“I guessed you’d say that,” Pickett replied, keeping his temper under control. “But please listen to me for a minute. My grandmother was Japanese, and when I was a kid she told me a story that I’d completely forgotten about until this week. I think it may save our lives.
“Sometime after the Second World War, there was a contest between an American with an electric desk calculator and a Japanese using an abacus like this. The abacus won.”
“Then it must have been a poor desk machine, or an incompetent operator.”
“They used the best in the U.S. Army. But let’s stop arguing. Give me a test—say a couple of three-figure numbers to multiply.”
“Oh—856 times 437.”
Pickett’s fingers danced over the beads, sliding them up and down the wires with lightning speed. There were twelve wires in all, so that the abacus could handle numbers up to 999,999,999,999—or could be divided into separate sections where several independent calculations could be carried out simultaneously.
“374072,” said Pickett, after an incredibly brief interval of time. “Now see how long you take to do it, with pencil and paper.”
There was a much longer delay before Martens, who like most mathematicians was poor at arithmetic, called out “375072”. A hasty check soon confirmed that Martens had taken at least three times as long as Pickett to arrive at the wrong answer.
The atronomer’s face was a study in mingled chagrin, astonishment, and curiosity.
“Where did you learn that trick?” he asked. “I thought those things could only add and subtract.”
“Well—multiplication’s only repeated addition, isn’t it? All I did was to add 856 seven times in the unit column, three times in the tens column, and four times in the hundreds column. You do the same thing when you use pencil and paper. Of course, there are some short cuts, but if you think I’m fast, you should have seen my granduncle. He used to work in a Yokohama bank, and you couldn’t see his fingers when he was going at speed. He taught me some of the tricks, but I’ve forgotten most of them in the last twenty years. I’ve only been practising for a couple of days, so I’m still pretty slow. All the same, I hope I’ve convinced you that there’s something in my argument.”
“You certainly have: I’m quite impressed. Can you divide just as quickly?”
“Very nearly, when you’ve had enough experience.”
Martens picked up the abacus, and started flicking the beads back and forth. Then he sighed.
“Ingenious—but it doesn’t really help us. Even if it’s ten times as fast as a man with pencil and paper—which it isn’t—the computer was a million times faster.”
“I’ve thought of that,” answered Pickett, a little impatiently.
(Martens had no guts—he gave up too easily. How did he think astronomers managed a hundred years ago, before there were any computers?)
“This is what I propose—tell me if you can see any flaws in it…”
Carefully and earnestly he detailed his plan. As he did so, Martens slowly relaxed, and presently he gave the first laugh that Pickett had heard aboard Challenger for days.
“I want to see the skipper’s face,” said the astronomer, “when you tell him that we’re all going back to the nursery to start playing with beads.”
There was scepticism at first, but it vanished swiftly when Pickett gave a few demonstrations. To men who had grown up in a world of electronics, the fact that a simple structure of wire and beads could perform such apparent miracles was a revelation. It was also a challenge, and because their lives depended upon it, they responded eagerly.
As soon as the engineering staff had built enough smoothly operating copies of Pickett’s crude prototype, the classes began. It took only a few minutes to explain the basic principles; what required time was practice—hour after hour of it, until the fingers flew automatically across the wires and flicked the beads into the right positions without any need for conscious thought. There were some members of the crew who never acquired both accuracy and speed, even after a week of constant practice: but there were others who quickly outdistanced Pickett himself.
They dreamed counters and columns, and flicked beads in their sleep. As soon as they had passed beyond the elementary stage they were divided into teams, which then competed fiercely against each other, until they had reached still higher standards of proficiency. In the end, there were men aboard Challenger who could multiply four-figure numbers on the abacus in fifteen seconds, and keep it up hour after hour.
Such work was purely mechanical; it required skill, but no intelligence. The really difficult job was Martens’, and there was little that anyone could do to help him. He had to forget all the machine-based techniques he had taken for granted, and rearrange his calculations so that they could be carried out automatically by men who had no idea of the meaning of the figures they were manipulating. He would feed them the basic data, and then they would follow the programme he had laid down. After a few hours of patient routine work, the answer would emerge from the end of the mathematical production line—provided that no mistakes had been made. And the way to guard against that was to have two independent teams working, cross-checking results at regular intervals.
“What we’ve done,” said Pickett into his recorder, when at last he had time to think of the audience he had never expected to speak to again, “is to build a computer out of human beings instead of electronic circuits. It’s a few thousand times slower, can’t handle many digits, and gets tired easily—but it’s doing the job. Not the whole job of navigating to Earth—that’s far too complicated—but the simpler one of giving us an orbit that will bring us back into radio range. Once we’ve escaped from the electrical interference around us, we can radio our position and the big computers on Earth can tell us what to do next.
“We’ve already broken away from the comet and are no longer heading out of the solar system. Our new orbit checks with the calculations, to the accuracy that can be expected. We’re still inside the comet’s tail, but the nucleus is a million miles away and we won’t see those ammonia icebergs again. They’re racing on towards the stars into the freezing night between the suns, while we are coming home…
“Hello, Earth… hello, Earth! This is Challenger calling, Challenger calling. Signal back as soon as you receive us—we’d like you to check our arithmetic—before we work our fingers to the bone!”