Does the Drake Equation Make Sense? Part 2.

If life originates, and the planet where this happens continues to reside in the liquid water zone, does it evolve to intelligent life? Are there certain conditions which are prerequisites for intelligence to evolve? Would they be common among such planets, or rare?

In this blog, and certainly elsewhere, it is supposed that tool use, starting with fire, then stone and wood, leads to the increasing capacity of the brain of some dominant organism. An equation, similar in form to the Drake equation can be written for this process, involving the evolution of increasingly complex organisms, starting from the first thing to form which constitutes life, a membrane enclosing some proteins that reproduce in some way, and which also produce more membrane. The steps might include the formation of more complex cells, with different features, the ability to exist in different environments and to consume different chemical energy sources. Then the shift to multicellular organisms has to happen, and many steps of evolution might be inserted into the new formula for the progressive development of capabilities of multicellular organisms. Then, back to single celled organisms, a step has to exist to be able to take energy from photons from the star, with the development of some primitive form of chlorophyll. And it goes on and on, as evolution is a horrendously complicated sequence. Regrettably, we do not understand the sequence completely, not even the conditions on the surface of the planet which are required to allow them to happen. The overall probability of producing intelligent species might be 1.0, meaning inevitable, or 0.000001, meaning intelligence is not a particularly useful capability for most creatures on an exo-planet.

The rise to intelligence is perhaps the most difficult of the probabilities in the Drake equation to estimate, as the evidence of most forms of life does not last for billions of years, with only a few exceptions. It should be one of the first orders of those who study it to come up with the new sets of probabilities, so that these can be studied from a normative sense, and then the whole combined into the Drake factor measuring it.

From intelligence to a civilization, mastering technology up to electronics, is another opportunity for sub-probabilities to be estimated. Here it is much easier, as there is history of our development, and it serves as one example, and a base upon which tangents may be followed. This blog includes, in many of the posts, speculation on the steps involved. There seems to be a natural order by which technology progresses, one stage depending on the previous, and there also seems to be a drive, reminiscent of evolution, which pushes creatures to develop successive stages of technology. Figuring out the steps up to the stage of civilization that we currently inhabit is not so difficult, but the postulation of what happens next is extremely controversial. There seems to be a tendency among modern-day humans to forecast dooms that might be imminent, and if one such doom really exists and is universal among intelligent species, reaching broadcast capability might be chancy, and staying there more chancy.

Another of the assumptions inherent in the Drake equation is that broadcasting is the end point of technology, and it would continue for some long period. It hasn't. There is still some, but the term, L, in the Drake formula may be very short as better ways of shipping large quantities of information around the planet have been found and have displaced broadcasting. This seems likely to continue, so L may be, for us, less than a hundred years. With that short a time, being so lucky as to be listening during the particular century out of billions of years of planetary existence is almost impossible to expect.

The Drake equation, if used with the retrospection of all the decades that have passed since it was first written down, may well indicate that the SETI project is hopeless and should never have been attempted. Many people's lives and careers were involved in it, and certainly some, perhaps many, were overwhelmed by the feelings that if they were successful, their fame would be writ large on the pages of scientific history. Some of the participants talked about the success of the project being a grand changer of the direction of human civilization. With such a result, it is not hard to see how the Drake equation was mis-evaluated in many ways so as to provide a justification for the search. Who wants to have their hopes of a glorious legacy be dashed?

The Drake equation, and indeed the SETI project, did have the value of focussing the attention of many individuals, scientist and non-scientists, on the various steps in the formula. It raises the interest level and provides some motivation for doing the hard scientific work necessary for our continued progress. There is little work going on in some very important areas, such as questions of the origination of life, but there might be even less if the burst of energy and excitement that the SETI project ignited had not happened. Understanding evolution is a continuing scientific task, and it might not have been greatly affected by SETI's popularity, but perhaps as the gaps and uncertainties in Drake's formula become more clear, there will be some effect, and some new Darwins will enter the field and erase the dark gaps in the theory.

Mankind has always tried to understand history, and the nature of man and the nature of civilization, but the Drake equation takes all this non-scientific palaver and demands that it be turned into a quantitative measure of how civilization develops. Historians typically do not make much use of the theory of technological determinism, which says that civilization is forced to adapt to technology, which is forced to follow a certain pattern of temporal stages. If history becomes scientific, this might be the result of the Drake and SETI activity with the greatest influence on the future of humanity. Once history becomes more scientific, a better forecast of the potential futures can be given and we would not have to resort to choosing between a dozen different predictions of dooms.

To summarize, the Drake equation inspires work in the following areas: orbital stability for small rocky planets, origin of life from either a unique event or ordinary conditions, the evolution of life through the millions of steps needed to lead to intelligent creatures, and the transformation of history from an art to a science. With the retrospective understanding we now have, the probability of success of the SETI project likely starts with many zeros, and there does not seem to be any redeeming factors in the equation which would raise it even to the order of a few percent or more. Given the amount of effort that was put into it, it was a good start, insofar as it provides motivation for more good science, and also makes non-scientists aware of the possibilities that we are not alone, and with a good amount of further work, we might know just how not alone we are.

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.