George and the Unbreakable Code

by Stephen Hawking

  In the Northern hemisphere, this happens between December 20 and December 23, otherwise known as the Winter Solstice.

  At the same time, in the Southern hemisphere, the South Pole is in full daylight for the whole 24-hour period. (In fact, a solar day is slightly under 24 hours, but we round it up.)

  As the Earth turns around the Sun, the tilt changes until it is the other way round. At the Summer Solstice (between June 20 and June 22), it is daylight for the full 24 hours at the North Pole. The rest of the world in between the poles receives a varying amount of light, lengthening or shortening the days.

  “Your dad said that looking for answers throughout the universe was like a man looking for his keys under a lamppost,” said George. “His keys aren’t there, but it’s the only place where there’s enough light for him to look.”

  “Yup, this is kind of the same.” Annie sounded sad. “Well, I don’t think we can wait any longer. Shall we try to get Ebot back before I shut the portal down?” She gave the command to zoom the portal in once more so that they could reach Ebot. But as she did so, George noticed a flash of red light on the comet.

  “Annie, stand back!” he cried.

  As she jumped back, away from the space doorway, they both saw a dot of bright red light latch on to Ebot’s chest. A moment later, robot pincer hands were pulling roughly at the makeshift peg structure they’d used to tether him to the comet.

  “They’ve got him!” George breathed. A second later, the space portal shut itself down as the supercomputer’s battery died.

  PICTURE FILES • CELESTIAL TWINS

  Gemini constellation, 1829 • Library of Congress/Science Photo Library)

  TWIN STARS

  Radio map of the double quasar

  Twin Quasar

  Twin star explosions

  Odd galaxy pair • NASA, ESA, and the Hubble Heritage (STScI/AURA)- ESA/Hubble Collaboration /SCIENCE PHOTO LIBRARY

  TWIN MOONS

  Double Helix • Phil Degginger/Science Photo Library

  Optical SETI © The Planetary Society

  Space junk • Roger Harris/Science Photo Library

  View of Earth • NASA

  UNIVERSE MARVELS

  Cosmic caterpillar • NASA, ESA and the Hubble Heritage Team (STScl/AURA), and IPHAS

  A collision: June 20 2013 • NASA, ESA and the Hubble Heritage Team (STScl/AURA)

  NASA, ESA and the Hubble Heritage Team (STScl/AURA) – Hubble/Europe Collaboration

  A brown dwarf – Jan 2013 • NASA, ESA and JPL-Caltech

  May 2012 – black hole swallowing a star • NASA, S. Gezari (JHU) and J. Guillochon (UC Santa Cruz)

  April 2013 – a Horsehead • NASA, ESA and the Hubble Heritage Team (STScl/AURA)

  “Ta-dah! I think I AM has captured Ebot!” Annie crowed.

  “So all we need to do is wait for them to take him to the mother ship, and then we can check in with the glasses to find out where it is!” replied George.

  Inside their space helmets, they were both beaming. They took them off and wriggled out of their suits.

  “We did it! We got our robot captured! Result!” Annie looked very pleased with herself.

  “Now we need to wait somewhere safe,” said George. “I don’t think we should stay in the tree house when it gets really dark.” As he bent down to pull off one of his space boots, he noticed something.

  “Annie … ,” he said slowly. “You know that slime—the stuff that I picked up on my boot in your kitchen …”

  “Yes.” She gazed at Cosmos’s blank screen.

  “It’s gone.”

  “What do you mean ‘gone’?” asked Annie, without looking up.

  “That goo on my boot!” said George, pointing. “It was covered in slime, which kind of looked like it was moving! And now it’s not there anymore!”

  “Whoa!” said Annie. “What if it was actually alive … and it’s wriggled its way onto the comet!”

  “We told Cosmos we were looking for the ingredients for life and said that was why we had to go into space! But instead, we’ve taken life into space and left it there … ,” said George slowly.

  “We?” said Annie, turning on her heel to glare at him.

  “Well, you’re the one investigating the ingredients for life,” he retorted.

  “Yeah, but it wasn’t me who stood in a great big puddle of living goo and then leaned through the space portal—only to find that it had crawled off to start its own colony.”

  In reply, George’s tummy gave an almighty growl, followed by some interesting gurgles and moans.

  The noise released the tension, and they both burst out laughing. Quickly they stashed their space suits and helmets in the tree house.

  Meanwhile Cosmos was now in his deep sleep, no longer able to hear or communicate with them.

  “What are we going to do?” Annie asked George quietly.

  “We need to look through the glasses to see if we can work out where Ebot has gone … and find a way to follow him.”

  “And we might need shelter overnight,” said Annie. “George, I’m almost scared,” she added.

  “I was,” he admitted. “But I’m not anymore. I was scared when I was wondering about what it would be like if everything in the world collapsed. It was way spookier when it was all in my head, but now that it’s actually happening … We’ve just got to keep going, that’s the main thing.”

  “Do you think we can use Cosmos to go after Ebot, once we work out where he is?”

