¹Seth and Jim came to Sam’s house. Kim and Jess came, too. Jim said to Kim, “What do you want to do?”

“We can play a game,” said Kim.

“We can eat a snack,” said Seth.

“We can play out in the yard,” said Jess.

“We can read,” said Sam.

“I do not want to read,” said Jim.

“Why not?” asked Sam.

“It is a bore,” said Jim.

“Yes, books are a bore,” said Kim.

Jess and Seth got out a game and started to play.

“Books are not a bore,” said Sam. “My books are fun.”

Sam showed Kim and Jim a book about a baby dragon afraid to attack its first castle.

“Do you know all these words?” asked Jim.

“Some of these words look very hard,” declared Kim.

“This is one of my favorite books,” said Sam, “so I know most of these words by now. When I first started reading it, my mom had to help me with a lot of the words, but I almost never have to ask anymore.”

“That does look like a fun book,” said Kim. “Let’s read it together.”

Sam and Jim and Kim sat down and took turns reading pages. Sam helped Jim and Kim with any words they didn’t know. When they were all done reading, Jim exclaimed, “That’s about the coolest book I’ve ever read!”

Kim said, “I love that the baby dragon decides that the lives of the people in the castle are as important as its own, and defies its parents. (Thanks, Sam, for telling me what ‘defy’ means!)”

Seth and Jess looked up from their game. “What kind of book are you reading?” asked Jess. “That doesn’t sound like the kind of book I ever get to read at home!”

“That’s because it’s not,” said Seth. “I’ve seen your books.” After a pause, he added, with a sheepish grin, “They’re just like my books!”

“I’ve told my mom that my books are boring,” said Kim. “She says that books will get more exciting when I get to be a better reader. I ask her how I’ll ever get to be a better reader if I never want to read now.”

“Good question!” exclaimed Jim. “What did she say back?”

Kim pouted a bit. “She says I’ll read whether I like to or not, and that’s how I’ll get better.”

“She’s right, I guess,” sighed Sam, “but you’ll get more practice if you like to read.”

“I heard some of the book you were reading,” said Seth. The dragons in that book talked like real people would talk, well, if they were dragons, I mean.”

“My dad says the people in my books don’t talk like real people because I don’t know all the real people words yet,” said Jess.

“Why are all those books so careful not to use any words I don’t know?” asked Jim. “I liked learning new words – the words I already knew how to say, but not how to read, like ‘dragon’ and ‘castle’, and the new ones I didn’t even know how to say yet, like ‘defy’ and ‘agonize’.”

“The baby dragon agonized over killing people,” said Kim. “The books I read make me agonize over being bored! Sometimes I want to defy my parents, too!”

“I liked the baby dragon story, too,” said Seth. “I stopped paying attention to the game. But Jess didn’t like it so much.”

“That’s okay,” said Sam. “We can’t all like the same things. What didn’t you like, Jess?”

“I guess I like books with more action. It seemed like the characters in this book didn’t do anything but talk.”

“I understand that,” replied Sam. “I still like this book, because I think about the action that might happen. Let’s look for a book you would like more!”

Kim smiled with sudden inspiration. “I know how we can find a book we’ll all like!” she said.

“How?” came a simultaneous chorus of four eager voices.

“We can write our own! We can act it out, and take turns writing down what happens!”

There is a moment of collective epiphany that occurs when a simple idea that had been just beyond the reach of everyone present is finally expressed. That moment had just happened in the family room of Sam’s house. As if they’d all been given a script, the players took the stage. Whatever character rotated out to be the scribe was instantly invisible to the others, and the walls of the family room soon melted away. A pristine white castle was visible on the horizon.

The baby dragon, Friedenfeuer, had made a mess of things. Her father, Menschenbrenner, and her mother, Frauenfresser, were not at all pleased with their daughter, and refused to take care of her anymore. Dragons are immune to dragon fire, or the little baby might have been burned up on the spot. Very likely, she escaped only because her parents figured they could find her later.

It was while she was wandering through the tall grass of the meadow near the forest that she came upon Lady Jessica and Lady Kimberly, who had come from the white castle on the hill. They didn’t see the unfortunate baby dragon until she was almost upon them, and she jumped back she when heard them scream. Sir Seth and Sir James, alarmed by the screams, rushed up to see what was wrong.

“’Tis a dragon, I’ll warrant!” exclaimed Sir James.

“No tizzing or warranting. We need to talk regular talk,” said Sir Seth.

“Okay, you’re right,” said Sir James.

The two knights and two ladies quietly examined the baby dragon, who did not seem inclined to attack. “What’s your name?” asked Lady Jessica.

