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Wednesday, July 20, 2011

Very Big Numbers

During the Great Budget Debate, we’ve heard some pretty enormous figures and values thrown around.  And I’m not being a smart-ass when I say it might be worth it to take a minute and talk about what those numbers truly mean.  If we don’t intuitively grasp the scale of these values at the same speed that we hear them, our ability to think critically about what they mean is diminished.

Unless you’re a financier accustomed to managing millions of dollars at a time, or an astrophysicist who measures a ray of light's path over billions of kilometers, you probably don’t have an easy understanding of really large numbers. 

Why would you though?  In our daily lives, do we rarely have occasion to even be able to count over a few thousand?  We don’t buy apples by the trillion, or measure our drapes by the quadrillionth of an inch.  We might vaguely know what the words mean, but without that frequent usage, we don't understand them on the natural, automatic level that we grasp smaller numbers.

I’ll let you in on a secret.  I’m not comfortable with huge numbers either. 

So here's a little trick I'll pass along to you:  to handle any number of any size, you only need to be able to count up to "1000."  You can always just take humongous numbers, and scale them down to good old "1000," and be whizzing around the number line in no time.

Here's the key to the "thousand trick."  Imagine any large magnitude base 10 value (aka an "-illion" number).  A billion.  A trillion.  Whatever. 

Now visualize that "-illion" as this...


...and think of all the "1"s, the single items of the above integer, the smallest ranking place it has, as the "-illion" that comes before the "-illion" you are looking at.

So for example, if we’re talking about “a billion dollars,” picture in your head:

1000 things

But keep in mind each one of those “things” is actually a “one million.”  (It might help to envision 1000 poker chips, each chip worth $1 million.) 

If you hear “a million,” think about 1000 again, but remember each one of those “1”s now is representing “a thousand.”

Then the pattern then just repeats and repeats all the way up:

If "1000" was read "one trillion," than "1" would be read "one billion."

If "1000" was read "one quadrillion," than "1" would be read "one trillion."

If "1000" was read "one quintillion," than "1" would be read "one quadrillion."

Example:  if we pretend for a second that "1000" is how you write "a billion," then "2" would be "two million" (million being the "-illion" that comes before a "billion").  "100" would be "one-hundred million."  "37.4" would be "thirty-seven million, four-hundred thousand."  You get the drift.  

So “500 million”?  Obviously, that’s half a billion (500 of "1000").  “3 billion”?  That would be three thousand millions.  “$14 billion”?  Imagine 14,000 individual millions, and your there.  

Think you got it?  Prove it!  Take the below quiz.  (To view the correct answer, place your pointer near the ->, click and hold the left mouse button, and drag your cursor straight across to the right.)

one and a half trillion = ? billion
                 ->     1,500

10000 billion = ? trillion
    ->    10

.002 billion = ? million 
    ->    2

1.781 trillion = ? billion  
    ->    1,781

Keeping this in mind, we can talk about the national debt in a language that we are familiar with, and at a scale we intuitively comprehend.  Neat trick, huh?

In 2011, the Federal government is going to be somewhere to the tune of one trillion (maybe even one and a half trillion) dollars short as it tries to pay to do everything a federal government does over the course of a year.   They'll have to borrow to make up that gap.

Put yourself, then, in the federal government’s shoes.  Imagine that you know over the next year you have $1000 dollars in bills coming up that you just won't have the cash for.  Either you'll have to cut expenditures, make more money (if you’re a government, you do this by raising taxes), or borrow funds from willing institutions, friends and relatives.

You and I know that one trillion can be written "1000" - as long as we keep in mind that each "1" is actually a billion – and now we've got you and the fed’s budget gap scaled down to the same size.

So, what would you do to fix your financial situation?  Sell your car?  Cancel the cable?  Pawn the furniture?  You'll have to do something drastic.  $1000 is quite a lot of scratch to pull out of thin air. 

There was a lot of mumbling this past year about NASA's eighteen-billion dollar a year budget.  Sounds like a big number.  But if the 2011 Federal Deficit was $1000, we know scrapping NASA completely would only save us $18.  We would still have another $982 to come up with...So where do you suggest we take it from?

