Tuesday, January 26, 2010

Cargo Cults (continued but different)

My college years were spend at Indiana University. I have some nice memories of being there,  but I really have no great longings for the place. Nor am I likely, as an alumnus, to contribute any further monies to them. 

Indiana University really should stop pestering me for revenue. When their cheerful little phone marketing coeds call up, I just tell them I'm unemployed and can't help them out. They get embarassed for me, and hang up pretty quickly, which is what I want them to do. 

As far as I can see, we had a business contract, which was fulfilled, completed, finished, and now we are done. They supplied me with a degreed certification, stating that I was vaguely qualified for some type of occupation, and I (ahem, my parents and I) supplied them with monetary reimbursement, and really, that should be the end of that.

I'm not entirely satisfied with my education. I started out with an art scholarship when I entered college. I came out the other end with a degree in mathematics. I'd prefer to think I don't know how that happened, but, of course I do. 

Primarily, it's because I'm lazy.

"Lazy?!" you exclaim, perhaps with a husky little uplifted squeak at the end, which you know I find so endearing, "but math is HARD! How can you call yourself lazy?"

Well, let me explain. When you are taught higher mathematics (calculus and up), you are shown a big bag of tools. And at first it all looks very confusing and intimidating, because the tools are all mixed up in the bag and you are not quite sure what each of them does. But as you go along, the tools are laid out one by one. The function and purpose of each is made clear, and it turns out that the tool itself, and how to use it, is not all that hard to grasp, once it is explained. 

It actually turns out that the hardest part of learning higher mathematics is algebra.  What is x? Well, x can be any number. You can plug any number into x and solve stuff like x2 - 2x +2. 

Once you've got algebra figured out, most of higher math falls into place. It is just repeating rules you've already learned, and usually through rote learning. The hard part of picking up algebra is something that we've all learned, or were supposed to learn, at a much younger age. It's when we learn to move from thinking about things in concrete terms to abstractions.

This is not to say doing higher math isn't hard. The actual hard part is knowing when to use the tools that a situation calls for. When should you, metaphorically speaking, use a screwdriver instead of a hammer. 

That capacity actually has nothing to do with mathematics. It has more to do with a certain style of thinking.

One of the best books I ever read was entitled "The Art of Probability" by Richard W. Hamming. The book is primarily devoted to probability, but I found, over the years, that the scope and importance extended well beyond this limited field, well, beyond math and physics, into, really a realm of thought and into an actual lifestyle. Reading Hamming over and over again, I came to finally understand this quote (you may, if you wish, substitute whatever activity you find important in your life for the word "probability", and then, perhaps, it makes sense):

"Probability theory provides a way, indeed a style, of thinking about such problems and situations... This style of thinking is an art and is not easy to master; both the historical evidence based on its late development, and the experience of current teaching, show that much careful thinking on the student's part is necessary before probability becomes a mental habit".

What I got from this is, a slow and measured examination of assumptions, and the resulting consequences of their adoption, is a far harder mental task than mere formal manipulation and rote repetition of logical and reasonable arguments. 

In other words, cutting though the bullshit is an art form. 

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