It Got Too Late

A story in two parts:

1. A Noontime Read

I went to lunch with one of those books the other day. One of those books that I pull off the shelf and put on my piles that accrete beside my bed and loom over me nightly. One of those books that I bought years ago because the title caught my eye. And because I liked the production values—the typeface they chose, the neat and simple diagrams, the width of the margins.

What Is Distance? was the title, and it was thin enough to qualify as I looked for a book to take in my backpack on my bike on my daily trek to some lunch time place not too far away. And what I found in that simple, little book was amazing.

Mind you, I've been dabbling in math books for years, guilty as I feel that I never quite mastered the deeper truths, shamed that all that time in grad school was never quite sufficient to make me competent in any significant sense. In real analysis I came close once, but topology and algebra and functional analysis stayed outside my reach although tantalizingly within view at times. And these unmastered subjects call to me from the bookshelves behind my back each day as I sit here typing at the keyboard. And they spoke to me from that little book.

For as I read that book today eating a juicy hamburger (without a pang of guilt, I might add, for I bravely passed on the fries which at times can out-call even a good wide-margined book), I read the chapter on metric spaces in which a simple definition was given and a related theorem proven in such clear language that there sitting in the middle of the restaurant with a glass of tea in my left hand and a hamburger in my right and that glorious little book sitting on the table before me, those epsilons and deltas of calculus finally lost their mystery, and it all finally made sense.

There in that hamburger joint, in my sweat-stained T-shirt (for that little bike ride is no mean feat in the hundred degree days of this 2008 summer) with a satiated look on my face, my long-felt calculus guilt was gone. It was gone because of those simple diagrams and that wonderful typeface and those straight forward words in that little book that I bought many years ago. The gaps were finally full.

But that isn't what I wanted to talk about. What I wanted to talk about was what happened as a result of that noontime read.

2. A Math Lesson

So it struck me some time later that the boy is taking calculus this fall. And it struck me that those epsilons and those deltas are hiding around the corner from him, waiting to pull on him what they pulled on me, waiting to burden him with at best a partial understanding and more likely a lifetime of suppressed guilt. And it struck me that we hadn't had a math lecture in a while.

Ok, it is summer, and he did just fine in his math class last year. And who lectures their kid on math in the summer when there's no reason to, anyway?

Well, um, we had a bit of an interesting conversation this evening over pizza in which I talked about the conclusions of the Columbia investigation board (actually the Diaz Report (pdf), but I digress) and about the need it revealed for credibility analysis to accompany simulations when decisions need to be made based on the simulated results. And I related that to the need, in general, for clear communication between people and how the inability to judge a speaker's credibility because they don't explain things well or because they don't supply enough evidence for their conclusions (or at least hint that such evidence exists) can lead to communications breakdowns at best and consequential catastrophes equivalent (in some sense) to the Columbia disaster at worst.

We talked about that over pizza. It's not a math lecture ... but then that's kind of picking nits, isn't it?

So the lecturing part wasn't new. He gets it periodically—mostly when I've been adequately caffeinated, which I certainly was in this case. And he's heard me talk about the fundamentals of math before, too. So I figured that even though it is summer (for a little while longer, anyway) that I'd give him a little lecture on math, on how they live in the world of abstractions, on how they weave great tapestries from little axiomatic threads. And I figured I'd top it all off by sharing that little bit from that little chapter on metric spaces in that little book that I read over lunch. A little head start on calculus.

He was on the phone. I was in the dining room with pencil and paper and a couple books for reference. (I can't do it on my own, man, even though those gaps have been filled.)

He chatted. I wrote. He chatted some more. Page 1 became page 5. More chatting and wandering around the house. More pages. And with page 11, I was finished.

"Ok," I said, "I'm ready!"

I had announced at dinner over pizza that I wanted to have a little math talk in the evening. But I knew it needed to be early, because we'd been thru late night math talks before, and I knew how that could go.

"I'm ready for the math talk," I said, and I looked up at him sitting in the chair in the living room.

Silence. There was silence in the house. Indeed, it had been quiet it seems for some time. His call had ended, and as I replay it in my head, I vaguely hear him playing with the dog and then all goes silent. He was sitting there in the comfy chair motionless with his head slumped down.

"Dang," I said audibly.

It got too late.

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