A Steel-Driving Man

I've been using my holiday break to catch up on my pleasure reading, which to the lay person, would be largely indistinguishable from school assigned reading. I just polished off one about econometrics called Super Crunchers. Econometrics, as near as I can tell, is what actuaries do, only hepped on on some powerful digital 'roids. Evidently, as Moore's Law continues to hold and computing power explodes, decision making that was once left to the "experts" is now being given over to fairly rudimentary mathematical formulas backed up by a whole lot of terabytes.

Chapter after chapter chronicled the successful usage of econometrics to predict things as diverse as good baseball players to Hollywood blockbusters to medical diagnoses. See as it turns out, those experts aren't really all that expert. Time after time, they fail to beat the predicting ability of simple equations, equations which boil down all of life's subtleties to bare bones. As I read, I found myself nodding in agreement. It is well documented how poorly doctors perform on tests of statistical reasoning. Why should patients trust in their abilities to prescribe treatment if they don't really understand the odds. If the use of a simple algorithm can help save lives, then why shouldn't doctors swallow their pride and admit defeat, as it were?

Of course, it wasn't my ox in the grinder. Until the chapter on education. Then suddenly, I was appalled. How can the process of teaching be boiled down to scripted lesson plans? What kind of robotic rote learning could possibly come out of that?

I've since come to my senses. These computer programs are not a threat, but a blessing. They allow us to do the things that we, as fellow humans, are uniquely suited to do. If a doctor is free from having to analyze symptom after symptom, if a diagnosis is less than a Google search away, then that medical professional can focus more on the healing process. They can spend a few extra minutes holding the hand of a scared little girl, or explaining the treatment details to her mother. Besides, the programs are still guided by the garbage in, garbage out principle. They are only as accurate as the information passed into them, and that will still require skilled human doctors. The same is true for teaching.

I have no desire to sit and read from a script all day, and frankly, it's silly for me to do so, even if it proves to be the most effective teaching method. The same computers that analyze the data behind these lesson plans can easily conduct the lessons as well. Sit the kids down in front of some powerful learning software. That's fine by me, because I know it doesn't render me obsolete. It empowers me to do all the "extra" things that I wouldn't ordinarily get to do. I would have the time to really get to know each of my students. I could allow them each to progress at their own pace, and have the ability to work one on one with each of them.

No one alive today would take offense at being beaten by a machine in a test of speed or strength. What John Henry learned the hard way is second nature to us. Yet we cannot seem to accept that certain intellectual feats are now better performed by cousins of those athletic machines. We feel as though our very humanity being stolen, when in fact, the machines are helping to teach us what being human really means.

Numbering from Zero

I've been noticing a trend lately, and I hope it's a fad. Several popular math books that I have read have begun with a Chapter Zero. I can rationalize several excuses for this, but I still think it boils down to nerds being nerdy.

The first excuse is that in modular arithmetic, a set of N numbers begins 0,1,2,3...N-1 so that it can include the identity. But a book isn't a clock. The chapters aren't going to start over at any point.

The second excuse is that the authors are also modern computer scientists. (Both of my computer science classes began with an Assignment Zero.) After the popular language C, all languages have begun their indexing sequences from zero rather than one. This is a consequence of the decision to have the memory address of an array element be the same as its index. But there's no reason why they couldn't have started indexing at 1 and defined the memory address using an imaginary number equal to one less than the index. So this isn't really any more rational.

The last excuse is that the numbers are meant to serve as markers instead of names, counting forward in a sort of greatest integer function scenario. Since the markers come at the beginning of the chapter, and the first page of the first chapter can be viewed as the origin of the book, it might make sense to label it Zero. However, if books were designed to be read from right to left (I know there are many languages which read right to left across the page, but I don't know if the books themselves read from right to left as well,) we wouldn't expect to start with Chapter Zero followed by negative chapters.

As far as I can tell, there is no good reason other than fashion why a math book should break the convention of using counting numbers to label chapters. I find it irritating and i wish it would stop.

Math for the Cosmo Girl

I wrote so many posts (here, here, and here) in anticipation of Danika McKellar's Math Doesn't Suck that many of you may be wondering why I haven't reviewed it yet. I have no excuse other than that I've been busy. But I finally got around to reading it tonight and it's about what I expected.

It looks and reads exactly like an issue of Cosmo. The front cover sports a sexy photo of McKellar with superimposed titles in a variety of fonts and sizes, exactly like the glossy covers of fashion mags. Inside, there are explanations and examples of math concepts, broken up by testimonials and horoscopes. I read it pretty much the way I read Cosmo*. I scanned through the testimonials, skipped over the quizzes, scoffed at the horoscope, and put it back on the shelf.

It is definitely geared toward the girly-girl and I think that's just fine. Boys have plenty of other books directed at them. Although, the quotes from school aged girls got a bit redundant, and Danika is not nearly as funny as she seems to think she is, the explanations were presented in a clear, concise manner with lots of great tips and short-cuts. The book will definitely be a powerful weapon against math anxiety for young girls.


*My girlfriend has a subscription and I like to know what manner of rubbish is going to somehow get me into trouble each month. And as an aside, she always manages to stack the issues out of order, which bugs me because it jumbles up the Guy Without His Shirt on the spines.

Redundancy?

This was staring me in the face at the grocery store check-out yesterday.

The jokes just write themselves.

Simple Arithmetic

Most of you probably think arithmetic is easy. All you computer programmers and tenured professors out there can add,subtract, multiply, and divide in your sleep, and you scoff at people who can't make change quickly in their head. Certainly, our nation's public schools think arithmetic is easy. They require elementary school teachers to have hardly any math background at all. And yet our elementary school students are using math technology 50,000 years in the making.

How Mathematics Happened by Peter Rudman explores in depth why and how civilized man came to depend on math. He focuses on the early years, beginning well before writing was invented, and giving an intriguing account of the birth of the science. I am in the process of reading it and it is truly fascinating. This isn't the first early math history I have read, but it is by far the most involved. Check it out. You'll never underestimate the power of the third r again.

Girly and Fabulous

Advance copies of Math Doesn't Suck by Danika McKellar are starting to circulate and the reviews are mostly positive. The general consensus seems to be that anything that gets young girls excited about math is a good thing. There has been a little bit of criticism of her marketing style. She is definitely exploiting her classic good looks (let's face it, she is pleasing to the eye,) and she uses topics like shopping and make-up to explain math concepts. Although her style may offend certain hard-core feminists or misogynistic men, neither of those demographics fall in the target audience. Aetiology over at ScienceBlogs has an interview with McKellar, where she puts forth the idea that it is possible to enjoy fun "girly" things like fashion and jewelry, while still developing an appreciation for math and science.

To Cogitate and Solve

One of my favorite PBS series of all time was Square One, a sketch comedy show devoted to making math fun. The highlight of the show was Mathnet, a parody of Dragnet in which Detective Monday and his partner solve crimes using their mathematical knowledge.

At the time, I thought it was just a funny show. Now I realize that it isn't far from the truth.

Experts in mathematics are regularly employed by all branches of law enforcement. Much of this occurs behind the scenes, but can be absolutely essential. Many cases hinge on purely mathematical evidence. But how exactly has this trend affected our justice system? The adversarial legal model that we brought with us from merry old England didn't exactly have a place for what we would today consider "expert testimony." A new book from the author of The Math Gene seeks to tackle that question.

Keith Devlin and Gary Lorden, the Caltech professor who serves as adviser for the hit CBS series Numb3rs, are co-authoring entitled The Numbers behind Numb3rs: Solving Crimes with Mathematics. Judging from what I know of the works of both authors, this should make for a fascinating read.