# Little Green Men

SETI is short for “Search for Extraterrestrial Intelligence”, or in other words, a search for the “Little Green Men”. The main thrust of SETI is to examine the light from other stars for signs of intelligent life, often on well known wavelengths such as wavelengths near the “water hole“,  a section of the electromagnetic spectrum associated with hydrogen and hydroxyl ions emissions lines. Hydrogen and hydroxyl together make water and water is supposedly necessary for life, so the thinking is that technically advanced life would possibly use this frequency to initiate contact with other civilisations.

The trouble is that this is just a guess and there are many possible frequencies that might seem plausible to technically advanced civilisations. If the little green men are not made of water, as we essentially are, they might pick a different frequency band to search. XKCD, my favourite web site has a cartoon which makes this point:

Suppose a remote civilisation did decide to broadcast in that waveband. If they are just announcing their presence, they would need to broadcast their signal in all directions, or they would need to pick out some likely looking star systems and send a directed signal in just a few directions.

If they broadcast in all directions, the power that they would require would be huge. The problem is that in any average stellar neighbourhood, there aren’t many stars. In the sun’s neighbourhood there is an average of 0.004 stars in a cubic light year. So the probability of finding a star one light year from a star in a neighbourhood like the sun’s is four in 1,000. If you look two light years out from the star, you will enclose a volume of eight times the volume of the search area up to one light year, meaning that the probability of finding a star in that volume is 0.032. You would need to look further than five light years out for there to be a fifty-fifty chance of finding a star in that volume, which would be 125 time the size of the original volume of one cubic light year. At 15 lightyears, there would likely be at least 10 stars within the search area.

That’s all very well, but most if not all of these stars will be of the wrong type to support planets of the type that will have free water on them. In fact it is extremely unlikely that a suitable star with suitable planets can be found within, say 200 light years of our hypothetical advanced civilisation. (That’s an out and out guess, but see later).

The trouble is that the signal gets weaker and weaker the further it travels. If you use the signal strength at one light year as the yardstick, the strength is reduced to one quarter at two light years, one ninth at three light years and one sixteenth at four light years and so on because the signal is spread over an area proportional to the square of the distance from the source.  So if the signal strength at 200 light years will be 1/40,000th of the strength of the signal at one light year. If the signal has to travel further it will be correspondingly weaker.

So likely systems are rare and the signal strength will be weak at the distance of a suitable system. This means that the signal needs to be very strong to be detectable.  Very strong means lots of energy. To broadcast to the Universe at large the civilisation would have to expend a considerable amount of its available energy to only potentially contact another civilisation. Imagine trying to get a project like into the planetary budget!

So the hypothetical civilisation is probably desperate to make contact. That may be because either they are in trouble themselves, or they want to warn all local civilisations about something. They are unlikely to do it on a whim, as they must know that the chances of success are pretty close to zero. There’s a faint possibility of a sort of “vampire civilisation” that must prey on other civilisations and so chooses to broadcast in the hope of finding a new victim. I consider that highly unlikely, since as I said the chances of success are nearly zero, and such a civilisation would need to find a new host in a relatively short period of time, astronomically speaking.

If a broadcast signal is very unlikely to find a receiver, how about a directional signal, maybe driven by a laser. The spread of a laser signal is much less than a broadcast signal, but the signal does spread. An advanced civilisation would still have to divert significant resources into sending the signal but it might be possible.

The civilisation would have an issue, though. If they wanted to get a signal to us and they used a ground based laser, their ground station would be in line with us once each local day, and our receiver would be in line with them once in every day too. Since it is unlikely that the day lengths would match, so the window for transmission would be short, even down to a minute or less.

The hypothetical aliens would most likely opt for an orbital laser. That could be pointed in our direction all the time, for every hour of every alien day, unless some local object got in the way. However we have a problem now. We would need to detect that a signal is coming from a point in space, in spite of all the extraneous noise that might mask it, and then we would need to concentrate our resources looking in that direction for a length of time. The hard part would probably be convincing ourselves that a signal is from LGM (little green men).

There’s an equation that purports to estimate the possible frequency of extraterrestrial civilisations, called the “Drake Equation”. It’s the sort of “equation” that gives mathematicians the heebie-jeebies, since it is derived from nothing and nothing is derivable from it. XKCD cruelly lampoons the equation, and while I don’t much like the sentiment expressed, I can understand why the Drake equation raises his ire – it is ad hoc, probabalistic, and presents as constants things which are fundamentally unknown. In other words, your guess is as good as mine, and both will fit comfortably in the Drake equation. I may return to the equation in a later post.