Welcome to the Universe: an infinity plus one

DW: 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…

Neil deGrasse Tyson: Yeah, bring it on!... [laughs]

… 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.
 

Now, you look at the Columbus voyages and that was the search for economic return, a quick way to India for trade for Spain. You look at the Apollo program, even though here in America no one really remembers it accurately ... again, they think, "We're Americans, so of course we're going to explore," without remembering that we were at war with the Soviet Union, basically, a [urinating] contest …

Which the Soviets won.        

[laughs] Well, so, they were first out of the box in almost every space achievement that you could list. And we got to the moon before they did and then we say, "We win!" But they had the first satellite, the first non-human animal, the first human, the first space station, the first woman, the first black person - a dark-skinned Cuban - the first space walk ... you know, all of this was Russian. So our space program was reactive to theirs,  not proactive. But my point is that that was militaristically driven. So now we want to go to Mars and you're going to tell me that corporations are going to do it, and I'm saying, "No, they're not." Not that I don't want them to do it. They're just not.

Why not?

Well, you have to ask what's the business model. Governments have much longer time horizons than do corporations. Corporations have quarterly reports; governments are in it forever. So if SpaceX ends up having one of its spacecraft go to Mars, my read of this is that it's not going to be because they found a business model to do it. It's because NASA bought it from them, because they made it cheaper than anything NASA could make out of the NASA factories. 
 

But that's been going on since the beginning, it's just a little more apparent now, and the rocket may still say SpaceX on the side, even though it's got a NASA payload.

So…

So you go from a space program to a space industry.

There's so much about space that we're all expected to understand, like the space industry ... like asteroid mining, gravitational waves, black holes, or sending a probe to the Alpha Centauri system. But what would you say should fascinate us most?

It's not what we should or shouldn't do, because that implies someone is value-judging research. I'm a fan of any research into the unknown in any academic subject, whatsoever. So we should just do it all. The 1920s saw the birth of quantum physics - a really obscure thing to do in the day. If you were around then, would you have said, "Should we be studying this hypothetical thing you're calling the atom?" It would take 50 to 60 years, but you must now recognize that the information technology revolution, which by some measures accounts for a third of the world's GDP, in the creation, storage and retrieval of information digitally, that that is enabled by quantum physics. There is no computer without quantum physics. Did anyone see that coming in the 1920s? Of course not.

Neil deGrasse Tyson is an astrophysicist, a professor and author, and the director of the Hayden Planetarium in New York. He wrote "Welcome to the Universe" with Professors J. Richard Gott and Michael Strauss. Their book is published by Princeton University Press.