It was the beginning of 2007 when I first heard about Normalized Google Distance being used for automatic translation and I started to understand how powerful linear algebra could be. I couldn’t understand the paper but I knew about the 25 billion dollar eigenvector and that the best way to get involved in any of the new and interesting developments I was reading about would be to understand linear algebra.
It is now 2011 and I feel like I am involved in some exciting projects and looking forward to being part of many more. We have been simulating fluids in our lab and we just got two kinects which we will bend to our will. Both endeavors require intimate knowledge of point clouds, manipulating, visualizing, and analyzing them to our nefarious ends. In the very short time since I was introduced to CT scan data and expressed interest in CT related research its become apparent that there is a huge need for software that can deal with essentially a whole bunch of points. The mathematics behind the techniques to look at every aspect of the human body at once, to scan your brain, read your thoughts and drive your car all depend on linear algebra to bring them to life. The reason your phone can solve sudoku and understand you when you speak to it is all because we can solve systems of equations. We don’t solve word problems anymore, the computer does that, we just have to come up with the right questions and the eigenvalues do the heavy lifting.
Four years after the beginning of my journey into math I feel increasingly closer to the edge. When I attempted to read the Normalized Google Distance paper the symbols and vocabulary slowed me to a halt. Since then many classes and lots of reading later I still lay no claim on understanding math, but I have been using techniques from papers as recent as one year ago. It wont be long before a paper from last year, and then a paper under review show me something I needed to solve a problem. After that there will be problems in front of me which haven’t been worked on before.