Does the Drake Equation Make Sense?

The Drake Equation was developed in the infancy of the SETI project. The Search for Extra-Terrestrial Intelligence was a US-sponsored project starting over sixty years ago, designed to listen for any kind of electromagnetic broadcasts than another intelligent civilization might be emitting. The equation is simplicity itself, just a product of conditional probabilities. Here it is:

N = R_*^.f_p ^.N_e ^.f_l ^.f_i ^.f_c ^.L

and N is the number of detectable alien civilizations in the galaxy,

R_* is the rate at which stars form in the galaxy,

f_p is the fraction of stars which develop planets,

N_e is the number of planets within a planetary systems which have the right conditions for life,

f_l is the fraction of planets with the right conditions for life which develop life,

f_i is the fraction of planets which develop life up to the level of intelligence,

f_c is the fraction of planets with intelligent life that build systems to radiate electromagnetic waves,

L is the length of time such civilizations persist in their radiation.

There are a number of assumptions made which permit the formula for N to be expressed this way. Let us discuss a few of them.

First, the Milky Way galaxy is chosen as the basis for measuring everything. We only know that life can originate on a spiral arm, far away from the bulge and the black holes which inhabit the center. It seems quite reasonable that life needs billions of years to evolve to the stage where a civilization emerges and starts emitting radiation, and in the bulge, distant stellar encounters happen much more frequently than in the spiral arms. A stellar encounter can create a gravitational pull on a planetary system to disturb it, and a planet which had conditions for life prior to the encounter may be moved either inward or outward relative to its star, where the conditions do not hold. Two solutions might be done for this, either change R_* to only count spiral arm stars or modify all the subsequent probabilities to take into account the different conditions between the spiral arms and the central bulge.

Second, the term detectable can be defined a number of ways. Since radiation dies off as the square of the distance travelled, without absorption, and worse with absorption, does detectable mean detectable with some particular equipment? Imagining a ten kilometer aperture radio dish out beyond Neptune's orbit, and compare that with the original SETI equipment. If one wants to be able to detect a civilization's emissions from the other side of the Milky Way, assuming the central bulge does not intervene, something huge would be required on both ends.

Third, the equation seems to be assuming roughly isotropic radiation, spreading equally in every direction, including the one direction that heads toward Earth. Why would any civilization do that? There might be some transitory period when they were broadcasting for their own planetary uses, but if they wanted to communicate from solar system to solar system, they would develop a narrow beam system that would require only a tiny fraction of the power of an isotropic radiator. But then detectable means that Earth is in the beam of such a system. That would be rather fortuitous.

Fourth, the fraction of stars which develop planets might be, as we now know, approximately one, but developing planets does not mean life can evolve on one of them, or certainly not to the threshold of EM emissions. Stars heavier than our star burn out quickly, and if one included them in the count, they could have planets and one could have the right conditions for life, but these conditions would soon change as the star evolved and died. On the other end of the scale, M dwarfs, the most populous kind of star, doesn't have enough energy output to have a planet with the conditions for life, except if it is close in, and there it would be likely phase-locked, with the same face always directed at the star. There are good objections to assuming life could evolve in such a system.

For the mid-range of stars, where our sun resides, there might be planets, and one or two with the conditions for life, but we know little about the migration of planets, even without the evolution of the parent star. Do smaller planets keep their orbits for billions of years in any planetary system, or does it take billions of years for them to gradually migrate inward or outward? If we change the definition to having a planet of the right size in the liquid water zone for billions of years, the number might drop from about 1.0 to 0.00001. Figuring out long-term stability of orbits should be a fairly simple task for the current state of mathematical astrophysics, but it does not seem to have been done in a comprehensive way that enables on to figure out this term in Drake's equation.

Fifth, exactly what does the “conditions for life” entail? If it is made very loose, the corresponding probability would be high, and the subsequent probability would be less to make up for the looseness. If it is made tight, the inverse happens. At the time the Drake equation was written, mankind did not know how life forms, nor what were the conditions needed for it. Now, sixty years later, the same situation exists. We don't know. It is appalling that so little work is done on the origination for life. One particular question is that, are there some conditions in which life forms over a period of time, something large compared to human lifetimes but small compared to solar lifetimes, like a million years? Or is the situation completely opposite, life only forms if some event happens, and the probability of the event might be very, very small.

Just suppose, as hypothesized in this blog, a mild collision with a large planetoid, which becomes a satellite, is necessary for life. The collision would have occurred in the early part of the solar system's existence. Earth-like planets which did not have that collision in their history might be similar in many conditions to ones which did, but, if the hypothesis is correct, only the latter could have life. There are certainly other events in the history of a planet which might affect the origination of life, such as the chemical composition of the crust, volcanic heating, and asteroidal bombardment.

To be generous, life originated three or four billion years ago, and we do not know the conditions of the Earth's surface, so we are limited in imagining how life could originate. The delay in life origination work might be caused by the delay in planet origination work. Neither is in a good state. There is no reason to think that current conditions on the Earth could lead to an origination of life, assuming all consequences of life were removed. One of the conditions discussed in this blog is the existence of organic oceans on the surface, able to nurture membrane formation as well as complex protein formation. Where might they come from? The mild collision hypothesis is a possibility for this.