Confessions of a Math Illiterate

This morning I was volunteering in my daughter’s gifted class. The students were given a handout with ten or so tricky math problems on it. Some dealt with deciphering the pattern in an unusual sequence of numbers, letters, or shapes and predicting the next entry. A few involved area estimations for odd shapes. My job was to help the kids out without giving away any answers.

For the most part it went fine, although I have to admit I was thoroughly flummoxed by one of the sequences, which ended up being almost painfully simple: the capital letters written using only straight lines went on top of the line, while those with curves went below. That’s one of those questions that seems like cheating to me, because it’s handwriting, not math! Or more accurately, it’s typography, because you will hard-pressed to find a single capital letter in my handwriting made up of only straight lines.

(Untold episodes of the television show Numb3rs have as yet failed to convince me that everything in the world is simply pretty pictures overlaid upon a skeletal framework of mathematics. Because if that were true, I would be guessing my way through life without showing any of my work. Read on.)

However, one very talented young girl who was all the way to the end of the sheet asked me a question that I could not answer for an equally simple reason: I had no idea what the math-specific terms being used in the question meant. We’re not talking sum and product here, but something edging closer to binomials or some such. I can’t be more specific because the word in question was literally a foreign language to me.

Under the impression that I am more or less competent (a hard-won impression among this group of children), this girl assumed I was just refusing to help her by feigning ignorance. Which left me in that dreaded no-man’s land of an argument with a precocious child: I could pretend to be deliberately unhelpful or admit to being ignorant. I went for honesty. “I don’t know what that means,” I said earnestly.

Her reaction was one of shock. “You’re a grownup. Don’t you need to know this?” The unspoken questions being, “Didn’t you go to college? Don’t you have a job?”

Having taken the first step on the slippery slope and feeling my footing giving way, I went for broke. “Truthfully? I haven’t used any of this stuff in years. Not even in graduate school.”

Her eyes were narrowing. I saw wheels turning behind them and began to hear the angry ringing of parental phone calls in my future. “Now, if you are an engineer, or a scientist, or a computer programmer, or maybe even a doctor . . .” I qualified hastily.

“My daddy is an engineer,” she nodded. The relief I felt washed away the details of her mother’s career. Based on this girl’s mind, mommy is probably a nuclear physicist.

“Well then, if you want to do something like that, then this is very important.” She didn’t seem fully convinced. Still sliding down that slope, I went for the most shameless ploy available in a grade school setting.

“Plus, all your test scores will be part of your permanent record. Where did you say you wanted to go to college?” There are some children under the age of ten who have actually considered where they might want to go college. At that age I wanted to be an officer on the Enterprise or a Rebel X-wing pilot.

“Harvard, maybe. Or Stanford.”

Of course. “Well, those are very selective institutions. Your knowledge of this kind of math lay an important foundation for excelling at the kinds of tests that will get you where you want to go.” She sighed. I saw the folly of my honesty in her eyes, resigned to the necessity of years of boring tests and jargon. “Or you could always skip this problem and work on one that seems more interesting,” I offered.

“Okay.” Her face brightened. “Neat, a graphing problem!” I retreated to the safety of a child using a calculator.

Those of us who aren’t comfortable with math like to make up and then perpetuate all sorts of stereotypes about the people who enjoy equations. They can't or don't read anything complex. Human emotions confuse them. They're physically awkward. Over the years I’ve found that most of these aren’t true. The starting center on my junior high basketball team was math whiz and the only one on the team who could dunk.

Some stereotypes do ring true at the extremes. Those that are true are not exclusive, however. You are just as likely to find a socially dysfunctional fanatic/lover of literature, religion, music, guns, or art who speaks about daily life in a foreign language as you are a number-crunching nerd who does the same. They all just dress differently and register at different degrees of "cool" on the popular culture thermometer. At a certain level it’s all about the obsession with perceiving reality through a particular lens.

