AIG bonuses = 165 million
As xkcd points out, there is a big difference between a million and a billion.
Many others have weighed in on the same point, the bonuses are only a minute fraction of what AIG got in bailout money. Others, Obama included, have pointed out that the amount of money is not really the point, but that the perception of those who got us into this mess being rewarded (with anything) is really stirring up the popular rage. I think also the very word "bonus" is also a problem point, which is why its defenders are trying to rechristen it "retention pay".
To me, this debate, and our popular understanding of the financial crisis also points out some limits of our national intelligence, but really about the constraints of human intelligence. In some ways, I think that this financial crisis is partly us flying too close to the sun, using the metaphorical wax wings of our limited number sense. I'll muse more about this in my next post, about why we are all bad at statistics.
Some of these points are taken from this piece by Jim Holt in the New Yorker on the work of Stanislas Dehaene (among others) in how our brain understands numerical concepts.
A few main points arise from the bulk of this work:
1) We are much better (faster, more accurate) at dealing with small numbers in our heads than big numbers. That doesn't sound like such bad news. But wait.... Big numbers start at 5.
2) The way that our brain represents addition and subtraction varies tremendously from how we represent multiplication and division (multiplication and division never come naturally).
3) The connection between number and physical space goes, as Dehaene puts it "very, very deep in the brain"
What does this mean for the financial crisis? Let's take number 1. The press can throw around "around 150 billion" and "around 687 million" and that actually means something very different to our brain than saying 1 or 2. Getting above 4 makes things more difficult for our brain, above 100 is like a second language you have a little practice on, above 1 million just doesn't really make sense. I think the big fuss about bonuses is because it is finally getting down to a scale that people can halfway understand. What much of the financial press, the politicians, and the financiers themselves do not understand, is that when they say the word "million" "billion" or "trillion" they are speaking in a different language than most of us understand. They have an understanding of these in the context of their business, in which they may have daily practice with scaling these numbers (it still doesn't come naturally to them, but they have extensive training). But most of us rarely think about numbers much larger than 20, and when we do, we probably need to sit down with a pen and paper. 1 billion is really more of anything than just about anyone ever has cause to think about.
For number 2, quick, what is 7 times 8? The only reason you know this is because you have memorized it as a fact. Just like the capital of North Dakota or what's the longest river in Africa. You may have memorized it well, but that doesn't make it any less arbitary to your brain that the other two facts. How many people in your high school class? How many of those would fit in 1 billion? Again, your brain has to go through a set of operations that you were taught, and this does not come naturally.
Number 3 illustrates why efforts to make us understand these numbers, like the example of your high school class above, will ultimately fall short. Our brain's understanding of number
is tied to physcial space (actually, our brain's understanding of just about everything is tied to something physical or related directly to our body). Which means, since your brain didn't evolve to understand what 1 billion is, it won't really help to tell you that it would be 20 million of your high schools. It doesn't help you all that much to understand that a stack of 1 billion one dollar bills would reach up to the moon (or wherever) and back. Why? Who can jump to the moon? Our understanding of physical space is related to our body, and again, anything over a small distance is quickly abstract and we need tools to understand it. What is a mile, really?
So, what is the message of all this? Well, first, people watching the news, etc, can't really understand what a billion or a trillion is. Maybe they can understand that in the past, when our government had to borrow money we had to borrow around 10 percent or so (oooh, percents, that we can understand, why? food). As the CBO says ( on "The Director's Blog" sounds like some awful DVD extra feature) :
Debt held by the public would rise, from 41 percent of GDP in 2008 to 57 percent in 2009 and then to 82 percent of GDP by 2019 (compared with 56 percent of GDP in that year under baseline assumptions).
Now wasn't that easier than me talking about trillions and billions?
So, using this as a model, I would really like to see a lot more pictures of numbers like this:
Here is one example. If more people understood this simple pie chart, I think we'd have a more honest debate about budget policy.
Or how about this one:
We have an Elements of Style for prose, which is built with around a sophisticated understanding of cognitive limitations for understanding language. Now what we need is an Elements of Style for presenting numbers with a similar understanding of our limited abilities.
Edward Tufte has been harping on this point for years (even trying to write that book), as are some out there designing great graphics. But I think there could be a lot more.
Again, this isn't necessarily because of a failure of our math education system (although it may be partly that) but it is at the root a limitation of the human brain. We should acknowledge that and try to design our expressions of numbers to be clear and to the point. In the same way news anchors and print journalists alike don't use five seven-syllable words in a sentence (see how that was actually much harder to think about than two three-syllable words?) they should stop using billion and trillion as if we all understand exactly what that means.