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Deconstruction of the Drake Equation

Posted by Karl Withakay on August 18, 2010

I’ve been scooped by PZ Meyers, but I’m still writing this post anyway.  It fits in well with my recent posts on space;

Cordial Deconstruction of Stephen Hawking? (Am I So Bold?)

Follow-Up: Energy Requirements of Interstellar Travel

Final Follow-Up on the Probability of an Alien Invasion

Where Does Stephen Hawking Think We Can Go?

On Monday  I read this article: Proof of Aliens Could Come Within 25 Years, Scientist Says on  The scientist, Seth Shostak, cites the Drake equation when attempting to support his prediction.

The Drake equation, in case you’re not aware, is an equation that is supposed to be used to estimate the number of intelligent civilizations in the Milky Way, and it’s utter garbage.

Form Wikipedia, the equation is:

N = R^{\ast} \times f_p \times n_e \times f_{\ell} \times f_i \times f_c \times L \!


N = the number of civilizations in our galaxy with which communication might be possible;


R* = the average rate of star formation per year in our galaxy

fp = the fraction of those stars that have planets

ne = the average number of planets that can potentially support life per star that has planets

f = the fraction of the above that actually go on to develop life at some point

fi = the fraction of the above that actually go on to develop intelligent life

fc = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space

L = the length of time such civilizations release detectable signals into space.

For the sake of argument, let’s assume the equation itself is basically sound, tough that’s debatable.  In that case, the accuracy of the number we can get from this equation depends on how accurate the values we plug into the individual terms are, so let’s look at  the terms and see how well we can estimate those numbers.

The first term, R*, we have an OK, better than order of magnitude estimate for, so we’re off to not too bad a start, understanding that we’re not looking for a terribly precise value here.

For the second term, fp, we really don’t have a good number for right now.  PZ says we have “growing evidence of values” for this number, and that’s not an inaccurate statement, as long as you understand that the evidence is not quite ripe for picking yet.  While we have been making a lot of progress in detecting extra solar planets,  we’re still only good at detecting larger giant type planets like Jupiter orbiting stars similar to the sun (the Kepler mission may change that).  Because the best way we have to detect planets right now is to detect the wobble the planets induce in their parent star while they orbit, it’s easier to detect planets with a large mass relative to its parent star.  Because of this, we haven’t yet been able to detected any planets of less than several Earth masses, which means what we currently have for this number is really a lower limit for this value, but we really don’t have a good estimate for an upper limit because we don’t know how many stars have only relatively low mass planets and no planets large enough to induce a noticeable wobble.  We’re only on the second term, and we already have a little problem, but as long as we use the lower estimate for this values, we should be OK.

For the third term, ne, we really have nothing but projections using our solar system as a model.  We don’t know how many rocky planets or moons are out there, we don’t know how many of them lie in the habitable zone of their parent stars, we don’t know how many of them have the right elemental composition, we don’t know how many have relatively circular orbits (to avoid extreme temperature variances), etc, etc.  Even if we get better at detecting terrestrial planets, there are so many factors that contribute to the suitability of a planet for supporting life, many of which will be very difficult to detect, that it will be problematic to ever come up with a good value for this number.

As little as we have to go on for the third value, we have basically jack nothing to go on for the all the remaining terms.  We have absolutely no clue about any of those numbers and any attempt to make an estimate for any of them is just wishful thinking or anthropically derived values by people wanting to find an answer.

What fraction of the unknown number of habitable worlds actually develop life?  How does one even make up a number for this and keep a straight face?  Without knowing how life arose here on Earth, how can we begin to  say how probable it is anywhere else?

What fraction of the planets from the previous term develop intelligent life?  Again, who knows?  Our sample of 1 doesn’t give us much to go on.  If the dinosaurs hadn’t died out, would we have intelligent dinosaurs now?  Who knows?  We assume we are the natural, logical conclusion of the evolutionary process because we’re here, but we could be an aberration, an exception to the norm.

What fraction of civilizations develop technology that releases detectable signals?  It might seem reasonable to suggest that if they survive, that this is an inevitable outcome, but we shouldn’t be overly anthropic and assume we are the norm.  We really don’t know.  We do know that when Europeans ventured forth and explored the word, they ran into a lot of pre-industrial and stone age civilizations several millennia behind them technologically.  We can’t even say if the native Americans would have ever developed technology in America under very similar conditions to what the Europeans had let alone say what would be likely on a planets of different conditions and abundances of resources.

How long do such technological civilizations release detectable signals into space?  We haven’t stopped yet, so we don’t even have an anthropic reference number to go on here.

Frankly the best evidence we have for estimating a number for N is the lack of evidence so far.  This is basically the Fermi Paradox.  The Fermi paradox is the apparent contradiction between high estimates of the probability of the existence of extraterrestrial civilizations and the lack of evidence for, or contact with, such civilizations.  I would say that this is not so much a paradox as an indicator that the estimates for N are probably unreasonably exaggerated.  N must be low enough that we’re not currently detecting signals from alien civilizations.  If they’re out there, we can at least say they’re probably not close by or we’d have detected them by now, which means alien civilizations probably aren’t as widely dispersed as the optimists project.

Honestly I’m amazed that anyone tries to invoke the Drake equation, given that we can only reasonably speculate the value for N is between 0 (if you don’t count us) and millions or even billions.  I automatically loose a little respect for any scientist who seriously invokes the Drake equation; the equation is junk science and probably always will be.


One Response to “Deconstruction of the Drake Equation”

  1. […] (the fraction of the habitable worlds that actually go on to develop life at some point) from the Drake Equation is 100%, which is extraordinarily unlikely to be […]

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