“I’m Friedenfeuer,” said the baby dragon, “but that’s my dragon name. I don’t want to be a dragon anymore.”

“I’m Lady Jessica, this is Lady Kimberly, and these two brave knights are Sir James and Sir Seth. You’re a dragon, and I guess you’ll always be a dragon. But why don’t you want to be one?”

“My mom and dad wanted me to attack that castle up on the hill.” A collective gasp escaped from the four humans as the dragon continued. “I wouldn’t do it. I didn’t want to kill all those people who never did anything to hurt me, ever.” Huge, sizzling tears slid down from her eyes. “But now I don’t know what to do. My mom and dad won’t take care of me anymore, and I’m afraid they’ll kill me if they find me again. I’m also afraid they’ll attack that castle tonight, and it won’t matter that I didn’t attack it earlier.”

There was a moment of silence as the four friends absorbed all that had been said. Lady Jessica finally spoke up. “We were all asleep in the castle last night – all of us. If you had attacked the castle, we would all be dead.” All four of the grateful young nobles stopped to hug the brave baby dragon. “What should we call you?” asked Lady Jessica. “You have a long name. You said … Feederfire … was your dragon name? Do you want a different name? You have to be a dragon, but you don’t have to have a dragon name.”

“Friedenfeuer is my dragon name. Can you call me Samantha? It’s the prettiest name I know.”

Lady Jessica smiled. “That is a pretty name. I love it. We will call you Samantha from now on. Samantha the Friendly Dragon.”

“Just Samantha, please; I don’t know if I want to be friendly yet. I just don’t want to kill people.”

“Just Samantha, then; but we can’t just stand around and talk. My daddy – father, I mean – is king of the castle up there. I have to warn him, so we can try to fight the dragons.”

Lady Kimberly paused, frowning, then smiled. “My father is a king, too – of a different castle. Jess – Lady Jessica – is my friend. I was sleeping over at her … castle. My father has a really big army, with lots of the best arrow-shooters…”

“Archers,” interjected Sir Seth.

“…archers in the land. But his castle is far away. Can you fly, Samantha?”

“Yes, but I’m just a little dragon. I can’t carry all of you.”

“Just carry me, then,” replied Lady Kimberly.

Samantha hesitated. Tears began to well up again in her huge, catlike eyes.

“It’s your mom and dad,” said Lady Jessica. “If the archers slay them, they might be dead.”

“Slaying is killing,” interrupted Sir Seth. “They would be dead.”

“Just let them talk,” said Sir James. “Nobody’s perfect.”

“They’ve got to learn sometime,” Sir Seth mumbled.

“Thank you for understanding,” said Samantha, as sizzling tears began to stream freely. “My mom and dad took care of me every day of my life. I never killed anybody, but some of the meat I ate might have been people you knew. I loved my parents. I still love them. But they’re not more important than you are. And they will kill me if they see me again.” She sobbed quietly. “Don’t hunt them down. I ask that much of you. But if they attack your castle, do what you have to do.”

“Then you’ll help us?” asked Lady Kimberly.

“I’ll help you,” said Samantha.

Carefully, the princess climbed onto Samantha’s back. The young dragon straightened her back, spread her wings, and gave a mighty leap. Not used to the extra weight, she wobbled in the air, flapped harder, and just barely cleared the trees as she reached the forest. The two knights returned to the white castle, with Lady Jessica safely between them. They told their story to King Tom and Queen Judy, Lady Jessica’s parents. They quickly prepared for battle, and made room for their expected guests from the neighboring kingdom. Then they waited.

Just as the sun began to set, King Tony arrived, leading his armies, with Queen Linda and Lady Kimberly at his side.

“Just in time!” said Sir Seth, as Lady Kimberly joined her friends. “Where’s Samantha?”

Lady Kimberly told her story. Samantha had stopped flying some distance from the castle, to avoid being shot down. Then the princess had jumped lightly off her back, and led the dragon to the castle. The castle guards were afraid that the dragon had Lady Kimberly under her spell, but finally allowed them to pass, noting that Samantha was only a baby dragon.

King Tony and Queen Linda looked very carefully at their daughter’s eyes for signs of dragon hypnotism, but the telltale swirling spirals were entirely absent, and the less-common wavy squiggles were also not to be seen. Lady Kimberly had to finish the tale, because Samantha was crying inconsolably in the corner. Steam rose slowly, and small flames brushed harmlessly against the stone walls.

In the end, Samantha could not bring herself to accompany them, and possibly watch either her parents or her new friends get killed. She was overcome by the conflict inside her, and crawled quietly down a hallway as everyone in the palace prepared to leave.

