Math

When I was in college (too many years ago to mention), I ran across an excellent book: Metamagical Themas: Questing for the Essence of Mind and Pattern, by Douglas R. Hofstadter. It's a collection of essays Dr. Hofstadter, a (or rather, as I think of him, the) Professor of Cognitive Science and Computer Science, wrote for the magazine Scientific American. This book should be a part of everyone's library; it is a fascinating collection of explorations into the way humans think, what creativity is, and the magic of music and math (yes, I did just say "the magic of...math"). Of the many articles that grabbed me, one of them is titled "On Number Numbness". In it, Dr. Hofstadter talks about very large (and very small) numbers, and how difficult it is for people to conceptualize them. In his discussion of trying to comprehend large numbers, he refers to a conceptual practice called chunking, in which you create a unit of something easy to comprehend, then describe very large numbers in terms of numbers of that unit. For example, while discussing the fact that at the time of his writing (he wrote the book during the Cold War), there were enough nuclear weapons in the world to equate to 25,000 megatons of TNT. That's another way of saying 25,000,000 tons (or 50,000,000,000 pounds). He pointed out that one ton (just 2,000 pounds!) was estimated to have been the amount that brought down the Marine barracks in Beirut (241 people killed), and so further estimated that ten tons, well-placed, could be expected to kill about 2,400 people.

Last summer when I visited Paris and climbed the butte of Montmartre, from the top of which, at the food of the Sacré Coeur, one has a beautiful view of all of Paris spread out below. I couldn't refrain from ruining my two friends' enjoyment of this splendid panorama by saying "Hmm... I bet one or two nicely placed megatons would take care of all of this."

He then points out: "Now if you just say to yourself 'one megaton equals Paris's doom' (or some suitable equivalent), then I think that the phrase '25,000 megatons' will become as vivid as the long string of zeros--in fact, probably more vivid."

This got me thinking. At the time I read his article, our deficit was 1 trillion dollars. I knew that that was a lot, but how much was it really? I broke it down and it turned out that you could buy a very nice $4,100 laptop for every man, woman and child in the United States (at that time, the population was 243 or so million people). Today, our population is just short of 300 million, but the prices have come down, so that a trillion dollars could roughly pick you up something like one of these $3,500 babies for everyone in the US.

I bring up all of this business about number numbness because last weekend was the 143rd anniversary of the Battle of Gettysburg. My husband and I went up there (by way of Manassas, stopping by Antietam on the way back home) and spent the weekend walking around. The big reenactment was, alas, postponed until this upcoming weekend, but we still got to see some reenactors and, of course, nothing beats just being able to explore. This is the second time I've been there (I first went there with friends James and Nathan) and the first time for my husband, Pat. A couple of things got me: one was the fact that many monuments (and, in fact, the Lincoln's Gettysburg Address) say things like "the world will little note, nor long remember what we say here, but it can never forget what they did here", and it's depressing to think that most Americans are aware of the Gettysburg address but a staggeringly large number can't even tell you in which century the Civil War occured, much less what happened. The other was the sheer scale of the war's effect on the population, especially in the number of people who died. The most common rough number I can find from various sources is around 620,000 deaths (from the low end of about 360,000 to the high end of 1 million). The park ranger at Antietam said that 2% of the total population (about 34.3 million people) died in the Civil War. That's a pretty big number. What does it really mean?

The Ohio section of Gettysburg National Cemetary:

Thank You, Sweet Buckeyes

I'm a big believer in walking the ground. Pat and I walked Pickett's Charge (something I'd done with James & Nathan) in order to get a real feeling for the distance. It doesn't seem far until you walk it and imagine being shot up by cannon the whole totally-no-cover-anywhere way. In the same way, I think that if you're going to think about large numbers that have to do with profoundly emotional events, you should relate them to profoundly emotional events you have personally experienced. September 11th was pretty emotional for me, so I decided to figure out the Civil War in units of "September 11" -- about 3,000 people dead, an almost too-large number by itself, but one I can still (horrifyingly) grasp.

First, I think the key number about the Civil War is this: 2% of the population. If we lost 2% of our population (300 million), how many would that be? That'd be 6 million people. How many September 11ths would we have to have to lose 6 million people? Let's see: 6x10⁶ divided by 3x10³ = 2x10³. That's 2,000. There are 365 days in a year (ignoring the occassional leap year, since we're estimating). Two thousand divided by 365 is about 5.5. In other words, 9/11 would have to happen every day for five and a half years in order to lose an equivalent of the population today as was lost during the Civil War. That's mind-boggling by itself. Can you imagine what that would be like? Over the three days of Gettysburg, about 50,000 people were lost, which was about .15% of the total population at that time. Today's equivalent: 450,000 people. That's one-hundred fifty 9/11's. And at Antietam, a one-day battle, about 23,000 people were lost (.07% of the population). Today's equivalent: about 210,000--seventy 9/11's in one day. So far in the Iraq war, about 2,500 soldiers have been killed. When Sedgwick's division barrelled into the West Woods near Antietam Creek to attack the retreating Confederates, he found himself enveloped on three sides and lost almost that whole number in ten minutes.

I don't say all of this to make light of the number of people who died in 9/11, or of the number of soldiers killed in Iraq. Instead, I mean to really understand, on this anniversary of the Battle of Gettysburg, what the scope of the Civil War was by relating it to something that has affected me personally and deeply. Even when chunking those numbers down, they are still incredible. This was one of the heavier prices of union, without which the US would not be where (or how) it is today, and it is something that should take some deep thought. For all of its faults (and there are always many), I think that the US is unique in the history of the world; I am glad to be here, and very mindful of the freedoms that I both enjoy and defend. Walking that ground had a profound effect on me. But the math did even more.