[Hat tip: JT at Between Two Worlds. If video isn’t displaying properly, look here.]
NOTE: This visualization applies to almost any “budget cuts” you hear about from any government administration, no matter which political party is in charge…
Related Links
I’ve mentioned this one before, but if you haven’t seen it, it’s well worth looking at:
And from the often rude and usually funny webcomic xkcd:
Denise Gaskins' Let's Play Math 
Dear Cartoonist (and video maker),
The fact that YOU have obviously recently discovered the mathematical difference between a million and a billion does not necessarily make the rest of the population as clueless as you are.
If you want to label FACTS as “dishonest,” so be it. My five-year-old would be good intellectual company for you.
Now, Joshua, you surely know the difference between facts and presentation! Do you really think that most people have an accurate mental grasp of different orders of magnitude? The “small pile out of a bigger pile” image in the video is exactly the way my mind works, even though I know better when I take the time to think about it.
The problem is that presenting the data in the way most people are used to seeing it does not make the presentation dishonest.
The implication–more from the cartoon than the video–is that someone is trying to pull the wool over our collective eyes. I don’t buy it.
Joshua – the point is that no one has to _try_ to pull the wool over our collective eyes. It happens because we are uneducated about numbers – I believe the term is innumerate. I have been teaching junior high, high school, college and university level, and now community college mathematics since 1962 (47 years) and I know that many of my students have no real idea of how much a billion or a trillion actually is. I will be sharing with them next week the one about what one trillion dollars looks like as well as the examples on this page.
I also think we often have the wool pulled over our eyes because those who present these things don’t know any better. A journalism student once wrote Marilyn Von Savant (world’s highest IQ, writes in Parade magazine) to ask why she needed to know math to write newspaper articles. Marilyn asked her how she would write about the GNP if she didn’t understand the underlying math. You cannot explain what you do not understand yourself.
Comparing things with the same unit is a basic tenet in elementary school math. You cannot compare feet to miles – you either make them both feet or both miles. Those of us who are numerate understand how important this is.
Joshua – the point is that no one has to _try_ to pull the wool over our collective eyes. It happens because we are uneducated about numbers – I believe the term is innumerate.
That’s actually NOT the point. People aren’t “uneducated” about numbers; they’re “uneducated” about big numbers. But that’s not ‘just there.’ There’s a reason–people don’t normally traffic in millions and billions.
So, that’s NOT the way “your mind works.” It’s not something you were born with. You just don’t have sufficient experience dealing with those “orders of magnitude.”
I have been teaching . . .
Let me just stop you there. Irrelevant.
I also think we often have the wool pulled over our eyes because those who present these things don’t know any better.
Really? Should the administration feel GUILTY about not making YouTube videos involving pennies in order to make it clear to those who think that their first, gut reaction to numbers must be the right one?
Comparing things with the same unit is a basic tenet in elementary school math. You cannot compare feet to miles – you either make them both feet or both miles. Those of us who are numerate understand how important this is.
Um, 5,280 feet = 1 mile. Look at that; I just compared them. Please.
By the way . . .
Now, Joshua, you surely know the difference between facts and presentation!
Spare me the school marm tut tut and tell me what you think. Be bold!
Well, that’s the first time I’ve been called a school marm. 🙂
Here is what I meant: The cartoonist is not calling the bailout facts “dishonest.” A fact is just a fact, and it cannot be honest or dishonest. The cartoonist is calling the presentation of the bailout facts “dishonest.” Perhaps “misleading” would have been a better term, since I’m not sure that he meant to imply any malicious intent. But being a provocative guy, he chose the stronger word.
News organizations are supposed to communicate information as clearly and accurately as possible. To ignore the fact that most people have no intuitive sense of the difference between million, billion, and trillion — to treat those words as if they actually have a meaning other than “big pile” to the average viewer — is to fail in communication.
Teachers also are supposed to communicate information as clearly and accurately as possible. As math teachers, one of our jobs is to help our students understand big numbers. I think the links in this article do a good job of that.
A fact is just a fact, and it cannot be honest or dishonest. The cartoonist is calling the presentation of the bailout facts “dishonest.”
I understand this. My point–or at least one of them–is what I said above: “presenting the data in the way most people are used to seeing it does not make the presentation dishonest.”
The cartoonist says: “Stop giving large numbers without context or proper comparison.”
What the hell are they SUPPOSED to say? People DON’T say “170,000 million.” I mean, really. It’s like me saying that I would like 5,670 cents on Pump 7, please.
The argument is that because ‘people’ don’t understand large numbers, it’s wrong to use the presentation of accurate place values, like billions or trillions, to make your case.
Can no one see how completely stupid that argument is?
Now we move beyond the math to argue ethics: Should the news reporter be trying to make a case — and if so, what case?
The obligation to communicate clearly is not satisfied by saying, “That’s how everyone says it.” There is always more than one way to say something. For instance:
* Would people have reacted as violently as some did, if the media had reported that “0.1%” of the money was spent to pay contractually-obligated employee bonuses?
* Would voters believe that politicians are trying their best to control spending, if the media reported that administration officials set aside 90 days to figure out how to chop “0.003%” from the federal budget?
If reporters (and if we as teachers) want to communicate accurately and clearly, we must use the numbers AND put them in context.
I disagree.
In the case of typical reporting, yes, one’s clarity obligations are pretty much met if one uses billions instead of millions to refer to a number that is in the billions.
Would people have reacted as violently as some did . . . ?
Why is the reaction important?
How the listener reacts is an indicator of what was communicated. Or of whether communication happened at all. As teachers, we know that information does not equal communication — we can put information in front of our students, but we have to watch their reactions to see if they understood what we meant.
We have to watch their reactions to see if they understood what we meant.
No doubt. But if they don’t get it, that doesn’t necessarily make you dishonest. Education (if we’re going to make this discussion about it) is not a one-way street. If what you’re saying to your kids isn’t working, that doesn’t give you license to make up a whole new set of “somethings” that DO make sense to them.
But forget education. What I’m responding to is a group of adults who seems to think it’s unfair that their government “communicates” to them with standard, accepted place-value indicators like trillions, billions, and millions.
No, no one came out and said, “Hey, just keep in mind that a million is a million times smaller than a trillion.” But why should they say this?
If you enjoy this sort of big-number visualization, the guy* who made the video above has another one:
The National Debt Road Trip.
*His bio: “I’m a lapsed math geek and and information visualization geek. I have my political opinions, but my real concern is getting the math right.”