“Everyone?” interjected Sir Seth.

“Yes,” replied Lady Kimberly. “We couldn’t leave anyone in the palace unguarded, so we took everyone with us.”

“Good idea!” exclaimed Sir James. “So that’s why there are so many people coming in!”

It was a full hour after the great castle gates clanged shut, two hours after sunset, when the unmistakable glow of dragon fire was seen far above the forest. Each deep orange jet of flame was closer to the castle than the last. It was soon clear that there were two dragons approaching, and everyone not ready to fight took refuge deep inside the castle. The fires disappeared from the sky, and every knight and soldier tensed for battle. Lady Jessica and Lady Kimberly had pretended to go inside, but were waiting near their friends.

The entire castle was swallowed up in darkness as everyone waited for the attack that was sure to come. With blinding light and searing heat, the moment finally came as the dragons attacked the main courtyard from opposite directions, saturating the area with deadly flame. As they passed, thousands of bowstrings were let loose, and thousands of arrows were heard whistling through the air. Empty, smoking armor still glowed in the courtyard.

But there was no time to mourn the dead. Two enormous crashes were heard, outside the castle grounds on opposite sides of the courtyard. Sir Seth and Sir James stood open-mouthed, leaning on their spears, staring at the smoking armor. Their fathers and uncles were among the archers who had stood ready to fight, and there was no way to know how many of them were reduced to ash in the courtyard right at that moment.

Realizing that their young friends were in shock, and could not be counted on to listen or to fight, Lady Jessica and Lady Kimberly held a very quick conference, then grabbed the speechless knights’ spears and rushed off in opposite directions to the top of the castle walls. Each saw an enormous dragon writhing on the ground, arrows sticking out like quills on a porcupine. Each watched as the dragon before her struggled to regain its composure, still shocked, gaping open-mouthed in disbelief. Each young lady hurled a spear deep into a dragon’s mouth.

As the dragons gasped, sighed, and collapsed, the knights on the walls rushed down as fast as they could climb, and finished the job. Then torches were lit, and the bravest knights went back to survey the grim remains in the courtyard. But all they found was armor and wood ash. As it turned out, the generals had not assigned anyone at all to the courtyard, but had instead ordered a few of their most trusted knights to place empty armor there, propped up to look like soldiers. The real archers were ready just beyond, in more protected positions. So, not a single knight or soldier was killed. Lady Kimberly and Lady Jessica were celebrated for their quick thinking, and a great feast was scheduled for the next day at King Tony’s castle. Nobody has ever figured out a good way to cook dragon, so the two dragon bodies were set adrift at sea, and were never seen by human eyes again.

As the procession reached King Tony’s castle late the next day, however, they could see that something was wrong. Smoke was rising from inside the walls. They got closer, and saw that no wooden roof or door, and not a stick of furniture, remained in the entire castle. They guessed that the dragons had seen the armies leave during the day, and had decided to attack the unguarded castle – but, finding it empty of all people, had rushed to their original target, the pristine white castle of King Tom, enraged at being tricked. There, they were tricked again, and their killing days were ended forever.

A frantic search was made for Samantha, who had stayed alone in the castle, unable to face the conflict to come. From the heights of the towers to the deepest dungeon, they searched and found no sign of life – until a large stone tile rose from the floor of an empty dungeon cell, with a dragon head under it. Samantha had buried herself under the dungeon, and was safe.

The reunion between Samantha and her four new friends was bittersweet. All her friends were fine, and she no longer needed to fear her ruthless parents. But her mom and dad were gone, and she had nobody left to care for her. But, of course, she did. Her friends would learn all they needed to know to feed her and see to her every need. She was a hero in both kingdoms, and was greeted with cries of joy wherever she appeared.

As the five fast friends quietly contemplated what to do next, they heard a telephone ring. The walls of the family room returned, and Sam’s parents – not the dead dragons, but her real, human parents, entered the room. “It sounds like there was quite a battle in here!” they said. “But Seth’s parents say dinner is almost ready and it’s time to go home. Dinner will be ready soon here, too, so Jim, Kim, and Jess, you should probably also go home.” Kim finished writing the last sentence of the story on a piece of paper, and handed it, along with a stack of other papers, to Sam, who was designated to transcribe all the notes and convey the whole story in her own words.

The next time they met, they each had a favorite book from the library. They’d convinced their parents to let them try books outside their stilted curricula, and they were all bursting with ideas for their next story. Some were more sequels to the baby dragon story, and others were entirely new stories, based on the books they all read to each other.

Whenever the walls of the room they were in melted away, you never knew where they would end up next.
_________________________
¹The new version, which attempts to make the beginning slightly less awkward, can be found here.

