## Sunday, 17 July 2016

### Where is Everybody? The Fermi Paradox and the Drake Equation.

Today, I want to have a bit of fun, but with a serious side. Among the silliness one regularly comes across is the seemingly perennial claims of being visited by aliens. Novelist Whitley Strieber, author of the brilliant The Wolfen (the only novel I ever found genuinely disturbing, notwithstanding the truly atrocious film adaptation starring Albert Finney), wrote a 'non-fiction' book entitled Communion, detailing his own alleged experience. There are those who give credence to such ideas, and can't seem to grok why sceptics might not take these tales at face value. Of course, the immediate answer is that they're sceptics, and that should end the discussion. Since the book that these meanderings are aiming toward is primarily going to be about how we got about assessing truth-claims, it will be instructive to treat this topic, a source of much amusement among sceptics and among those scientists working in the relevant fields of cosmology, astronomy and astrophysics.

I know that many professionals in those fields are often confronted with the sincere question 'do you believe in UFOs?' I've had it levelled at me by people who discover I have an interest in physics and cosmology.

So, as properly trained sceptics, how would we go about assessing this question, and the underlying claims concerning alien visitation? I've said in a previous post that philosophy is the art of ensuring that we're asking the right kinds of question, so clearly the best place to start is by analysing the question itself.

There are several issues with the question as framed. The obvious one is that the questioner rarely questions what the initials stand for, particularly the first letter, U. It stands, of course, for 'unidentified', and this should be a big clue. Do I believe that there are some things that fly that have yet to be identified? Given that entomologists, coleopterists and lepidopterists are identifying new species of flying insects all the time, it seems a bit of a silly question on that basis alone. Of course, the believer doesn't really mean unidentified, not least because they think they've already identified what they are: Flying saucers, which means that they're committing the fallacy known as petitio principii (begging the question).

There's also the issue of the source of these claims. Of course, it's important not to slip into the genetic fallacy but, as properly trained sceptics, we have to consider the source as at least being a factor in arriving at any conclusions, however tentative those conclusions might be. The real question concerning source is the question of why the sources claiming these sightings never come from a particular demographic. There are many recorded instances of, for example, Venus being mistaken for a flying saucer, lots of aeroplanes - especially military (it's informative to note how many of these sightings are in the dry states in the US, coincidentally also the area containing a fair few top secret military bases such as Roswell, in New Mexico), atmospheric phenomena such as sundogs, ball lightning, and other well-understood (by some) optical effects. The one group of people that seems not to have a preponderance of UFO sightings, is the one group that spends most of its time staring at the sky; astronomers, which is telling in and of itself. Why? Because they know what they're looking at, and don't make such mistakes.

It's also worth bearing in mind that these reports, pretty much unheard of prior to Yuri Gargarin's famous flight, have gone through cycles of waxing and waning as activity in space has waxed and waned. Also, our immediate vicinity has been strewn with satellites for several decades now (you wouldn't believe how many man-made objects there are orbiting the planet these days), including sophisticated instruments trained out in the universe looking in all areas of the electromagnetic spectrum, yet the nearest we've gotten to anything in science that really looked like aliens was by a ground-based telescope in 1967, the famous LGM-1 observation by Jocelyn Bell-Burnell, which turned out to be a kind of star we hadn't seen before, a pulsar, PSR B1919+21.

There's a famous story in the history of physics on this subject. Nuclear physicists Edward Teller, Emil Konopinski, Herbert York and Nobel Laureate Enrico Fermi, while working at Los Alamos National Laboratory, previously home to the Manhattan Project and scene of a large number of Richard Feynman's practical jokes and safe-cracking escapades, were walking to lunch one day in 1950. They were discussing the following cartoon that had appeared in the New Yorker, which suggested that a recent spate of disappearances of dustbins in New York was the work of aliens.

The conversation turned to other topics, and they sat down to lunch until suddenly, so the story goes, Fermi leapt out of his seat and exclaimed 'Where is everybody?'

Teller notes that, although this came seemingly out of nowhere, everybody at the table knew what he was referring to. The reactions of other people in the canteen were not recorded.

Fermi wasn't the only one to have asked the question, of course. It was famously iterated by Russian rocket scientist Konstantin Tsiolkovsky, famous for deriving the equation dealing with variable thrust under expenditure of fuel.

Anyhoo, Fermi did some back-of-the-envelope calculations (like beermat calculations, but not as much fun), and concluded that we should have been visited by aliens many times, so 'where is everybody?' This is now known, somewhat inaccurately, as the Fermi Paradox. This question knocked about for a while, and eventually, in 1961, some of these variables, along with some others, found their way into the work of Frank Drake and the famous 'Drake Equation'.

