March 2, 2006


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The Infinite Book: A Short Guide to the Boundless, Timeless and Endless, by John D. Barrow (Pantheon Books, 2005, 275 pages plus notes and index)

I fail to see the need for mind-expanding drugs when all you need to do is ponder the question “How big is the universe?” for five minutes.

If you do it right, you should completely freak out.

If the universe is a certain size, then what’s outside it? What’s it contained in? And how big is that? And if that is a certain size…
OK, then the universe is infinite. Sure, you can accept that on principle, but can you picture it? What does it mean really? It leads to my favorite question: why is there something instead of nothing? (Corollary questions: Can you imagine there being nothing? Is all the something placed inside a space of nothing? So what’s nothing?) But I digress.

John Barrow, a professor of sciences at the University of Cambridge, talks us through these questions with a minimum of freaking out in The Infinite Book.

There is some debate, he notes, over whether or not “actual infinities exist.” I’m thinking it hardly matters. As far as the human mind is concerned, you can always add one to a number to get a higher number; so what would it mean if “actual infinities” do not exist? Freaking out yet? Sorry.

So. Either the universe is finite, which we can’t get our heads around, or it’s infinite, which we can’t get our heads around, or it’s somehow both or neither, which certainly isn’t any easier to get our heads around.

But insofar as you can fit any of this into your head, Barrow is your man.

He starts with elementary conceptions of infinity (endless counting and Zeno’s Paradox), tours briefly through Georg Cantor’s woes as a mathematician who dared contemplate infinity (his peers thought it more rigorous to deny the whole idea their attention) and neatly explains the difference between countable and uncountable infinities and the concept (or mathematical fact) that some infinities can be bigger than others. (This is for real. I ask you, who needs Quaaludes?)

The chapter on “The Infinite Replication Paradox” made me feel like I was repeatedly, though finitely, hitting my mind against a padded wall. It says that if the universe is infinite then it must contain infinitely many of every thing that is possible, and every thing that happens has already happened. I get hung up trying to define “thing” in this context. Don’t laugh; it is harder than you think. You get into the recursion of things containing themselves and… and… and… oh bosh. But it’s a good sort of pain.

Infinite time, infinite space; infinitely large, infinitely small… Barrow covers them all.

Yet The Infinite Book is manageable and finite – comfortable, even. Too often the only sources of discussion on this stuff are broad volumes covering much of modern physics. If you find infinity intriguing (and come on, how can you not?) but are not in the mood for a sandtrap of discourse on relativity theory – in other words, if infinity is enough – try this.


—Lisa Parsons

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