What does set the math folks apart is their insistence that their obsession describes the world in empirically concrete terms. (Well, some of the gun fanatics are pretty confident of this as well and more than happy to demonstrate.)

I’m willing to concede the "math explains reality" theory for pretty much anything involving electronics, mechanical parts, or laws of nature that I can actually feel. (Okay, and x-rays and hard radiation as well. I grew up on White Sands Missile Range and everything in the category of "invisible rays that pass right through you" still scares the crap out of me.) When you get to dark matter and alternate quantum universes, the process moves into the self-referential realm of math proving or disproving other math as far as I can tell.

I simply try to muddle through with my mathematical dyslexia, with the full knowledge that in a few years my daughter will be working on math problems I do not understand. This knowledge hangs over my head like a polygonal sword of Damocles. (Oh yes, I went mythological on you—that’s just one of my own conceits. We’ve each got our boulders to roll.)

Until then I enjoy my Sudoku and marvel daily that a calculating machine capable of thinking only in ones and zeros can be such a diabolical pain in my ass.

Being/Loving in the Moment: The Children's Gift

Every Thursday afternoon I volunteer at my son's class. He's four years old and has been diagnosed as a high functioning autistic, most likely with Asberger's Syndrome. If you are told that your child is autistic, that's about the best diagnosis you can hope for, so my wife and I feel very fortunate. He's a very loving, very intelligent, very wonderful little boy.

My son is in a developmental preschool program with nine or so other children whose diagnoses fall along a similar spectrum. Some have greater physical challenges, some greater speech and mental challenges, and some you would not suspect have issues at all until you see them emotionally disturbed.

Generally I assist the physical therapist in working with small groups of children from the class and help the teacher and her aide run the classroom. This involves helping children with craft projects, doing some individual occupational therapy with them, and a lot of taking kids to the bathroom.

I also volunteer every other Tuesday morning for my daughter's Highly Gifted 3rd/4th grade class. This is also a small group of ten children, but these kids are considered to be on the high end of the spectrum, with skills in reading, writing, and arithmetic far above their age peers. At the same time, these children are also fragile in their own ways. Some have trouble making friends, some have attention deficit or sensory overload issues, and some (like my daughter, in many ways) are simply young children struggling with expectations of social maturity based on their academic achievement rather than their real age.

I find these volunteer experiences very rewarding. The specific nature of my interaction with these two sets of children is very different. In my son's class he is the only child who can read. Some of them have trouble with identifying basic colors and shapes. In my daughter's class there are children who can multiply in base three and read at a very high level.

But my basic goals in each class are basically the same. I help the children individually, I praise their achievements, I try to ease their self-consciousness about their eccentricities by accepting them as they are, and I try to make them laugh. Sometimes it is challenging and frustrating. But it puts my mind in a place that is very healthy.

The teachers have a much greater challenge than I do. They need to think about the overall progress each child is making, which with these children is typically a very individualized set of benchmarks and goals. In much the same way I have to keep a careful eye on the progress of my own children in and out of the classroom. I have to be prepared to meet and advocate for their special needs on a constant basis.

But when I volunteer, all I do is think about what will make this particular child happy or successful right now. And I find the easiest way to do that is to love them for that moment as selflessly as I can. I just try to accept them, because in many ways these children are outsiders. Yet they are still young enough that if you treat them with kindness and patience, they will let you in and tell you what they need or want.

There is a girl in my son's class who can't really speak, at least not intelligibly. She's quite shy and has some sensitivities to touch and temperature that can make her uncomfortable at times. But she watches the world around her closely. One day I stumbled across a little game I could play while swinging her on the therapy swing at the start of class that would make her burst into peals of laughter like the chiming of little bells. Now she smiles at me and asks me for help in her singsong voice whenever I am in the class. I can't always help her. Sometimes I'm not allowed to, because she needs to master certain self-reliance skills. Often I can't even understand what she wants from me. But she trusts me, and that trust is a wonderful gift.

