Joe: I’m not sure I agree with you Blow in denying that nature contains the infinite. But to settle this, why don’t we start out by defining infinity.
Blow: That’s a piece of cake. The infinite is that which is not finite.
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.