Contents
Cover
About the Book
Also by Lucy and Stephen Hawking
Title Page
Dedication
Latest Scientific Ideas!
Chapter One
Chapter Two
Chapter Three
Chapter Four
Chapter Five
Chapter Six
Chapter Seven
Chapter Eight
Chapter Nine
Chapter Ten
Chapter Eleven
Chapter Twelve
Chapter Thirteen
Chapter Fourteen
Chapter Fifteen
Chapter Sixteen
Chapter Seventeen
Chapter Eighteen
Chapter Nineteen
Acknowledgements
About the Authors
Praise for the GEORGE series
Copyright
George’s Secret Key to the Universe
George’s Cosmic Treasure Hunt
George and the Big Bang
For details of Stephen Hawking’s books for adult readers, see:
www.hawking.org.uk
www.randomhouse.co.uk
GEORGE AND THE UNBREAKABLE CODE
AN RHCP DIGITAL EBOOK 978 1 448 17469 0
Published in Great Britain by RHCP Digital,
an imprint of Random House Children’s Publishers UK
A Random House Group Company
This ebook edition published 2014
Copyright © Lucy Hawking, 2014
Cover artwork, design and lettering © Blacksheep-uk
Spacesuit photographs on cover © Blue Jean Images / Superstock
Illustrations by Garry Parsons
Illustrations/Diagrams copyright © Random House Children’s Publishers, 2014
First Published in Great Britain by Doubleday Childrens, 2014
The right of Lucy Hawking to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988.
This ebook is copyright material and must not be copied, reproduced, transferred, distributed, leased, licensed or publicly performed or used in any way except as specifically permitted in writing by the publishers, as allowed under the terms and conditions under which it was purchased or as strictly permitted by applicable copyright law. Any unauthorized distribution or use of this text may be direct infringement of the author’s and publisher’s rights and those responsible may be liable in law accordingly.
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A CIP catalogue record for this book is available from the British Library.
In this chapter, I would like to talk to you about the development of life in the Universe, and in particular, the development of intelligent life. I shall take this to include the human race, even though much of its behaviour throughout history has been pretty stupid!
We all know that things get more disordered and chaotic with time. This observation even has its own law, the so-called Second Law of Thermodynamics. This law says that the total amount of disorder, or entropy, in the Universe, always increases with time. However, the Law refers only to the total amount of disorder. The order in one body can increase, provided that the amount of disorder in its surroundings increases by a greater amount.
This is what happens in a living being. We can define life to be an ordered system that can keep itself going against the tendency to disorder, and can reproduce itself. That is, it can make similar, but independent, ordered systems. To do these things, the system must convert energy in some ordered form – like food, sunlight, or electric power – into disordered energy, in the form of heat. In this way, the system can satisfy the requirement that the total amount of disorder increases while, at the same time, increasing the order in itself and its offspring. This sounds like parents living in a house which gets messier and messier each time they have a new baby!
A living being like you or me usually has two elements: a set of instructions that tell the system how to keep going and how to reproduce itself, and a mechanism to carry out the instructions. In biology, these two parts are called genes and metabolism.
What we normally think of as ‘life’ is based on chains of carbon atoms, with a few other atoms such as nitrogen or phosphorous. There was no carbon when the Universe began in the Big Bang, about 13.8 billion years ago. It was so hot that all the matter would have been in the form of particles, called protons and neutrons. There would initially have been equal numbers of protons and neutrons. However, as the Universe expanded, it cooled. About a minute after the Big Bang, the temperature would have fallen to about a billion degrees, about a hundred times the temperature in the Sun. At this temperature, neutrons start to decay into more protons.
If this had been all that had happened, all the matter in the Universe would have ended up as the simplest element, hydrogen, whose nucleus consists of a single proton. However, some of the neutrons collided with protons and stuck together to form the next simplest element, helium, whose nucleus consists of two protons and two neutrons. But no heavier elements, like carbon or oxygen, would have been formed in the early Universe. It is difficult to imagine that one could build a living system out of just hydrogen and helium – and anyway the early Universe was still far too hot for atoms to combine into molecules.
The Universe continued to expand, and cool. But some regions had slightly higher densities than others and the gravitational attraction of the extra matter in those regions slowed down their expansion, and eventually stopped it. Instead, they collapsed to form galaxies and stars, starting from about two billion years after the Big Bang. Some of the early stars would have been more massive than our Sun; they would have been hotter than the Sun and would have burnt the original hydrogen and helium into heavier elements, such as carbon, oxygen, and iron. This could have taken only a few hundred million years. After that, some of the stars exploded as supernovas, and scattered the heavy elements back into space, to form the raw material for later generations of stars.
