Infinity

March 7, 2010

First Aired: February 24, 2008

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Infinity is a puzzling concept. Mathematicians say there are as many odd numbers as there are numbers altogether. That seems like saying there are as many men as there are people altogether – which we know is untrue. And if you subtract infinity from infinity, you are still left with infinity – but which infinity? Some infinities are larger than others – how can this be? John and Ken unravel the paradoxes of infinity with Rudy Rucker, Professor Emeritus of Computer Science at San Jose State University and author of Infinity and the Mind: The Science and Philosophy of the Infinite.

Infinity is a pretty big concept. We come across infinity when we talk about God, space, numbers themselves, and even in the division of matter. Surely then, we can define infinity with some precision. Yet, Ken points out that it’s easy to list what infinity is not, but a real definition can be far more elusive. John seems skeptical that we’ll ever even find such a thing.

Rudy Rucker, a computer scientist, mathematician, philosopher, and author joins John and Ken to get to the roots of infinity. The notion of infinity is an old one indeed, but people didn’t always think of it as we do today. For instance, the ancient Greeks saw infinity in a rather negative light. After all, what’s more frustrating than a number you could never count to? During the middle ages, though, infinity became a more appealing idea as people pondered the connections between infinity and God. St. Augustine was one notable advocate of the view that God, being all-powerful, could create infinity.

These days, mathematicians view infinity as a property of certain sets. Set theory, Rudy says, is the theology of mathematics. John is a bit hesitant to swallow the ‘fuzzy’ math. Callers raise a few good questions, asking about the nature of our cognitive representations—that is, can we even conceive of infinity at all? And moreover, why do we need more numbers? Don’t we have enough already? John, Ken and Rudy tackle these questions and more.

Roving Philosophical Reporter (seek to 5:54): Zoe Corneli stops by San Francisco State University to listen in on some of the student’s deep thoughts. What is infinity? One theater student thinks that in some sense, perhaps life itself is infinite. Other students wonder if infinity is even worth thinking about—after all, we never need to deal with it in real life. Or do we?

60 Second Philosopher (seek to 49:50): Ian Shoales reports in with a few witty remarks about the nature of infinity. What is infinity? Can we ever find words to capture it? It seems like the concept of infinity has given us some deep thought experiments and some tough riddles to crack. For instance, a monkey at a typewriter could write Hamlet if we gave it an infinite amount of time. Why a monkey though? Maybe it could type Hamlet faster than a human . . . .