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.
He was not a gentle man, as her father had been, and he had no idea what a sense of humor was.
When anyone assumed that she was Staughton's daughter, she would be outraged. Her mother and stepfather never suggested that she change her name to Staughton; they knew what her response would be.
Occasionally there was a little warmth in the man, as when, in her hospital room just after her tonsillectomy, he had brought her a splendid kaleidoscope.
“When are they going to do the operation,” she had asked, a little sleepily.
“They've already done it,” Staughton had answered. “You're going to be fine.” She found it disquieting that whole blocks of time could be stolen without her knowledge, and blamed him. She knew at the time it was childish.
That her mother could truly love him was inconceivable. She must have remarried out of loneliness, out of weakness. She needed someone to take care of her. Ellie vowed she would never accept a position of dependence. Ellie's father had died, her mother had grown distant, and Ellie felt herself exiled to the house of a tyrant. There was no one to call her Presh anymore.
She longed to escape.
“Bridgeport?” said I.
“Camelot,” said he.”
CHAPTER 2
Coherent Light
Since I first gained the use of reason my inclination toward learning has been so violent and strong that neither the scoldings of other people… nor my own reflections… have been able to stop me from following this natural impulse that God gave me. He alone must know why; and He knows too that I have begged Him to take the light of my understanding, leaving only enough for me to keep His law, for anything else is excessive in a woman, according to some people. And others say it is even harmful.
I wish to propose for the reader's favourable consideration a doctrine which may, I fear, appear wildly paradoxical and subversive. The doctrine in question is this: that it is undesirable to believe a proposition when there is no ground whatever for supposing it true. I must, of course, admit that if such an opinion became common it would completely transform our social life and our political system; since both are at present faultless, this must weigh against it.
Surrounding the blue-white star in its equatorial plane was a vast ring of orbiting debris—rocks and ice, metals and organics—reddish at the periphery and bluish closer to the star. The worldsized polyhedron plummeted through a gap in the rings and emerged out the other side. In the ring plane, it had been intermittently shadowed by icy boulders and tumbling mountains. But now, carried along its trajectory toward a point above the opposite pole of the star, the sunlight gleamed off its millions of bowl-shaped appendages. If you looked very carefully you might have seen one of them make a slight pointing adjustment. You would not have seen the burst of radio waves washing out from it into the depths of space.
For all the tenure of humans on Earth, the night sky had been a companion and an inspiration. The stars were comforting. They seemed to demonstrate that the heavens were created for the benefit and instruction of humans. This pathetic conceit became the conventional wisdom worldwide. No culture was free of it.
Some people found in the skies an aperture to the religious sensibility. Many were awestruck and humbled by the glory and scale of the cosmos. Others were stimulated to the most extravagant flights of fancy.
At the very moment that humans discovered the scale of the universe and found that their most unconstrained fancies were in fact dwarfed by the true dimensions of even the Milky Way Galaxy, they took steps that ensured that their descendants would be unable to see the stars at all. For a million years humans had grown up with a personal daily knowledge of the vault of heaven. I the last few thousand years they began building and emigrating to the cities. In the last few decades, a major fraction of the human population had abandoned a rustic way of life. As technology developed and the cities were polluted, the nights became starless. New generations grew to maturity wholly ignorant of the sky that had transfixed their ancestors and that had stimulated the modern age of science and technology. Without even noticing, just as astronomy entered a golden age most people cut