A boy in my daughter's class is somewhat emotionally fragile. He's prone to stepping away from the group and isolating himself when he feels embarassed about a situation. During a school Christmas party I saw him pull away to the corner of the room. So I went over to sit by him. We sat next to each other in silence as I tried to think about what to say to console, encourage, or cheer him. Then it dawned on me that for the moment being there was enough. After a while I asked him about the pattern on his shoes, then the picture on his shirt, giving him a chance to be the expert, to teach me, to feel a little confident again. And then I thanked him for sharing with me. He went back to the group and started to play with the others.

And the thing was, I was grateful to him for sharing with me. Being helpful was the best feeling that I had that entire day. And not just because I gave to someone else. It was as though I reached back through time and gave encouragement to the lonely and isolated little boy that I often was.

I try, with limited success, to remind myself on a daily basis to embrace the people I love with love in my heart. To see their frailties and mistakes with compassion and understanding. To see myself and my own mental and emotional challenges in the faces of my children. To try to be helpful because, in truth, it simply isn't always possible to help another person, though you want to with all your heart. So the opportunities to help those you love are little gifts that make life more meaningful.

And maybe, in the end, to become a better person. Because for all the ascetic teachings in the world and the tales of lone artists pursuing their passion, I don't think you fulfill your true promise as a human being on your own.

On Writing and Other Compulsions

Lately I've been struggling with the question of whether I have what it takes to write and publish fiction. For a very long time this has been not simply a dream, but an almost unconscious expectation of mine.

I make my living, such as it is, from writing nonfiction. From my days as a mediocre technical writer, to my rather more successful years as a textbook writer and editor, to my current phantasmal existence as a ghost writer and freelance editor for everything from elementary school science to high school history, writing has paid my bills since I received my undergraduate degree.

So on a fundamental level I know I have the basic skills and discipline needed to communicate in writing. I understand the process of revision. I've stared at many a blank page with a deadline looming and produced something that passed muster.

I also have what might be called a hyperactive imagination. I read a lot of nonfiction on a fairly wide range of topics. Everything I read suggests ideas to me for settings or characters. I find it hard these days to read anything without thinking about how to fold, spindle, and mutilate the more interesting anecdotes or facts into some kind of narrative or imaginary milleu.

The same thing happens to me walking around. For while I tend to be oblivious to much of my environment, certain details will jump out at me and change in my head. When I was in college there was a very large tree outside the window of the main library whose branches and leaves used to dance wildly in the wind. It always made me think of a great Chinese dragon gyrating to its own music. I used to collect weathered brown leaves from that tree like so many scales Beowulf might have stepped over on his way to face his doom.

Years later I went for a hike by myself in Muir Woods. I lost track of time and walked for hours, which was a bit foolish as I hadn't brought nearly enough water. Yet I can't remember what the redwoods themselves looked like. The only sensations I recall are the smell of their peeling bark and the brilliance of the shafts of light that pierced the canopy here and there like spotlights. The only specific memory I have is of suddenly coming upon a spider dangling in midair, suspended above the path by an invisible silken thread that stretched up into the vault of trees. The thought of that spider still amazes me. On one level I'm certain that my memory must be faulty, that surely there was a nearby branch I've forgotten. But this how I remember it.

And this is me: surrounded by majestic trees hundreds of feet tall, I am engrossed by a spider the size of my thumbnail.

So surely I can harness the escapist energies of my wandering mind to the wheel of my professional craft and turn out a vessel that can hold a reader's interest like so much precious oil or a draught of wine.

Except I can't seem to hold my own interest. When I turn my mind's eye loose from an assignment, it wanders. Every shiny idea it comes across seems suited to fit into the mosaic of whatever story I think I have to tell. So the task becomes overwhelming. And when I seem to solve the puzzle, to figure out how it will all slide together and form a recognizable whole, I'm no longer drawn to it.

