Cornut turned to relish the construction Pascal had first written down, centuries before. 'You will note,' he said, 'that each number is the sum of the two terms nearest in the line above it. The Pascal Triangle is more than a pretty pattern. It represents—' He had them. Their faces were rapt. The class was going very well.
Cornut picked up the ivory-tipped pointer that lay on his desk, clustered with the ceremonial desk furnishings of the instructor - paper cutter, shears, pencils; all there for appearance - and with the aid of every audio-visual help possible to man, began explaining to three million viewers the relation between Pascal's Triangle and the binomial distribution.
Every line on Cornut's face, every word, every posturing ballet dancer or animated digit that showed itself on the monitor behind him, was caught in the tubes of the cameras, converted into high-frequency pulses and hurled out at the world.
Cornut had more than a hundred live watchers - the cream; the chosen ones who were allowed to attend University in person - but his viewers altogether numbered three million. In the relay tower at Port Monmouth a senior shift engineer named Sam Gensel watched with concentrated attention as across the dimpled tummies of the five girls in the fourth line of the Pascal Triangle electronics superimposed the symbols
He was not interested in the astonishing fact that the signs of the five terms in the expansion of (p + q)4 were 1, 4, 6, 4 and 1 - the same as the numbers in the fourth line of the triangle - but he cared very much that the image was a trifle fuzzy. He twisted a vernier, scowled, turned it back; threw switches that called in an alternate circuit, and was rewarded by a crisper, clearer image. At some relay point a tube was failing. He picked up the phone to call the maintenance crew.
The crisper, clearer signal was beamed up to the handiest television-relay satellite and showered back down on the world. On the Sandy Hook texas a boy named Roger Hoskins, smelling seriously of fish, paused by the door of his room to watch. He did not care about mathematics, but he was a faithful viewer, his sister was in the class, and Mom was always grateful when he could tell her that he'd caught a glimpse of their very fortunate, very seldom encountered daughter. In a creche over lower Manhattan three toddlers munched fibrous crackers and watched; the harried nursery teacher had discovered that the moving colours kept them quiet. On the twenty-fifth floor of a tenement on Staten Island a monocar motorman named Frank Moran sat in front of his set while Cornut reviewed Pascal's thesis. Moran did not get much benefit from it. He had just come off the night shift. He was asleep.
There were many of them, the accidental or disinterested dialers-in. But there were more, there were thousands, there were uncounted hundreds of thousands who were following the proceedings with absorption.
For education was something very precious indeed.
The thirty thousand at the University were the lucky ones; they had passed the tests, stiffer every year. Not one out of a thousand passed those tests; it wasn't only a matter of intelligence, it was a matter of having the talents that could make a University education fruitful - in terms of society. For the world had to work. The world was too big to be idle. The land that had fed three billion people now had to feed twelve billion.
Cornut's television audience could, if it wished, take tests and accumulate credits. That was what Sticky Dick was for; electronically it graded papers, supplied term averages and awarded diplomas for students no professor ever saw. Almost always the credits led nowhere. But to those trapped in dreary production or drearier caretaker jobs for society, the hope was important. There was a young man named Max Steck, for example, who had already made a small contribution to the theory of normed rings. It was not enough. Sticky Dick said he would not justify a career in mathematics. He was trapped as a sex-writer, for Sticky Dick's analysers had found him prurient-minded and creative. There were thousands of Max Stecks.
Then there was Charles Bingham. He was a reactor hand at the 14th Street generating plant. Mathematics might help him, in time, become a supervising engineer. It also might not - the candidates for that job were already lined up fifty deep. But there were half a million Charles Binghams.
Sue-Ann Flood was the daughter of a farmer. Her father drove a helipopper, skimming the ploughed fields, seeding, spraying, fertilizing, and he knew that the time she put in on college-level studies would not help her gain admittance to the University. Sue-Ann knew it too; Sticky Dick measured abilities and talents, not knowledge. But she was only fourteen years old. She hoped. There were more than two million like Sue-Ann, and every one of them knew that all the others would be disappointed.
Those, the millions of them, were the invisible audience who watched Master Cornut's tiny image on a cathode screen. But there were others. One watched from Bogota and one from Buenos Aires. One in Saskatchewan said, You goofed this morning, and one flying high over the Rockies said, Can't we try him now? And one was propped on incredibly soft pillows in front of a set not more than a quarter of a mile from Cornut himself; and he said, It's worth a try. The son of a bitch is getting in my hair.
It was not the easiest task ever given man, to explain the relationship between the Pascal Triangle and the Binomial Distribution, but Cornut was succeeding. Master Carl's little mnemonic jingles helped, and what helped most of all was the utter joy Cornut took in it all. It was, after all, his life. As he led the class, he felt again the wonder he himself had felt, sitting in a class like this one. He hardly heard the buzz from the class as he put his pointer down to gesture, and blindly picked it up again, still talking. Teaching mathematics was a kind of hypnosis for him, an intense, gut-wrenching absorption that had gripped him from the time of his first math class. That was what Sticky Dick had measured, and that was why Cornut was a full professor at thirty. It was a wonder that so strange a thing as a number should exist in the first place, rivalled only by the greater wonder that they should perform so obediently the work of mankind.
The class buzzed and whispered.
It struck Cornut cloudily that they were whispering more than usual.
He looked up, absent-mindedly. There was an itch at the base of his throat. He scratched it with the tip of the pointer, half distracted from the point he was trying to make. But the taped visual aids on the screen were timed just so and he could not falter; he picked up the thread of what he was saying; itch and buzz faded out of his mind...
Then he faltered again.
Something was wrong. The class was buzzing louder. The students in the first row were staring at him with a unanimous, unprecedented expression. The itch returned compellingly. He scratched at it; it still itched; he dug at it with the pointer.
—No. Not with the pointer. Funny, he thought, there was the pointer on his desk.
Suddenly his throat hurt very much.
'Master Cornut, stop!' screamed someone - a girl ... Tardily he recognized the voice, Locille's voice, as she leaped to her feet, and half the class with her. His throat was a quick deep pain, like fire. A warm tickling thread slipped across his chest - blood! From his throat! He stared at the thing in his hand, and it was not the pointer at all but the letter-opener, steel and sharp. Confused and panicked, he wheeled to gaze at the monitor. There was his own face, over a throat that bore a narrow trickling slash of blood!