“Ten poems in one night? Wow! How can you do it?”
“I’m fast at poems. There’s nothing to it.”
“But haven’t you had this assignment a while?”
“But I’ve got the whole night to finish the pile.”

“It’s quite a long haul. You’ll pull an all-nighter.”
“Yes, true, I might, but I’m a tough fighter.”
“Won’t your quality tend to suffer?”
“They’re not too bad, and I’ve written rougher.”

“Well, after tonight, your poems will be done.
You’ll catch up on sleep, go out, and have fun.
But your teacher will suffer when you’ve gained your freedom.
You had to write ‘em, but HE has to read ‘em!”

And Jesus, surfing on a site in Galilee, saw two brethren, Simon called Peter, and Andrew his brother, casting their words upon the net: for they were bloggers. And he tweeteth unto them, Follow Me, that ye may ever know my status. – Matthew 4:18-19 (paraphrased)

Some of you may have seen that before, but I couldn’t resist using it again. I’m putting out my call, too. “Follow Me, for when I tweet, thou shalt know when Steve should be read.” I won’t be telling anybody what I’m having for breakfast, or when I’m going out clubbing. This will be reserved for ReadSteve type news. What kind of news is that? You can’t know what you don’t follow!

http://twitter.com/ReadSteve will get you there, or you can just search for ReadSteve (no spaces) on Twitter. I’m pretty easy to find.

Saying: If you don’t stand for something, you’ll fall for anything.

My answer: Speak for yourself!

I believe in my ability to have an open, yet critical mind. I think that too many of the world’s evils come from people taking rigid, inflexible stands for which they have no logical support. I’m sure I have some unsupported beliefs. Maybe we can’t even function without them – but I think it makes sense to at least recognize our unsupported beliefs, and realize they could be wrong.

I resent the implication that openness to change of opinion through learning makes me a gullible fool. Users of this Saying, if you need to stand up for something through thick and thin in order to function in this world, then, by all means, do it. Recognizing your limitations, and working with them, is important. But don’t go telling me that I need the same thing. I don’t think I do – and there are all kinds of things I don’t fall for. That’s why I say, “Speak for yourself!”

I do think that, to make sense of the world, you need a way of filtering through all that the world throws at you, and finding truth in the whirlwind of irrelevant and misleading information that surrounds us continuously. But to refer to that method as “standing for something” seems to me very narrow indeed.  There are other ways to filter.

Finally, this saying qualifies for my Truth Through Wordplay Alert. In this instance, the content of the saying bugs me a lot more than the wordplay that “supports” it.

I enjoy wordplay. I pun more than most people would want me to, and I enjoy a good pun when I hear it. I don’t think puns are mindless like many people do. I think that puns are an outgrowth of our pattern matching skills, and that people who are good at puns are also good at recognizing more useful patterns, and maybe changing the world.

Wordplay is a poor substitute for wisdom and deep thought, however. When someone says “Forgiving is for giving away”, with a straight face, as if imparting the most profound wisdom, I want to throw up. I realize I may have some growing up to do. I know that wordplay can be a useful mnemonic device, a reminder of truth, just as rhyme can make a poem easier to memorize and more fun to hear.

I’m not against all sayings with wordplay. I had a German professor who used to say “Wirklichkeit ist das, was wirkt.” Roughly translated, it means “Reality is that which has an effect.” It’s a very useful saying when reading Kafka, where you never really know what’s in a character’s mind and what’s in the real world. In a sense, it doesn’t matter. What affects your world is real. It is debatable, and I have to say that I believe there’s a big difference between thinking you’re being stabbed in the heart and actually being stabbed in the heart. The former might kill you, and the latter will. But phantoms of the mind can ruin your life, and they can kill you. They may also improve your life and make you happy, too, but you’d never learn that by reading German literature.

Back to the topic, the original German has wordplay. The noun Wirklichkeit (reality) and the verb wirken (to have an effect) appear to have the same root. The sentence appears to be as obvious as “Snowmen are made of snow.” I want to say that the reason I like this particular saying is that it has substance on its own. It has meaning and truth even in English, where the wordplay is stripped away. But maybe I like it also because it’s in another language, and has to be explained to most people I know. I don’t like to think that, but maybe there’s some truth to it.¹

In any case, I’m not likely to change much on this. When someone tells me “Yesterday is history, tomorrow is mystery, and today is a gift – that’s why they call it the present,” I balk. No, that’s NOT why. Everybody knows that – even the pseudo-sages who peddle this crap. And here I face a real dilemma when I challenge my gut. I actually believe that the present moment is a valuable thing. I believe it’s when everything happens – it’s the one time you have any control over. But the wordplay takes something away from it for me. I also believe that forgiveness shouldn’t have to be earned, but I’m not sure that’s very profound.

