World Without End

The journey to infinity begins. Published by Legend Books 1987. Cover design by Dennis Barker.

Getting your head around the concept of infinity is not easy.  We look into this subject, in so far as our finite minds are capable of doing so, in the latest edition of Odyssey, which has just been issued.

In his popular science book from 2005, The Infinite Book: A Short Guide to the Boundless, Timeless and Endless, John D Barrow, Research Professor of Mathematical Sciences at the University of Cambridge, provides an account of how the idea of infinity has been contemplated throughout the ages, and reaches some wide-ranging conclusions (in the literal sense) on what it means today.

Understandably given the subject matter, he tackles issues of cosmology.  Whilst providing some convincing reasons why our universe is not actually infinite, he discusses the problems arising from the assumption of infinite density in the singularity from which the Big Bang originally exploded.  Space and time are destroyed at such a place and so, with reference to Stephen Hawking’s view on the matter, if the laws of physics could break down there, couldn’t they break down anywhere?

But the existence of an infinity in any physical property at a singularity, including the conclusion that the curvature of space itself would be infinite, is critical to our understanding of the universe within Einstein’s view of spacetime.  It helps explain the large-scale structure of everything.  Even though it may be hard to grasp, we need to be able to appreciate what infinity really is in order to progress.

One writer of fiction whose work stands out in the field is the Argentine writer Jorge Luis Borges.  In his 1941 short story The Library of Babel, he describes an infinite Library with no two identical books.  The librarians recognise that all possible combinations of the letters of the alphabet in books of similar size, even given the many meaningless combinations (which comprise most of the books), are still not infinite.  Some travellers in the Library believe that one day they might encounter a repetition of the sequence of books.  And in The Garden of Forking Paths he envisages a story where divergences in the narrative lead to an endless series of all possible futures.  The analogies with our own universe, and with the “many worlds” interpretation of quantum physics, seem clear.

On the other hand, in the realms of hard science fiction, Greg Bear’s 1985 novel Eon, the first in his series in the universe of The Way, looks into the infinite after its own fashion.  Astronauts investigate the inside of an asteroid which has been hollowed out to provide a succession of huge cylindrical chambers, and rotates to simulate gravity on the inner surface.  It is all intriguing enough as they explore the first six chambers but, when they reach the seventh, they discover that “the asteroid was longer on the inside than it was on the outside.  The seventh chamber went on forever.”

How these explorers get to grips with a vast tunnel that seemingly never ends (and, needless to say, they are by no means the only ones there) makes for a great story, but a memorable aspect is how the immensity of the Way gradually becomes clear.  First, tentative steps a few metres or kilometres along it, then travelling hundreds of kilometres down the corridor, then much, much further…

In a sense, when we try to understand infinity ourselves we go along much the same route, taking the idea forward step by step.  Which probably misses the point.  “Infinity” isn’t something we could ever reach since, as many of the thinkers described in Professor Barrow’s book have said in the past, it doesn’t actually exist in any practical way.  It’s something towards which things tend to progress, be they number sequences, timescales or whatever, but they can never get there.  Not because it’s a long way away, but because it isn’t there at all.  And yet, we need to understand it to appreciate the universe around us – one reason why cosmology is exciting, but not easy.

Richard Hayes, Assistant Editor (Odyssey)

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