Our own solar system was formed about four and a half billion years ago, or about ten billion years after the Big Bang, from gas contaminated with the remains of earlier stars. The Earth was formed largely out of the heavier elements, including carbon and oxygen. Somehow, some of these atoms came to be arranged in the form of molecules of DNA. This has the famous double helix form, discovered in the 1950s by Crick and Watson in a hut on the New Museum site in Cambridge. Linking the two chains in the helix are pairs of nucleic acids. There are four types of nucleic acids – adenine, cytosine, guanine, and thiamine.
We do not know how DNA molecules first appeared. As the chances against a DNA molecule arising by random fluctuations are very small, some people have suggested that life came to Earth from elsewhere – for instance, brought here on rocks breaking off from Mars while the planets were still unstable – and that there are seeds of life floating round in the galaxy. However, it seems unlikely that DNA could survive for long in the radiation in space. There is fossil evidence that there was some form of life on Earth about three and a half billion years ago. This may have been only 500 million years after the Earth became stable and cool enough for life to develop. The early appearance of life on Earth suggests that there is a good chance of the spontaneous generation of life in suitable conditions. Maybe there was some simpler form of organization which built up DNA. Once DNA appeared, it would have been so successful that it might have completely replaced the earlier forms. We don’t know what these earlier forms would have been, but one possibility is RNA.
RNA is like DNA, but rather simpler, and without the double helix structure. Short lengths of RNA could reproduce themselves like DNA, and might eventually build up to DNA. We cannot make nucleic acids in the laboratory from non-living material, let alone RNA. But given 500 million years, and oceans covering most of the Earth, there might be a reasonable probability of RNA being made by chance.
As DNA reproduced itself, there would have been random errors, many of which would have been harmful and would have died out. Some would have been neutral – they would not have affected the function of the gene. And a few errors would have been favourable to the survival of the species – these would have been chosen by Darwinian natural selection.
The process of biological evolution was very slow at first. It took two and a half billion years to evolve from the earliest cells to multi-cell animals, and another billion years to evolve through fish and reptiles to mammals. But then evolution seemed to have speeded up. It only took about a hundred million years to develop from the early mammals to us. The reason is that fish contain most of the important human organs and mammals – essentially, all of them. All that was required to evolve from early mammals, like lemurs, to humans, was a bit of fine-tuning.
But with the human race, evolution reached a critical stage, comparable in importance with the development of DNA. This was the development of language, and particularly written language. It meant that information can be passed on from generation to generation, other than genetically through DNA. There has been some detectable change in human DNA, brought about by biological evolution, in the ten thousand years of recorded history, but the amount of knowledge handed on from generation to generation has grown enormously. I have written books to tell you something of what I have learned about the universe in my long career as a scientist, and in doing so I am transferring knowledge from my brain to the page so you can read it.
The DNA in human beings contains about three billion nucleic acids. However, much of the information coded in this sequence is redundant, or is inactive. So the total amount of useful information in our genes is probably something like a hundred million bits. One bit of information is the answer to a yes/no question. By contrast, a paperback novel might contain two million bits of information. So a human is equivalent to about 50 Harry Potter books, and a major national library can contain about five million books – or about ten trillion bits. So the amount of information handed down in books or via the internet is a hundred thousand times as much as in DNA!
This means that we have entered a new phase of evolution. At first, evolution proceeded by natural selection – from random mutations. This Darwinian phase lasted about three and a half billion years and produced us, beings who developed language to exchange information. But in the last ten thousand years or so, we have been in what might be called an external transmission phase. In this, the internal record of information, handed down to succeeding generations in DNA, has changed somewhat. But the external record – in books, and other long lasting forms of storage – has grown enormously.
Some people would use the term ‘evolution’ only for the internally transmitted genetic material, and would object to it being applied to information handed down externally. But I think that is too narrow a view. We are more than just our genes. We may be no stronger, or inherently more intelligent than our caveman ancestors. But what distinguishes us from them is the knowledge that we have accumulated over the last ten thousand years, and particularly over the last three hundred. I think it is legitimate to take a broader view, and include externally transmitted information, as well as DNA, in the evolution of the human race.
