A selection of the best from recent issues of the Philosopher

If you are not familiar with The Plurality of Worlds, it is really the philosophical development of Cantor's Theories of Infinity. For those of us who are not mathematicians, in the 1890s a Danish mathematical genius - Georg Cantor - developed a series of ideas around the concept of infinity. This included the concept of there being hierarchies of infinities. 

For example, an infinite series of numbers that consisted exclusively of even integers 2, 4, 6 etc., would be smaller than the infinity that was made up of all the integers 1, 2, 3, 4 and so on.  Though both groups would be infinite.

Lewis develops an attractive idea that in an infinite universe, there is an infinity of worlds, an infinite number of which resemble ours, though the infinity that resembles ours will probably be less than the total number of worlds in existence.

In other words, according to Lewis, there are an infinite number of people with your name, physical appearance and personal history 
who are reading this article - or one identical to it -on infinite worlds - as you read this.

Lewis develops this further, in a fascinating way, examining concepts such as universals, and questions of identity.

For example, in a world where Hubert Humphrey won a US election, is that Hubert Humphrey the same as our local Hubert Humphrey? His answer is no. If someone looks exactly like you, has an identical personal history and identity - they are still not you any more than - say- an identical twin brother.

As science moves towards the Theory of Everything, with its thirteen dimensions and the 'M-Theory' of a Mulitiverse - rather than Universe - the idea of infinite worlds, populated by random and varied beings is infinitely attractive. Recently, an American University set up a computer programme that started with a world like ours, yet through random variation, produced an intellectually dominant species that were not humanoids like ourselves, but intelligent, feathered flying snakes.

In a sense, this is rather like a kind of  back door Catholicism. In the Middle Ages, a Catholic Westerner could look up in the sky, and the visible Universe was alive for them. The stars were not mysterious distant fires, but like the lights of a distant and familiar city. The Milky Way was made of St Mary's milk. If the observer were a classicist, he knew that the constellation of Orion was the remnant of a hunter torn to pieces by his own hounds for glimpsing the goddess Diana naked, etc., etc.

For all its modernity, Lewis's ideas seem very like this. The apparently lifeless universe that you see beyond our planet is an illusion, due to lack of knowledge. In fact, it contains countless worlds populated by people - infinite numbers of which are just like us.

You can turn Lewis's idea on its head: As far as we can see, there is no other life in our Solar System. Although the University of Arizona searches the skies as part of its SETI programme, and astronomers have studied the skies since the days of Ancient Babylon, or Stonehenge, there is no evidence of any other intelligent life in the entire universe.

We tend to think of only ourselves keeping records of significant events and looking skywards, but the Roman and Chinese Empires have no records of space ships or creatures from other planets. In the fossil records, we have not stared like Robinson Crusoe, at a strange Man Friday, or Man Doomsday, footprint.

Recently, when NASA was searching for funding a piece of rock turned up which some scientists claimed contained evidence of life, while others disagreed. It was hardly evidence of creatures from Star Trek, just tracks of some single cell bacteria, hotly disputed by many scientists who said that they were not even that, but chance formations.

If Lewis were right, and our Universe were infinite, would there not,  therefore be evidence of intelligent life in it -  indeed an infinite amount of intelligent life? Would you not expect something? I am not talking about evidence the size of the Great Wall of China, or even the Book of Kells. A single item would do. It could be the size of a biro or a beer can, even a solitary Morse bleep. Yet we have nothing so far.

In cosmic terms, Earth is less than a speck of dust. It is one part of a great spiral arm on the end of the Milky Way. Also, in cosmic terms, the lifetimes of Roman and Chinese Civilisations as bases for observation, are the batting of an eye. For all this though, would you not think, that if the Universe were infinite there would be some small trace of alien intelligence or civilisation?

A friend once said to me that it is unlikely that space travellers would go unnoticed in the Van Allen belt, since this is around 4000 miles above the Earth and is scanned by multiple ranging and surveillance devices. Given the enormous size of the Universe, we are not even talking about an alien civilisation contemporary with our own, just one that sent signals, hundreds or thousands of years ago.

It is probably worth examining the concept of infinity at this point. There are two: one that assumes that had you the technology you could cut things in half, endlessly, until you had a fractions of a quark, or whatever. The second is that however large a number you think of, you can add a 1 to it. There is cultural one too. This is the apparently infinite; the impossibly huge number that is, in reality, finite. Supposing a maniac who had the power to enforce his will over you, Hitler - or Emperor Caligula or someone, told you to empty the oceans using a glass tumbler - and amazingly-provided you with a receptacle large enough into which to tip them all. 

You might assume, even if you could live forever,  that this is impossible, as there are an infinite number of glassfuls of water in the sea. You would be wrong. As, while there are more molecules in a tumbler of water than there are tumblers of water in all the World's seas, this number is still finite.

Let us assume that our Universe is vast but still finite, that its combinations of planets and stars are like the result in an enormous Bell fruit machine. Someone pulled a handle and we ended up with this particular combination: pear, apple, planet, or whatever. As the Universe continues to expand, so too does the fruit machine result grow larger, in terms of matter and the spaces between matter. As the Universe formed, perhaps it so happened that very few planets developed life forms. Perhaps only our own has done so. Had the Universe been infinite, then there would have been infinite numbers of planets like ours. There would be infinite planets that were partially like ours-and so on, infinitely.

Sadly, this does not - as yet - seem to be the case.
 

Reviewed by Michael Brett.