Tuesday, 14 June 2022

Revisiting the Drake Equation

Dr Drake in Repose

In this blog, I have previously addressed 'The Extra Terrestrial' question from a variety of perspectives. I have considered the Fermi Paradox and the elegantly simple Drake Equation as well as the problem of travelling vast interstellar distances and the plausibility of extra-stellar space travel. 

According to the Drake equation, it has been estimated that there should exist, in the order of 50,000,000 advanced technological civilisations in our own galaxy alone. This is before we extrapolate to the number of galaxies in the known universe (2 trillion?). And again his can be expanded as the universe, as a whole, is considered to be immensely and mind-bogglingly huge. Of course, if the universe is infinite, then we will have to think anew. Personally, I'm in favour of a finite Cosmos, for reasons I will expand upon in a future post. Before continuing I'll just review Drake's original insight.

The equation first formulated in 1961 can be represented as:

The above parameters are those considered most important when calculating the number of extant intelligent civilisations floating about within our Milky Way galaxy.

Some may find this equation wonderfully simple, and of course, it is. Although I'm a great fan of keeping explanations as simple as possible, sometimes simplicity can belie and mislead the beholder. I suspect this is one of those occasions.

Many folk support Drake's findings, although to be fair, these days, most cosmologists are more circumspect in their opinion. It needs to be recognised that certain, critical, assumptions necessary to populate five out of seven equation terms are highly speculative; only the initial two terms have a foundation in science. For instance, consider the term, ne, which refers to the fraction of planets that are able to support and develop life, at some stage in their existence. This number is no more than a guess. At this juncture, it is noteworthy to state that in 1961 we didn't even have reliable quantities for the first two terms (R* & fp), although nowadays we are better placed to make scientifically valid estimates. 

Scientific principles are, at their best, based on the existence of solid and repeatable data sets. The whole 'concept of scientific endeavour' is based on the empirical method. Without data collection, science, at least as we know it, would not be possible. Having stated this fundamental principle we need to ask how data is able to assist with the variable, fg. And of course, here is the rub, the grand total of our data gathering comes down to the grand total of 1. As far as we know, we are the only planet that supports life. I'm not saying that life does not exist elsewhere in our galaxy, I'm saying we have no firm evidence for the existence of life apart from our own. To base our equation on such a miserable paucity of hard data removes us from the realm of speculation into the land of 'wand-waving and wizardry'. In other words, any number that we plug into the equation for fg is without any foundation. On the basis of this single term alone, the equation becomes meaningless. We expect better from our mathematics. After all, mathematics is ultimately a logical construct and needs to be unfettered by unproductive speculation. This only refers to the possibility of life elsewhere, not the actual formulation of intelligent life (fi). If we have no idea or regard for the possibility of extra-terrestrial life then our ability to populate fi is not even a bag of lemons (that is, fruitless). It gets worse: As said, of the seven variables comprising the Drake equation we only have reasonable estimates for the first two. The remaining five are unknown quantities. Here we have the illusion of precision. Mathematical equations tend to offer the prospect of logical impermeability and immutability, and so they should, with one very crucial caveat: The equation may be sound and logical, in principle, but the quantities entered should also be reliable and sound. As the old adage states- 'Bollocks in, Bollocks out'.

To be fair to Dr Drake he, initially at least, didn't expect his equation to be taken as seriously as it has subsequently become. As I understand it, Drake didn't devout much thought to the situation. It seems he scribbled his thoughts on the back of an 'envelope' prior to a scientific cosmology meeting. The equation was a simple tool to stimulate discussion on the topic of extraterrestrial organisms amongst his peers. I'm not suggesting that Drake was insinuating that his colleagues were xenomorphs. Regardless of Mr David Icke's contention that we are surrounded by extraterrestrial lizards, there is no evidence to support his conjecture, royalty excluded. Moving on. The fact that others have read into the equation more than was originally intended is no fault of the esteemed Dr Drake. 

I think I will leave the subject at this junction however, I will be interested in what others have to say. Please append opinions in the comment field. I thank thee. 


  1. I am not keen on these 'simple' equations... They are not proper equations, just peoples' thoughts presented in the form of an equation, but without the rigour of mathematics. You can find this sort of pseudo-equation in economics, history, and (my favourite trash in sparkly clothes) self-help.

    A key test (after the 'proof' of the terms) is whether or not you can add new terms without restriction. So you could spilt f(c) into civilizations that produce technological evidence (f(c1)) and those civilizations who hide under a stone (f(c2)), or whose technological prowess does not broadcast itself (f(c3)). I have added nothing to the 'equation' by doing this.

    Our galaxy is a *big* place (nearly 53,000 light years across). I suspect other life is probable, and other intelligent life is likely, but there is a very narrow time window for us to detect it through, and that assumes the window is open and looking in the correct direction.

    1. Drake's equation is too simple. I'm sure we could think of lots of useful parameters.

  2. Humans have been detectable from space for only a few hundred years - many potential civilizations may have come and gone in the nearly 13E9 years since stars formed. We're just a twinkle in universe-time, easily missed should any intelligence be looking.

