Drake equation and calculating the odds of intelligent life in the universe

So far all we have asked is does life exist beyond earth? There are many scientist and astrobiologist working on this. Our first step is to find microbial life on mars or the ocean under the frozen surface of Jupiter’s moon Europa, or on Saturn’s moon Titan which has liquid hydrocarbon lakes. Even though all telescope are indirectly looking for evidence of life, there is one institution which is actively looking for alien intelligent like. This institution is SETI (Search for Extraterrestrial Intelligence). Researchers at SETI are trying hard to detect some evidence that intelligent life elsewhere have used transmitter of some sort. Considering the vastness of the universe, there are no guarantees that we will detect such signal. There are many odds involved but thanks to Frank Drake we can have some ideas about the odds of finding such signals.

Drake equation contrary to many other equation we have seen in Physics have too many unknowns so the answers coming out of it has some uncertainties. The variables in Drake equation are based on our best guess or estimation. So, as we increase our knowledge of the universe, the result coming out from Drake’s equation becomes more certain and dependable. The most definite answer to Drake equation can only be achieved only if institution like SETI succeeds in finding other intelligent species in vastness of the universe. The Drake equation tries to find the number of technological civilizations in the Milky way galaxy by using the equation

N = R^* \times f_p \times n_e \times f_l \times f_i \times f_c \times L
All these factors multiplied together helps us to find the intelligent civilizations that we might detect right now.

R^* is the rate of formation of stars in the Milky way galaxy over the last few billion years and hence it is the number of stars per year. Since Milky Way is about 10 billion years old, in earlier time stars’ rate of formation was different. All the f factors in Drake equation are fractions hence each one is less or equal to 1.
f_p is the fraction of stars having planets.
n_e is the average number of habitable planets in a solar system
f_l is the fraction of planets where life actually starts
f_i is the fraction of the life which develops intelligent life
f_c is the fraction of that intelligent life developing a civilization and uses some sort of transmitting technology
L is what we called as longevity factor or the factor deciding the transmitters’ continuous operation.

The first three factors are easier to predict as we are finding more exoplanets everywhere. The product of first three terms are more certain at this point. The more difficult factor is the fractions dealing with life and intelligence and technological civilizations. At this point the only known planet harboring intelligent life is right here on Earth. As we explore Mars, Europa and Titan, any kind of life detection in these places means that life will be abundant in the Milky Way because if life can start twice in one solar system than in suitable condition life will happen.

The unknown and uncertainties are great at this point but we think that R^* and n_e are both numbers close to 10 and f factors are less than one and some way less than one. Among the unknowns, the biggest one in L. Unless L is large, the chance of N being large is slim. But on the other hand if we detect sign of intelligent life in small portion of sky then we can extrapolate that L is large in the bigger scale.

Since the speed of light is finite, any signal for intelligent life we receive will tell us about the past of that civilization and not what happening now. The biggest source of predicting the value of L is humans itself. In our very short existence in cosmic scale, we have developed technologies to go to the moon and on the other hand we have also developed weapon of mass destruction, chemical weapon, biological weapon etc. Will this development help us or hinder us in long lifetime will give an idea to fate of other civilization as well.

At this point Drake equation have a lot of unknown and there is no right answer to this equation so far.

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