jumpingfish

We devoured the Narnia books, my brother and I, when we were young. My aunt had given them to all four cousins. My brother read them faster than the rest of us. That was years ago. Of all the wonder in those books, two images remain strikingly vivid.

1. Lily Pads

At the end of The Voyage of the Dawn Treader, Reepicheep climbed over the side of the ship to a rowboat. The ship could go no further, so he rowed alone toward the rim of the world. The surface of the water was green with lily pads extending to the horizon.

Once upon a time during a summer in Michigan, we paddled a canoe thru what felt like an infinite expanse of lily pads. We pulled hard on our paddles, barely making forward progress to what in a way was the end of our world where the lake water ran over a small dam down to Cooper Creek. Our canoe would go no further.

In the summer, they spray herbicides on the lake to counter the algae blooms that come from fertilized lawn runoff, herbicides that kill the algae and the lily pads and anything else green. I wonder about the far end of the lake where the lily pads used to thrive. I wonder what it will look like when summer comes. 

Last year, they seemed better than the year before. Perhaps the men in hazmat suits throttled their spraying. That gives me solace, and I look forward to the lake this summer.

2. Burnt Civilization

In The Magician’s Nephew, upon stepping into a pool in the wood between the worlds, Digory and Polly found themselves in an empty city. There was only a pathetic queen alone in the emptiness beneath a dim glow of a dying sun, a place whose time was over. The silent desolation haunts me to this day.

And then I stop to think about what this place will be like as the planet broils, whether it be from changing climate or an end-of-life sun much later. I wonder what it will be like for the last of us to linger. What will it be like to remain as Earth nears its end? As the rivers run dry. As the rains stop. As the heat soars. I try to imagine what I would do, and then I think that we are doing it.

We are doing it, you and I. You with your lovingly tended tomatoes and broccoli bursting forth and the other seeds waiting to germinate in the safety of the shelter you provide them. Me with my sticks and piles of wood and other hidey-holes where leaves might stay damp and the little creatures find refuge from the heat. We are doing it. And it gives me solace, and I look forward the fruits of our labor this spring.

1. Kitty’s Retest

Kitty stayed after school. She had not done well on Tuesday’s test, and she was taking it again for extra points. When she was finished, she closed her laptop and stood up. We made eye contact.

“Can I see how I did?” she asked.

These tests get automatically graded. So I opened my laptop and scrolled down to her name.

“You got a 100.”

She was relieved.

“I guess I should have done the review before I took it the first time.”

Yes, there is that.

2. Peter’s Insight

Peter stayed after school so that he could work on today’s worksheet while I was in the room. He picks things up quickly, and he only had a few questions. When he was finished, he turned his work into the purple box. Then he turned to me and asked about retaking the test, as Kitty just had done.

“What days are you here after school?” he asked.

“Every day,” I said.

“Every day. I see.” He paused for a moment and then asked (in a sympathetic tone), “Mr. Hasan, do you get to have a life outside teaching?”

The fair and industrious Trudy wants to know if I tell them my wife wonders likewise.

3. Erica’s Question

Once a week I pull my better students into my room for 30 minutes of “enrichment.” We’ve done this a few times, and although I started out with great hopes, their reactions have been underwhelming. I should have expected this, of course, since there are no grades associated with this time, and so most of the kids couldn’t care less.

On this day, the kids were rotating squares to investigate rotational symmetries, although I did not say that. I asked questions. They answered. I drew pictures on the board. Some of them dutifully drew the pictures on the papers that they were manipulating. And by the end of class we had a Cayley table for the C4 cyclic group, although I definitely did not tell them that.

We finished about 10 minutes early, and they instantly buried their noses in their phones. Then from the back of the room Erica asked a question.

“Mr. Hasan, what do you call that, what we just did?”

I smiled. 

“Group theory,” I said. 

Next week: Dihedral groups.

4. Jenny’s Eyes

Jenny finished the worksheet we were working on in class. But she had one remaining question. I walked over to where she and Jasmin had been working together, and we talked about her question.

Jenny just recently dyed her hair a reddish-maroon color. More red than maroon, but somewhere in-between, and fairly striking. She also had a strikingly bloodshot left eye. I kneeled down next to her.

“Jenny. Your red hair matches your eyes. What happened?”

“Mister,” she said. “It was from the glue for my eyelashes.”

“The glue!? Does it hurt?”

“Both eyes, Mister. It hurts.”

And then so did mine.

5. Annie’s Artwork

Annie is an artist. She’s quite good. She sketched a picture of me the other day. Evidently this is what Annie’s math teacher looks like by sixth period.

Do I look tired? Ask a teacher. 

#silentsunday

That morning, a fierce wind howled. We could hear its moaning thru the walls of the house. 

Shrub and tree branches whipped dramatically left and right and up and down. A large limb lay on the ground at the base of the Walnut tree. The garbage cans fell over. The sticks and trimmings in the yard waste can were gone, evidently having been blown down the street and maybe piled up in the corner of someone’s yard.

The car shook as I commuted east in the pre-dawn light.

The rising sun struggled to shine.

Let’s talk about “sawbucks” again. Steely-eyed mjb observed that they seem to be the same as “sawhorses”. I mean there are sawhorses and there are sawbucks.

Go look. I’ll wait.

Same thing, right? But no. Check out this  article about building a sawbuck out of logs, and take a moment to look at that the guy’s sawbuck.

Not a sawhorse.

I’m reminded (no surprise perhaps) of linear algebra. It was all about matrices. We added, subtracted, and inverted them. We diagonalized and decomposed them. We did all this, and then we were done … until I find out later, in the twilight of my years, that a matrix is just a particular way to calculate a linear transformation. The matrices are mere representations. The important concepts are the transformations. I missed the memo!

So don’t wait until your twilight years! Read the memo. Know your concepts. A sawhorse is a sawhorse, and a sawbuck is something else.