Skip to content

about me

Cabin Fever Cure


Read and comment on my blog.

The ancients knew what they were about making February shorter than other months. Short as it is, it still seems the longest. Since Christmas with its reds and greens, all we’ve seen are somber browns and grays and blacks and blinding whites. The snow has lost its charm, and all of us, cooped up together for the past two months, have too often lost our tempers. We needed to get out. We needed to renew our faith in the coming of spring with its lush growth and wanton colors.

Saint Paul mercifully provides a place where those weary of winter’s doldrums can refresh their souls. The Como Park Conservatory operates year around, but in February, it’s like water in a desert. We all went yesterday to marinate ourselves in the tropical weather under its glass dome. We breathed the drenched air of the fern room. We saw the stately Christmas palms and the not-so-stately bottle palms. We saw oranges on an orange tree and cacao pods on a chocolate tree and coffee berries on a coffee tree. We saw allspice and red ginger and black pepper. We saw a Panama hat tree, so called because its young leaves are used to make Panama hats.

We always save the best for last, of course, and the best is the Sunken Garden with all the flowers. I like flowers, but I’m not very good with their names. I do fine with marigolds, daffodils, and tulips, but I can never seem to remember cyclamens, rhododendrons, or bromeliads. So, to my chagrin, I can’t remember most of what we saw. All I know is that they were beautiful. There were crimson blossoms sprung from drooping heads that twisted their petals upward as they unfurled. There were star lilies as big as my hand. There were blossoms shaped like tiny vases.

And there were carp in the pond. When the children were young, they would race past the flowers to see the fish, to touch the fish. Certainly, the carp are fascinating: their glittering scales, whiskered faces, and round toothless mouths. Lithe and slippery, they glide over and under one another looking shamelessly for a handout.

After walking through the garden, I sat down on a bench where the winter sun dazzled me. I relaxed. For, lo, the winter is past. The rains are over and gone. Flowers appear in the earth, and the time of singing has come.


Math Is Fun


Read and comment on my blog.

In grade school I hated arithmetic. More accurately, I hated repetitive drills in arithmetic. I never had trouble remembering facts, and by second grade, I had discovered that if I remembered what my teachers said and what I read, I could do well in school. I had no trouble learning the basic facts of addition, subtraction, multiplication, and division. It wasn’t enough to know the facts, however, I had to demonstrate that knowledge over and over again with mind-numbing pages of arithmetic problems. I remember doing timed tests of long division problems where we were supposed to complete 50 problems in 15 minutes. I was so busy silently fuming at the injustice of it all that I would finish only 8 or 9 problems. It wasn’t that I couldn’t do them; it was that they presented no challenge.

One day, my older sister came home and showed me what she was learning about. She showed me how 3 could be written as 11 in binary. It was like switching on a light. Suddenly, math was fun. I started tinkering with different bases on my own, writing familiar numbers in unfamiliar ways:

1, 2, 3, 4, 10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 30, … 44, 100, …

I made multiplication tables for different number systems:

× 0 1 2 3 4
0 0 0 0 0 0
1 0 1 2 3 4
2 0 2 4 11 13
3 0 3 11 14 22
4 0 4 13 22 31

I created new arithmetics using the new bases. I even found ways to convert familiar constants such as π to different bases.

π(10) = 3.14159265…

π(5) = 3.03232214303343…

What I liked best about math, though, was the comfort it gave me. Mathematics gave me access to an abstract world, a world where the rules were absolute, where absolute certainty was not only possible but necessary. I could divide the 21 abstract cookies in my math problems among 7 abstract friends because the cookies were all the same, and the friends all wanted an equal number. I didn’t have to deal with the odd, misshapen cookie or with Paul, who wanted an extra cookie for being my best friend.

Measurements were always exact. Squares and circles and prisms and spheres were always perfect, and cylindrical tanks could always be filled exactly full. You never had to worry about cutting a 20-foot board into five 4-foot lengths only to find that the last length was actually only 477/8” because the saw took out 1/32” with every cut. The mathematical world was pristine and pure, beautiful and symmetrical. Every operation had its inverse. Every number had its own unique qualities. Every theorem had its own peculiar applicability.

While other boys were discovering girls, I was discovering the five platonic solids. While they tinkered with their cars, I taught myself how to use a slide rule and how to solve problems involving logarithms. I fell in love with the ideal and had neither time nor concern for the real. The ideal world was consistent, logical, and true. The interior angles of an n-sided polygon always summed to n−2 straight lines. I could trust the ideal world.

Math is still fun. The ideal world turned out to be less ideal than I had thought. Kurt Gödel saw to that. But the real world turned out to have in it more beauty than I had at first noticed: fractal beauty.


West Saint Paul Song


Read and comment on my blog.

Even though I don’t live in West Saint Paul—(I live in Saint Paul on the West Side)—this video made me laugh so much that I had to post it. For those who don’t know, the Mississippi River takes a sharp U-turn through Saint Paul before flowing generally south again. The result is that the west side of the river is actually due south of downtown. So West Saint Paul is south of Saint Paul, and South Saint Paul, where my kids have gone to school, is east of West Saint Paul, still south of Saint Paul and still west of the river. The West Side neighborhood, where I live, is sandwiched between the river and West Saint Paul.