But we still have the instincts, and in particular, the aggressive impulses, that we had in caveman days. Aggression, in the form of subjugating or killing others and taking their food, has had definite survival advantage, up to the present time. But now it could destroy the entire human race, and much of the rest of life on Earth. A nuclear war is still the most immediate danger, but there are others, such as the release of a genetically engineered virus. Or the greenhouse effect becoming unstable.
There is no time to wait for Darwinian evolution to make us more intelligent, and better-natured! But we are now entering a new phase of what might be called self-designed evolution, in which we will be able to change and improve our DNA. We have now mapped DNA which means we have read ‘the book of life’. So we can start writing in corrections. At first, these changes will be confined to the repair of genetic defects – like cystic fibrosis, and muscular dystrophy, which are controlled by single genes, and so are fairly easy to identify and correct. Other qualities, such as intelligence, are probably controlled by a large number of genes, and it will be much more difficult to find them and work out the relations between them. Nevertheless, I am sure that during the next century, people will discover how to modify both intelligence, and instincts like aggression.
If the human race manages to redesign itself, to reduce or eliminate the risk of self-destruction, it will probably spread out, and colonize other planets and stars. However, long-distance space travel will be difficult for chemically based life forms – like us – based on DNA. The natural lifetime for such beings is short, compared to the travel time. According to the theory of relativity, nothing can travel faster than light, so a round trip to the nearest star would take at least eight years, and to the centre of the galaxy about a hundred thousand years. In science fiction, they overcome this difficulty by space warps, or travel through extra dimensions. But I don’t think these will ever be possible, no matter how intelligent life becomes. In the theory of relativity, if one can travel faster than light, one can also travel back in time, and this would lead to problems with people going back and changing the past. One would also expect to have already seen large numbers of tourists from the future, curious to look at our quaint, old-fashioned ways!
It might be possible to use genetic engineering, to make DNA-based life survive indefinitely, or at least for a hundred thousand years. But an easier way, which is almost within our capabilities already, would be to send machines. These could be designed to last long enough for interstellar travel. When they arrived at a new star, they could land on a suitable planet and mine material to produce more machines, which could be sent on to yet more stars. These machines would be a new form of life, based on mechanical and electronic components, rather than macromolecules. They could eventually replace DNA-based life, just as DNA may have replaced an earlier form of life.
What are the chances that we will encounter some alien form of life, as we explore the galaxy? If the argument about the timescale for the appearance of life on Earth is correct, there ought to be many other stars whose planets have life on them. Some of these stellar systems could have formed five billion years before the Earth – so why is the galaxy not crawling with self-designing mechanical or biological life forms? Why hasn’t the Earth been visited, and even colonized? By the way, I discount suggestions that UFOs contain beings from outer space, as I think that any visits by aliens would be much more obvious - and probably also, much more unpleasant.
So why haven’t we been visited? Maybe the probability of life spontaneously appearing is so low that Earth is the only planet in the galaxy – or in the observable Universe – on which it happened. Another possibility is that there was a reasonable probability of forming self-reproducing systems, like cells, but that most of these forms of life did not evolve intelligence. We are used to thinking of intelligent life as an inevitable consequence of evolution, but what if it isn’t? Is it more likely that evolution is a random process, with intelligence as only one of a large number of possible outcomes?
It is not even clear that intelligence has any long-term survival value. Bacteria, and other single-cell organisms, may live on if all other life on Earth is wiped out by our actions. Perhaps intelligence was an unlikely development for life on Earth, from the chronology of evolution, as it took a very long time – two and a half billion years – to go from single cells to multi-cell beings, which are a necessary precursor to intelligence. This is a good fraction of the total time available before the Sun blows up. So it would be consistent with the hypothesis that the probability for life to develop intelligence is low. In this case, we might expect to find many other life forms in the galaxy, but we are unlikely to find intelligent life.
Another way in which life could fail to develop to an intelligent stage would be if an asteroid or comet were to collide with the planet. It is difficult to say how often such collisions occur, but a reasonable guess might be every twenty million years, on average. If this figure is correct, it would mean that intelligent life on Earth has developed only because of the lucky chance that there have been no major collisions in the last 67 million years. Other planets in the galaxy, on which life has developed, may not have had a long enough collision-free period to evolve intelligent beings.