  “I don’t think so,” said George. “Cosmos is just too dangerous. We have to assume that whoever is messing around with all the computer systems on Earth has also gotten into Cosmos and is making him behave strangely. And anyway, he’s run out of power. Even if we wanted to use him, we couldn’t … at least, not that Cosmos! C’mon, Annie, follow me! I’ve had an idea… .”

  Even as he spoke, he was already climbing down the rope ladder again. He jumped the last few rungs down onto solid ground and started to make his way across the garden to his back door.

  “Careful!” he whispered to Annie, hearing a sharp crunch underfoot. “Broken glass—smashed windows.”

  Together they gingerly edged their way into George’s kitchen, stepping lightly over the trapdoor that led down to where their families were hiding. They paused for a second but could hear only the soothing murmurs of their mothers chatting.

  George shook his head violently at Annie, to make sure she didn’t say anything. But she just crept on, catlike, feeling her way toward the front door, with George following close behind. The front door had been torn off its hinges, so it wasn’t totally dark inside. A small amount of ambient light, just enough for them to locate and pick up their skateboards, shone through.

  “This way,” whispered George, looking out into the empty street. “And quickly!”

  Both Annie and George had learned to skateboard the year before, when they had befriended skateboard champion Vincent, who had not only taught them some basic moves but left behind two of his boards when he moved back to Hollywood with his film-director parents. They would never be as good as him, but they could both skate quickly and safely. However, they’d never tried skating in near total darkness before, and now they stood outside George’s front door, holding their boards nervously.

  “Where are we going?” whispered Annie.

  “Your dad’s office at the Department of Math in town,” said George. “You know how to get in, right?”

  “Yup,” said Annie. “I can open the front door. But why are we going there?”

  “We’re going to find Old Cosmos!” said George. “Your dad’s original computer! The first ever supercomputer. That’s where he is, isn’t he—in the basement at the Math Department? He’s our only hope—if he’s still working, that is. But we’ve got to go and see. Has Ebot come through with any visuals yet?”

  “Ooops!” Annie fumbled in her shorts pocket and brought out the remote-access glasses. She put them on and flicked through
the screens using the eye-gaze technology.

  “Nope, nothing,” she said. “Hang on—what’s this?”

  “What?” George wondered if Ebot had suddenly popped into view.

  “It’s like I’m seeing everything around us clearly,” said Annie, “but the world’s turned a really pukey kind of green.”

  “It must be night vision!” George realized. “You must have night vision on your glasses!”

  “Amazing!” said Annie. “That means I can lead the way. Are you going to be able to see me if I go ahead?”

  “If I stay close enough, I can just see the reflectors on your sneakers,” George told her.

  “Let’s go, then. There’s no time to waste.” Annie zoomed off ahead of George, but kept checking behind her to see if he was following. She looked right and left through her night-vision glasses as she sped down the middle of the road. There were no cars about, but even so, she didn’t follow a direct route. Several times she had to veer off down side roads to avoid groups of people ahead. Fortunately, with her goggles, she could spot them well before they were aware of anyone coming their way. Turned green by the night-vision technology, they looked pretty scary; the sort of people she and George did not want to encounter.

  The riots were still simmering; those people who were still out on the streets were searching for anything they could lay their hands on—and George and Annie didn’t want the booty to be them.

  As they traveled through the center of the ancient university town, past the colleges with their grand columns, arches, and courtyards, they came across a sight that showed them how far and how fast Foxbridge had changed. Right outside the gate of one of the larger colleges—an impressive group of buildings with turrets and stained-glass windows, surrounded by sweeping lawns—a group of people sprawled around a bonfire; it looked like they were cooking scraps scavenged from the garbage bins they had emptied onto the sidewalk.

  This time Annie figured they simply needed to get past these people as quickly as possible; to avoid them would mean taking a very long way around. She pushed her skateboard along as fast as she could, and hurtled toward them, George following close behind.

  As they flew along, one or two people looked up at the sound of the skateboards, but made no move to intercept or follow them. They shot past, curving along the narrow street in a graceful arc.

  “That was easy!” said George. “No one’s interested in us!”

  But he had spoken too soon.

  As they carried on toward Eric’s office, he heard a noise behind them, getting ever closer. Turning while skateboarding at top speed isn’t easy, but George managed to peer behind him enough to see …

  “We’re being followed!” he shouted to Annie, not caring if whoever it was heard him.

  “Who by?” Annie’s voice flew back to him on the breeze.

  “It’s a robot,” yelled George. “Like the one from the Moon! And it’s catching up!”

  The robot was still a fair distance behind them, but just as it had on the Moon, it was eating up the ground as it strode along.

  “Faster!”

  George and Annie were moving so quickly now that the town was a blur around them. Behind them, the robot stumbled on the cobbles, its advanced technology seemingly unable to cope with the uneven surface of the ancient street.

  “It’s stopped!” said George as they scooted up to the doorway of the Department of Math. “Quick, Annie—get the door open!”

  “This is so weird!” she panted as she turned toward the entrance, and saw that the building was dark and empty now. “Were we wrong? Do they want us and not Dad?”

  “Don’t look around,” urged George. “Just unlock the door.” Peering through the darkness, he saw the sinister silver figure pick itself up and set off toward them again.