I have not yet found the story that I feel compelled to write. Instead I feel only the compulsion itself, voices in my head that won't be silent. And I wonder if I want to write because I want someone else to tell me those voices are not worthless, that they have something of value to offer, if only entertainment. Or if I've simply internalized the voices of all the people who have told me since I was a little boy that I wrote well and had a vivid imagination. Writing would satisfy those voices as well.

So I'm not sure that the words "I want to write (story/novel/poem) X" are really being spoken in my own voice. Not yet. And I have to decide if a lifetime of wandering imagination is its own reward or if it has to take some tangible form on the page to have been worthwhile.

Personal Post: I Have Become El Asso Wipo

Several friends commented that my first couple posts are rather heavy. That is undoubtedly going to remain the case. I am a heavy dude.

Seriously, this blog is my way of talking about subjects and thoughts that nobody in my daily life typically has the time or interest in listening to (and there are the references to speaking again!). I’m imagining that there is an audience out there interested in these topics.

That being said, it’s not all deep. For example . . .

My son has been diagnosed with high functioning autism, which will most likely be translated into an Asberger’s Syndrome diagnosis as he gets older. He’s smart, loving, and wonderful.

He also loves routine and is slowly mastering certain life skills. Recently he made a breakthrough with his potty training. He graduated from pull-ups and night time diapers and rarely has an accident during the day or evening. This is a big step of which he and we are justifiably proud.

However, he either does not grasp or does not approve of the idea of wiping his own bottom after Number 2. He does recognize that this is a necessary step, but he insists upon me performing it. Given that he shows a remarkable talent for delaying his urges until he is at home or I am nearby and that I usually have several other things going on when he requests this service (“Daddy! Come wipe my bottom!”) he often gets his way.

(As a result I do possess a knowledge of my son’s bowel movements and stool on par with that of a medieval physician perusing the effluence of a noble client.)

Thus, I am truly “El Asso Wipo, wiper of other people’s bottoms.” (Those of you who used to watch Mad TV will get the reference. For the rest, here’s a pertinent link—scroll down to find the name on the list of recurring characters. For those unfamiliar with Mexican wrestling, here's some more context.)

Not a title I aspired to, but one I bear with pride. Now to learn how to "break people's backs on my knee, like so."

Considering the Topic of Hard Fantasy

I first came across the term Hard Fantasy in a reference to Michael Swanwick’s essay “In the Tradition,” which may well have coined the term. (I tracked down a used copy of The Year’s Best Fantasy and Horror Eighth Annual Collection, which reprinted the essay.)

Swanwick’s own definition of Hard Fantasy as presented in the essay is unclear. He refers to the stories within this nebulous genre as “those strange and shaggy literary creatures that have no ilk or kin.” He sees their role within fantasy fiction as akin to that of hard science fiction within the broader s.f. genre and in opposition to styles such as High Fantasy and Urban Fantasy (though some of the authors he cites seem within the realm of Urban Fantasy). The essay itself is very eloquently written and references many books I’d never heard of before and for the most part still haven’t found the time to read.

The very term Hard Fantasy was a helpful jumping off point for my own ideas about how to go about writing in the fantasy genre. The analogy to hard science fiction suggested the application of rigor and logic grounded in scientific principles to the realm of the fantastic. In other words, unless otherwise specified, the laws of science as we know them apply. More critically to me, the principles of social organization and cultural structure that we see apply.

The best examples I can think of for what I’m getting at are three short stories by the incomparable Ted Chiang: “Tower of Babylon,” “Seventy-Two Letters,” and “Hell is the Absence of God.” These are all collected in his wonderful short story anthology “Stories of Your Life and Others.” In each story the social, personal, and physical ramifications of a central fantastic conceit (it is possible to build a tower that reaches all the way to the vault of heaven; the principles of kabbalah can be combined with philology to animate inanimate matter; the world is regularly visited by old testament style angels, terrible in their wrath and beauty) are explored with relentless insight.

