Studying in Retirement – “Metrics”

I am taking Point Set Topology. This is, for me, challenging math, and I’m liking it.

Last fall was my first “term” of retirement. (I was on terminal leave). In many ways it felt like an extended summer vacation. Fun. At first. But it got long.

So for the spring I committed to create a schedule for myself.

• I was looking at forming a math reading group.
• I wanted to pick up work one or two days a week – work with kids and math.
• I wanted to regularize reading (I’d almost completely stopped reading my last years of teaching).
• I wanted to regularize walking.
• And I wanted to take courses – when I was on sabbatical a decade ago, I loved being a student again.

I had partial success.

• Sue and I formed a reading group, which I have enjoyed, but has been irregular. I will try again, soon, to create a slightly larger group.
• I didn’t get work for the spring, but landed something I am really interested in for the summer.
• Reading has been mixed. I AM reading much more – both books, and making progress in my magazines (New Yorker, Economist, Scientific American) – but I have not succeeded in making a regular time – and I am uneven. I’ll take the progress, and work on more.
• Walking has been good. I am out most days. There are hikes. There’s loops around the neighborhood (usually around the reservoir). And there’s days in the New York Botanical Gardens (the grounds are free to Bronx residents.) And there’s days in Van Cortlandt Park, which I love.
• And I signed up for a course. Turned out to be a math course, Point Set Topology, at Queens College.

I scrambled in January – I got back from a trip January 6, and courses were starting in a few weeks. Out of lack of imagination, I chose mathematics. Cost pushed me to CUNY. I was divided between Lehman for distance and Queens for course offerings – and Queens was where I’d been on sabbatical. In fact, I’d forgotten, Queens had admitted me to their masters program. Now, do I want to earn another masters? I don’t know. But it made registration easy.

I love being a student. I like sitting in class. I do not have most of the right answers. This is challenging for me. But I get some of it right. There’s actually a freshman (this is mixed graduate/undergraduate) who runs rings around us (rings in the “runs rings” expression sense, not in the math sense, where I know what a ring is, but don’t know how to run one). A few weeks ago me and two people around my level formed an open study group – and it is nice to hang out in the library after class, and slowly go over ideas and problems.

Also, this is Queens College. The class, and the study group, are integrated. We have a fascinating mix of backgrounds. It reminds me of the high school I worked at, when it was just starting (not like today).

I’d love to tell you about the course. I got an okay grade on the first quiz. A perfect grade on the second. But if you’ve taught, you know. Getting a high grade << Being able to explain. And I am laser-focused on not being able to explain what Point Set Topology is. It is a goal. I cannot do it here, today. I mean, I could use the right words, maybe, and a math person would understand, and assume I really knew what I was talking about. But no, they would be filling in the blanks. I am not ready. I am not there.

But a few weeks ago we ran into a topic that I really did understand. So I’m going to share that with you.

Distance

Think of distance as a function – the input is two places – the output is a number – the distance between the places. “How far is it from the movie theater to the liquor store?” – we have “how far” and two places, the movie theater and the liquor store.

OK, good enough for math people? Nope.

Abstract rules (axioms)

First they need some abstract rules. And they always start with the things that are so obvious that there’s no proof of them. Math people call these “axioms.” And for distance they come up with three of them, plus an obvious fact.

• Obvious fact: Distance is never negative.
• Rule 1 without proof: If the distance between two places is 0, then they must be the same place.
• Rule 2 without proof: The distance from home to work is the same as the distance from work to home (or whatever two places you want, they don’t need to be home and work)
• Rule 3 without proof: The distance from home to work to the bar has to be the same as or more than the distance from home straight to the bar (could be from school to the skate park to your friend’s house, or really any three points)

I see other people describe these or break them up a little differently. I wonder what’s that about – although small differences do seem to crop up among math people about a wide range of things.

Not just distance, “Metric”

Math people need this to be more general. So I write distance(theater to store) = 8 blocks, or d(x,y) = 7 and say “the distance from x to y is 7”.

And we call a function that follows the same rules as distance “a metric.”

“Metric” sounds like “metric system” – and for good reason. “Metric” means of or related to the either the metric system, or measurement in general.

By the way, I am writing “distance” – but I mean regular, normal distance. Math people call this Euclidean distance or the Euclidean metric. I think when I come back to writing about this topic (I will!) I’ll start with Euclidean distance. (which is just regular distance).