A story with some scary parts

My four-year-old and I decided to collaborate on a book. I was surprised when she decided the story should have some scary parts in it. Like a dragon, she said. Or the dark, I said. Like a dark cave, she said.

Here's what I ended up writing.

The snow fell harder and harder. I remembered that polar bears dig dens in the snow. So to escape the biting wind, I begin to dig.

Suddenly the ice and snow collapsed. I slid. I fell.

Where was I? It was very dark. I was in a cave of ice.

I thought I saw two large, pale, gleaming eyes. Trembling, I crept closer. What was it?

It was a dragon. It saw me. I was afraid. Then I saw that the dragon was trapped in the ice, frozen in place.

The dragon's scales over its heart were warm. I could feel the heart beating, very faintly, very slowly. Thump. Thump.

I stayed there a long time.

The storm passed. I came home safely. That was one year ago. Now I am returning to find the cave again. The zoo wants the dragon for their collection.

As we got near the end, I asked her if the heroine should set the dragon free from the ice. Her eyes grew wide and she smiled and said no in an small tense voice.

Later J. read it and said it was pretty good. I wonder if he felt it was scary. The uneasy feeling I get from this story comes from all the questions it leaves open. Is the dragon a person, an animal, or a monster? Is it safe to take it to live in a zoo? Is it humane? To me those are the scary parts.

Mathematicians in training

First off, if you haven't played Set, you really should, because you're just the sort of person who would love it. It's a clever idea elegantly executed, and it just happens to be great competitive fun. I taught the kids to play, and the four-year-old has a definite edge on the six-year-old. I couldn't be more pleased.

We had a bit of a drive yesterday, and along the way we gave the kids some analogies to puzzle over. You know the sort of thing: “Ice is to water as rock is to what?” This turns out to be engrossing and surprisingly fun. (I might try it with adults sometime. I sense opportunities for nerd humor.) Here the kids were not evenly matched at all. The four-year-old would get the easy ones (cow : moo :: pig : x) but would guess random related words on the harder ones, apparently with equal confidence. The six-year-old saw more clearly what the game was about, so he was able to bring his greater general knowledge to bear.

Why is this post titled “Mathematicians in training”? Well, Set is a transparently mathematical game. There are 81 cards because 81 is 3⁴. The deck is the Cartesian product of four three-element sets. They form some kind of algebraic structure with extraordinary symmetry (of a kind I don't really know anything about—it's not a group—such that I'm tempted to get completely sidetracked here). But the kicker here is, the gameplay itself is mathematical. As far as I can tell, the only good strategy is to try to prove there are no sets.

Analogies are just little homomorphisms, which is to say, structure-preserving transformations. The idea that deep sameness is more interesting than superficial differences is more important to mathematics than numbers.

On the surface it seems like analogies are less mathematical than Set. Appearances can be deceiving.

(P.S. Figured it out. The sets in Set are the cosets of cyclic subgroups of (Z/3Z)⁴. The symmetry I was referring to above was that after you erase the underlying group operation, there's no privileged element. There are isomorphisms on the deck of cards, preserving the sets, mapping any given card to any other given card.)

Milestone

I probably learned about variables from playing around with a Commodore 64 when I was about the age you are now. But I didn't see them used in mathematics for many years, until they were finally introduced, in about 7th grade, as a tool for solving problems. Take a problem, write down the equation, putting variables for the unknown quantities, and then you have something you can solve.

A little while ago I realized that this isn't the only way, or even the most important way, that variables are used in math. Variables are used to write laws.

The other day you were getting a shower, and I told you that letters could stand for numbers, that you can use letters to write rules about numbers. The letter could stand for any number, and the rule would always be true. I wrote in the condensation on the glass:

A + 0 =

Then I stopped and said, well, A plus zero equals what? You said zero. I said I didn't think that was right, because what if A was seven? Seven plus zero equals zero? So then you said A. And I couldn't be sure but I thought you really got it. That's right, I said. I'm sure you could tell I was very pleased. Actually I was surprised and excited.

Later I wrote some math pages for you to solve. The first one said,

Here is a rule:

0 < A

Do all the numbers follow this rule?

If there is a number that doesn't, that's called a counterexample. It means the rule is false.

In math, a true rule is always true, for all numbers.

The other one had some mathematical statements on it and asked you which ones were true.

You surprised me.

(Click for a larger image.)

You got them all right. I asked you about the rule on the first page, A < 0, and you had to look up what the < symbol meant, but then you told me right away that it was false, because zero isn't less than zero.

I was amazed. I asked your mother, “Did you see those pages J. did today? What does this mean?” She wasn't surprised. “It means first-graders can learn pre-algebra,” I said, insistent.

“Some can,” she said.

She is half right: you are special; you are bright; and you are interested. But I know there are millions of special, bright, curious kids like you in this country, and I think by and large their schools are selling them short. You sure are lucky you've got me, kid. But not as lucky as I am to have you.

