard within an individual human lifetime, and even if what we hear represents the distant past (an extreme form of time-shifting communication). Thus SETI continues. The “odds” are slim. The potential rewards are enormous, even if it is nothing more or less than the joy of knowing that we are not alone in the Cosmos.
Practice problems of this concept can be found at: The Search for Extraterrestrial Life Practice Problems
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