Sunday, October 22, 2006

The Fun Things

Three Hundred Seventy Third Post: The Fun Things

A while ago when surfing the Net for comparisons between art and math, I had a great fine. It was of a bunch of carefully written and very influential essays. The site is . These essays not only explain the art of computer programming, they explain how to approach any type of creative work be it drawing, math, programming, or any other creative discipline. It is definitely worth the several minutes it take to read the articles.

Two things stood out to me when reading these articles. First I am not familiar with the Lisp programming language, but now I’m convinced it is the best language ever. (LOL, you have to read the articles.) Second and more importantly was the article on fun things. You know, the things you do for fun when not working. It seems that most of the time the fun things are a whole lot more interesting than work. But even though they are fun doesn’t mean they are not important. In fact Graham states that some computer companies wouldn’t hire those programmers who work on side projects such as open source software. Graham on the other hand wouldn't hire anyone who didn’t have a side project. To him it shows a love of the work. It is proof that a person’s desire is more than putting in an 8 hour day.

For me the arch doorway was my fun project. In class the necessary evil is the standardized test. These test are to determine how well you mastered the material. In an ideal classroom we would need this. A student would just relax and learn the things they wanted and have fun doing it. This would be great if it would work. But all types of work have to have some way to measure them. I guess in the ideal class, the measurement would be the projects they completed.

Anyway, in my trigonometry class, the arched doorway was one of the fun projects. We often explored “fun” things each week. But these fun projects often have to be done on your own time because of the amount of material to cover in class. If I could have solved this problem then I would have gotten an automatic A in the class. I remember studying for the final. There was so much to review, but I was interested in the arched doorway. I had a hunch that the higher the chord in the center was from the horizontal was related to width of the door. Unfortunately I decided to study for the final instead, since it was thought that there was no solution using elementary mathematics.

Now the problem is easy and solved many ways. But that is not the point. The point is the fun things. It can be tricky to know when to pursue them and when to do the standard work. But as Paul Graham’s essays document: the difference between ordinary and extraordinary is in the passion of one’s working on fun things.

Tuesday, October 17, 2006

Absolute Involutes

Three Hundred Seventy Second Post: Absolute Involutes

I’ve found that Logarithms can sometimes be confusing. It is supposed to be simple once you know how to work the chart, but there are so many numbers it answers can get jumbled. But I like to look for the creative part of math. There is so much grunt work adding, factoring, and remembering rules, it can be nice to realize what the problem solves. I think of ways to relate logarithms to other things. If you think about it, logarithms are just like logs stacked exponentially.

Seriously though, I find it beneficial to find a relationship between the geometry and the less tangible numbers. In trigonometry for instance, we have a unit circle which is simple once a person is familiarized with it, but may not be clearly pictured when learning it. The key is to think of something circular. In this case a dog tied to a post works. As the dog moves with respect to the pole his chain stays the same length. And what we see is the length and width vary with his position and the dog has just walked a circle. There it is! The unit circle is now given a visual picture. But wait... what if the dog’s chain is wrapped around the pole? So when he runs the opposite directions his chain is lengthened as it unravels. When the dog’s chain is drawn on paper an involute is created. This is a visual representation of how angles change proportionally. And as we know, it is related to length change in a parabola.

Often math is not thought as creative as the arts because math often has rules that are guidelines on how a problem is solved. This is similar in the sciences. However, even a child makes theories. They make them all the time to explain how things work. Sometimes we as people make less of these theories because we have work. But there is no time you ever learn as much as you do while you are young. So just maybe we shouldn’t have stopped our inquisitive nature.

Admittedly, when you’re an adult making theories is a little more complex. The theory must explain the mysteries in a way that answers the known questions. So it’s a little more work but the theories are only limited by the imagination.