# Pencils Down!

After noting that mackenab.com was up and running again, Andy sent me a link to relative new blog, Pencils Down, created by our mutual high school friend Tony. I promptly added it to my feed reader (the incomparable Google Reader) and my blogroll. And last night, I spent an hour or two after Charlie went to bed (when I should have been doing something else) reading through all of his posts so far. (His blog started in February. It currently has 183 posts. Some of them are substantial.)

I really like Tony’s blog. I won’t try to tell Tony’s life story here. He and I lost track of each other for long enough that I couldn’t do it justice if I tried. But, suffice to say, he hiked the Appalachian Trail last summer and moved to Maine. This fall, he starts back to college at the University of Southern Maine for a second bachelor’s degree with the ultimate goal of becoming a math teacher.

Two particular themes of his blog really resonated with me.

First, Tony insists in several posts on the importance of teaching probability and statistics in K-12, even if it means displacing some other topics. He rightfully points out (though not in these words) that these are topics which interact with people’s lives and in which our culture’s math illiteracy is most easily exploited. I agree completely. Probability is the primary mathematical tool that I use in my work. I mostly use random processes in my research, especially Markov chains and Markov decision processes, but in trying to teach these subjects I have been shocked at the poor preparation that many of our new graduate students have in probability. So, in a graduate course that is supposed to introduce students to random processes, we wind up trying to review all of probability up to that point.  And this is for graduate students in electrical and computer engineering.

This brings me to a slightly funny story. While I was at Cornell in graduate school, I found out that an acquaintance from high school was also there. (Tony and Andy might know him, in fact, but I will do him the courtesy of not naming him here.) We hadn’t been friends in high school, exactly, but I liked him well enough, and he was also in graduate school at Cornell studying, I believe, Chemistry. In any case, I ran into him on campus, and we agreed that we should get together. As it happened, Bela Fleck was coming to a nearby town, and he invited me to join him and another friend of his (also an acquaintance from our shared high school, as it happens) who would be in town for the concert. I’m not a Bela Fleck fan, exactly, but I like his music pretty well and so I agreed. In any case, on the drive to the concert I made an offhand comment about how important and misunderstood I think probability is. I probably overstated my case a bit, claiming, as I recall, that probability was the most the important area of mathematics. He disagreed, saying that differential equations were much more important and useful for modeling the world. I stood by my position, and he got quite angry. I can’t remember if he outright said that my position was idiotic, but he certainly strongly implied that it was deeply and obviously so. I sent him an email once or twice after the concert, but I never saw or heard from him again.

In any case, I think this is what our argument ultimately comes down to: If you are a physicist or a chemist trying to construct a precise mathematical model of the world, then differential equations may the most important tool in your toolbox. In my opinion, though, ordinary folks can get along just fine without them. A failure to understand the basics of probability, though, causes ordinary folk to make bad decisions on a regular basis.

The second theme of Tony’s that really resonates is his discussions of getting girls more excited about and interested in math. We have certainly struggled with the difficult issue of increasing the representation of women in our ECE department. It’s also the issue that has caused the most contention on this blog back in the deep archive. I’m glad that Tony and others in his community are thinking about it, though, because one thing that’s obvious is that no matter how hard we work to improve the status of women in ECE at Virginia Tech (and there’s lots that we need to do), this is a problem that often stretches back to girls’ early encounters with math and science.

I want to say more about a couple specific posts that Tony has made, but alas, I also have a lecture to prepare on mathematics in finite fields. (I’m teaching error control coding this semester, and all math for error control codes is traditionally done in finite fields. Since most students haven’t seen them before, we start there. In short, the first thing I try to teach my students is that, in the fields that we care about for this course, 1+1=0. They are surprisingly resistant.)

## 3 thoughts on “Pencils Down!”

1. Andy

Allen,

 I'd love to audit that error control course.  Regarding the arithmetic of finite fields, I'd really hammer the concept of Exclusive Or (XOR) and hope for the best.

2. Tony

Good to have you back in the blogosphere, and glad to have your approval.

I WOULD argue that statistics is the most important field of mathematics. Whether we realize it or not, we are using some form of intuitive understanding of statistics and probability to make every decision. Let me repeat that. Every decision. It can’t be avoided. Even if you give up your free will and resort to a coin toss, you’re still using probability!

3. Allen Post author

Exclusive Or (XOR) works fine for understand the binary finite field (a.k.a. GF(2)). Unfortunately, it isn’t quite good enough for the higher order finite fields, such as GF(256) which are important for some types of codes.