So what is the Drake Equation? Well, it's actually more like a thought experiment designed to show what information we would need to robustly calculate the number of communicating civilisations in our galaxy. The equation is made up almost entirely of unknown variables. It's formulated as follows:

$N=R^*\times f_p\times n_e\times f_ℓ\times f_i\times f_c\times L$

Where:
N = the number of civilizations in our galaxy that may be communicating
R* = the average rate of star formation per year in our galaxy

fp = the percentage of those stars that have planets

ne= the average number of planets that can potentially support life per star that has planets
f= the percentage of the above where life independently evolves
fi= the percentage of those where life develops intelligence
fc= the percentage of civilizations that develop a technology that can be detected
L = the length of time such civilizations release detectable signals into space

As we can see, all the variables in this equation are unknown, with only the exception of R*, for which we can generate a reasonably robust figure, although not that robust, in reality. We can also, in light of recent observations, begin to put a figure to
fp. It may be that, as time moves on, we can put figures on some of these variables. At the moment, however, they remain 'guesstimates'. So, here's how it works in practice.
If we take our starting figure for the number of stars in our galaxy as 300 billion (it's actually estimated at somewhere between 200 and 400 billion, so this figure will serve well enough for our purposes here) Then:

$N^* \approx 300\space bn$
$f_p \approx 20\%$

After this, things get really woolly, and we can only really guess. No matter, we'll take those two as our starting figure and put in some estimates for the other values. So let's assume that:

$n_e = 1$ (based on the only example we know of)
$f_ℓ = 50\%$ (wild stab)
$f_i = 20\%$ (wild stab)
$f_c = 20 %$ (wild stab)
$L = 10,000\space years$ (wild stab: We hope it will be at least this, but we only have one example to go on, and an asteroid - among other things - could seriously curtail that figure).

The output here would be 1,200. That means that, based on this equation with those figures as input, there should be about 1,200 communicating civilisations in our galaxy right now. That looks like a pretty big figure, but that's peanuts to space (RIP DA). Our galaxy is 100,000 light years across. Via πr2, that gives us an area for the galaxy of 7,850,000,000 square light-years. Dividing this by the number of communicating civilisations in the galaxy (assuming a uniform distribution), we get an average distance between communicating civilisations of approximately 7,000 light-years.

Now, given that we have been transmitting radio for about 80 years, give or take - and listening for signals from space for considerably less - and that radio signals propagate at c, this means that, on average, our signals will have made it approximately 1% of the distance to the nearest civilisation. So, for example, if the star 72 Herculis A weren't well within our average distance between communicating civilisations, any aliens watching our signals would just about be able to receive footage of Neil Armstrong's moon walk. On Delta Trianguli A, they're amusing themselves with the Cosby show, and will not be aware of Cosby's disgrace for some years yet. On HR5566, they will be watching Leni Riefenstahl's Triumph of the Will, while some of their neighbours a bit closer will be watching the horrific war that followed the rallies commemorated therein.

Similarly, if we were actually to have received a signal from a communicating civilisation, that signal would have to have left its source in precisely the right 80 year window 7,000 years ago to arrive during the window of time in which we've been able to detect such signals. If any civilisation on the edges of the past light-cone* went extinct prior to the 80 year window corresponding to their distance in space from us, even were they capable of communicating, their signals would have passed us before we were capable of detecting them, and we'd never know they'd been there.

A final consideration in terms of propagation of radio waves has to do with the fact that we live in a cosmos with three spatial dimensions.

Radio waves are made of photons, and photons travel in straight lines, radiating out from a centre. In a one-dimensional universe, you would receive the same number of photons from a source, regardless of how much you were separated from that course, because there is only line they can travel. In a two-dimensional universe, the light falls off in direct proportion to separation, because the lines they travel are uniformly spread on a circle, and the circumference of the circle is proportional to its radius. In a three-dimensional universe, the fall-off follows an inverse-square law because again, the lines travelled are uniformly spread over the surface of a sphere whose area is proportional to the radius. In a universe with four spatial dimensions, the fall-off would be inversely proportional to the cube of the distance, for exactly the same reasons. What this means, in terms of our current discussion, is that the number of photons received by any given civilisation follows exactly the same inverse-square law as gravity. For any given distance, a civilisation twice as far away will receive a quarter of the photons, which means that, should a civilisation be able to receive them (or the reverse) the further away they are, the weaker the signal intensity will be. This is also why, for instance, distant stars are fainter than nearer ones.

It should also be noted that if any of those variables in the Drake equation tend toward zero, which is a very real possibility, then that output goes down dramatically, meaning that the average distance between communicating civilisations goes up just as dramatically. Indeed, it is far from being beyond the realm of possibility that we are the first communicating civilisation in the galaxy. If we were to rigorously deal with some of those variables above, we'd quite probably find that our estimates are too generous. Intelligence isn't the only requirement for a communicating civilisation, after all. Opposable thumbs (or some equivalent trait), curiosity, motivation, etc, are all factors in what fc ultimately looks like.

Finally, I should point out that the area calculation is treating the galaxy as a flat disc for simplicity. Given that the galaxy is not a flat disc, suggesting that we have to in fact employ a volume calculation, we have to be aware that the average distance between communicating civilisations again ramps up considerably.

I hope that the above clarifies what the Drake equation's limitations are, and why the Fermi paradox isn't a paradox.

* See previous post, The Idiot's Guide to Relativity for more on this.