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How big is a trillion dollars?

| 9 Comments

I saw an article yesterday that tried to break down the idea of a trillion dollars into something the reader could visualize.

The article pointed out that if you stacked a trillion $1 bills (US) on top of each other, you'd form a stack that reached a quarter of the way to the moon--the stack would be nearly 70,000 miles high. (Alternatively, if you formed a hundred stacks of $100 bills, each stack would be 7 miles high.) As the article noted, that distance is still kind of unimaginably big by our normal scale.

So here's another way of looking at it:

Imagine laying out dollar bills, on flat ground, edge-to-edge, so that they cover the ground. Wallpapering the ground with dollar bills.

A dollar bill's dimensions are about 2.6" x 6.1" x .0043"

If my calculations are correct, it would take about $253 million to cover a one-mile by one-mile square. So a quarter of a billion dollars is a square mile of money. (In $1 bills.)

So $700 billion in one-dollar bills would cover an area of about 2700 square miles, or a 52-mile-on-a-side square. That doesn't sound like a lot to me in those terms. But think about it: Draw a line 50 miles long. Now draw three more 50-mile-long lines to turn it into a square 50 miles on a side. If you're familiar with the eastern US, you could take the state of Connecticut and draw a line down the middle of it; each half is about 2700 square miles. Now cover every single inch of the eastern half of Connecticut with dollar bills, and you've got $700 billion.

If that still doesn't sound like a lot of space to cover, note that it would take about 20 hours to walk along one edge of the square. Or think about driving, at freeway speeds, for 45 minutes, with nothing but a field of dollar bills stretching out further than the eye can see in all directions.

Okay, one more try: $700B in one-dollar bills (if packed perfectly) would fill a volume of about 28 million cubic feet, which is roughly half the interior volume of the Metrodome, the Minneapolis sports stadium. Fill a football stadium halfway to the brim with dollar bills, and there's your $700B. (I suspect that if you just tossed them in, rather than packing them perfectly, you'd fill the whole stadium. Though I imagine they would also compress somewhat with weight.)

Note: This entry is purely an exercise in visualization; it should not be construed as making any kind of political argument about whether it's a good idea or a bad idea to spend $700B. Also, this entry ignores all sorts of real-world constraints, like weight, and land not being completely level, and so on.

9 Comments


Jed,

Your descriptions are excellent--helps a lot to visualize it. How about another technique to understand what a trillion is...a couple years back, I wrote a blog entry about about how long it would take to hand over a trillion dollars at the rate of one $10 bill every every ten seconds (answer: about 31,700 years; a billion would take a mere 31.7 years). Below is a link (and just scroll past the first half of the entry, on Ray Bradbury). Come to think of it, I have just stolen my own thunder, so maybe there's no need to click on the link. But in any event, thanks again for showing me how to search a site on Google...it took about five seconds to find this entry:

http://www.journalscape.com/X_Zachary_Wright/2007-02-06-18:17/


Although the visualization part of it is, of course, interesting (at least to me) on its own merits, the point of the article, and of lots of similar articles, is to use the visualization as a rhetorical trick to convince people that the deficit (or debt, or stimulus bill, or whatnot) is unacceptably high. One rarely, for instance, sees an article asking us to visualize the market capitalization of the Coca-Cola company in dollar bills (more than $100B) or the GDP of the United States (nearly $14T) or the money spent on Super Bowl commercials (no idea, don't really want to know).

And as a rhetorical trick, it seems to me to be one of those things that is persuasive without logical merit. I mean, why dollar bills? Why not hundred-dollar bills? Why not bars of gold or pennies or Big Macs? The point is to show just how much a trillion is, but based on the idea that a dollar is a fixed size, which of course it isn't--the dollar bill is a fixed size, but the value is not fixed.

Thanks,
-V.


V,

I think visualization is a valuable tool because for most of us, it's hard to comprehend off the top of our heads what a trillion dollars actually is--it's not like a million dollars, where you can easily imagine it, or imagine the home (or ten Teslas, or what have you), that a million dollars would buy.

So it's hard to reach a conclusion or even an informed opinion on, say, the size of our national debt if you can't even imagine what a trillion dollars represents. You can always do things like compare our debt to GDP, or measure it per capita, but there's no good substitute for thinking about how much money $10.6 trillion (the current size of our national debt) really is.

Of course, I think the debt is too big and we are abdicating our moral responsibility to future generations by making it bigger every year. We spend over one billion dollars per day on interest alone on the debt, and it's about to get worse. A lot worse.

