### Diversions

IRA FLATOW, host:

For the rest of the hour: trying to get your head around a figure the size of a trillion. How much is a trillion?

This week, President Bush unveiled a budget, a proposed budget for 2009 - budgets are not unusual. What was really unusual to see on this fund was the size, the price tag of it: $3.1 trillion dollars. And to paraphrase former Senator Dirksen, a trillion here, a trillion there, pretty soon it adds up to real money. Of course, he was talking about billions back then. It seems like a little small change now.

So getting a real handle on huge numbers like trillions isn't easy, but we've got the guy to do it. David Schwartz. He's the author of many books for children, including "How Much is a Million," "If You Made a Million," and "Millions to Measure." He's also the winner of the 2008 AAAS/Subaru science book and film prize for "Where in the Wild?: Camouflaged Creatures Concealed and Revealed." He joins us by phone from California. Welcome.

Mr. DAVID SCHWARTZ (Author, "How Much is a Million"): Hello, Ira.

FLATOW: Hi, there. Now, you've written about millions. How do you write about trillions?

Mr. SCHWARTZ: Well, actually, how much is a million talks about million, billion and trillion. And one of the things I think is most fascinating about these numbers is what happens when you compare them to each other.

FLATOW: Mm-hmm. Is it possible to get your mind around the trillions, something that big? Tell us how we would do that.

Mr. SCHWARTZ: I think you have to start a little bit smaller, so I'll give you an example.

FLATOW: Okay.

Mr. SCHWARTZ: Well, start - let's talk about time and let's talk about seconds. If you were to clock out a million seconds, a million seconds. A million is a thousand, thousand. Easy to define these numbers, it's harder to really understand it. A million of thousands, thousand. A billion is a thousand million. A trillion is a thousand billion or so a million, million. But if we were to clock a million seconds and figure it out, do the math and we'll turn out that that's about eleven and a half days. So what about a billion seconds? That turns out to be about 32 years. And then a trillion seconds is 32,000 years. So the difference between a million, a billion…

FLATOW: Wow.

Mr. SCHWARTZ: …and a trillion is like the difference between eleven and a half days, 32 years and 32,000 years. Sometimes I say I have a pretty good idea of what I will be doing a million seconds from now. I have no idea of what I will be doing a billion seconds from now. But I have an excellent idea of what I'll be doing trillion seconds from now.

(Soundbite of laughter)

FLATOW: 1-800-989-8255, if you want to talk with David Schwartz about a trillion. So that's how long it would take you to count out the trillion $1 bills if you can do one a second.

Mr. SCHWARTZ: If you could do one a second. And there's something with dollar bills also because I was thinking about this $3.1 trillion budget. So, yesterday, I went to my bank and withdrew $100 and asked for in singles. I didn't really get any strange looks. I thought I might. So I took this $100 bills and in Chinese restaurant in Tucson, which is where I happen to be right now. I do live in California, but I'm visiting schools, speaking at schools to children about big numbers in Tucson, Arizona, right now.

So in a restaurant last night, I took my stack of $100 bills and measured them, touched them down because I think, okay, we have a trillion of these dollar bills, they'd compress. And - so I just kind of squished them down and I measured them, then it came out to be about a half an inch for a hundred of these bills. And I felt, okay, well, let's suppose these were $100 bills. And I did the math to figure out that $1 million in a stack of $100 bills would come out to be about four feet high. That's a million dollars in $100 bills.

A billion dollars in the same $100 bills would be 4,000 feet high, almost three Sears Towers on top of each other. And then here comes the trillion dollars in $100 bills is about 789 miles or 144 Mount Everest stacked on top of each other. So the $3.1 trillion budget were up to 446 Mount Everests. That's a trillion dollars in a stack of $100 bills. And compare that to the billion and a million and, yeah, we're talking about real money, Ira.

FLATOW: Well, how can you spend it all in one year?

(Soundbite of laughter)

FLATOW: If that three trillion…

(Soundbite of laughter)

Mr. SCHWARTZ: Spending it is another…

FLATOW: How much would you have to spend per second to spend it all in one year?

Mr. SCHWARTZ: Well, there's math formula I have to think about a little bit.

(Soundbite of laughter)

Mr. SCHWARTZ: But the one I did think about was I thought, well, suppose you spent $1,000 a day…

FLATOW: Okay.

Mr. SCHWARTZ: …how long would it take you to spend a trillion dollars comes out to be 2.7 million years.

