You might argue, on the basis of the limited knowledge we have, that it is so incredibly difficult that it has only happened once, here on Earth. Or you might argue that it is just a tiny bit easier than that. But as soon as you allow for even the faintest possibility that life has emerged more than once, you have to confront the vastness of the Universe. In our Milky Way galaxy there are, roughly speaking, a couple of hundred billion stars more or less like the Sun. In the Universe at large, there are several hundred billion galaxies like the Milky Way visible to our telescopes. Even a tiny probability that life might have arisen somewhere else, multiplied by the total number of stars in the Universe, gives you an extremely high probability, indistinguishable from 1, that there is intelligent extraterrestrial life.
In the absence of evidence either way, which option you choose is entirely subjective. But the point is that it is an all-or-nothing situation. Either the Universe is teeming with life, or we are alone. So the discovery of even one other Earth-like planet with signs of life on it would tip the scales dramatically, ruling out the option that we are unique. As one of my tutors used to be fond of pointing out, "you cannot extrapolate from a sample of one", so the existence of life on Earth in itself tells us nothing about the probability of finding intelligent life elsewhere. But the existence of life on two planets would mean that you could begin to extrapolate, and in this case the extrapolation immediately leads to the inevitable conclusion that life is far from unique.
As the title of his book suggests, Amir Aczel is firmly of the school of thought that says that we are not alone. Writing as a statistician, he spells out the probabilities involved in each step of the argument (the chance of a star having an Earth-like planet, the chance of life evolving to the point of intelligence on that planet, the chance of life spreading from one planet to another, and so on). This is done in an entertaining and informative fashion, but it still boils down to the argument that out of some hundred thousand billion billion stars, there must be more than one that is accompanied by an inhabited planet.
Much of this is familiar to anyone who has followed discussions about the possible existence of extraterrestrial life in recent years and decades. Aczel moves on to less familiar ground when he tackles the possible role of mathematical chaos in changing the way we think about some of the probabilities, but he stops short of reaching any conclusions about what this may tell us about the emergence of DNA as the molecule of life.
Indeed, "tantalising" is an apt word to sum up the whole argument. Aczel's book is to be recommended not for its conclusion, or even for the pains- taking statistical analysis which lends credence to that conclusion, but for his skill as a storyteller. His previous book was (in my view) the best popular account of Fermat's last theorem, but it got elbowed aside (in the UK at least) by a more artfully packaged version of the same story.
In his latest book, he tells you a lot about probability and a little bit about life and the Universe, and weaves everything together with his personal account of how he approached the subject as an outsider with no experience of the long-running astronomical debates about extra-terrestrial intelligence. The result is an ideal blend for anyone else who is interested in the subject but knows nothing about those debates, and it deserves to be as successful as the "other" book about Fermat's last theorem.
The reviewer's latest book is 'The Birth of Time' (Weidenfeld & Nicolson)