Monday, March 03, 2008

The Fermi Paradox and the Drake Equation

You can’t read any serious book on xenoscience without coming across the Fermi Paradox and the Drake Equation. They may sound like Robert Ludlum thrillers but they’re actually a brace of thought experiments that, in different ways, pose questions about the likelihood of life in the universe. I’ll explain the Fermi Paradox first. Drake can wait until later.

While having lunch with some colleagues back in 1950, physicist Enrico Fermi posed this question (although maybe not in these exact words): ‘Given the extreme age of the universe and the vast numbers of stars, it seems almost inevitable that the universe should be brimming with life. And, by the law of averages, in an almost infinite universe of life, there must be extraterrestrial civilisations that are technologically on a par with, or in advance of, our own. They’ve had more than enough time to litter the galaxy with their presence. So where is everybody?’

From that conversation we got the Fermi paradox, which continues to taunt us nearly 60 years later. It 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. To put some numbers to this, there is estimated to be 250 billion (250,000,000,000,000) stars in our own galaxy, the Milky Way, and 70 sextillion (70,000,000,000,000,000,000,000) stars in the visible universe (source: Dr Simon Driver, Australian National University). Oh, and in case all of those zeros are hard to relate to, one sextillion seconds equates to around 300 billion years … and to put that into perspective, the Earth is only 4-5 billion years old and the universe itself is only 13-odd billion years old. That’s a lot of stars.

The signal we send out from the Arecibo Radio Telescope. Will aliens even know that this is a coherent signal?

So, if only a tiny number of stars had planets around them, and intelligent life only occurred on a tiny, tiny proportion of those planets (or other environments), there should still be a huge number of civilizations in our galaxy alone. So you can see why Fermi’s Paradox bugs the hell out of the astrobiologists. They’re aiming their radio telescopes and satellites at stars likely to have ‘Earth-like’ planets and hoping to hear a transmission from our alien brethren. But ET ain’t on the phone. A number of possibilities for this silence have been put forward, all of which have generated thousands of academic papers, books and studies. I've tried to group them here under four easy to grasp categories:

Firstly, there is the faintly uncomfortable idea that we are the first life form in the universe to achieve a sufficiently advanced technology that allows us to attempt contact with other worlds. This is sometimes called the Rare Earth Hypothesis; the idea that we are a cosmic rarity.

Secondly, it could be that there are advanced civilisations out there but their technology does not resemble ours in any way; therefore they may not recognise our signals as signals and we don’t recognise theirs. I personally favour this idea as I am of the xenoscientific view rather than the astrobiological view.

Thirdly, it may be that intelligent aliens have anticipated the sorts of activities we’re currently involved in (radio signals, unmanned probes etc.) and choose to ignore it or hide themselves from detection (I call this the Peek-a-boo Principle). The more pessimistic philosophers among us, however, came up with the far more sexy-sounding Doomsday Argument; that technological civilizations usually or invariably destroy themselves before or shortly after developing radio or space flight technology.

Lastly, there is the simple and unfortunate fact that the universe is very, very large and, therefore, civilisations may just be too far away from each other to communicate. We’ve been chucking signals out into space for just a hundred-odd years and there’s only so far they can have travelled even at the speed of light (186,000 miles per second). Who knows … far out in the depths of deepest space our signals and theirs may be crossing even now, but we won’t hear them for another hundred years (For a more detailed look at the many theories I’ve tried to simplify, check out the links at the bottom of this post.)

It's extraordinary that one fairly innocuous lunchtime comment could generate so much thought. But as astronomer and science writer Seth Shostak says: ‘The Fermi Paradox is a remarkably strong argument. You can quibble about the speed of alien spacecraft, and whether they can move at 1% of the speed of light or 10% of the speed of light. It doesn't matter. You can argue about how long it would take for a new star colony to spawn colonies of its own. It still doesn't matter. Any halfway reasonable assumption about how fast colonization could take place still ends up with time scales that are profoundly shorter than the age of the Galaxy. It's like having a heated discussion about whether Spanish ships of the 16th century could heave along at two knots or twenty. Either way they could speedily colonize the Americas.’

I just hope that if aliens are looking for us, they're not using the plaque devised by Frank Drake (of the Drake Equation) and Carl Sagan and attached to the Pioneer 10 and 11 probes (see illustration at top of post). The plaque depicts a solar system with a sun and nine planets. As you know, we've added several bodies to our solar system since then ...

Perhaps they are looking for us and they've got lost?

And now, the Drake Equation. Ten years after Fermi upset the astrobiologists with his paradox (but no doubt ingratiated himself with the religious fundamentalists), Frank Drake dropped another bombshell – the so-called Drake Equation.

Drake, now Emeritus Professor of astronomy and astrophysics at the University of California, Santa Cruz, was musing about the possible number of extraterrestrial civilisations in our galaxy (and no doubt considering Fermi’s Paradox) and decided that there had to be a way for scientists to quantify the uncertainty factors that determine the possibility of extraterrestrial civilisations. What emerged from his cogitation was the Drake Equation (sometimes also called the Green Bank Equation). It looks like this:

And this is how it works:

  • N is the number of civilisations in our galaxy, with which we might hope to be able to communicate;
  • R* is the average rate of star formation in our galaxy;
  • fp is the fraction of those stars that have planets;
  • ne is the average number of planets that can potentially support life per star that has planets;
  • fl is the fraction of the above that actually go on to develop life at some point;
  • fi is the fraction of the above that actually go on to develop intelligent life;
  • fc is the fraction of civilizations that develop a technology that releases detectable signs of their existence into space; and
  • L is the length of time such civilisations release detectable signals into space.

You can have a go at running the equation at home; the only really difficult parameter to identify is the R* (which only an astronomer – like Drake – would be able to work out). Which is why another version of Drake’s Equation turns up quite often which solves the problem by replacing the R* with N* (the number of observable stars in the galaxy) and by dividing the L by a new value of Tg (the age of the galaxy). So this variant equation looks like this:

There is a lot of speculation about what values to assign. In 1961, Drake thought that the values should read as:

N = 10 (stars formed per year) × 0.5 (half of these stars will have planets) × 2 (planets per star capable of supporting life) × 1 (where life develops) × 0.01 (intelligent life develops) × 0.01 (are able to communicate) × 10,000 (alien civilisation lasts 10,000 years) = 10.

So, according to Drake, there are at least 10 alien civilisations out there sufficiently advanced enough to talk to us and understand us. But the truly remarkable thing about the Drake equation is that by plugging in different plausible values for each of the parameters, the resulting value of N is often much higher than one … which is a great motivator for organisations like SETI (Search for Extraterrestrial Intelligences), who are already desperately trying to find an answer to Fermi’s Paradox!

Fancy a go at Drake’s Equation yourself but don’t like maths? Visit the SETI site and have a go.

Other sites worth visiting:

No comments: