# Frank Drake and the Drake equation

I was saddened to find out about the recent death, at the age of 92, of Frank Drake, one of the pioneers of SETI. One of the things he is most famous for is the equation bearing his name which estimates the number of intelligent civilisations in our galaxy, the Drake equation.

As a tribute to him I have reposted the blog post on this topic I wrote  back in 2014.

Revised Original post

The Earth is one of eight planets which orbit the Sun. The Sun is an ordinary star among the 100 billion or so stars in our Milky Way galaxy.  The Milky Way itself is an average-size galaxy. To me one of the most fascinating questions is :

How likely is it that there are other intelligent civilizations within our galaxy ?

The Milky Way- Image credit ESO

Drake’s Equation and the seven numbers

Frank Drake (1930-2022) was an American astronomer who was often known as “The ‘Father of SETI”‘ In 1960, he was the first person to conduct a serious scientific search for radio signals from alien civilisations.

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Frank Drake- Image credit Wikimedia Common

In 1961 he invented an equation to estimate the number of intelligent civilizations within our galaxy that we could communicate with, which he gave the symbol N.  To arrive at N,  Drake multiplied together seven other numbers.

N=  R*  x  FP  x  NE x FL x FI x FC x L

Drake’s seven numbers are follows:

• R* is the number of average number of stars formed per year in our galaxy. This has a value of about 10.
• FP is the fraction of the stars within our galaxy which have a planetary system with one or more planets, expressed on a scale of 0 to 1. A value of 1 means that all stars have planets. 0 means that no stars have planets. Current estimates are around 0.2 to 0.5.
• NE is the average number of bodies, either planets or moons of planets, with the right conditions to support life. Current estimates for this vary widely, but it is sometimes considered to have a value of 0.4, meaning that out of every 10 stars which have planets, 4 have bodies which could support life.
• FL is the fraction of bodies with the right conditions to support life on which life actually evolves, expressed on a scale of 0 to 1.  A value of 1 means that on all  planets with the right conditions life will evolve.There is no consensus among astronomers about the value of FL. If, in the future, life is found in other places in our solar system which have the right conditions  e.g Mars, or in the warm underground oceans of Saturn’s moon Enceladus (see here for more information) then it would be reasonable to assume that, given the right conditions, in general life will evolve and FL is nearly 1.

A geyser of warm water erupting from an underground ocean on Enceladus. Image from NASA

• FI is the fraction of bodies having life, on which life has evolved into intelligent civilisations, expressed on a scale of 0 to 1. Again, there is no consensus among astronomers about what this value should be. Enthusiasts for extra terrestrial intelligence such as Drake believe that the value is close to 1, meaning that intelligent life will always evolve. Others who believe that it was a highly improbable chain of events which led to the eventual evolution of man from single celled creatures believe the value is very low.
• FC is the fraction of bodies with intelligent life which develop a technology that releases signs of their existence into space. For example, on Earth TV and radio signals escape into space and could be picked up by a nearby alien intelligence with a sensitive enough receiver tuned to the right frequency. No one knows what the value of FC is, but current estimates are around 0.2.
• L is the average lifetime of a civilisation in years. This could be very short if civilisations end up destroying themselves once they have discovered nuclear weapons – or it could be hundreds of millions of years.

The Optimists’ View.

As said previously, no one really knows what the values of most of the terms in the Drake equation are. If we go for values at the high end (FP= 0.5, NE=0.4, FL=1, FI=1, FC=0.2, L= 100 million) then we get the following:

N= 10 x 0.5 x 0.4 x 1 x 1 x 0.2 x 100,000,000

which works out as 40 million intelligent communicating civilisations in our galaxy!

One of the problems with such a large number is that we would expect a significant fraction of civilisations to be more advanced than us. Humans have only been civilised for a few thousand years and have already travelled into space.  If a civilisation had been around for more than 1 million years, for example, it is likely that they would have developed the ability to travel the vast distances to other planetary systems and would have already attempted to make contact with us. The fact that they haven’t may mean that civilisations much more advanced than us are rare.

Indeed for over fifty years, since the pioneering work of Drake in 1960, astronomers have been looking for radio signals from nearby civilisations over a wide range of radio frequencies and have failed to find anything.

Could we be alone ?