J. listens to a story

I started to read J. the story of Moses last night. As a kid I probably scorned story bibles, but someone gave us this one when J. was a baby, and flipping through it I was pleasantly surprised. Now I think you can probably do a whole lot of deleting and clarifying without hurting much. You do lose the texture of the Bible. But we've already read the kids D'Aulaire's Greek Myths (miraculously told without any hint of debauchery) and Julius Lester's version of the Br'er Rabbit stories (retaining occasional cruelty but excising the stories' roots in a culture enslaved). So much for texture.

Still, just setting the scene for the story of the little baby in the bulrushes requires a whole new vocabulary of evil and suffering. J. did not know the words slave, taskmaster, or anguish. Also I forgot that the first thing of note Moses does is murder someone.

When J. is surprised, he doesn't look surprised. Just very thoughtful.

I think we'll proceed. J. likes being challenged. And, though I am not religious, there's a message here. The Israelites are not a particularly well-behaved people. Their relationship with God is anything but smooth. Sometimes they are stubborn and refuse to do as God tells them. Sometimes God abandons them to the consequences of their actions. Sometimes He punishes them rather arbitrarily (it seems to me). At one point they get a “time out” that lasts forty years. He never stops loving them.

Did I just write a whole paragraph comparing myself to the Almighty? I'm just saying I can relate. I expect J. can relate too.

J. writes a song

The handwriting is our babysitter's.

Squares

Yesterday, apropos of nothing, J. announced that 9 is not the only square number. 4 is, too. Even 1, he added. It turns out he didn't hear the phrase “square number” anywhere. He's just been playing with blocks.

Today I got out some extra blocks and showed him that 16 is a square number, too. He wondered, apparently at random, if 100 was a square number. So we counted out one hundred blocks and as it happens, it is.

He's been watching some math videos. We borrow one from the library each week. Last week's video, on division, explained that any number divided by 1 is itself. I doubt J. has any real conception of what division is and where it applies, but he liked that rule.

Properties of the integers, man. Before you know it he'll be telling me that 7 and 13 can't make any rectangles, except for long skinny ones...

Curlicues

J was writing his sister A's name for her on a piece of construction paper. J is 4 years old and A is 2, and somebody recently taught J that he can decorate his letters with outrageous curlicues. So J says, “Do you want me to put curlicues on it?” And A replies, in her tiny stern voice, “There are no Qs in my name!”

A bad guy in a lose-lose situation

I guess there's no point denying that J, my four-year-old, has a bit of an aggressive streak. Paraphrased from memory:

J: I'm going to try and splash him into that swimming pool. He's a bad guy. (The “bad guy” is a toy car.)

If he misses, he's going to be shot out of a cannon that will shoot him so hard, he will crash into the sun, and then he will blow up and his car will blow up.

(J. rolls the car off the table at a mixing bowl; it falls in.)

Me: Hey, you got him into the swimming pool.

J: (casually) Yeah, there's sharks in there.

I'm just glad he has it in for the bad guys.

Black-Eyed Pea Dip

Heat and drain:

• 1 can Bush's black-eyed peas

You can just zap them in the microwave for 2 minutes.

Mash them, then mix in:

• 1 tsp. seasoned salt
• 2 tbsp. chopped onions
• 1 tbsp. jalapeños (or salsa or diced tomatoes)
• 1½ cup grated cheddar
• ¼ cup unsalted butter, softened
• 1 3-oz. can of deviled ham

Pour the mixture into a 9-inch baking dish. Sprinkle on top:

• 3 oz. grated mozzarella cheese

Bake at 350° for 25 minutes. Serve with corn chips.

Overheard in a car

Buzz (not his real name) is 3; Woody is 22 months.

...
Buzz:  Yes you are!
Woody:  I'm not a are!
Buzz:  Yes you are!
Woody:  I'm not a are!
...

Concerning gifts (and other puzzles)

What can you conclude from the following three premisses?

1. If something is not gift-wrapped, it's not a gift.
2. Nothing that's gift-wrapped is entirely unlike a box of chocolates.
3. Life is a gift.

Lewis Carroll published a book of about a hundred puzzles like this one. Read it online: introduction; puzzles. My nephew IM and I stumbled upon them in Memphis last week. He pretty much knocked them out of the park one at a time.

They're fairly easy to make, if you know some logic and some algebra. Here are a few more (but Lewis Carroll's are the most sublime nonsense—you should probably try those instead.)

Concerning fashion

1. Anyone lacking impeccable fashion sense might wear a rhinestone sombrero.
2. Anyone who might wear a rhinestone sombrero can't dance.
3. All penguins can dance.

Concerning animals

1. Animals that are active during the day are either featherless or tasty—or both.
2. No creature is both nocturnal and naturally funny.
3. Chickens have feathers.
4. Chickens are naturally funny.

Concerning the inhabitants of this town

1. All the monsters in this town are carnivores.
2. A carnivore would eat anything made of meat.
3. No creature in this town would eat any other creature in this town.
4. Humans are made of meat.