So maybe I just need to get over myself, as far as my dislike of certain sayings goes. Some contain wordplay, and some don’t. Some rhyme and some don’t. Some make allusions to classic literature and some don’t. Shouldn’t I just take them all for whatever little nuggets of wisdom they offer, and not worry about the decorative bits that make them easy to remember?

Perhaps, but I still think my gut is telling me something. Wordplay should be used playfully. There’s nothing wrong with imparting wisdom playfully, but it’s also important not to give the playfulness any more weight than it deserves. So, when I see wordplay in a saying, I’ll be extra careful to evaluate it on its own merits, and not give it extra validity because it has extra cleverness in it. I’ll flag it with a Truth Through Wordplay Alert, and then move on to get what I can from it, independent of the wordplay.

_______________________

¹The same professor used to ask, “Ist es dicht?” (“Is it dense?”) when referring to poetry. He argued that poetry takes many forms, but the very definition of it is that poetry makes efficient use of words – the words are packed with more meaning than the average word. The German word for poetry is dichtung. As far as I know, there’s no etymological connection between dichtung and dicht, but my professor used to talk as if the relationship were a given. I also liked the insight that poetry is dense – another instance of wordplay imparting insight, which I like despite that.

John Dryden long ago received the bid
To translate Virgil’s stately Æneid
From freely flowing Latin lyric verse
To courser English lines, both crude and terse.
He bravely strode ahead and did his part –
Translation’s not a science, but an art.
So, to preserve the meaning, I suppose
He could have brought the work to us in prose.
Instead of this, the scholar took the time
To render it for us in rhythmic rhyme.
He showed amazing and persistent strength,
Under such constraints and at such length,
To bring the poem to English readers whole,
Preserving its heroic, epic soul
Across the gulfs of language, time, and space,
Into its current standard-setting place.

Among those English readers, I’m now one.
I bore the task of reading it for fun,
Trying to appreciate today
In my very simple, humble way,
A building block of culture, ages old
Whose influence cannot be fully told.
The lines of Dryden’s Virgil filled my head,
Yet soon I found that I had lost the thread.
The poets’ rhythm pounded through my brain,
Intensely, not far short of causing pain.
Even when I’d set the book aside,
The rhythm’s power could not be denied.
My words and thoughts, obedient, fell in line,
Until they were no longer really mine.
How long until this passes, no one knows.
Until then, though, I cannot write in prose!

When I was in college, and beginning to despair about the fact that I was too lazy to do the work necessary to get into the College of Engineering, much less get a degree, I took some economics courses, toward what would become a strange liberal arts degree, a Bachelor of Science in Social Science.  I can address at a different time whether I was actually lazy, or just in the wrong field at the time.  Right now, I want to concentrate on the economics courses.

As is the case many places, the intro econ courses were divided into two parts: microeconomics and macroeconomics.  I took the micro first, as is most common.  Microeconomics takes the view of an individual household or business, and looks at what effects market forces have on it.  Businesses and consumers work together to create a supply/demand curve that more or less determines the best price for any item.  We discussed what shifts the curve up and down, what makes it steeper or flatter, what a monopoly looks like, and how close substitutes can affect the curve.

There was a lot of complexity to a simple idea, and there was also discussion about when a business is worth keeping afloat and when it isn’t – how fixed and variable costs all work into the mix.  But, despite that complexity, it was all mathematical, and you could work it all out.  It was uncontroversial.  Liberals and conservatives have no fundamental differences on how to run a small business.

The reason for this is one small assumption – that neither the action of a single household nor the action of a single business can affect the economy at large.  This assumption excludes some large businesses, that have to be considered under macro, but it’s extremely useful.  It’s akin to predicting the trajectory of a projectile near Earth without considering its effect on the Earth.  A cannonball, in its arc, will attract the Earth, and actually pull it a tiny bit closer – but there is no way to measure such a small effect, and it may be balanced out by other cannonballs elsewhere on Earth, anyway.  You can predict the trajectory as if the Earth were immovable, and exerted a constant, unidirectional force on the cannonball.

The relationship between a business or household and “the market” is similar.  The market may change over time, but the actions of a single entity are assumed not to have much of an effect.  This means that you can judge the outcome of a business decision based solely on where the business is heading, and what the market is doing.  The business’s actions will not turn around and change the market, and this greatly simplifies things.