FLATOW: So to spend it a three trillion at a $1,000 a day is…

Mr. SCHWARTZ: Yeah. So we're all up to, you know, eight million years or so or something like that. So the numbers are fun to think about, you know? What I like to do in books and when I'm speaking to children, is I like to, you know, take some examples that they - that people, adults and children, can relate to. You know, the height of a child…

FLATOW: Right.

Mr. SCHWARTZ: …four feet high, you know? The $100 bills, a million of them, four feet high. That's a height of maybe a 6- or 7-year-old. And then, expand it to the unthinkable proportions of billions and trillions and we can have a lot of fun with that.

FLATOW: Well, let's say I have a kid who was four feet high.

Mr. SCHWARTZ: Yeah.

FLATOW: And you had three trillion of them, how far would that go to?

Mr. SCHWARTZ: Well, let's see. Three trillion times four feet, so that'll be 12 trillion feet. If we want to do that in miles divided by, oh so, if there were 10 trillion feet divided by 5,000 that would be, I think two billion miles, something like that. Oh, man, that's way out there.

FLATOW: That's out toward Jupiter, so.

Mr. SCHWARTZ: Towards that edge of our solar system, yeah. In "How Much is a Million," what I did was I said if we had a trillion children standing on each other's shoulders, they would extend almost to Saturn's rings. And what's really funny about that is that kids love that - those kinds of examples, and once in a while, they get into exploring them on their own, and they'll write me letters. And they'll say things like, well, we saw how you figured it out -because I explained the math in the back of the book - and you said that the average height of an elementary school child is 4'8. And, therefore, the shoulders of these children would be about four feet above the ground, and we don't think that average height of an elementary school student is quite that much and we went and we found the mean, the median and the mode of everybody in our school, and it was only 4'4. So I love to have kids do their own investigations, their own mathematical explorations…

FLATOW: Mm-hmm.

Mr. SCHWARTZ: …ways like that. One person said, you know, you forgot the kid at the top because if they're all in each other's shoulders, I said the shoulders are four feet above the ground and I multiply four feet times a million. And said, you know, you forgot the kid…

FLATOW: Yeah.

Mr. SCHWARTZ: …at the top. You have to include his head. That's another eight inches.

(Soundbite of laughter)

FLATOW: What if you went in the other direction? One trillion.

Mr. SCHWARTZ: Yeah.

FLATOW: Can you think…

Mr. SCHWARTZ: That's really interesting. You know, one trillion or one part per trillion. I think a BB(ph) and a swimming pool is one part per million. And so, one part per billion and one part per trillion is going to be so much smaller than that.

FLATOW: Let me go the phones. Hi. Russ(ph) in Kansas City, welcome to SCIENCE FRIDAY.

RUSS (Caller): Hi there.

FLATOW: Hi there.

RUSS: Actually, a BB is not quite that - I think 100 by 100 by 100 BBs, yeah, or about 8 feet by 8 feet by 8 feet would be - or those 6 by 6 by 6 would be…

Mr. SCHWARTZ: Yeah. You're right about that.

RUSS: But a million - take I happens to with marbles, and if you took a trillion of them and put them in a perfect conical stack, like you'd have an hour glass, it will be just a shade under a 1,000 feet high.

Mr. SCHWARTZ: Wow.

FLATOW: Wow. Russ, I think you're doing too much thinking about this.

RUSS: I'm an engineer. It's my job. I get paid.

(Soundbite of laughter)

RUSS: I'm on my job. From point A to point C, I'm servicing a customer and I'm thinking about numbers.

FLATOW: Yeah. Well, give us some other ideas. What are the kinds of comparisons you have come out with?

RUSS: Well, there's all kinds of comparisons. But it's easy to think about if you think about it in smaller terms.

FLATOW: Yeah.

RUSS: A million is only a hundred cubes, so if you'll think of anything, a hundred by a hundred by a hundred, it's a million a hundred of those by a hundred of those by a hundred of those. So, you know, a hundred by a hundred by a hundred inches is big and, you know, a hundred of those is bigger. But if you think in terms of small like a BB. I mean, a BB is 0.166 inches, so a hundred of them would be, you know, 16 somewhat inches, I guess, actually, yes, 16 caliber. So that could be 16 by 16 by 16 inches. So 1,600 inches or, you know, about 250 - I'm sorry, about 160 feet by so forth cube would be that many BBs.

FLATOW: Wow.

RUSS: It's actually pretty easy to think about if you just divide it into a hundred by a hundred by hundred because it can wrap our names - our minds around a hundred easily enough. And then seeing the size, X-size, a hundred times, a hundred times that.

FLATOW: All right.

