ET is out there, according to maths

If you fill out Drake's equation, life beyond Earth is highly probable. Patrick Short and Graihagh Jackson do the math...

Patrick - ...he actually didn’t intend it to really be his legacy or to be the thing that he was remembered for.  It was basically intended to drum up conversation at a conference and the idea was basically to put a rough, back of the envelope calculation on what is the probability that we find life somewhere in our galaxy.

Graihagh - At this stage, I think it would be a really good idea to go through Drake’s equation to understand a bit more about what these limitations are.  So what is the first item in the equation?

Patrick - So the first item is the rate of star formation in the galaxy.  So they express this in terms of the number of stars per year.  So the Milky Way is about 13 billion years old and Drake puts his first estimate at 1 star per year.  So that’s the first step.

Graihagh - So 13 billion - let’s write that down.

Patrick - So this would be 'n' and star I guess…

Graihagh - OK.  What next?

Patrick - So next is what proportion of these stars have planets around them. So not all stars have planets and Drake put this at somewhere between ⅕ and ½.  And then we’ve also got the number of planets per star.  So given that it’s got a planet, how many does it have in general and he puts this at somewhere between one and five. Given that you’ve got a star that’s got planets we’ll assume conservatively that it’s got one planet and we’ll assume aggressively that it’s got five habitable planets per star.

Graihagh - And when we’re talking habitable we mean the right sort of temperature, that it’s got an atmosphere, and it doesn’t spin too fast or spin too slowly.  All these types of things that are needed for life.
Patrick - Yes, exactly.

Graihagh - So we’ve got the number of stars and then how many habitable planets around those stars. So what’s next after that?

Patrick - Then we’ve got the probability that a habitable planet will result in life.  So, I guess, you can consider it the probability that given all the right conditions to find that habitable planet that life will arise on that planet and Drake puts that at one.  So he’s quite an optimist - he says if we’ve got a star with a habitable planet then life will arise on that planet.  And then this follows quite closely by the second term which is the probability that that life will develop into intelligent life, which Drake also puts at one.  So he thinks that it’s inevitable that if life is created it follows to intelligent life.

Graihagh - After this, there’s still more isn’t there?

Patrick - Yes.  So then there’s the probability that they don’t develop communication skills so Drake was specifically interested in looking for civilisations that would have made contact with us or that we could make contact with.  And he puts their probability of developing communication at between 1/10  and ⅕, so 0.1 and 0.2.

Graihagh - OK - communication. Surely that’s the final one?

Patrick - No - we’ve actually got one more.  So Drake has factored in exactly how long these communications will last. We’ve been doing our search for extraterrestrial intelligence listening not broadcasting but only for a few decades so he places his lower bound and upper bound between somewhere between 1,000 and 100 million years.

Graihagh - OK. So if we take this equation and we do the conservative estimate, what do we get?

Patrick - So the conservative estimate which is: 13 billion stars, ⅕ of which have planets, one of which is habitable in which we develop life 100% of the time, intelligent life another 100% of the time,  10% of the time they develop communication tools and they only use these communication tools for 1,000 years.  Then Drake estimates that we would have actually only have about 20 habitable planets in our galaxy, which is the Milky Way.

Graihagh - That doesn’t seem like very many.  What about on the other end of the spectrum?

Patrick - On the other end of the spectrum if you want to go with Drake’s most optimistic estimates, then Drake arrives at a maximum of 50 million intelligent species within our galaxy and again, that’s just within the Milky Way. So we’ve got another hundred billion of these galaxies out there so, even if we pick Drake’s lowest estimate which is 20, then we’ve got in the order of 2 trillion intelligent species that we could get in contact with.

Graihagh - I mean that sounds incredibly high so why the heck have we not been able to make contact with any of these civilisations or, indeed, they make contact with us?

Patrick - Yes, so that opens up a whole other famous chapter of physics history. So this question was asked by Enrico Fermi, he’s a physicist and, I think the exact terminology he used is “if this is the case then where is everybody.” And his point being that if we accept that somewhere between this conservative and aggressive estimate of the amount of life out there that surely either we should have heard somebody, detected something or had somebody get in contact with us.  And especially the extra layer of evidence is that we’re actually somewhat young in terms of the history of the universe.  So, if we can imagine our society fast forwarding just a few hundred million years, then we should most certainly be able to colonise the galaxy and do all these intergalactic travels and certainly communication but, the fact of the matter is, we haven’t heard from anybody. So the paradox here is if we can accept that the universe is teeming with life then what are the possible explanations for why we haven’t heard from anybody?

Graihagh - Jim Al-Khalili thinks the answer lies in the sheer size of the Universe.

Jim - ...despite searching for so many decades, we are only sampling a tiny, tiny fraction of what is out there. After all, we are only looking towards star systems that are close enough to us - you know, hundred or so light years away or nearer. That’s only our little neighbourhood within the Milky Way galaxy. Just because we may never find evidence of life elsewhere doesn’t mean there isn’t life out there.
Just from the laws of probability, the universe is big enough that it must be teeming with life. It’s just whether there’s anything close enough to us that has evolved and become sentient, and developed civilisations, and developed technology enabling it to send signals out to us. So there are lots of steps along the way that would explain why we’ve heard nothing yet.