So, why do people talk about economics as if it’s unscientific?  Why do they say that, whenever you gather three economists, you get at least four opinions?  I didn’t know until I took macroeconomics.  I left micro feeling pretty good about things.  Even now, years later, I feel like I could regain everything I forgot about that course within a few days.  I never, for a moment, had the same feeling of confidence about macroeconomics.

The essential difference is that you are now dealing with governments and large businesses, who have enough clout to actually change the market on their own.  Now, instead of launching a cannonball near the earth, it’s more like launching a large asteroid, or even the Moon.  Both bodies noticeably affect each other, and things become much more complicated.

I’m reminded of some experiments Douglas Hofstadter did with video feedback – first back in the 1980’s, illustrated in his book Gödel, Escher, Bach: An Eternal Golden Braid; and then much more recently, with much better equipment, in I Am a Strange Loop.  He basically aimed a video camera at the monitor it was hooked to, and watched what happened.  I didn’t find any links to it that looked sufficiently permanent, so I’ll leave you to Google them yourself if you want to see some results.  Mr. Hofstadter was making a larger point about self reference and feedback as a basis for thought, but I think I can take a simpler point from it: when a model refers to itself, strange and unpredictable things can happen.

This strange and unpredictable behavior, counterintuitive to the point of almost seeming like magic, is why so many different economic theories can stand, internally consistent, with rules that make sense, each claiming to represent the actual economy on some level or another.  Just change a few variables, tweak a few parameters, and you can change the entire nature of your model.

All this is why I have so little patience with arguments like “You can’t spend your way out of debt,” or “You can’t reduce the deficit by cutting taxes.”  Both of these arguments, presented just as they are, are microeconomic arguments applied to the macro economy.  In fact, I’ve seen microeconomic analogies (“My bank would laugh me right out of the building!”) used to support both of these proposals, and many similar ones.

When a hurricane’s path is predicted, several completely separate computer models are consulted.  Forecasters don’t feel like they have a solid prediction until most of those models agree.  I’m starting to think that economic forecasts and policy should be set like that.  My impression is that too many people’s sense of the economy is more akin to the old man who predicts the weather by how the corns on his feet are feeling.  He may be right a lot, but would you stake your life on it?

I would suggest we do the same thing with our most predictive economic models, except that I don’t think most of our dialogue centers around things that our models could possibly cover.  The weather models we use to predict the path of a hurricane are based on very complex interactions, but they are set under conditions that have happened before.

The economic scenarios that most pundits are talking about aren’t in the realm of the familiar.  The pundits want to take us in whole new directions, and hold fast to the belief that the only reason their points of view have not been proved conclusively is simply because there has not been a real trial.  The market has never truly been free.  Socialism, in its true spirit, has never been tried.  The government has never been big enough or small enough to test everything out.

I’m not ready to suggest a way out of this mess.  I don’t know if I ever will be.  But I am convinced that the mess has nothing to do with anybody’s inability to see simple reason.  The economy is more complicated than common sense, and common sense approaches to the economy may well be as dangerous as any of the 20th century’s vast social experiments, performed by visionaries who were dead sure they knew the answers.

Even if a picture is worth a thousand words, sometimes words are all you have. I got a new phone last week, and it took me until Thursday to put a memory card in it – so, on Wednesday, when the Samsung Moment happened, I could not take pictures. Instead, here’s my picture, in words.

Wednesday was a cool, sunny day, possibly one of our last relatively dry days for a while. In the Seattle area, once the winter rains start, even a day when it doesn’t rain will still be wet from the previous day’s rain, and just as cloudy. So this day was worth doing something with. Still, I was willing to let it go – my daughter had had an after school fitness class, so I knew she’d gotten some exercise – so I spared her the “beautiful day – you should go out and enjoy it” speech.

It didn’t matter, though. Within 45 minutes of getting home, she actually asked to go to Idylwood Park, which is about five minutes’ walk from our house. It’s a park on Lake Sammamish. She was going to get insistent, I could tell, and very disappointed if I didn’t deliver on this. Plus, of course, I knew I should take her out, given how nice it was. Who knows when we’ll get another day like that? “Okay, you can go,” I said, “but no swimming.” She looked at me weird.

But I decided that, if I was going to spend the rest of the afternoon at the park, I was going to get some work out of it. So, it was off to my teenage son’s room. “One of us is going to unload and load the dishwasher, and clean up the family room downstairs, and one of us is going to take Dani to the park,” I announced.

“I’ll clean,” he said, clearly not happy about the choice, but also clearly believing he’d chosen the lesser of two evils. So I told Dani to get her shoes on, and I walked with her to the park, toting my Kindle to pass the time, and a sweatshirt for Dani, in case it got chilly later.