RUSS: We got things like red boxes and BBs in buildings that we can wrap our mind around.

FLATOW: All right. Russ, thanks for calling.

Our number: 1-800-989-8255. Talking with David Schwartz this hour on TALK OF THE NATION: SCIENCE FRIDAY from NPR News.

A lot of different ways, David, to think about these numbers.

Mr. SCHWARTZ: Yeah, there are. And, of course, you know, when we're talking about something like a trillion dollars, we can think about what it can buy.

FLATOW: Right.

Mr. SCHWARTZ: And I saw a calculation that $1 trillion would be enough to buy thousand box of girl scout cookies for every person in the United States. If I tell you where to use the money.

FLATOW: It's only two years of the Defense Department budget, though.

Mr. SCHWARTZ: Yeah. That's right.

(Soundbite of laughter)

Mr. SCHWARTZ: It's sobering thought, isn't it?

FLATOW: Yes. It gives you an idea how fast that money is being spent when you think about…

Mr. SCHWARTZ: Oh, yeah.

FLATOW: …how fast you have to spend it to get rid of it.

Mr. SCHWARTZ: Per second, right.

FLATOW: Yeah.

Mr. SCHWARTZ: If people used to like to do calculations about how fast Bill Gates earns money, you know? They figured out that if he were on his way to work and he saw a thousand dollars on the ground, it wouldn't be worth his while to pick it up because he earns more per second than the time we'll take to pick up a thousand dollars and put it in his pocket.

(Soundbite of laughter)

FLATOW: 1-800-989-8255. Let's see if we can get another phone call in here before we have to go. Hi. Let's go to Jias(ph) in Berkeley. Hi.

JIAS (Caller): Hey. Hello, guys. I'd suggest people who want to communicate the scope of scale should lean on exponentiation but in a visual way of being express. The classic book on this is called "Power of 10."

FLATOW: All right. Thanks for your…

Mr. SCHWARTZ: "Power of 10" is a fabulous book. I love that book, and I drew upon that in a book I wrote called "On Beyond a Million." The idea - it zooms out…

FLATOW: Yeah.

Mr. SCHWARTZ: …10 times starting with a scene one meter by one meter and then 10 meters by 10 meters and if you keep going further out, many turns around comes back into inner space.

FLATOW: Is that Phil Morrison's book?

Mr. SCHWARTZ: Yes. Morrison and Charles and Roy Eames.

FLATOW: Here's a question from Renophin(ph), of "Second Life." How big is trillion nanotubes? If a nanotube is billion, right?

Mr. SCHWARTZ: Right.

FLATOW: So a trillion would be a thousand?

Mr. SCHWARTZ: Well, a trillion times, a billion would be a thousand. Yeah.

FLATOW: So.

Mr. SCHWARTZ: Tenth to the ninth times - tenths of 12 times, tenth of a minus ninth, so that would be tenths of third. Yeah.

FLATOW: Is there a number bigger than a trillion that it's almost impossible to get your head around?

Mr. SCHWARTZ: Well, of course. The numbers keep on going. Kids always like to say what's the biggest number and, of course, there is no such thing. No matter what number you name, we can name one bigger. But there is somebody - came out with this name, googol, and it's spelled G-O-O-G-O-L. It was actually a 9-year-old boy who came out with the idea of polling(ph) one with a hundred zeros a googol. And this is - kids love this. There are a lot of times were I go to schools and children know about the number googol and their teachers and their parents don't.

FLATOW: They think it's a search engine.

Mr. SCHWARTZ: It's such a fascinating huge number, but it's actually useless because there isn't a googol of any kind of physical object. The estimated number of atoms in the universe is way less than that. The estimated number of atoms in the universe is about tenth of a 72nd or 73rd power and googol is tenth of a hundred power. So, of course, it's way more. Yet, someone thought, well, we need a name for an even bigger number and they came out with googol plot(ph). You know what that is, Ira? A googol plot? That's a one with a googol zeros after it.

FLATOW: Wow.

Mr. SCHWARTZ: See if you write all those zeros.

FLATOW: Wow. We're going to start writing that now because we have to take time and say goodbye to you. We're running out of time.

Mr. SCHWARTZ: Well, thank you.

FLATOW: So that's the assignment for tonight - is to write a googol plot.

Mr. SCHWARTZ: A googol plot.

FLATOW: David Schwartz is author of many books including "How Much is a Million," "If You Made a Million," and "Millions to Measure."

Thank you, David, for taking out to be with us today.

Mr. SCHWARTZ: Yes.

FLATOW: And good weekend to you.

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