An artist-turned-scientist gradually understands her mother's message.

FOR A GRADE SCHOOLER, learning how to color within the lines is an important academic milestone, just as significant as mastering subtraction or learning how to write in cursive. Being able to color neatly shows that you're in control. You're not a baby anymore. A picture colored tastefully, with no stray marks, communicates a sort of worldliness, achieved only through experience with a well-worn box of Crayolas.

By the time I was eight years old, however, I still hadn't mastered this skill, and it caused me a great deal of anxiety. I realized my incompetence one day in the third grade when I dropped off a coloring assignment on my teacher's desk. I caught a glimpse of the work done by my classmates, and my heart sank. Their pictures looked as if they had been colored by professionals: the black outlines traced in a thick, dark ribbon of crayon and each shape filled in with light, parallel strokes. My picture, on the other hand, resembled the immature scribblings of a kindergartner. My cheeks flushed. My classmates obviously had a competitive edge over me.

For the rest of the year, I tried to imitate the two-part technique of my more skilled colleagues. I got the tracing down fine, but for some reason, I could never make my crayon strokes behave and stay within the black lines. Many times, I would be coloring away, concentrating, brushing the stubby, paper-wrapped wax stick across the paper, carefully stopping each stroke at the border. But then suddenly -- inevitably -- a spasm would overtake my hand and the tip of the crayon would leap across the great divide. Frustrated, I would revert to my former omnidirectional technique and scrawl out the rest -- anything to fill up that empty white void.

Looking for a scapegoat, I silently blamed my mother for my woeful lack of ability. A former art teacher, my mother didn't let me have coloring books when I was young. She said they discouraged creativity. Clearly, I was at a disadvantage. How was I supposed to know how to color within the lines? I was too young to know anything about developmental psychology, but I was sure the explanation lay in early coloring book deprivation.

When it comes to lines, there actually is evidence that during a short window of time, the brain can be trained to see some lines and not others. In 1964, two psychologists, Colin Blakemore and G.F. Cooper, conducted a kind of feline virtual reality experiment. They fitted two newborn kittens with two different pairs of goggles: one showing black vertical lines on a white background and the other horizontal lines. The kittens spent the first five months of their lives wearing these goggles, gazing at what must have seemed to be a very strange world.

The psychologists then removed the goggles and tested the kittens' ability to move through two different boxes, each containing a series of obstacles. In one box, horizontal poles stuck out from the sides at various heights, while the other had a forest of vertical poles running from top to bottom. The kittens acted like they could not see the lines that they had not been exposed to. The kitten who had seen nothing but vertical lines its whole life couldn't move through the box with horizontal poles, and the opposite was true of the other kitten. Although I don't believe I suffered as severe a fate as these kittens, I felt vindicated by the story.

Fortunately, by high school, I recovered from the coloring book trauma and signed up for a drawing class. But here, the concept of lines eluded me again. My fellow students and I would often spend the class time sketching the contours of still lifes planted in the middle of the tables in the room. The radio would murmur in the background (to stimulate our creative right brains, I suppose), and my teacher would stroll around the room, peering over our shoulders and dispensing advice on how to capture the subtle shadings of the forms in front of us.

Most of her words washed right by me as I concentrated on moving the soft charcoal pencil across the paper. But one day she said something that caught my attention: "Remember, class: lines don't exist in nature." I raised my head from my paper and looked at her. What did she mean? Of course they exist -- just look around -- they're everywhere. She explained that lines only represent a contrast between a light area and darker area, the boundary between the two. She was trying to get us to see the forms, the shapes that filled the space, not the space in between. She was trying to cure us of the coloring book mentality of drawing an outline and then filling in the rest -- a way of looking at the world my mother had hoped I wouldn't develop in the first place.

My art teacher probably borrowed her insight from a 19th-century painter named Thomas Eakins, who said, "There are no lines in nature...there are only form and color. The least important, the most changeable, the most difficult thing to catch about a figure is the outline." Eakins liked to paint human beings in motion -- especially lean, muscular rowers in their sculls, slicing through the calm waters of Philadelphia's Schuylkill River. Eakins focused on capturing the substantive flesh of his subjects with his paintbrushes, rather than their ephemeral outlines that shifted with every oar stroke.

Another more modern artist, Barnett Newman, specialized in painting what he called "zips" -- vertical stripes that ran the length of his canvases. Yet the space around the zips were the real subjects of his pieces, not the zips themselves. "Instead of using outlines, instead of making shapes or setting off spaces, my drawings declare the space. Instead of working with the remnants of space, I work with the space," he once said. Newman was interested in what was on either side of the lines rather than the lines themselves.

Artists have the luxury of thinking about lines in any way that suits them: as a concrete element of a figure, like Eakins did, or as an abstract concept, like Newman. But the way the eye physically sees objects also supports the idea of lines as artificial things created by humans. The retina of the eye is a dense carpet of light receptor cells called rods and cones. When light reflects off of an object, enters the eye and hits the retina, it switches on chemical reactions in the cells which then fire off electrical signals to the brain. The brain interprets these signals as an image and sees the object.

The lines that seem to be all around us in nature actually are coded by the eye as a contrast between light and dark, just as my art teacher said. The rods and cones continually send signals to the brain, spontaneously, even when there's no light to stimulate them. When we look at something with a sharp contrast, like the border of a white square on a black background, the white square causes the receptor cells to fire at a rate over the spontaneous level, which the brain registers as a bright area. But the dark background on the other side of the border doesn't stimulate the cells at all, and the rods and cones continue firing at the same level. No brightness there. Instant contrast is created, and you have a line.

Furthermore, the eye itself actually enhances the contrast at the border. With a process called lateral inhibition, the cells stimulated by the white square actively cause their neighbors to decrease their firing rate. On the white side of the border, away from the middle of the square, the cells are inhibited by only half as many of its neighbors since they're next to the dark area. The white side seems brighter. The cells on the black side of the border get inhibited by the cells on the white side without any direct stimulation of their own. The black side seems blacker. The eye itself creates the contrast -- the line -- rather than reflecting what is actually there.

I find it easier now to appreciate my mother's distaste for coloring books. I see that she wanted me to ignore the lines, the restrictions, and to create my own pictures. Though I haven't picked up a crayon or a charcoal pencil in years, the lessons taught by my mother and my art teacher have given me another, much-loved hobby: going to museums, staring at the paintings and not seeing the lines in them. I'm grateful, too, because in art as in nature, there's so much to look at in between.