For a while, she played contentedly on the playground equipment, but there weren’t that many kids out, and she grew bored. She urged me out to play with some leaves under two large trees nearby. Leaves out here get big, and the area under the trees was covered in three or four inches of bright, colorful leaves. At first, we played catch with the leaves, a difficult aerodynamic feat, even standing only four feet apart. But then a thought struck me. “Do you want to make a pile?” I asked.

She was agreeable. There were no rakes available, but I was able to gather a pretty sizeable pile fairly quickly just shuffling my feet to gather them. In just a few minutes, we had a pile of red, yellow, and orange leaves big enough for a six-year-old to jump in. I continued to gather leaves to make the pile bigger, when two younger girls – one either a smart two-year-old or a small three-year-old, and one under two, still in diapers – caught sight of the pile.

They were both shy, the younger one even more so, so I hung back away from the pile, gathering leaves ten to fifteen feet away, and letting Dani carry armfuls of leaves to the pile. That distance was all the bigger girl needed, and she got into the pile. Her mother started snapping pictures of her, posing her in the colorful leaves, and getting everything just right. I had to ask Dani to refrain from jumping until a few good pictures were taken. That’s when I realized I couldn’t take pictures.

But now Dani was jumping into the pile, missing the other girl each time amid numerous reminders from her father to be careful. The girl’s mother didn’t seem too worried, so I let Dani keep jumping. The only time I worried was when Dani’s head came within six inches of the tree the pile was under. But nobody was hurt the whole time.

“Bury me!” urged Dani, and I gathered a huge armful of leaves, big enough to do the job, and dropped it on her head. She laughed. “Do me! Do me too!” yelled the other girl (I’ll call her Allison), her shyness completely gone. She was a smaller girl, so I grabbed a wad of leaves about twice the size of her head in my hands, and dropped them on her head. She giggled, and her mother seemed unconcerned. So, I continued dropping leaves, in amounts appropriate, respectively, for a six-year-old and a three-year-old, amid squeals and giggles. At one point, Allison said to me, “I’m gonna put some leaves on YOUR head!”

“MY head?” I asked, as if astonished by the very idea – but I fell into the pile, burying Dani as a pretext, to make my head available for Allison’s leaf attack. That’s when the third girl, Noelle, toddled over, diaper peeking out of her leggings, and dropped a handful of about four leaves on my head. Her grin was huge. Now, I had to be even more careful with Noelle than with Allison, so she got small handfuls of leaves dropped onto her head from a foot or so above.

Allison’s mom continued snapping pictures. At this point, Dani and I must have been in some of them. I was now playing on three simultaneous intensity levels. But then Allison crossed a line her mother didn’t want her crossing. Laughing with sheer delight at the fun she was having, she tried to push me down. “Allison, don’t do that.” her mother said.

“That’s okay,” I said, but just once – I was going to respect the limits her mother set for her. “That’s not YOUR daddy,” Allison’s mom reminded her. So, I stood up from the pile, to remove temptation, and the kids played for a short while longer. When they had left, the girls all saying goodbye to each other, Dani and I played some more, tossing leaves furiously at each other.

A two-year-old Chinese boy was drawn to the pile, and Dani and I quieted our play again. The boy’s mother was as playful as he was, and tossed armfuls of leaves into the air, to his delight. When they were done, Dani and I decided we were done, too, and walked down to the lake. She looked for fish and followed ducks up and down the shore until it began to get dark, and we headed home.

I did have one regret, that I’d captured no pictures at all. But somebody has pictures, and I have this now, which I hope to enjoy just as much. Thursday, it rained, and I’m sure the pile was no longer any fun to jump in. I’m glad we grabbed the moment while we could.

Not all my thoughts on infinity involve trying to teach the concepts to a six-year-old.  My daughter’s questions are definitely what got me thinking about infinity again, but this is a question that has been intriguing me for years – since high school, in fact.  I’ve tried to pose it to others many times over the years.  Some “don’t want to think that hard”, and others, many of whom are much better at math than I am, dismiss it without giving me a satisfactory reason why.  Of course, what may be satisfactory to a math expert may not be satisfactory to me.

Anyone with knowledge of high school algebra should be able to follow this.  Whether you want to or not is another matter.  But, to those who do choose to take an interest, I have a request.  Can you tell me what you think?  If you have no opinion, can you refer this article to someone who might?  I’d love to have a genuine mathematical perspective on this, if one exists.

