NAA: S is for Symmetry

29 October 2009

New post at Not About Apples.

It’s been a long time already since A was for Abstraction. Today another contribution to the mathematician’s alphabet, S is for Symmetry. I claim that, just as the mathematical language of numbers fulfills a human need for the abstraction-act of counting and quantifying, the appreciation of symmetry, both geometric and not, is a thing we all do instinctively but which longs for the right language.

Permalink: S is for Symmetry


NAA: More Math with Aliens

22 October 2009

New post at Not About Apples.

Last time, the aliens’ notion of number was a lot like ours. In particular we could find a shared metaphor of a “real number line”. What if we couldn’t? What if the aliens have much “different-er” ways of thinking about numbers? Turns out what happens is we find the starting point for a very deep and beautiful theory.

Permalink: Thought Experiment: Talking to the Other Aliens


NAA: Math with Aliens

20 October 2009

New post at Not About Apples.

Suppose you were responsible for establishing communications with an intelligent but very different alien race. Starting from scratch, how might you establish common vocabulary for basic math concepts?

Permalink: Thought Experiment: Talking to the Alien


Matroids

20 October 2009

One thing that consistently brings me joy is when a funny story or thought from long ago dislodges from the rest of the gumballs in the gumball machine of my mind and rolls to the front of my mind

After my shower this morning, I found myself recalling an incident from grad school.

I was taking a course in combinatorics, and one day the professor decided that we should learn about matroids, a somewhat exotic combinatorial structure which combines and generalizes some aspects of vector spaces and graphs.  (Don’t worry if you’ve never heard of them, neither had I–and anyway the only thing that matters is the word anyway.)

The most common pronunciation among Americans is MAY-troid, but the professor this day had a subtle accent, which distorted some vowels a bit, so it was pretty hard for people of my generation who’ve spent any time playing video games not to be thinking of a different word.

So there was sporadic stifled chuckling and exchanged glances as the lecture went on.  The basic gist of the lecture was that even though relatively few people know what a matroid is, they actually show up in problems more than you’d expect, and now we would know to be looking for them, and have some basic techniques for analyzing them.

So when the professor said to be alert, since you never know when there might be a matroid lurking under the surface of a problem and asked if, now, we would know what to do with a matroid when we saw it, several of us answered as one.

Freeze it! And shoot it with missiles!


Pretty sure I have at least one class level in Pinball Wizard.

19 October 2009

I like pinball. I like pinball a lot. Which is why I know that in Fenton, MI, where I live, there are three pinball machines. The Arby’s has a Monopoly table (in good working order; the ball save is disabled for some reason, but it’s hard to hold that against it when they leave the replay set so low–3 mil–that it’s easy to play for ages on four quarters), and the Fenton House has an Addams Family (a very good game, dare I say cult classic, but this particular table is in horrible disrepair, with the flippers so weak it’s unplayable) and a Baywatch (which I haven’t been able to bring myself to play, I mean, it’s Baywatch; if the Arby’s Monopoly breaks, we’ll talk).  The bw-3 used to have an Elvira, but now they don’t.  Stupid Fenton b-dubs.

On days when I actually take a lunch break, it’s very often spent at Pinball Pete’s, an arcade with something-teen pinball machines in the back.  (My favorites there? Pirates of the Caribbean, Spiderman, Medieval Madness.  Addams Family and Elvira when I want to be a little more retro.  Used to like Lord of the Rings, which is a work of art in many ways, but without padding on the out lanes, unpreventable ball loss is way too common to stay fun for long.)

Funny story: it came up once when talking to a student that I go to Pinball Pete’s.  He said his friends go for DDR, and asked what I went for.  I said I play pinball.  His response was priceless, “Pinball?!? Like where you stand up and flip the things?  Do people still play that?”  I said that yes, some people do, and he said “Man, Dr. Cap, you’re like the oldest school guy I know, and you’re not even thirty!”

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NAA: Algebraic completeness

15 October 2009

New post at Not About Apples.

Today I look at algebraic completeness, as contrasted with the topological completeness I talked about last time. Works as a segue into Galois theory. Plus, I use the word transcendental.

Permalink: Now there’s completeness and then there’s completeness . . .


NAA: Dedekind cuts

15 October 2009

New post at Not About Apples.

What is the real number line, anyway?

Permalink: Dedekind cuts