But if something as big as the Earth turned once a day, it had to be moving ridiculously fast. Everyone she knew must be whirling at an unbelievable speed. She though she could now actually feel the Earth turn–not just imagine it in her head, but really feel it in the pit of her stomach. It was like descending in a fast elevator. She craned her neck back further, so her field of view was uncontaminated by anything on Earth, until she could see nothing but black sky and bright stars. Gratifyingly, she was overtaken by the giddy sense that she had better clutch the clumps of grass on either side of her and hold on for dear life, or else fall up into the sky, her tiny tumbling body dwarfed by the huge darkened sphere below.
She actually cried out before she managed to stifle the scream with her wrist. That was how her cousins were able to find her. Scrambling down the slope, they discovered on her face an uncommon mix of embarrassment and surprise, which they readily assimilated, eager to find some small indiscretion to carry back and offer to her parents.
* * *
The book was better than the movie. For one thing, there was a lot more in it. And some of the pictures were awfully different from the movie. But in both, Pinocchio–a life-sized wooden boy who magically is roused to life–wore a kind of halter, and there seemed to be dowels in his joints. When Geppetto is just finishing the construction of Pinocchio, he turns his back on the puppet and is promptly sent flying by a well- placed kick. At that instant the carpenter’s friend arrives and asks him what he is doing sprawled on the floor. “I am teaching,” Geppetto replies with dignity, “the alphabet to the ants.”
The seemed to Ellie extremely witty, and she delighted in recounting it to her friends. But each time she quoted it there was an unspoken question lingering at the edge of her consciousness: Could you teach the alphabet to the ants? And would you want to? Down there with hundreds of scurrying insects who might crawl all over your skin, or even sting you? What could ants know, anyway?
* * *
Sometimes she would get up in the middle of the night to go to the bathroom and find her father there in his pajama bottoms, his neck craned up, a kind of patrician disdain accompanying the shaving cream on his upper lip. “Hi, Presh,” he would say. It was short for “precious,” and she loved him to call her that. Why was he shaving at night, when no one would know if he had a beard? “Because”–he smiled–“your mother will know.” Years later, she discovered that she had understood this cheerful remark only incompletely. Her parents had been in love.
* * *
After school, she had ridden her bicycle to a little park on the lake. From a saddlebag she produced The Radio Amateur’s Handbook and A Connecticut Yankee in King Arthur’s Court. After a moment’s consideration, she decided on the latter. Twain’s hero had been conked on the head and awakened in Arthurian England. Maybe it was all a dream or a delusion. But maybe it was real. Was it possible to travel backwards in time? Her chin on her knees, she scouted for a favorite passage. It was when Twain’s hero is first collected by a man dressed in armor who he takes to be an escapee from a local booby hatch. As they reach the crest of the hill they see a city laid out before them:
“`Bridgeport?’ said I…
“`Camelot,’ said he.”
She stared out into the blue lake, trying to imagine a city which could pass as both nineteenth- century Bridgeport and sixth-century Camelot, when her mother rushed up to her.
“I’ve looked for you everywhere. Why aren’t you where I can find you? Oh, Ellie,” she whispered, “something awful’s happened.”
* * *
In the seventh grade they were studying “pi.” It was a Greek letter that looked like the architecture at Stonehenge, in England: two vertical pillars with a crossbar at top–?. If you measured the circumference of a circle and then divided it by the diameter of the circle, that was pi. At home, Ellie took the top of a mayonnaise jar, wrapped a string around it, straightened the string out, and with a ruler measured the circle’s circumference. She did the same with the diameter, and by long division divided the one number by the other. She got 3.21. That seemed simple enough.
The next day the teacher, Mr. Weisbrod, said that ? was about 22/7, about 3.1416. But actually, if you wanted to be exact, it was a decimal that went on and on forever without repeating the pattern of numbers. Forever, Ellie thought. She raised her hand. It was the beginning of the school year and she had not asked any questions in this class.