It’s a well-known fact that you can’t get a meaningful answer dividing any number by zero.  Even dividing zero by zero is problematic.  So, look at dividing 1 by any number greater than zero: the smaller the denominator (the number on the bottom), the greater the result.  It would appear that 1/x approaches infinity as x approaches zero.  Now, the fact that infinity isn’t a real-world number might be enough reason to question that answer.  You can’t fit an infinite number of anything in the known universe, and you can’t plot infinity meaningfully on any conventional graph.

But it’s worse than that.  If you approach x = 0 from the negative side, the result approaches negative infinity.  The graph of y = 1/x looks roughly like the drawing below.  It illustrates a bizarre result, scornfully challenging intuition to get any grasp on it whatsoever.  If you approach zero from the positive side, 1/x approaches positive infinity.  If you approach zero from the negative side, 1/x approaches negative infinity.  This is why, when you ask most people what 1/0 is, they’ll say that it’s “undefined”.  Math functions in microchips have a special error condition for dividing by zero – they won’t even attempt it.  Who can blame them?  What two “numbers” could be further apart than positive infinity and negative infinity?

Very rough plotting of y = 1/x

Now, let me digress for a moment, and talk about the most common way to produce flat glass.  It was developed in the mid-twentieth century, and involves letting the glass solidify on a pool of molten tin, or some other metal with a melting point lower than that of glass.  The glass comes out a uniform thickness, and very, very flat.  The glass isn’t actually flat, however.  It’s only as flat as the pool of tin, which has the curvature of the earth.  However, even on the scale of a very large window, the curvature of the earth is very slight.  By a quick calculation, you’d need a window about 70 feet long for it to dip a tenth of an inch.  That is very, very flat.

The point is, the greater the radius of curvature, the flatter the curve.  So, what might an infinite radius of curvature yield?  Might we not get a perfectly flat curve?  A circle with an infinite radius might be the same as a line.  A sphere with an infinite radius might be equivalent to a plane.  Certain non-Euclidean geometries might become Euclidean again.

To further clarify (I hope) the issue, consider if a two-dimensional space were mapped to the surface of a sphere, as shown below:

A Two-Dimensiona Space on the Surface of a Sphere

This becomes a finite two-dimensional space, but it’s one that I’ve seen quite often in lay discussions of non-Euclidean spaces.  The X and Y axes here are great circles on the sphere, perpendicular to each other, and they meet both at the “origin” (arbitrarily chosen) and at the maximum distance from the point, halfway around any great circle passing through that point.  We can’t call this point infinity, because it’s a finite space.  It should be noted that this is a two-dimensional space, equivalent to a plane (or part of a plane), and traveling through the sphere is not possible – entities in that space can travel only along the outside of the sphere.

Along the sphere, we can map a function like y = 1/x, which meets at the maximum distance on the other side of the sphere.  I won’t bother figuring out what the function is – we can define it very artificially if we want to.  But such a function would plot something like this:

The "plot" thickens!

Now, I think those of you who’ve kept reading probably know where I’m going with this.  The bigger the sphere gets, the flatter the curve gets, and the more the actual function mapped can resemble y = 1/x.  If the radius is infinite, then each great circle could be a straight line, and the sphere could be a plane.  Granted, this is a fudge.  I don’t think that the appearance of a totally flat surface is the only possibility.  Multiply the infinite radius by two pi to get circumference, and you get the exact same infinity.  It’s hard to get a definite shape from that.

This reminds me of problems I heard of in some quantum theory models, where infinities are canceled out by dividing them by other infinities.  It’s mathematically possible for them to work out, but not mathematically required – so it feels messy.

But, all messiness aside, if you do think of the number line as a circle of infinite radius, is it not possible for infinity and negative infinity to occupy the same point on a number line – and thus, in effect, to be the same “number”?  If we allow this, it either makes better intuitive sense of the y = 1/x equation as x approaches zero, or it wreaks havoc with the concept of infinity, or at least the intuitive sense of it.  Maybe it does both.

Is it possible that the transfinite numbers transcend positive and negative?  Is infinity just too big to have a plus or minus sign attached to it?  What other implications might such a trans-Euclidean geometry have?  Anyway, that’s about all I have for now.  So, what do you think?

Thrilled with senses one through five,
And happy just to be alive,
I skipped about the house with glee,
Quite heedless of velocity.

As joyful as you’ve ever seen,
I bounded through my set routine.
Down the stairs, as quick as light,
I jumped the last few – joyous flight!

Thump!

Pain!
Stars!
Where did that door frame come from?
Owwwwww!!!

I lay crumpled in a heap.
I’d failed to look before my leap.
I wasn’t limp, impaired, or dead.
A bleeding lump adorned my head.

I pondered then, and found it strange
How quickly happy moods can change.
Nothing else on earth can rain
On my parade like sudden pain.