There has recently been a proliferation of online "test-your-mental-gender" psychological profile tests, and I took one last night at about 3 AM. It showed my profile to be at exactly the average female mental profile. Despite my almost 20 years of experience working with blueprints and architectural rendering, I didn't do well at the "rotate the shape in space" test which is said to prove your mind's manliness. But I was great at the "remember where everything is" test, which proves that I know how to keep house like a neat lady concerned with details. I also was good at the "find synonyms" test, which proves that I'm nice and verbal and chatty like a girl, rather than strong and silent like a guy.

From the beginning, I've viewed my mathematical and physics journey through the lens of gender. The whole noise over the remarks of Harvard president Lawrence Summers, which I mentioned in an earlier post, has finally brought this matter into the popular attention. No matter how many times the "reasonable" people try to tell us that gender differences don't (or shouldn't) matter in learning and practicing math and science, there are other voices, also citing scientific evidence, often involving testosterone, that say that they do. I feel trapped between these social forces, as if no matter what I do, I cannot help be defined mentally by my gender. As a female, I must struggle to achieve what a male presumably can do "naturally" with far less effort. And when I falter, I always wonder whether it's because I'm a female, trespassing in archetypal men's intellectual territory where my little brain was not meant to go.

I am currently working on vectors. This is the third time I have tried to understand this subject. I solved two-dimensional vector problems while I was doing trigonometry. I dutifully drew the diagrams and solved the triangles. The introductory vector problems set the vectors at right angles, so that the sums could be found with simple trigonometry. The later problems, which I also did, set the vectors to be summed, at non-right angles, so that you had to invoke the laws of sines and cosines, also known as the sine formula and the cosine formula, or even more arcane laws made up by Hellenistic mathematicians in ancient Alexandria. These problems I solved as well, if you remember my posts about the British trigonometry book and the Red-Spine trig book from February and March of last year.

Now I am doing vector problems about weights on inclined planes. These are in chapter 2 of my Barron's physics study book. Now there are not only vectors of gravitational forces, but there is the so-called "normal" force which is perpendicular to the inclined plane, and the "parallel" force which is, uh, parallel to the inclined plane. And there is the force of friction and the force of pulling or pushing the weight up the incline. I had no clue what they meant by "normal" force. What's so "normal" about it? Was there such a thing as an "abnormal" force?

I could not figure out the diagrams in the Barron's book. They drew a triangle representing the inclined plane and its vertical and horizontal dimensions, but I didn't get that those were not the verticals and horizontals they wanted me to figure out. Finally I went to the great oracle of our day, and revisited an excellent website out of the Chicago area called The Physics Classroom which is one of the best high school-level teaching sites I've found. Their unit on inclined planes gave me the very helpful information that "normal" means "perpendicular." Sure enough, when I looked up the word "normal" in my etymological dictionary, I found that it comes from the Latin word norma which means "carpenter's square" or "ruler." The square tool gives perpendicularity to a construction, or regularity, hence "normality."

Diagrams often confuse me. I don't know which gender they are supposed to confuse, but I think it's my visual artist's mind that gets misled. I expect these diagrams to somehow be pictorial representations, but they are not meant to be. The length of a vector line expresses magnitude, an abstract quantity, but I see it as a literal picture of something. With inclined planes, there is a starlike cluster of interacting forces diagrammed: forces perpendicular and parallel to the plane, as well as the up-down forces of gravity. A hypothetical block or wagon moves up and down an angled line. The gravitational forces acting on it have to be diagrammed in right-angle vectors to it, because since it's sitting on something that's holding it up (that angled line), it can't go straight down.

Force equals mass times acceleration, but which part is the mass and which is the acceleration? I tried re-drawing these diagrams in the margins of Barron's book, but I kept getting the concepts wrong and I had to use white-out to eliminate my scribbles. I should never annotate a math or physics book in an un-erasable medium. I have only tried to solve a few inclined plane problems, and so far I've gotten most of them wrong. I have to take into account the acceleration of gravity, the co-efficient of friction, the angle of incidence, and the mass of the block, and find the net force. I wish I had more net force. Right now I am struggling up that inclined plane, against a heavy force of gender friction and intellectual gravity.

Posted at 3:00 am | link