Add It Up

Today, another rant about a Newsweek column; this time, it's not Anna Quindlen, but the topic is definitely strongly related to feminism.

Sharon Begley, Newsweek's science columnist takes a moment to speak up on a subject near and dear to my own heart: sexism and stereotypes about learning ability. ("Math is Hard, Barbie Said") See, just in case you're not aware of it, American girls have a hard time with math, generally finding it too challenging for them, and thus we find that there is a clear gender gap in ability and achievement in this area. The thing is, though, it's all (as they say) in their minds.

I love parenthetical statements, don't you? (Okay, maybe it's just me.) "As they say" is really the operative phrase here. The fact is, while girls in America and Japan have consistently lagged behind men in mathematical ability, that gap has been far narrower in communist nations where supposedly they take a more liberal view of the ability and worth of the individual, regardless of gender. It would seem--and to many of us, there's no surprise to this--that girls do badly in math because society has told them that they will have this failing.

The result, according to Begley is something more than simply a self-fulfilling prophecy of "Tell somebody they can't do something, and they probably won't be able to do it," but actually an emotional response. Tell a girl she can't do something, and even if she doesn't believe you, the fact that you gave her discouragement will cause a distracting emotional reaction. How well are you going to be able to focus on factoring a polynomial when half your brain is screaming out to you, "How DARE they say that!"

This fact is very personal to me for two reasons. One of them is that despite that my degree is in mathematics and I know I tend to be very good at it, there was a time around fifth and sixth grade when I struggled with math. I had a couple of math teachers who, instead of encouraging me to do better, essentially took time and effort to embarrass me and tell me I was a failure. I never considered the fact until just now what a boon it was for me to have a seventh-grade math teacher who was completely incompetent. I've always wondered how a guy like that ended up teaching math when he obviously had no skill in the subject, but in retrospect, I wonder if it helped stroke my ego to recognize that my own ability was better than the teacher. (This was the first of many teachers that I had the habit of viciously correcting on a daily basis, pointing out his errors at every opportunity, which came frequently. On the same note, it was probably oddly useful for his ego that he clearly just didn't care.) I realized long before seventh grade that mathematics was the method of understanding reality on a basic, foundational level, and seeing it taught with such ineptitude goaded me into always being the best I could be.

But I was lucky. As a boy, when I showed ability in math and science, society approved and egged me on to greater achievement. The second thing that's always bothered me about this topic, and this one even more so and more repeatedly at every chance it had to come into my mind, was the fact that my sister did not go into a college major in math or science. Sure, all things being equal she might still have chosen the path she did, and I'm not aware of any regrets on her part; she's been very successful in the things she's set her hand to as far as I am aware. What irks me is that I do feel she was shorted in the area of praise for her abilities. I became the math major in college, I was the one that people actually called a "math genius" repeatedly in high school. (Note that when you go to a small-town high school, and then graduate to a large university, you tend to find that most areas where you were considered excellent are now areas in which you are merely average; I don't claim to be anything special today.) Nobody ever called my sister a "math genius", but I always suspected that she was far superior to me.

Once when visiting home from college, I was rummaging through some papers in my mother's house, and came across some standardized test scores. A test taken sometime towards the end of elementary school revealed that while I was above average in my mathematical aptitude, my sister was truly the cream of the crop. Yes, my sister was the real "math genius", but where did that genius go? Fast forward from elementary and rewind from college to the beginning of my senior year. This is the time that you start looking at your grades and test scores and pick what schools you want to look into. The school guidance counselor called me into his office and informed me of what was supposed to be great news. I knew my SAT scores were good, but apparently, in my small rural county of Northern California, I had set the record of highest-ever SAT score. I might have reveled in that announcement if it weren't for the very following sentence with came before the first had a chance to sink in.

"And the person who previously held the record was your big sister!" I was told with a big grin. How about that, Brucker? Consider the irony! Oh, I did.

"Uh... Was my sister informed when she had set the record in the first place?" I asked. "This is the first I've heard of it."

The smile disappeared. "Um, well, I guess not."

"Why the hell not?!" I responded through gritted teeth, and I got up and left. I was always somewhat aware of the problem, but that day, it hit home in a special way. Friends come and go, but my sister will always have a special place in my heart, and I couldn't forgive the injustice done to her or to all our sisters everywhere. As I said, I get the impression that my sister was satisfied with the academic course her life took her on, but I can't help but feel that nonetheless she was robbed of a full set of options.

Thus comes the real problem, the larger problem as I see it. Sexism and racism aren't just bad, but hurtful things that cause often nearly irreparable harm. Our society is closing down gaps all over the place, but will the wounds of the past ever be healed? Within a few months, it appears we will likely have our first black President, but will a single black President make up for centuries of slavery and oppression? When the day comes that a woman is placed in the Oval Office, will that make up for all the years they were treated as slaves in attitude, if not in name?