Other astronomers believe that some of the values in the Drake equation are very low. There are a large number of steps which occurred between the emergence of the first primitive single-celled life forms and the evolution of man. Each of the individual steps may have a very low probability. So FI the probability of life evolving into intelligent civilisations would be extremely small. For most of the Earth’s lifetime there were only single-celled organisms and perhaps on most planets where there is life, it never gets beyond this point.

Another point is that mammals only become became the dominant lifeform after the extinction of the dinosaurs 65 millions years ago. Before that large small-brained reptiles were the dominant life form. Having greater intelligence does not always give an advantage over other traits such as size, speed and physical strength in the survival of the fittest.  There is therefore no guarantee that evolution will result in life forms with the intelligence necessary to develop civilisations.

In addition, dramatic events such as sudden changes in climate can cause any species to become extinct. Roughly 70,000 years ago, an enormous eruption occurred in what is now Sumatra, leaving behind Lake Toba. This triggered a major environmental change which caused the near extinction of the human race. At one stage there were only 2000 individual humans alive on the planet.

Lake Toba, site of a supervolcano eruption 70,000 years ago – Image credit Wikimedia Commons

For these reasons, some scientists, such as the late British theoretical physicist and popular science writer John Barrow (1952-2020) , believe that FI could be around 0.000000001 or even lower. If it were this low, and we take the low end values for for the other parameters, then the expected number of intelligent communicating civilizations in the galaxy would be 0.000016. What this means that if we took 60,000 galaxies similar to our own Milky Way we would on average expect to find only one communicating civilisation. Ourselves!

If this is the case then the Earth would not be just be an ordinary planet orbiting an ordinary star in an ordinary galaxy, it would be a very special place indeed. It would be the only place for tens of millions of light years where intelligent life exists!

## 10 thoughts on “Frank Drake and the Drake equation”

1. I wonder if maybe the reason we haven’t heard anything yet is because the aliens, in surveying planets and coming to ours, then watching a few moments, are thinking, “Ok. Let’s go ahead and pass on this one for about, oh maybe 100,000 years or so, shall we?”. Then quietly leaving whilst erasing any traces they might have left just to make sure we don’t try to contact them 😉

I think the late Carl Sagan alluded to this in an interview on the Johnny Carson show (it’s about 10:55 seconds in).

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2. It is a fascinating rational approach to a fundamental question of existence, I found myself thinking, what if the equation were applied not just to our ‘home’ galaxy but included estimates from the other galaxies that we are currently aware of? Would it just mean broadly similar results on a vastly multiplied scale? Or would it throw up some real surprises; e.g if advanced imaging of the cosmos revealed that actually the number of planets with Enceladus-like features is actually far, far more than has been estimated, and what about the factor of time, or ‘deep’ time – millions of aeons- past, present and future, and the possibility of ‘civilisations’ having been and gone; as ours surely will, whilst others are still in the ‘primordial’ state as we once were with hazard leading to our current ‘civilised’ state…I am getting carried away, as these questions always do- RIP Frank Drake; – you made us think.

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1. Thank you Graham. You make some interesting and very deep points.

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3. Hi Steve, Thanks for that – I missed your original 2014 posting.

Sorry to hear abour Frank Drake. People tended to be scornful of his equation for the reason alluded to by Ggreybeard – that you can get almost any result you want from it according to your mood on that day. But it has certainly prompted some useful thinking & analysis.

Still, we’re in a postion now of firming up the first two -and nearly three- terms: Fp (no. of planetary systems) is much nearer to 1 than it was in 2014. No comment on Ne (habitable planets) except that it’s creeping up year by year.

It’s sad that he didn’t survive slightly longer; he’d have been gratified to see a reasonable amount of data from JWST – and maybe a year or two of SKA results.

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1. Thank you David,

Some interesting observations

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4. Sad to lose Frank Drake. He did a lot for SETI.

I had the pleasure of attending a public lecture he gave here in Sydney about thirty years ago, which left me with a strong impression of the man.

I always found it astonishing that such an important cosmological question as the number of advanced alien life forms could be estimated using an easy equation which is probably less complex than most other equations in astrophysics!

Yet it is so easy to plug in optimistic figures and get an optimistic result, which has not been confirmed, despite five decades of sophisticated research.

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1. Yes it is sad he is no longer with us. The drake equation doesn’t of course give a firm number, but it us certainly a useful tool to consider all the factors involved

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5. I remember when I was kid and decided to do a presentation on the Drake Equation. It was so much fun to look into, and it’s so sad to hear of his passing.

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1. Very true. But his equation will live on

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