A third possibility is that there is a reasonable probability for life to form – and to evolve to intelligent beings but the system becomes unstable, and the intelligent life destroys itself. This would be a very pessimistic conclusion and I very much hope it isn’t true.
I prefer a fourth possibility: that there are other forms of intelligent life out there, but that we have been overlooked. There used to be a project called SETI – the Search for Extra-Terrestrial Intelligence – which involved scanning the radio frequencies to see if we could pick up signals from alien civilizations. But we need to be wary of answering back until we have developed a bit further! Meeting a more advanced civilization, at our present stage, might be a bit like the original inhabitants of America meeting Columbus – and I don’t think they thought they were better off for it!
Stephen
‘Like a Dr Who adventure, inspiring curiosity and amazement’ Sunday Times
‘a dramatic adventure story for any young cosmologist in the aking . . . Lucy and Stephen Hawking’s first venture into the world of children’s books offers a lucid and imaginative lesson in the physics of space and time’ Guardian
‘a delightful book for young readers’ Independent
‘a novel anyone who devoured Captain Underpants a year or two ago will appreciate’ Los Angeles Times
‘A rollercoaster ride’ Junior
‘Gripping, informative and funny’ Bookseller
‘Miss it at your peril!’ Carousel
To all those who have looked up at the night sky and wondered . . .
As you read the story you will come across some fabulous science essays and information. These will really help bring the topics you read about to life, and they have been written by the following well-respected scientists:
My Robots, Your Robots
by Professor Peter W. McOwan
Queen Mary University of London
The History of Life
by Professor Michael J. Reiss
Institute of Education, University of London
Quantum Computers
by Dr Raymond Laflamme
Director of the Institute of Quantum Computing at the University of Waterloo
The Building Blocks of Life
by Dr Toby Blench
Research Chemist
3D Printing
by Dr Tim Prestidge
Totempole Consulting
Life in the Universe
by Professor Stephen Hawking
Director of the Institute for Theoretical Cosmology, University of Cambridge
With special thanks for the additional material to:
Dr Stuart Rankin
High Performance Computing Service, University of Cambridge
ON ANOTHER PLANET, the treehouse would have been the ideal spot for star-gazing. On a planet with no parents, for example, it would have been perfect. The treehouse – halfway up the big apple tree in the middle of the vegetable patch – was the right height, location and angle for a boy like George to spend all night staring up at the stars. But his mum and dad had other ideas, involving chores, homework, sleeping in beds, eating supper or spending ‘family time’ with his little twin sisters, none of which were of any interest to George.
All George wanted to do was take a picture of Saturn. Just one teeny photo of his favourite planet – the enormous frozen gas giant with its beautiful icy, dusty rings. But at this time of year, when the sun set so late, Saturn didn’t appear in the night sky until nearly midnight. Which was so far past George’s bedtime, there was no hope of his parents leaving him out in the treehouse until then.
Sitting with his legs dangling over the edge of the platform, George sighed and tried to calculate how many hours and days it would be before he was old enough to be free . . .
‘’S up?’ His train of thought was broken as a slight figure dressed in long baggy camo shorts, a hoodie and a baseball cap bounded onto the treehouse platform.
‘YOLO!’ George cheered up instantly. ‘Annie?’
Annie was his best friend, and had been ever since she and her mum and dad had moved to Foxbridge a couple of years ago. She lived next door, but that wasn’t the only reason why they were mates. George just liked her: Annie, the daughter of a scientist, was fun and clever and cool and brave. Nothing was beyond her – no adventure could be shunned, no theory go untested and no assumption stay unchallenged.
‘What are you doing?’ she asked.
‘Nothing,’ George muttered. ‘Just waiting.’
‘Waiting for what?’
‘For something to happen.’ He sounded miserable.
‘Me too,’ said Annie. ‘D’you think the Universe has forgotten about us now we’re not allowed to go on space adventures any more?’
George sighed. ‘D’you think we’ll ever get to fly in space again?’
‘Not right now,’ said Annie. ‘Perhaps we’ve had all our fun already; now that we’re eleven, we’ve got to be really serious all the time.’
George stood up, feeling the wooden planks rock slightly under his feet. He was almost sure that the tree-house was safe and that there was very little chance they could both go crashing down to the hard ground below. He’d built it with his dad, Terence, out of stuff they’d scavenged from the local tip. And once, when they were busy constructing the ‘house’ part where he and Annie now sat, his dad had plunged his foot through a rotten plank. Fortunately he hadn’t fallen through entirely, but it had taken all George’s strength to pull him back up again, while below, on the ground, his twin sisters, Juno and Hera, shrieked with laughter.
