Wednesday, February 22, 2006

About a math opinion.

This is a rather interesting article on math. I invite you to read it, and then read my commentary, which is as follows:

I thought the author had a few important points to make; certain others are ridiculous. For example, the claim that computers can do math is quite misleading. Computers compute. Computation is only one part of math. Math is really all about recognizing patterns in a quantitative way. It's not about formulae. No computer that I know can translate a word problem (practically any math problem worth doing has its origins in a word problem) and spit out the answer. You, the human, if you want to use the computer, must translate the word problem yourself; that is a problem of interpretation which requires its own brand of intelligence. While modern education theory is mostly bunk in my opinion, there is one thing I like: the theory of multiple intelligences. I think this idea in its current form was originated by Howard Gardner and here they are:

Linguistic intelligence (as in a poet);
Logical-mathematical intelligence (as in a scientist);
Musical intelligence (as in a composer);
Spatial intelligence (as in a sculptor or airplane pilot);
Bodily kinesthetic intelligence (as in an athlete or dancer);
Interpersonal intelligence (as in a salesman or teacher);
Intrapersonal intelligence (exhibited by individuals with accurate views of themselves).

The reason I like it is because to me it squares with the idea of different gifts that Paul discusses. Naturally, there is overlap between these.

The author's points here: "Writing is the highest form of reasoning. This is a fact. Algebra is not. The proof of this, Gabriela, is all the people in my high school who were whizzes at math but did not know a thing about history and could not write a readable English sentence." is a rather funny example. It is true that there are many people good at math who can't write at all. However, the fact that people can be good at math and not at writing in no way is support for the statement that writing is the highest form of reasoning. To say so is to be guilty of a non sequitur. The author also reasons in a circle. Second, because this is so, the author has just damaged his own case by a bad form of reasoning, thus showing that writing has its own problems. Logic is logic; we get it from the Bible, and its applications, while not exhaustive, are not limited to any one field. You must use logic in English, math, history, music, art, etc. What is a good mathematician? Well, in the current context, I would classify them into two broad groups: those who do research well, and those who do scholarship well. The distinction is this: researchers work on new stuff, while scholars make clear what is already known for the benefit of others. Thus you can have people quite good at one but not the other. It is rare to find someone good at both, though I know at least two. One good scholarly paper is worth a hundred research papers, in my opinion, but maybe that's just because I'm lazy, and prefer to read clear stuff versus unclear stuff.

I think ultimately, the author is committing the fallacy of the false dilemma: either you're good at math or you're good at writing, but not both. Or at least, the author is trying to say that there's no need to be good at math in today's world. In that case, I would dispute the meaning of the word "need." It depends on who you are, and what are your expectations. I believe bachelor's degrees should not be awarded to anyone who hasn't seen the Fundamental Theorem of the Calculus. Why? Because that theorem is responsible for the modern technological age. A bachelor's degree has been traditionally thought of as being "in the liberal arts." Those are the arts that free. Not to know something as important as FTC seems to me to break with the tradition of the liberal arts. Math is a liberal art.

I think if he rephrased himself a bit, he might get on better. I think it's important for everyone to know how to write. It's not important for everyone to know the Spectral Theorem for Hermitian Operators. While you can get on in life knowing the latter and not the former, your usefulness to society is greatly hampered. You may get the great ideas, but if you can't communicate them effectively, they won't go as far. Classically speaking, I think the following are important: grammar (nuts and bolts of a subject), dialectic (or logic; how the nuts and bolts fit together), and rhetoric (how to express yourself clearly in the context of that subject). As I have said, take anything out of there, and the structure is weakened.

Those are my thoughts.

In Christ.

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At 2/24/2006 12:43:00 PM , Blogger zan said...

Well, I hope to get a bachelors in nursing someday so I can teach but, I sure hope I am not required to learn FTC.


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