Concerning monsters

1. Only monsters can make the ground tremble.
2. Two-year-olds and raccoons get into everything (two-year-old raccoons doubly so).
3. If something gets into everything, but it doesn't emit terrifying shrieks, it must be a raccoon.
4. All firebreathing creatures are monsters.
5. Opera singers can make the ground tremble.
6. Raccoons are not human.
7. A creature that isn't a monster doesn't have slavering fangs.
8. If a creature emits terrifying shrieks, then either it breathes fire, it has slavering fangs, or it's an opera singer.

A speaks

A's first words are: book, apple (“ap”), bump (“bup!”), up, ball, drink (“guk”), hat (clear as a bell), and something that sounds like bite or eat.

Observation

J, who is three, enjoys A Light in the Attic. O says Shel Silverstein's best poems are the ones that are really about himself. This led me to a new appreciation of his stuff.

I've never dealt draw poker

In a rowdy lumber camp.

Or got up at the count of nine

To beat the worlds champ.

I've never had my picture on

A six-cent postage stamp.

I've never scored a touchdown

On a ninety-nine yard run.

I've never winged six Daltons

With my dying brother's gun...

Or kissed Miz Jane, and rode my hoss

Into the setting sun.

Sometimes I get so depressed

'Bout what I haven't done.

—Shel Silverstein, Never

J. turns 2

This is J. He's my son, as you can tell; he looks just like me.

J.'s grammy bought him a table for his birthday and came up for the party. (That's J. on the right.)

There were a few balloons at the party. One of them was a very large two, or as J. says, “five”.

D. & M. gave J. this very cool cardboard box. It was even more fun after we got the green Winnie-the-Pooh chair out of it.

J. wasn't the only one to get presents for his birthday. O. and I got some Legos. Here's O. putting the finishing touches on an ostrich.

We were previously unaware that all you have to do to get Legos is raise a screaming baby to age two. This is an important revelation. Sign us up for another!

Abby chillin'

The kids get little uncles

I called Dad the day Abby was born to break the news, but he trumped me. He and C. are expecting twins. Two boys, to arrive in November.

They'll be James's half-uncles, but two years younger. He'll have little uncles. They'll have a big nephew and a big niece.

James thinks it over

Of course, we tried to prepare him.

Months ago, we told James about the baby in Mommy's belly. We told him what the baby would do, where it would stay, and what it would look like. But there's really no way to prepare a first child for the arrival of the second.

When James first saw Abby, it was clear from his expression that he had to reevaluate the whole proposition. He reserved judgment for several days. He became silent and thoughtful when O. or I brought up the subject.

Now he has gotten used to her. Sometimes he's curious. Sometimes he's sweet. He's still generally crankier than usual.

Abby is born

Olivia woke up at 3:30 last Sunday morning with contractions. At 9:10 AM on 31 July 2005, she gave birth to a perfect baby girl, Abigail Parks Orendorff.

She's sleeping now.

M. plays Blank White

My sister M. was in town a week ago. We did the tourist thing and played 1000 Blank White Cards. I guess we should have used the rejects the gang sent back with us from Florida, but we decided to start from scratch.

Normally this game is something of a free-for-all, but with the card set we ended up with, it was surprisingly stable. For me, this makes the game even more fun. After the last hand, we ended up with:

• six plain point cards
• six point cards that actually do something
• eight action cards
• six counterspells

This is a good mix. I've been thinking about doing the counterspell thing for a long time. My impression is that it really helps the game. It also helped that very few of the cards had you doing something every turn. I think the game works better when it can move along pretty quickly.

Favorites:

Evil Thieving Monkeys - Steal another player's card in play and play it on yourself. (inspiration)

Turn to the Dark Side - Flip any card in play face-down. On the back (if it's blank), draw a cruel, evil version of the front.

Let it all hang out - All new cards must have a PIG theme! +3 pts. (There was a Star Wars theme card, too. Never managed to get both in play at the same time, alas.)

In Triplicate - +3 pts. Whenever you play a non-point card, triple its effects.

I'd better stop here. James wants to look at motorcycles.

James wants to look

James's first four-syllable word was avocado, but only because he long ago started saying “cycle” for motorcycle. Yesterday he said, “momocycle”—a conscious effort on his part.

I showed James some pictures of motorcycles on Google Image Search and it's now one of his favorite things to do. “Look—cycle?” he'll say. Whenever he's in the computer room he demands to see pictures. It's becoming quite difficult.

Some of his favorite searches are purple fish, red motorcycle, and blue bus. (James is into two-word phrases these days.)

I had forgotten—you do find some strange and beautiful things when you spend time aimlessly wandering on the Web.

A rift in the Ross Ice Shelf. “At the narrow end, [these rifts] are covered by a snow-bridge and are nearly invisible. As a result, they can be quite treacherous, as some covered portions of the cracks are large enough to swallow tracked vehicles.” (more)

A child's toy filled with gasoline - Not for sale in the land of the free, for obvious reasons. But what a cool toy. You can take it apart and rearrange the pieces to make this. The same page has a picture of the most beautiful motorcycle I've ever seen. This motorcycle could star in its own movie.

A search for big rock turns up lots of nice pictures, including this one.