Thursday, September 29, 2011

As the Cookie Crumbles: Algebra

One of the insights for which I am grateful to Howard Gardner's theory of multiple 'intelligences' is that it helped me to understand my own ineptitude with mathematics.

Not arithmetic. No, no...I went to Catholic grammar school. I can DO me some arithmetic! Them addin', an' subtractin' and multiplicatin and divising--I'm top o'de heap! I can do three-digit by three-digit multiplication in my head. I had to memorize the squares to 25. Estimating fractions is my MEAT. Everything was going FINE til sixth grade Algebra...

Just as my skill and courage surfing runs out at about 10 foot waves, so such skills as I possess in arithmetic exhaust themselves in "higher" mathematics. Especially algebra, which--for reasons I'll mention later--made calculus impenetrable to me.

"Algebra" is an Arabic word, around the root 'gebr,' which means (among other things) "to straighten." It became a component of the formal mathematics system devised by Arab mathematicians during the flowering of Muslim culture along the fringe of the Mediterranean in the 9-11th centuries, more or less.

The system, designated Al-gebr we'l mukabala, was formulated and formalized by one Mohammed ibn Musa Ab Jefar Al-Khwarizimi, sometime around 830, CE. It was in this way--through the Arabic expansion across the straits of Gibraltar, and in through Italy, that "the West" came to learn how to do decimals, among other things. The Muslim expansion is credited with preserving and developing the knowledge of the Greeks through the Dark Ages of pre-medieval Europe.

(Parenthetically: During the FIRST Gulf War, I recall seeing a debate between an officious, supercillious Brit and an Arab spokesperson for some institution or another, wherein, the Brit accused the Arab of being uncivilized, the arab replied, with wonderful aplomb: Civilized? Sir, WE were doing algebra while your ancestors were still painting themselves blue to make it rain.")

The first time anyone in the English-speaking world would have encountered the word, it would have had the form "Algebrist," and it would have identified the party being referred to as a "bone-setter."

Algebra is basically a puzzle-solving activity: you have a formula (one of the parts of the puzzle is determining which formula you need) and some values, and you have to figure out which values to plug in what slots in what formula, which is always the form "x = (Something). All the homework in the WORLD will not improve the facility of someone who does not have such a puzzle-solving aptitude to do the desired task.

It occurred to me one day that the only really practical application of algebra in 'everyday' life is in another mathematical activity: calculus. Algebra is the "grammar" of calculus. And calculus is the LANGUAGE of power. It is NOT in the interests of "power" that too very many people should understand just HOW it works. There are a lot of KINDS of knowledge, but the most useful is "know HOW."

That's one reason why it's often taught as if the student were a supplicant before the "mysteries." It's because "calculus," (a Latin word, meaning 'little stone,' used in tallying) is the branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series.

Any of those terms ring a bell, hippies? Wall Street bells?

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