The good thing about the mini-accident was that the treehouse was judged dangerous enough by George’s parents for his toddler sisters to be banned from coming up the rope ladder. Which made George very happy. It meant that the treehouse was his kingdom, protected from the chaos of the rest of his house. Under strict instructions to pull up the rope ladder to stop eager small people from shinning up to join their beloved brother, George was very careful about security. He never left the ladder down. Which meant . . .
‘Hey!’ He suddenly realized that Annie shouldn’t have been able to appear out of nowhere like that. ‘How did you get up here?’
Annie grinned. ‘I was bitten by a spider when I was just a baby,’ she intoned dramatically. ‘Which gave me special magic powers that I am only just coming to understand.’
George pointed over to the knotted rope that he had just spotted lassoed onto the end of the thickest branch. ‘Is that your work?’
‘It is,’ admitted Annie in her normal voice. ‘I just wanted to see if I could do it.’
‘I would have let the ladder down for you,’ George told her.
‘Last time I asked you to do that,’ she complained, ‘you made me guess about a thousand million different passwords and I still had to give you half my Kit Kat.’
‘That wasn’t a Kit Kat!’ George reminded her. ‘It was a piece of “chocolate”’ – he used his fingers to make comma marks around the word – ‘you’d tried to create under lab conditions, done up in a Kit Kat wrapper to see if I could tell the difference.’
‘If a mouse can grow an ear on its back,’ protested Annie, ‘then why can’t I grow a Kit Kat? It’s got to be possible to make self-replicating chocolate molecules that just keep on doubling.’
Annie was a budding experimental chemist. She often used the kitchen as her own personal laboratory space, which drove her mother, Susan, crazy. Her mum would reach into the fridge to get a carton of apple juice, and encounter crystalline protein growth instead.
‘FYI,’ said George. ‘Your Kit Kat tasted like a dinosaur’s toe—’
‘It did not!’ interrupted Annie. ‘My home-grown chocolate was delicious. I don’t know what you mean. And when have you ever chewed a dinosaur’s toe anyway?’
‘Toenail,’ finished George. ‘Seriously gross. Like it had been fossilized for a trillion years.’
‘ROFL,’ replied Annie sarcastically. ‘’Cos you’re, like, so gour-may.’
‘You don’t even know what gourmet means,’ George retorted.
‘Do so.’
‘What is it, then?’ George was pretty sure he’d won this one.
‘It’s like when you have some gours,’ explained Annie, ‘and it’s the month of May. It makes you go all gour-may.’ She just made it to the end of the sentence before bursting out laughing – so hard that she fell off the beanbag.
‘You’re an idiot,’ said George good-naturedly.
‘With an IQ of 152.’ Annie picked herself up off the floor. She’d had her IQ tested the week before and she wasn’t about to let anyone forget the results. Suddenly she spotted the line-up of George’s possessions. ‘What’s all this?’
‘I’m getting my things ready.’ George pointed at the equipment, which had been rescued from the tiny hands of his twin sisters and borne up to the treehouse for safety. There was a 60mm white telescope with black bands at each end, and a camera which he was attempting to rig up to the telescope so that it could take a picture. The telescope had been a present from his grandmother, Mabel, but amazingly, the camera had come from the tip. ‘So I can get photos of Saturn when it gets dark. If my boring mum and dad don’t make me go in. It’s my half-term project.’
‘Cool!’ Annie squinted into the viewfinder of the telescope. ‘Ew!’ she exclaimed immediately. ‘It’s got something sticky on it!’
‘What!’ shouted George.
He looked at the telescope more carefully. Sure enough, around the viewfinder was some kind of gluey pink substance.
‘That’s enough!’ His temper suddenly exploded. He started to climb down the rope ladder.
‘Where are you going?’ Annie scrambled after him. ‘It’s no biggie! We can clean it off!’
But George had steamed ahead, back into his house, his face red with fury. He barged into the kitchen, where his father was attempting to give Juno and Hera their tea.
‘And one for Dadda!’ Terence was saying to Hera, who opened her mouth, accepted the green goo and promptly spat it back at him. Hera then shrieked with laughter and banged her spoon maniacally on the tray of her high chair, which made all the other bits and bobs of food jump around like Mexican beans. Juno, who tended to copy her twin, joined in, banging her spoon and making a disgusting wet farting noise with her lips.
