TIME'S 1999 Man of the Year, Jeff Bezos, indicated that the primary reason for starting Amazon.com was not the lure of fame and fortune, but regret minimization. He started the world's largest Internet store because he would have regretted not starting an Internet store. I must admit that regret minimization is the same motivation for starting this web site-Descriptive Mathematics.
In 1982, a month or so after my twentieth birthday, I was taking a painting class and studied the art of visual perspective. During the class, I realized that it would be easy to derive the basic principals of The Calculus from a model of visual perspective. I quickly put together an outline for a book called the "Calculus in Perspective" (what a clever pun!). I believed that such a book would be more interesting and accessible to students than the rigorous Cauchy method.
I switched my major from arts to mathematics, and within two years flunked out of school. My main problem was that my work on the Calculus put me on the losing side of an argument that had been raging in the mathematics community for the last century. This conflict, of course, is the schism between logicists and intuitionists. Yes, that's right, "The Calculus in Perspective" bears the ugly moniker of intuitionism. As such it is basically unpublishable.
My idea of creating a class that woud combine visual perspective and calculus was caught up on a fundamental disagreement on the nature of the calculus. The traditional approach to the calculus holds that derivatives and integrals are limits. That means the only way to establish the foundations of the calculus is by teaching limits and transfinite theory.
I saw transfinite theory as fundamentally flawed, and the overall confusion between means and ends as backward step in mathematics. Columbus used a boat to discover America. This does not mean that American continent is a boat. The American continent is a thing unto itself. If Columbus had used an airplane or submarine to discover America, the American continent would still be a mass of land. It would be neither a plane or submarine.
I held that derivates and integrals were separate from the means used to find them. You can use algebra, fluxions, infinitesmals, limits, geometry, wild guesses, or what ever tool you desire to find the derivative. The destination exists independent of the means of discovery.
If we accept that the end is different from the means, then we get down to the next important question: What is the best means for teaching the Calculus?
In my opinion, limits are the strongest and most versatile tool for finding derivatives. However, I have noticed the students tend to get hung up on the concept of the limit, and that many students never learn the elegant concept the slope of a curve, because they could not master the concept of a limit.
I saw "The Calculus in Perspective" as a introductory work that could help ease students over the large intellectual chasm that you must cross to master limits. I saw it as a beautiful work that combined mathematics, history and art in a simple and easy to read text.
But we must get back to the unfortunate reality that by holding such a position, I turned myself into a pariah, and pretty much ended any hopes of a career in mathematics.
Anyway, after losing my argument. I failed school and spent the next decade a half working custodial and clerical jobs for near minimum wage. In the 90s I was fortunate to find a company that let me hack on their computers as part of my minimum wage data entry job. Since then, I have been able to pay rent by working with companies willing to hire second rate programmers at below market rates.
Unfortunately, I keep finding my mind drifting to the Calculus in Perspective.
Applying the concept of regret minimization, I finally decided to register the domain descmath.com, and launched in on the long involved task of making such a dream a reality.
Since I have my own domain, I decided to broaden the scope of the project. Rather than simply looking at one branch of mathematics, I thought I would look beyond the world of academia, and write a web site about the way people actually used mathematics in their day to day lives.
In school, the main goal of mathematics is to separate the smart kids from the stupid kids. In the real world, people use mathematics to communicate their ideas. Since I have absolutely nothing to do with the world of academic mathematics, I thought I would complete the break with academia and weave a web about using mathematics in the real world.
The Internet is the largest vanity press in the world. It lets average people do something they could have never done in the past. It lets them self publish their unpublishable words. I hope you enjoy reading these unpublishable words, and hope that they have a positive impact on your day.
If math ain't your bag, you can read some of my short stories at rgreetings.com.
December 31, 1999