  Annie nodded. She concentrated on the combination lock that would open the Math Department for them: the small metal wheel protruded through an ancient brass panel next to the front door.

  Inside his head, George gave a silent scream. He couldn’t risk breaking Annie’s concentration as she worked on the lock, but the robot was nearly upon them—they were backed against the door and there was absolutely nowhere for them to go.

  Finally she got the correct code, and the lock—a mechanical rather than an electronic device—sprang apart; the grand old door swung open. They both ran through and breathed a sigh of relief as it slammed shut behind them. It was still pitch black inside the offices, and given the way the robot was now battering on the front door, they were far from safe.

  “Old Cosmos … ,” whispered George. “We need to find him.”

  Using the night-vision glasses, Annie steered them through the gloom, down to the door that led to the basement, where Old Cosmos was kept. Here they came to a stop. The door was locked.

  From upstairs, they heard the sound of breaking glass as the robot smashed the windows around the front door.

  “How do we get in?” whispered Annie. On the side of the door, an entry pad glowed faintly.

  “What’s the entry code?” George asked her.

  “Um, we’ll have to guess… .” She typed in a stream of numbers.

  “What was that?” George was trying to control his panic. He knew it would ruin everything if he made Annie lose her focus.

  “I just tried Dad’s birthday,” she said, “but that didn’t work. Then I tried Mom’s. And now …”

  She tapped away—and this time the door slid back, allowing them to enter.

  “That was my birthday,” said Annie, nearly crying with relief, “and it worked!” The door closed behind them with a satisfying slurp.

  The robot might still be able to break it down, but at least they had bought themselves some time.

  Inside, the enormous, ancient-looking machine was waiting for them. He took up most of the basement with the towers and stacks that contained his extensive circuitry. Looking at him, George thought it was a marvel that computers were now small enough to carry.

  Welcome, Annie, Cosmos said via a ream of old-fashioned computer paper—the sort with a series of punched holes along the edges. This Cosmos didn’t have a speaking voice—he had to print out whatever he wanted to say on paper. I’m glad to see you again.

  WHAT IS A COMPUTER?

  Mathematical laws

  It is a marvelous feature of the universe that everything in it seems to follow mathematical laws—anything from a planet to a beam of light or a sound wave—so we can predict what it can do by performing mathematics.

  A computing machine turns this around—we design and assemble a collection of parts that will behave according to some mathematics of our choosing. We allow the machine to then behave naturally (to “run”), and it performs the mathematics and gives us an answer. If the theory behind the machine, the way it is built, and our measurements are all sufficiently accurate, we can trust the final answer to be accurate.

  Nowadays, we are used to the idea that a computer can be programmed to do almost anything if it has enough memory and processor power, and that the programs themselves are just more data. But the computer you use today is a long way from the earliest designs… .

  A very early analogue computer

  Way back in second-century Greece, a very early computing machine—the Antikythera Mechanism—was built to simulate the cyclic behavior of the Sun, Moon, and planets, using rotating gear wheels. The designer of the machine drew an analogy between the celestial objects moving around the sky and bronze wheels, carefully arranged through a complex mechanism so that they would accurately reflect the arrangement in the sky of those celestial bodies at different times. Since it is based upon an analogy with a specific physical system, it is an example of an analogue computer.

  A slide rule—a ruler with a sliding central strip—is also an example of an early analogue computer. This handheld device was invented in the seventeenth century and widely used until the arrival of pocket-sized electronic calculators in the 1970s. It is based upo
n the mathematics of logarithms.

  But analogue computers have clear limits. The main disadvantage is that, once created, an analogue computer can only solve one type of problem with a fixed accuracy. A different problem may require different mathematical behavior, and so a different analogy, a different design, and a different machine.

  A human being, on the other hand, approaches calculation differently. He or she might start by writing down a set of equations, then transform these equations into other equations step by step using the rules of mathematics—a familiar process that you will know from school—for example, solving quadratic equations.

  A new form of computational device was needed to tackle problems in this way.

  A computer powered by steam!

  Mechanical calculators followed—Pascal’s of the seventeenth century was groundbreaking at the time. Then, in 1837, Charles Babbage designed an Analytical Engine that (if it had been built) would have been the first programmable computer—it would have used punched cards for programs and data, used only mechanical parts, and been capable of performing like a Universal Turing machine—although it would also have been 100 million times slower than a modern computer! And it was powered by steam… .

  From Turing to the first digital computers

  A digital computer is a machine designed to automatically follow algorithms (like a human being might follow an algorithm, only much faster). In practice, it turns an input whole number (possibly very big) into an output whole number.

  Why whole numbers?

  It is easy to turn text into numbers—for example, in the ASCII scheme, “A” is represented by 65 and “Z” by 122. For actual numbers, in practice we always want to deal with fractions to a certain number of decimal places (or precision), e.g. 99.483. This is the same as 0.99483 times 100 (or 10 x 10, written mathematically as 102). So a digital computer only really has to store the whole numbers (integers) 99483 and the number 2, which tells us the power of 10 that is used (102).