“How could anybody know that the decimals go on and on forever?”
“That’s just the way it is,” said the teacher with some asperity.
“But why? How do you know? How can you count decimals forever?”
“Miss Arroway”–he was consulting his class list–“this is a stupid question. You’re wasting the class’s time.”
No one had ever called Ellie stupid before, and she found herself bursting into tears. Billy Horstman, who sat next to her, gently reached out and placed his hand over hers. His father had recently been indicted for tampering with the odometers on the used cars he sold, so Billy was sensitive to public humiliation. Ellie ran out of the class sobbing.
After school she bicycled to the library at the nearby college to look through books on mathematics. As nearly as she could figure out from what she read, her question wasn’t all that stupid. According to the Bible, the ancient Hebrews had apparently thought that ? was exactly equal to three. The Greeks and Romans, who knew lots of things about mathematics, had no idea that the digits in ? went on forever without repeating. It was a fact that had been discovered only about 250 years ago. How was she expected to know if she couldn’t ask questions? But Mr. Weisbrod had been right about the first few digits. Pi wasn’t 3.21. Maybe the mayonnaise lid had been a little squashed, not a perfect circle. Or maybe she’d been sloppy in measuring the string. Even if she’d been much more careful, though, they couldn’t expect her to measure an infinite number of decimals.
There was another possibility, though. You could calculate pi as accurately as you wanted. If you knew something called calculus, you could prove formulas for ? that would let you calculate it to as many decimals as you had time for. The book listed formulas for pi divided by four. Some of them she couldn’t understand at all. But there were some that dazzled her: ?/4, the book said, was the same as 1 – 1/3 + 1/5 – 1/7…, with the fractions continuing on forever. Quickly she tried to work it out, adding and subtracting the fractions alternately. The sum would bounce from being bigger than ?/4 to being smaller than ?/4, but after a while you could see that this series of numbers was on a beeline for the right answer. You could never get there exactly, but you could get as close as you wanted if you were very patient. It seemed to her a miracle that the shape of every circle in the world was connected with this series of fractions. How could circles know about fractions? She was determined to learn calculus.
The book said something else: ? was called a “transcendental” number. There was no equation with ordinary numbers in it that could give you ? unless it was infinitely long. She had already taught herself a little algebra and understood what this meant. And ? wasn’t the only transcendental number. In fact there was an infinity of transcendental numbers. More than that, there were infinitely more transcendental numbers than ordinary numbers, even though ? was the only one of them she had ever heard of. In more ways than one, ? was tied to infinity.
She had caught a glimpse of something majestic. Hiding between all the ordinary numbers was an infinity of transcendental numbers whose presence you would never have guessed unless you looked deeply into mathematics. Every now and then one of them, like ?, would pop up unexpectedly in everyday life. But most of them–an infinite number of them, she reminded herself–were hiding, minding their own business, almost certainly unglimpsed by the irritable Mr. Weisbrod.
* * *
She saw through John Staughton from the first. How her mother could ever contemplate marrying him– never mind that it was only two years after her father’s death–was an impenetrable mystery. He was nice enough looking, and he could pretend, when he put his mind to it, that he really cared about you. But he was a martinet. He made students come over weekends to weed and garden at the new house they had moved into, and then made fun of them after they left. He told Ellie that she was just beginning high school and was not to look twice at any of his bright young men. He was puffed up with imaginary self-importance. She was sure that as a professor he secretly despised her dead father, who had been only a shopkeeper. Staughton had made it clear that an interest in radio and electronics was unseemly for a girl, that it would not catch her a husband, that understanding physics was for her a foolish and aberrational notion. “Pretentious,” he called it. She just didn’t have the ability. This was an objective fact that she might as well get used to. He was telling her this for her own good. She’d thank him for it in later life. He was, after all, an associate professor of physics. He knew what it took. These homilies would always infuriate her, even though she had never before–despite Staughton’s refusal to believe it–considered a career in science.