Finally, you ask a good question--why not hundred dollar bills? Well, in my example, it would still take 3,170 years to hand over a trillion dollars at the rate of one $100 bill every ten seconds. That's a lot of lettuce.



Just to keep this going, Josh Micah Marshall over at TPM has a nice chart showing the height (in miles) of a stack of dollars equal to the estimated cost of the stimulus bill versus the height (again in miles) of a stack of people equal to the number of unemployed Americans at this time.

The money is dwarfed by the people.

I hope that is a lesson to us all.

Thanks,
-V.


Sorry to have neglected this discussion.

Jay: Good visualization; I had forgotten that one of yours.

V: Yeah, true that this kind of visualization is usually used as a rhetorical device. But I'm more interested in visualization for its own sake. I have a sense of how much money a million dollars is; once we start talking about a billion, or anything larger, it becomes meaningless to me. So the part I'm interested in is the "on its own merits" part you mention--visualizing large numbers in terms of things that are familiar to people. To make that work, I probably should've chosen $20 bills instead of singles, and I probably should've given parallel images for a thousand, a million, and a billion.

Jay again: Yeah, I agree. I don't understand enough about economics to have a valid opinion on your third paragraph (I've even seen an economist argue that having a large national debt is a good thing)--but you know way more about economics than I do, so I'm happy to yield to your opinion on that bit.

V. again: Nice! Okay, so part of your point is, I believe, that a physical representation of size isn't the right approach to visualizing large amounts of money in real-world terms. A fair point. I would say that it's one useful approach, but that you're right that other useful approaches would talk about it in terms of buying power. But even that gets tricky. Jay pointed out that a million dollars is ten Tesla Roadsters--so a billion dollars is ten thousand Teslas, and a trillion is ten million Teslas. I don't think I can imagine ten million cars much better than I can imagine a trillion dollars.

But I think Jay's hand-over-money approach is a good example of an alternative approach: it's not showing buying power per se, but it's also not based on the physical size of the bills; it's giving a sense of the quantity by breaking it down into easily understood chunks of time. I think that's kinda neat.

Peter: You posted an insulting comment. I deleted it. If you post a replacement comment that isn't insulting but that argues that there's no need to visualize large numbers, I'll be happy to leave that in place, even though I'll continue to disagree with you.


Well, and Peter's argument was well worth deleting, not only being insulting, but clearly showing no understanding of the original post. Which, in case anybody else happens by, very clearly and explicitly is about visualizing a large number, rather than being about the stimulus bill or the deficit or any specific thing.

And I think that visualizing big numbers is both tricky and interesting. I think it's particularly difficult for people to grasp the difference between a million, a billion and a trillion--I mean, people know that a billion is a thousand million, but I still have a sense that a million here and a million there and pretty soon you're talking about real money. And you aren't. You're unlikely to leave a million dollars in your pants pockets every day for three years. Or, say, all the other 49 states could get a million-dollar-earmark every day for a month, and my state would just get one little billion. You know. Fair. And then to go from a billion to a trillion, well, that's huge.

But if you stop at a trillion, then you give the impression that a trillion dollars, being unimaginably huge (and it is) must be too big in some absolute sense. In fact, the trillion is dwarfed by the problem, which is very difficult to visualize because it doesn't come in 2.6" x 6.1" stacks. And, to be fair, the actual cost of spending a trillion dollars down the line also dwarfs the number. While your visualization gives the number a trillion meaning by visualizing it, that meaning is illusory at best, misleading more likely, and that illusory meaning gives it rhetorical power that I don't want it to have.

So while I'm all in favor of your visualization and Jay's and the work you both put into it as divorced from a policy discussion, I actually agree with Peter (tho' again, I'm glad you deleted his comment, and I feel bad about agreeing with his point even whilst recognizing his bad behavior) that visualizing large numbers in the context of a policy discussion is wrongheaded. The question becomes, then, whether it's possible to divorce such a visualization from policy discussion. Well, and whether the positive aspects of your visualizations outweigh the negative ones I see. Actually, there are a bunch of things to be taken into account, I suppose, if one isn't going to be an insulting jerk.

Thanks,
-V.


Interesting points, V. But I guess I'm not clear on what the alternative is.

Say you have a policy decision to make: say you want to determine whether to spend $x on something. Now say x is a number so big that it's hard to understand how big it is.

