Proofiness: A look into how mathematics relates to American political life

Dearest readers,

This is my first post on The Virtuosi, so I thought I’d take a moment to introduce myself.  I’m a first year physics graduate student at Cornell, recently joined after 2 years working as an engineer first at a private firm and then at a national lab.  I myself have had lots of fun following the exploits of my estimable colleagues here on The Virtuosi, and I thought I could bring a new angle to the content here.   I would like to use this space to discuss how science interacts with everyday life in a cultural sense. How does science appear in popular culture?   How do political or social issues relate back to science? Those sorts of questions.  (I understand that there are plenty of other resources elsewhere that offer far more intelligent insight into these matters than I can, but in the very least this will give people a chance point them out to me as they yell at me in the forum below.)

Enough intro, here begins my very first blog post:

Being interested in how science is communicated to the public, I am an avid reader of popular science.   While academic types sometimes dismiss this kind of writing as shallow or otherwise uninteresting, I think science writers perform a very important function serving as a way to convey information about conceptually challenging topics to a general audience.   At their best, I find that these books serve as examples for how I can communicate my own ideas better, and in addition challenge my understanding of how science relates back to society in general.

A Sense of Scale (in Dollars and Cents)

I hate politics, but for some reason I obsessively read about it.  I don't know why I do this, but I assume it's the same reason people slow down for car wrecks and pay to see the geek [1].  Anyway, the big thing in political news now is that if Congress can't pass a budget [2] by the end of the day Friday, the government will shut down.

Shutting down the government means that 800,000 federal employees will go without pay [3], lots of services will be put on hold and you won't be able to go to the Smithsonian or the Grand Canyon.  So it's kind of a big deal.  Since the ramifications of a government shutdown are so serious, there must be some really important disagreements holding it up, right?  Right?

A quick search (for example, here), shows that the big hold-up in passing the budget comes over a disagreement on how much money should be cut from the budget.  Republicans want to cut $40 billion dollars and Democrats are willing to cut $34.5 billion dollars.

So the hold-up is over $5.5 billion.  Let's consider how utterly and stupidly insignificant this is.

The Law and Large Numbers

Human beings are not equipped for dealing with large numbers. Honestly, 7 thousand, 7 million, 7 billion and 7 trillion all register about the same in my mind, namely 7 big. Unfortunately, there is a world a different between each of these, three whole orders of magnitude, a thousand, the difference between lifting me and a US quarter.

This lack of respect for orders of magnitude has really been rearing its head recently with most of the political discussions surrounding the US budget.

Turns out the US Budget is really large. In 2010 it weighed in at $3.55 trillion. Thats big. Really big. So big that I can't fathom it.

Without getting too political, there has been a site going around recently; the You Cut program, which invites public suggestions for cuts to be made to the budget to try and fix the deficit. Now, personally, I believe we ought to do something about the deficit. To this end, I think it is useful to point out the scales involved. In particular, the link I gave above is to one of the suggested cuts: federal funding of NPR (Disclaimer alert: I love NPR), which weighs in at 7 million dollars.

Seven million dollars is a lot of money. A lot of money, more than I can imagine having personally. But to suggest that a 7 million dollar cut is any sort of progress towards solving a $1.2 trillion dollar deficit is a little amusing. As a fraction, this comes out to

\[ \frac{ 7 \text{ million} }{ 3.55 \text{ trillion} } = 2 \times 10^{-6} \]

Two parts in a million. To give a sense of scale to this, the gravitational influence of the moon on my weight is:

\[ \frac{ \frac{ G M_{\text{moon}} }{ R_{\text{earth-moon}}^2 } }{ 10 \text{ m/s}^2 } = 3 \times 10^{-6} \]
Three parts in a million. So, suggesting that you have made real gains in reducing the US budget by cutting federal funding for NPR is as silly as suggesting that if I want to lose weight, my first concern should be the current tides.

[I want to point out that I don't really mean to get too political, and that I've noticed both parties pulling these kinds of numbers tricks.]

So, wanting to get a little better understanding of the numbers at stake, I collected some data (all from the 2010 budget). My goal is to attempt to represent how the US government spends its money.

Before I begin I need to plug two great tools towards this end: Here the NYTimes graphically represents government spending, helping to give a sense of scale to different categories. Here the NYTimes lets you try and balance the budget, not only for next year but down the line, letting you choose from a wide array of proposed changes.