Prejudice says, "We're not going to allow you to be equal." When pressed, it says, "Okay, you can have the right to be equal, but you will never really be equal." Eventually, after centuries of beating down the oppressed, be they members of a race, gender, or other social group, the members of the oppressive group ask the oppressed group, "Why are you so bitter about all that stuff? It's in the past!" There is a tendency to miss the fact that the fight against oppression is an uphill battle, and even when the playing field is leveled, it's hard to shed the weight of the past.

When Begley points out that the very fact of being told that you can't do something impedes the brain from doing it, she points out that it doesn't have to be personal. A girl doesn't have to be told that she is incompetent in mathematics, she need only be told that historically, women have underachieved in comparison to men, and the discomfort that sets up in her mind is sufficient to impede her thought processes. This is the sort of thing that goes beyond self-worth, and turns into an evaluation of the worth of the group to which one belongs. We tell people that they are inferior for long enough, and some of them believe it; among those who have the determination to not believe it, more than a few will still be burdened by the injustice of the sentiment.

You don't have to be a member of an overtly downtrodden group to experience this for yourself. Think about the situation we have here in America with respect to the learning of foreign languages. There's a joke I've heard a few times that goes like this: "A person who speaks two languages is called bilingual; a person who speaks three languages is called trilingual. What do you call someone who speaks one language? An American." Why is it that Americans have such a hard time learning foreign languages, but so many Europeans and Asians seem to typically speak three or four languages? I know Americans in general won't accept the argument that these people are somehow intellectually superior to us. I personally believe that we as Americans don't learn foreign languages because we've decided it's just too hard. This is not something indicative of any subset of the culture of the United States, but seems to pervade us in general. We either believe that we just can't do it, or we think we might be able to, yet we look around and note that few people are doing it and get discouraged. This isn't even the result of anyone acting prejudicial towards Americans, but merely a culture that has shifted into a sort of self-prejudice. Imagine if it were a matter of prejudice; instead of simply struggling through your language classes worrying about how difficult it is to conjugate verbs and learn the gender of nouns, you also have to keep thinking about how everyone's expecting you to fail.

But here's where my cynicism cuts in and takes over again. Begley points out that things are getting better for women, and they are beginning to be accepted more often as the intellectual equals of men, but will equality--true equality--be realized in our lifetime, if ever? If we as Americans can slip into a feeling of hopelessness over our inability to acquire languages without any sort of external oppression, how can people who have been actively pushed into a state of hopelessness rise above it? Perhaps asking such questions is largely adding fuel to the fire, but it needs to be said anyway.

I don't believe that we escape the evils of the past by simply trying to forget that they ever happened. We escape from them by actively fighting to overcome them. As a father of two daughters, there's a significant battlefront of this culture war located within my own household. It's a hard responsibility that's been given to my wife and me to see to it that our daughters are never told that they are any less capable of anything simply because of their gender. Really, that's the only thing we can do: try our best to raise up a new generation better than the past. Do we do this by never mentioning the sins of past generations towards their mothers and grandmothers, or by entreating them to actively strive to overcome the vestiges of that shameful past? I don't know the answer to that. Maybe it would take a woman to figure it out?

The book of numbers

I remember many years ago, a couple of people came knocking at my door. I seem to recall they were Jehovah's Witnesses, but I may be remembering wrong; it's not important.

"Do you know what the most popular book in history is?" they asked me, their way of starting up a conversation. This is the sort of conversation I enjoy greatly; not the theological conversation, which I also enjoy and of course they were aiming towards, but the conversation of interesting but ultimately pointless trivia.

"That's an easy one," I replied, "The Bible of course. Now here's a stumper for you: what's number two?" See how I did the very thing that so often annoys me (probably most people, actually)? I took their train of thought and switched it off to a different track so they had no idea where we were going. Next stop: Trivialand.

Actually, the funny thing about pointless trivia is that often enough, it's not even so vital that it's true, which, in thinking about the story lately, I realized that I may have been incorrectly parroting back what I had been told. I'm fond of asking the trivia question: "What's the only animal with four knees?" This confuses people, who mostly don't notice that most quadrupeds don't have knees on their front legs. The answer is supposedly "elephants", but I not only don't know if this is true, but I don't know if even elephants truly have four knees. I don't think they do, actually.