    1. Might be a good idea. They could be just like us. Steven Hawkings thought communication was a bad idea.

  3. Yes, an elegant solution no doubt, but my major problem with that equation is that it does not take into account the necessity of several extinction level events over the epochs to give evolution a bump start and increased impetus on any given world orbiting in the 'Goldilocks' zone of a given star. Humanity evolved what passes for its intelligence because of these pressures that the equation never seems to factor in.

    However, I've long had the notion that other intelligent species might, given our propensity for wars etc, do the equivalent of winding up the windows and not stopping as they pass through our solar system.

    1. Yes, the equation as proposed is way too simple. But as mentioned in the post, it was originally a means to initiate discussion. You may be right with 'keep away' theory. I think it is called 'Dark Forrest'.

  4. Yes, the only things we actually know are that there are a lot (a LOT!!) of stars and planets.

    We know an awful lot about life and how it works, but there is no model of abiogenesis that can be tested, or even hypothesised around. Without that it may as well be a discussion of how many angels can fit on the head of a pin. You can decide on whatever conclusion you want and – from the sample of 1 – construct a very plausible sounding case.

    As cool worlds correctly puts it, the only honest answer is, we simply don’t know: https://www.youtube.com/watch?v=PqEmYU8Y_rI

    The two things I do truly struggle with are the concepts of deep space and deep time: the sheer inconceivable vastness of space around us and time both back into the past and that has yet to be.

    A civilization could have arisen and spread across ten thousand galaxies over billions of years and then, for some reason died – and we might never have any clue that it had ever existed.

    1. But there are hypotheses about abiogenesis, some of which have been evaluated then discarded. A Google search will pull them up. e.g.


      A simple primer, with rather more scientific rigour elsewhere in various papers.

    2. I'm currently writing a post about abiogenesis- a fascinating topic, indeed.

    3. Not really, and in the context of the Drake equation (or the discussions instigated by it), for factors 3 and 4 its still very much how many angels can fit on the head of a pin, and will be until we actually start finding other examples. The cool worlds link does mention the Miller-Urey experiments, and the limitations of what we can draw from them.

      Even the simplest life (when does a collection of molecules actually become alive?) we could find (or find the signature of) is massively complex compared to the raw chemicals of which its made. How many examples of life would we need to find to begin to construct any sort of meaningful theory as to how it might originate?

      I wish I could come back in a hundred or a thousand years and find out.

    4. Interesting......you must read this https://flaxensaxon.blogspot.com/search?q=angels+on+the+head+of+a+pin

    5. Yes, I do recall this, and thanks for the reminder!

      No two angels can occupy the same space, so 2.448x105 become a band of angels. A conduction band or a valence band? Moving between by surfing on the luminiferous aether presumably? Maybe that’s what the more supernaturally minded mean when they talk of the cosmic computer.

      As you say, the question was subtle and interpretable in many ways (although in 1332 I would imagine many interpretations remained the private thoughts of those that made them).

      I’ve always been fascinated by this sort of metaphysical/philosophical type question and I certainly don’t share the disdain for philosophy that seems to be part of the depressing dumbing down that is corroding just about anything that requires that requires a brain more than a kelvin above absolute zero.

      The Drake (let’s call it) question is very much in this ballpark and it may remain there forevermore. There are so many scenarios where we may just never know. Maybe we are the first, or perhaps there are civilization and life bearing worlds but they are so far apart that we may never be able to physically reach them or develop the means to analyse data at what might be hundreds or thousands of light years (although who knows what means may be possible in a few hundred years).

      Neils Bohr, some would argue the greatest physicist of the 20th century, would let his imagination run wild Monday, Wednesday and Friday. He would then apply the most austere examination of these imaginings on Tuesday, Thursday and Saturday. Doing so enabled him to be creative and rigorous, both to an extraordinary degree.

      We can perhaps look at the Drake question in the same way.

      The imagination can run wild theorising about alien life and its possibilities (which is one of the things I have always liked about sci fi) but we must always acknowledge that – for now certainly – none of this can really have any rigorous scientific basis.

      Our Tuesday, Thursday, Saturday could be a rigorous exploration of that bit of the cosmos we can analyse and where we know that there is life. Mars and Venus may well have had distinctly earth like conditions several billion years ago and perhaps have fossilised life. And then there are the postulated oceans of Europa. To find and be able to definitively identify a three billion year old fossil stromatolite in a dried up former sea on mars for example would be perhaps the most profound scientific discovery to date.

    6. The dumbing down of the population is a worry. Look at Youtube where ordinary young folk are asked simple general knowledge questions....

    7. A worry indeed, but it's also evil, and I don't think that's too strong a word!

      So much of the education system in much of the western world (all of it?) has been systematical removed over decades - a process that is still ongoing - and replaced with debased and degraded ideology. I have seen many of those videos and these young folk have been abused, there is no other word for it.