Saying that "visualizing large numbers in the context of a policy discussion is wrongheaded" seems to me to imply that we should make policy decisions without regard to how big the numbers are. But the size of the numbers makes an enormous difference. A policy decision about whether to spend $1 is (for a government, anyway) much easier than a policy decision about whether to spend a quadrillion dollars.

So if you don't believe it makes sense to try to try to think of gigantic numbers in contexts that we're familiar with, and if you do agree that "it's particularly difficult for people to grasp the difference between a million, a billion and a trillion," then on what basis should policy decisions involving large amounts of money be made?

If it's true that "the trillion is dwarfed by the problem," then to me that suggests that there should be a visualization comparison. Put together a way for people to make sense out of the phrase "trillion dollars"; put together a comparable way for people to make sense out of the cost of the problem; compare them. If you have to spend money to solve a problem, then you're putting a financial value on the problem; I like the idea of giving people tools to help them decide whether the amount of money being spent is worth it.

To put it another way, where you're seeing two options here (pure visualization of a large number divorced from context vs rhetorical use of visualization to claim that a number is objectively too big), I'm seeing three: those two, plus a middle ground of using visualization to get a grasp on very large numbers in order to make some sense out of them in real-world contexts. It sounds like you only encounter these visualizations in the context of someone making a rhetorical point, so I can see finding that annoying. But I think they can also be a valuable tool for people who aren't arguing for a specific course of action.


Well, and I don't think that we need to visualize a trillion dollars to decide whether it's the right amount or not for a particular problem, any more than we need to visualize 10,779,215,329 to know that it's 47 to the sixth power. In fact, I don't think that visualizing ten billion helps with that at all. Imagine having, say, 47 pennies, a handful, more or less, and asking what that number to the sixth power was. Now visualize ten billion pennies; I won't bother doing the actual visualization, but clearly it wouldn't fit in your house. That's obviously too many pennies.

In a more serious example, let's say you wanted to figure out how much to save for retirement. You want enough to maintain your lifestyle, for some actuarial number of years, but there is a point at which the marginal benefit of adding to the retirement account is less than the benefit of using the dollars now on entertainment, education and easy chairs. In what way would it help to visualize a million dollar bills?

The CBO is projecting a $2.9 trillion shortfall (according to Paul Krugman) in output over the next three years, so we could use that. Now, we could just say: the projected shortfall is almost three trillion dollars, the planned stimulus is well under one trillion dollars, so it clearly is dwarfed by the basic economic problems. Or we could say that the stimulus falls short of the shortfall by enough dollar bills to fill the Metrodome up to the roof, even if they were stacked perfectly. The latter has more rhetorical power, but it's not any more accurate or easier to understand, and it's that unearned rhetorical power that gets up my nose. And the two things being compared are not really comparable; the spending being definable by Congress and the shortfall being an estimate of a constantly changing real situation.

And the policy arguments shouldn't focus on the size of our stacks. We should be debating (a) what sorts of spending will actually alleviate the problems most effectively, and (2) where we should choose the point between the ultimate cost and the near-term benefits. It isn't just putting a financial value on the problem. If we could buy Problem-Solving Dust by the ton, and it was just a question of how much we buy, that could be a visualization issue. But it's not. It's--well, I don't want to lecture about all the various things that are in the package, as I'm not even following it all that carefully, and you can get better information elsewhere. My point is that the visualizations are reductive, which doesn't make them bad as visualizations, but makes them bad as policy arguments.

Thanks,
-V.


..."what sorts of spending will actually alleviate the problems most effectively"...

I would also suggest we should not just consider what sorts of spending will help, but will ANY sort of government spending help. Everyone seems to be focused on the 'how much' and not even looking at 'should we'.

Visualizations are great mental exercises, but when dealing with the economy, I don't think we should forget people's natural reactions in times of uncertainty.

If you are unsure as to how long you will have a job or if unsure that your company will have capital to use, if I then come along and give you cash (or hire you for a job) - say $1,000 - most people's initial gut reaction is to store it away safely in case it gets worse later and it's needed for survival, not necessarily looking at that $1,000 as something to loan out or use now.

So you'd have to ask, how much money would the government have to print to convince people that this one-time windfall will fix the economy and the people don't have to save what they get for future survival. If it's not actually going to stimulate the economy, is it doing anything but spending money that our kids who will have to pay off? The money DOES have to be paid back at some point.

--Obviously, I'm not an economist...
Thanks,
-B


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