One of the most fascinating questions that occurs when contemplating the universe is whether there other life exists, equally or more intelligent than we. Are there alien eyes looking at our star or our galaxy and do these creatures ask the same cosmological questions we ask? Nobody knows, although the straightforward application of the Copernican Principle suggests that we cannot be unique in the universe.
Is there other life in the universe? How can we begin to answer that question, in the absence of direct evidence to answer the question in the affirmative? One way is through something known as the Drake equation, named after the astronomer Frank Drake. It is not really an equation to be solved, so much as it is a way of systematizing the unknowns. Here is how it works. Let us say we wish to estimate the quantity N, the number of technological civilizations in the galaxy. Of the n stars in the galaxy, only some fraction   fp  of them will have planets. Only some average number of planets per star, (H), will be potentially habitable. Of the habitable planets, there is a fraction   fl  that will develop life. Now of the planets that develop life, how many will develop intelligent life? Use   fi  for that fraction. Only some fraction of intelligent species   ft  will develop technology. So given all these things, we can write
N = n ×   fp  ×   H  ×   fl  ×   fi  ×   ft
Some of these factors are easier to estimate than others. There are about 100 billion stars in the Milky Way so we will use that for n. There now seems to be some direct evidence for planets around other stars, but as yet we still don't know what fraction of stars would have planets. If we are optimistic, then we would take a fraction near one, essentially saying that all stars have planets. What number of planets per star would be habitable? The planets would have to be located at a distance from their star that is neither too hot nor too cold. In our solar system there are three that are potentially habitable, Venus, Mars, and the Earth. Some stars would support fewer, or possibly no, habitable planets. Let's say that, on average, only one in 10 stars with planets has one planet that could support life. What have we got so far?
N = 100,000,000,000 × 1 × 0.1 ×   fl  ×   fi  ×   ft
This still leaves a lot of potentially life-bearing planets!
The next three fractions are the especially tricky ones. If life can develop, does it? Opinions differ widely on this topic. This is where the recent Life on Mars issue has some application. If this development holds up, then life developed on both Mars and the Earth and it becomes much more problematic to say that life is incredibly difficult to get started on any given planet. If you believe life is inevitable, given habitable conditions, then make   fl  =1.
Now, if life forms, does it become intelligent? A difficult question. Life has been around on Earth for billions of years and we (modern humans) came on the scene only in the last 100,000 or so years. And any life on Mars that may have once existed (if it did) died out completely. For purposes of an estimate, let's take the ratio of 100,000 years of humans to 1 billion years of life, giving us 1 in 10,000 planets with life that develop intelligence.
Does intelligent life inevitably develop technology? Good arguments can be made either way. There doesn't seem to be anything particularly inevitable about humanity's rise to technological prowess. Although it happened rapidly once it got going, did it have to happen? Could an intelligent creature stay as a hunter/gatherer or simple tool-user for the entire length of its existence? Who knows? Let's adopt the attitude that intelligence necessarily leads to technology and say that   ft  = 1. So we have
N = 100,000,000,000 × 1 × 0.1 × 1 × 0.0001 × 1 = 1,000,000
One million planets with technologies!
OK, we stacked the deck by choosing all the optimistic numbers. Go back and put in some numbers of your own. You only have to insert one pessimistic number to drop the number of planets in the Milky Way down to around 1, which would be the Earth. For example, humanity has been technological for only 100 out of its 100,000 years of existence. If you find the thought of a low number of life-bearing planets depressing, that we might be alone in the Milky Way, bear in mind that there are more galaxies in the visible universe, than there are stars in our galaxy. So if there were only one life bearing planet in each galaxy there would still be trillions of life bearing planets. But we will never communicate with or visit other galaxies.
And how likely are life-bearing planets that can lead to intelligent life? Do they require a large moon, such as the Earth has? Such double planets may well be rare, particularly if the Moon formed as the result of a huge impact early in the history of the solar system. Does intelligent life require dry land as well as oceans? What are the odds that the Earth would end up with both oceans and dry land (as opposed to all oceans or all dry land)? We don't really know, but once you start thinking about it, things become rather tricky quite rapidly.
So who knows? But it does tend to make you want treat our planet and its unique inhabitants with some respect.