Closeness

In the “real” world you can cover a distance. You can visually tell how close together two points are to each other; even if the points are far away from you, your brain can process the visual information so you can tell the distance between points.

In the truly wonderful and beautiful world of math, these things are not as easily true. Xenos’ Paradox tells us that you can never transverse the distance between points. You can try to get from one point to another point by dividing the distance between the two points in half, and then divide the half closest to the other point in half and so on…to infinity. Essentially, you never reach the other point! There are an infinite number of points between any two points.

On the Cartesian coordinate system, which uses a flat plane, you can calculate the distance between two points and therefore judge the closeness between two points. However, Xeno’s Paradox applies here too.

In mathematical terms, if you try to evaluate the closeness of two points independent of the Cartesian coordinate system which exists only on a flat plane, it is difficult to do. Dividing the distance in half does not work. Imagine two sets of two points out in space where there is not even any type of surface such as a flat plane or the surface of a sphere. How can you tell which points are closest together?

What a great thing to think about!

Greatest Compliment Ever

While I was taking down my three-piece self-portrait, one of the other UVA teachers stopped by to talk to me. She wanted me in her Drawing 2 class in the spring and then to give serious consideration to trying printmaking, her area of specialty. Wow. This is an amazing compliment. I am thrilled! I am giving consideration to perhaps trying for a second BA degree at UVA (or maybe an MA).

Amir Aczel

Ever since reading Descartes' Secret Notebook, I have decided that Amir Aczel is one of my favorite authors. As history is one of my least favorite subjects, this surprises me. Aczel writes his history books as if there is a great mystery being solved by his research. This approach makes his books compelling, even to those who do not like history such as moi! Pick one of his books up and read it today. It will be hours of learning and fun! At the moment I am rapidly reading The Artist and The Mathematician. Awesome book.

Cramer's Rule

I have become fascinated by Cramer's Rule which makes solving systems of linear equations very easy! This has also made me more interested in linear algebra than I have been before. perhaps there are new ways of using matrices out there yet to be discovered. So, now I must decide which math is next.....

Final Display

Gravity, Esh and I all attended the final display for my drawing at UVA, Drawing 1. Gravity was so impressed that he said it did not look like the results of a beginning drawing class, and I agree. The drawings are really good! Here are some pics.

Art 21

The PBS series, Art 21, is great. It focuses on artists of the 21st Century. I have previously made two posts focused on two of the artists, Matthew Richie, and Cai Guo-qiang. The artists talk about their work along with videos of them creating the work and images of various gallery shows/installations of their work. Most of the artists are very articulate and learning what thoughts or feelings are behind their creations. A worthwhile watch.

Yet Another Change

So the final version of spring classes is the Friday drawing class at UVA, a watercolor class from a professional artist, and Calculus A from Stanford U. This should be a nice balance as the two art classes will probably have little out of class work.