You've just published a new book, "Welcome to the Universe" with co-authors J. Richard Gott and Michael Strauss. It's based on a course you taught at Princeton University. And it starts with a thought exercise in numbers as a way to describe the size and scale of the universe. So I wanted to try one out on you…
… and I'm sure you're scared! Thing is, I was talking to this kid the other day, and I tried to describe the universe as this endless expanse. But I also said how that confused me, because surely the universe has to exist in something. And he said, "Well, what about endless - plus one?" And I was totally stumped by that, so I thought I'd hand it over to you. Endless plus one? Is that possible?
Well, that sounds like a variant of what we all did as kids, which is to say, "What's the biggest number you know?" And you'd say, "A million." And the other kid would say, "Okay, how about a million and one? That's bigger." Then it goes on with, "A billion." And there's always a kid who's adding one to your number to best you. And then you learn infinity and you say, "Infinity plus one!"
But that's kind of what you do at the start of the book with numbers that are no longer real, they're mathematical concepts more than anything …
Yes, exactly. It's an adult version of what kids do.
There's a limit to the number of countable things in the observable universe. That would be, like, the number of particles in the universe - you could count those - and we give that estimate. It's around 10 to the power of 80 or something like that. So, then, of what good are numbers bigger than that if there's nothing to count them with? It turns out bigger numbers have value when you consider events. So we asked: what's the total number of legal, complete chess games you can play? Well, we estimate that as well, and it's 10 to the power of 25000 - that's way bigger than 10 to the power of 80, and, again, you're not counting things, you're counting events. And so [the idea of] "endless plus one" is like infinity plus one, and it is true that some infinities are bigger than other infinities. I know it sounds crazy, but it's true. Endless plus one would put you into the realm of the next infinity, for example. Although, strictly speaking, infinity plus one equals infinity. But that requires a careful mathematical proof to demonstrate it.
Well let's head deeper into infinity. You headed a commission for the Bush administration in 2001 on the Future of the US Aerospace Industry. Later there was the "Moon, Mars, and Beyond" commission. And I wonder whether we're now at this point where we will allow certain actors to get into space, actors who aren't necessarily interested in the fundamental science of space, and we'll just say, "Well, why shouldn't they go there?"
Well, they should. My skepticism here is … well, let me roll back a bit … Twenty years ago I wrote an essay that explored how exploration has changed over the centuries. I came up with only three drivers. Only three… of civilization's doing hugely expensive things. And one of them is war, the "I don't want to die" driver. The other is economics, "I don't want to die poor." And the third one, which you don't see much today, because the world is different, is praise of royalty or deity.
