What I Learned Doing The Leap Day 2016 Mathematics A To Z


The biggest thing I learned in the recently concluded mathematics glossary is that continued fractions have enthusiasts. I hadn’t intended to cause controversy when I claimed they weren’t much used anymore. The most I have grounds to say is that the United States educational process as I experienced it doesn’t use them for more than a few special purposes. There is a general lesson there. While my experience may be typical, that doesn’t mean everyone’s is like it. There is a mystery to learn from in that.

The next big thing I learned was the Kullbach-Leibler Divergence. I’m glad to know it now. And I would not have known it, I imagine, if it weren’t for my trying something novel and getting a fine result from it. That was throwing open the A To Z glossary to requests from readers. At least half the terms were ones that someone reading my original call had asked for.

And that was thrilling. It gave me a greater feeling that I was communicating with specific people than most of the things that I’ve written, is the biggest point. I understand that I have readers, and occasionally chat with some. This was a rare chance to feel engaged, though.

And getting asked things I hadn’t thought of, or in some cases hadn’t heard of, was great. It foiled the idea of two months’ worth of easy postings, but it made me look up and learn and think about a variety of things. And also to re-think them. My first drafts of the Dedekind Domain and the Kullbach-Leibler divergence essays were completely scrapped, and the Jacobian made it through only with a lot of rewriting. I’ve been inclined to write with few equations and even fewer drawings around here. Part of that’s to be less intimidating. Part of that’s because of laziness. Some stuff is wonderfully easy to express in a sketch, but transferring that to a digital form is the heavy work of getting out the scanner and plugging it in. Or drawing from scratch on my iPad. Cleaning it up is even more work. So better to spend a thousand extra words on the setup.

But that seemed to work! I’m especially surprised that the Jacobian and the Lagrangian essays seemed to make sense without pictures or equations. Homomorphisms and isomorphisms were only a bit less surprising. I feel like I’ve been writing better thanks to this.

I do figure on another A To Z for sometime this summer. Perhaps I should open nominations already, and with a better-organized scheme for knocking out letters. Some people were disappointed (I suppose) by picking letters that had already got assigned. And I could certainly use time and help finding more x- and y-words. Q isn’t an easy one either.

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Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there.

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