...and I'm going on a tangent again, and from a tangent off of a story about going off on tangents, at that! So, back to my first tangent, the one I gave the poor confused representatives of the Watchtower Society: I had been told repeatedly in college that the #2 book--whether it was supposed to be in popularity or influence or what, I do not know--was Euclid's Elements, an ancient textbook on the fundamentals of mathematics. Wikipedia says it is "second only to the Bible in the number of editions published", which may be the basis for its supposed #2 slot.

I definitely think there's something very significant in the fact that a math textbook holds such a vital place in world history. The average person may find mathematics a very dull subject, but it has been said, and I believe quite truly that "Mathematics is the only true universal language." Some people find it strange for a Christian to say such things, but I believe that even God cannot subvert some of the basic principles of mathematics. As Galileo said, "Mathematics is the language with which God has written the universe."

Numbers interest me deeply. They have a power in them that people do not realize. I've worked for years as a computer programmer, not because I love computers, but because there's something in me that greatly distrusts computers, and wants to know as much about them as I can. Understand HTML, JavaScript, PHP, ASP, etc., and you understand how the web works. Understand mathematics, and you understand how reality works.

People shy away from understanding numbers and how they interrelate, but they don't realize the vulnerability it gives them. As a someone who has also worked as a statistician, I also understand that. Another famous quote is "There are lies, damned lies, and statistics." People who control the numbers can have power over those who don't understand the numbers. Even my father, who was not good at math, understood the principle. He once told me, "I noticed there was a brand of soup in the local supermarket that nobody wanted to buy at 25¢. The managers of the store took away the 25¢ sign and put one up that said '4 for $1', and they couldn't keep the stuff in stock!" Lack of a basic understanding of mathematics clearly leaves one wandering in the wilderness of confused ideas. And manipulation of statistics can be even worse than this sort of amateurish manipulation of simple fractions.

Statistics is a "science" of mathematics that involves sometimes a process of incredibly complicated calculations and delicate statements of degrees of confidence that are actually quite precise and accurate. But most people don't operate on that level, and don't want to operate on that level, so statistics tends to come at people with a simple pecentage, or a cutesy chart; a method that tends to simplify things to the point of meaninglessness.

Case in point: a friend elsewhere on the web posted a link to an article suggesting that statistics show gun ownership decreases the rate of "hot" burglary, i.e. burglary that happens while the residents are in the house. Here's the article. Can you spot the problem with this? In the first paragraph, we are told, "In studies involving interviews of felons, one of the reasons the majority of burglars..." Now a citation is given, so the original study may show more, but here we are told about "studies" which may mean anything. When I was in high school, I was fond of bolstering my arguments in research papers by interviewing classmates and citing useful responses. There's no good reason to assume that's what's going on here, yet there's not really any reason to assume something better. As far as the numbers go, "one of the reasons the majority" is worded so nebulously I'm not even sure it's safe to say that 50% of the interviewed felons feel this is important. Of course on top of that, we also don't know if this claim holds true in real life. Some felons (and which ones? I assume these are felons who were caught; who knows if those who got away with their crimes have the same feelings?) may claim that they behave this way, but how do we know how they act in real-life situations?

Here's where the numbers come in, right? The numbers were compared to Britain and the Netherlands in the second paragraph. Questions here that occur to me are: How do we know that theses are reasonable comparisons at all? What are the actual levels of gun ownership in those countries versus the U.S.? Do criminals know the statistics before they approach a house to burglarize it? What was the computation used to come up with the number of 450,000, and assuming this is a reasonable computation, what's the current number? I mean, is this 450,000 "hot" burglaries that would have still ocurred, but would not have been "hot", or brand-new burglaries that simply wouldn't have happened? Are we talking about doubling the number of burglaries, or increasing by 50%? (For that matter, do you know that those aren't the same thing?) That last statistic of 30% is tossed in with no comparison to the other two countries, so what's the significance?

The most important question to ask, however, is whether guns are really the deciding factor behind these numbers. Another article my friend linked to pointed out that in Britain, many people are getting high-tech security systems for their homes, making it a necessity that burglars need to strike while someome is home. Many years ago, I remember hearing that the proliferation of "The Club" device for securing one's car was causing a rise in carjackings. Does that mean security systems are bad? I don't know much about the Netherlands other than the fact that drug use is much higher there. Could that have something to do with crime rates? Look, the conclusion that the article is trying to support may actually be true, but the numbers and info given are largely meaningless. How many people realize that, though? People love to say, look, I've got statistics! I am right! But who knows what numbers really mean, and who knows when numbers are misleading, whether intentionally or accidentally?

Our whole world is made of numbers. Numbers to count items, numbers to measure time and distance, numbers to represent complicated concepts. They're simultaneously the most abstract concepts of our minds and the most fundamental building blocks of concrete reality. They're powerful, they're meaningful, and they're there whether you try to understand them or not. Ignore their power at your own peril.