User:DavidCBryant/Rants

Well, I've only been working on this Wikipedia stuff for about two weeks now, and already I have issues. The first of these may be a bit silly, but it matters to me. A lot.

Rant #1 -- Continued Fractions
The continued fraction is one of my favorite mathematical objects. I think that a formula like this one



\pi=3 + \cfrac{1}{6 + \cfrac{9}{6 + \cfrac{25}{6 + \cfrac{49}{6 + \cfrac{81}{6 + \cfrac{121}{\ddots\,}}}}}} $$

is not only beautiful; it also expresses a very deep relationship between the natural numbers and the symmetries inherent in the structure of the complex plane.

So when I first signed on to Wikipedia, I naturally took a look at the article about continued fractions. I was absolutely shocked to find that objects like this one are not continued fractions, by definition. Apparently a "continued fraction" can only be used to represent irrational real numbers uniquely, and rational real numbers in two essentially identical ways. At least that's what the Wiki gateway to the subject of continued fractions says right now.

Now I've read quite a bit about continued fractions, and I've spent more than a few hours playing with them myself. From all the reading I've done I know that the standard nomenclature for an object like this



\pi=3 + \cfrac{1}{7 + \cfrac{1}{15 + \cfrac{1}{1 + \cfrac{1}{292 + \cfrac{1}{1 + \cfrac{1}{\ddots\,}}}}}} $$

is regular continued fraction, or simple continued fraction. Since I want to contribute some new articles about continued fractions in complex analysis, I began by broaching the subject of the restrictive definition in the gateway article. This provoked some fairly strong reactions. If you're interested you can view those discussions here, and also over here.

I cooked up the paragraphs that follow, intending to add them to the Wikipedia_talk:WikiProject_Mathematics page. But then I thought, "Why bother? Those guys have their minds set in concrete already." But since I still care about the issue, I'm posting it here where one day you, gentle reader, may find it.

---

Well, I've listened to you guys, and it appears that I've been con-censored. I can accept that. But I've also listened to Dylan Thomas, so I'm going to "rage, rage, rage, against the dying of the light". And before I even do that I'd like to tell y'all a little story.

I was born and grew up in a tiny little town called Palmer, Alaska. Odds are your atlas doesn't even note the fact that it exists. There were only about 800 people in Palmer when I was a kid.

Anyway, I have always loved mathematics. I learned to count to 100 and beyond when I was just 3 years old. I remember counting sheep when I was little, to put myself to sleep. I don't think I ever got beyond 7,856, but I might be wrong -- it was a long time ago.

Now there were only two schools in Palmer when I was growing up. Central School housed grades 1 through 8. The little kids (grades 1, 2, & 3) attended class on the ground floor. The middle grades (4 - 6) were mostly in the basement, along with the furnace and the cafeteria. Junior High School was mostly on the third floor.

One day in January, 1961, I was sort of bored. I was in the fourth grade, and my teacher was named Miss Boese. Dee Boese. Our classrooom was in the basement, on the southwest corner of the building. It was lunchtime, and most of the kids were on recess. I wanted to read some more about mathematics, but I had already read all the books about math in the little kids' library. So I screwed up my courage and took a hike to the third floor, to invade the Junior High library.

There was no one in the room. It didn't take long to find the shelf that housed the math books -- the library was organized according to the Dewey decimal system. I pulled out the biggest and fattest book I could lay my hands on and started to read.

Suddenly a big black shadow fell across my book. It was cast by Mrs. Wallace, who was about 250 years old and big, and tough, and mean. "Young man," she demanded, "What are you doing in this library? This library is for Junior High, and you're too little to be in here."

I couldn't think of anything else to say, so I just blurted out the stuff I had been reading about. "Look, Mrs. Wallace. It says right here that some guy named Cardano discovered how to solve the general cubic equation in 1545, more than 400 years ago! And this book shows the intermediate steps he used, and explains how it all fits together, so now I can do it myself!! Isn't that amazing?"

Mrs. Wallace staggered, as if she'd been pole-axed. Then -- and I'll never forget this -- she spoke slowly and deliberately in a very low voice. "Well, it's all Greek to me. Nobody has checked that book out in the last five years. But if you like it, I suppose I ought to get you a library card." And she took me over to her desk, and she filled out a Junior High School library card for me, and from that day forward I never took another math book out of the little kids' library.

So what has this got to do with Wikipedia, and the article about continued fractions? Well, there's a celebrated formula that reads as follows:



\pi=3 + \cfrac{1}{6 + \cfrac{9}{6 + \cfrac{25}{6 + \cfrac{49}{6 + \cfrac{81}{6 + \cfrac{121}{\ddots\,}}}}}} $$

Call me biased, or prejudiced, or whatever, but I think that formula, the one with all the 6's and the odd perfect squares, is much more interesting and beautiful than the only possible "continued fraction" representation of π, according to the Wikipedia:



\pi=3 + \cfrac{1}{7 + \cfrac{1}{15 + \cfrac{1}{1 + \cfrac{1}{292 + \cfrac{1}{1 + \cfrac{1}{\ddots\,}}}}}} $$

You know what? I'd bet my bottom dollar that there's a little child out there somewhere who is going to be reading Wikipedia someday soon. And if he could see a really interesting continued fraction, like the one with the 6's and the odd perfect squares, he just might get hooked on mathematics instead of getting hooked on drugs. But instead he's going to see some boring stuff about a "natural" way to express every real number, and he'll wander away without giving it a second thought. And that's very sad.

I know that the articles in Wikipedia have to address the target audience. I think the most important target audience is the next generation. What good is all the knowledge of mankind if there's nobody new to whom we can pass it along?

I also know that kids don't yet have the vocabulary necessary to absorb really difficult mathematical concepts. But I still think we do them a terrible disservice when we assume they have no innate ability to appreciate beauty and truth. DavidCBryant 23:50, 5 December 2006 (UTC)