Hard Fantasy for me is an approach to the creation of stories and settings as much as a method of writing them. It is a sort of mental alchemy by which I try to transmute my modern sensibilities into a perspective that can encompass the fantastic and the magical without losing my bearings.

You might think that by trying to define the fantastic in rational terms one would rob the resulting stories of the essential elements of fantasy. For me, at least, these are the ability to evoke a sense of mystery, fear, and awe/wonder in a reader. Things need to be a little unbalanced, with the unexpected waiting in the dark woods. There is a lot of darkness in the human past, a certain brutality to the old religions and fairytales that is often lost in the present. (Today I heard a wonderful interview on the radio program "Fresh Air" with Spanish director Guillermo del Toro that touches upon some of these points.)

Personally I also think magic should be a bit frightening, chaotic, and unpredictable. But it can still function according to certain principles, or be seen (perhaps with fingers crossed) to follow those principles. And you can extrapolate what sort of society would develop from a reliance upon and/or a fear of such a means of manipulating reality.

But the logic used to define the parameters of a setting does not have to be embraced by the characters and cultures who inhabit it, nor explicitly stated to the reader. Consider how many different interpretations of natural laws existed in ancient cultures around the world. So a “hard” perspective on the principles of fantasy can be the hidden scaffolding for the rest of the setting.

I’m interested in depicting the essence of ideas like faeries, goblins, werewolves, and vampires without necessarily worrying about being true to any particular interpretation of the folktales that have grown up around them. I want to think about what it would mean if they could and did exist in real ecologies and societies that last, as well as what they mean psychologically.

But I’m not so concerned with trying to explain why a vampire might, say, be unable to enter a home without being invited. I want to think about what a vampire or an elf represents as a cultural concept. Why are they fascinating? What reactions do they evoke in “mundane” people? How would that change if they were more commonplace?

Most critically, how would such beings see the world around them? Why would they act as they do? How are they being misinterpreted? The same holds true for concepts ranging from druidic worship to mushroom eating to cannibalism to Dionysian rites to visions of archangels blazing with holy fire in the desert.

I’m not suggesting that other people haven’t done this sort of thing. It’s just what drives my own interest. The intersection of my interests in anthropology, history, cognitive science, literature, mythology, and science, I suppose.
Why think about writing Hard Fantasy as I’ve struggled to present it here, as opposed to Hard Science fiction, “Soft Science Fiction” or “Science Fantasy?” That’s a subject for another post.

First Post

"Thinking is more interesting than knowing, but less interesting than looking."
--Goethe

I'm anticipating taking the middle route here. That is, thinking in print about stuff that I've looked at but don't really know all that well.

I had to stop myself from writing the words "thinking out loud" above, realizing that this is a soundless exchange. (Or rather, it has no predefined sound associated with it--I'm surrounded by noise as I write this and I have no idea what you might be listening to.)

I use speech-related euphemisms a lot when writing electronically. It seems imprecise to me but habits are hard to break.

This brings to mind some reading I've been doing recently. Walter Ong's Orality and Literacy has a few chapters that examine the differences between the way literatre, preliterate, and semi-literate cultures perceive and describe the world around them.

As with most of the nonfiction that I read, I immediately think of this in terms of story and character. Take a standard fantasy "barbarian," for example. Rather than acting and speaking like an illiterate person from a literate society, wouldn't such an individual have a viewpoint based on oral culture?

Ong and others I've read suggest that such a viewpoint includes elements such as (A) a lack of general, Platonic definitions to apply to specific items in the surrounding world (for example, a picture of something round would not be described first as being a circle, but as some other specific round object like a plate) (B) an overriding pragmatism when dealing with hypothetical questions and (C) the belief that stories, laws, and such are being repeated verbatim when in fact they are slightly different every time, which might provide a greater flexibility over time, given that the rules and stories are adaptable to new circumstances by their very nature.

Oh well, dinner time approaches. Enough rambling for the first entry.