If the 2011 Federal Budget gap was scaled down to $1000, than proportionally speaking:
o   The Department of Defense budget would be worth $640 (only $160 of that is for the Overseas Contingency Operation, aka The Global War on Terror)
o   Medicaid appx. $250
o   Medicare appx. $600
o   Social Security $700
o   The Department of Homeland Security $55
o   The National Science Foundation $7
o   The Department of Agriculture $100 ($60 of that for Food Stamps and WIC)
o   The entire Peace Corps $0.0004
o   The Department of Education $32
o   The Department of Housing and Urban Development $44
o   The FBI $8
o   The FAA $16
o   The US Department of Transportation $79
o   The Environment Protection Agency $10

The list goes on.  I encourage you to get online, go to these programs’ websites, or to Wikipedia even, and search for the budgets of other federal programs.  See how they stack up against the US’s one trillion, 1000 billion, 1000000 million problem. 

*NOTE: Most of these values are the past year’s expenditures.  Its the best I could do.  For most federal programs, this upcoming year’s budget is still a big question mark.

Politically speaking, it’s easy to suggest making up the gap in our budget by cutting those peripheral, lower profile programs.  In the long run you'll get less resistance and more successes, since they aren't the sacrosanct "American institutions" that we are so averse to altering. 

          However, even cutting those government side projects completely out of the budget would just be bailing out the Titanic with a teacup.  Any serious discussion about America’s financial situation needs to address our major expenses, those being defense, Social Security and healthcare.


  1. Great post, Dan...

    The National Science Foundation $7

    Oh, oh my, it hurts. It looks like congress will let us poor non-health scientists get away with no budget increases. We should consider ourselves lucky. Shrimps on treadmills indeed.

  2. Thanks Dave!

    I remember the shrimp on the treadmill! That one was a lightning rod, I bet because it was so damn bizarre. I looked it up online, found that one cost $560000, so $0.00000056 of America's "$1000" (by which I mean a trillion bucks) shortfall!

  3. So, I decided to take your $1000=the $1 Trillion Dollar Gap example a little further.

    I was able to find that the total budget at the moment would be $3,820. Okay, so we need to cut a third of the budget. Adding up your Defense, SS and healthcare costs above (the big programs), I get $2190... so there's $1630 in the other stuff.

    Not clear to me whether the remainder is made up of small programs or if there are any identifiable big fish in there. I've tried doing internet searching, but I can't find any .gov site that just gives just a simple list of the money spent on all programs. I know it exists; I remember printing out an excel spreadsheet of the 2001 budget when I was a first-year honors student at UB. Just can't find it.

    While searching around, I did find two very good visualizations of the budget:

  4. I actually had a post on my facebook wall about the shrimp... turns out the program was about doing disease ecology of shrimp, and the way to figure out how infected a shrimp is to put it on the treadmill and see how much oxygen it is using to keep pace. The fact that it produced great youtube videos of shrimp on treadmills was a happy accident.

  5. Very cool links!

    I might as well make this public: that death and taxes poster, I'm really into that. I have a copy of that poster hanging up in my living room, and used it in a previous post on the National Debt (

    The only caveat I'd make though is these are both PROPOSED budgets. The final product could wind up looking much different. BUT not trillions of dollars different! I have heard the 3.8 trillion figure a bunch, but I'd guess that in the end it will clock in closer to 3.5 trillion (3,500 billion), but hey, what do I know?

    You're right though, Defense spending, Medicaid/Medicare, Social Security, Welfare and Unemployment have made up about 75% of the Fed's spending in recent years.

    Go here to check out LAST years budget to get an idea of what our spending typically looks like:

  6. I knew I'd seen it somewhere! I kept thinking it was a post office, but now I realize it must have been your living room...

  7. I love this trick. When I read about government spending and such, I usually skip over numbers and substitute in the words "some ridiculously big amount."

    Thanks for the perspective. Now if you could explain Greece in a way I could understand...

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