Terence turned to look at George, an expression of mixed suffering and joy on his face; green slime dripped off his beard and down his home-made shirt.
George took a deep breath to start on his angry tirade about small people who messed up other people’s stuff, but Annie managed to squeeze past him just in time.
‘Hola, Mr G!’ she sang cheerily to Terence. ‘Hello, baby girls!’
The girls banged their spoons and gargled eagerly at this new distraction from dinner time.
‘Just wanted to ask if George could come over to mine!’ chirped Annie. She reached out a hand to tickle Hera under her soft sticky chin, which made the little girl dissolve into helpless giggles.
‘What about my telescope?’ George muttered crossly behind her.
‘We. Will. Sort. It,’ she said firmly back to him in a low voice. ‘So lucky to have baby sisters,’ she cooed over the twins. ‘I wish I had lovely ickle baby sisters. I’m just a one and only lonely child . . .’ She pulled an exaggeratedly sad face.
‘Hmph.’ George would have liked nothing better than to live in Annie’s quiet, geeky, techno-obsessed household, with her scholarly father and her increasingly career-minded mother. Where there were no babies, no noise, no organic vegetables and no mess – except, perhaps, when Annie had been conducting one of her more ‘interesting’ experiments in the kitchen.
‘Er, yes, you can go – but make sure you’re back in time to do your chores,’ said Terence, trying to sound like he was in charge.
‘Great!’ shouted Annie enthusiastically, pushing George back out of the door.
George knew that when Annie was in bossy mode, he just had to go with the flow. So he followed, which wasn’t so hard: he didn’t feel like hanging around at home in a bad mood when a visit to Annie’s house was on offer.
‘Bye, Mr G and baby Gs!’ bellowed Annie as they ran off. ‘Have a wonderful time!’
‘Don’t forget, George, you need to fill in your reward chart by completing your weekly tasks!’ Terence called weakly after the departing figure of his oldest child. ‘You’ve still got three fifths of the pie-chart left!’
But George was gone, swept away by Annie to the exciting domain of Next Door – the home of all things techno, cutting edge, scientific, electronic and amazing in George’s eyes.
THEY REACHED ANNIE’S house by means of a hole in the fence between the two gardens. The hole had been made when Freddy the pig – another present from George’s enterprising Granny Mabel – broke through from the Greenbys’ back garden in a bold bid for freedom. Following Freddy’s hoof prints that afternoon had led George to meet Annie and her family for the first time – her dad, mega-scientist and super-boffin Eric; her mum, musician Susan; and their super-computer, Cosmos, who was so powerful and intelligent, he could draw doorways through which you could walk to any part of the known Universe you wanted to visit (provided you were wearing a spacesuit, that is). Since that day, George had surfed the Solar System on a comet, walked on the surface of Mars, and had a showdown with an evil scientist in a distant solar system. It was fair to say that his life had never been quite the same since.
‘Hey!’ said Annie as they ran. ‘You shouldn’t be mean to your sisters.’
‘What?’ George wasn’t thinking about his baby sisters any more. ‘What are you talking about? I wasn’t mean!’
‘Only ’cos I stopped you,’ accused Annie. ‘You were going to say something horrible.’
‘I was angry!’ George replied indignantly. ‘They’re not supposed to touch my stuff or go up to the treehouse!’
‘You’re lucky to have a brother or a sister at all,’ said Annie piously. ‘I haven’t got anything.’
‘Yes you have!’ George burst out. ‘You’ve got so much stuff! You’ve got Cosmos the computer, you’ve practically got your own science lab, you’ve got an Xbox, you’ve got a smartphone, a laptop, an iPod, an iPad, an i-everything; you’ve got that mechanical dog; you’ve got a scooter with a motor on it . . . I dunno . . . You’ve got the lot.’
‘It’s not the same,’ said Annie quietly, ‘as having a real-life brother or sister.’
‘If you actually had one,’ said George dubiously, ‘or even two, I bet you wouldn’t want it. Them.’
The two friends hurried through the door into the kitchen.
‘Huzzah!’ Annie skidded across the floor towards the huge fridge, reaching out to grab the handle.
Even the Bellises’ fridge didn’t look like a normal fridge – more like the sort of thing you might find in a laboratory: massive and made of steel, with cavernous drawers and separate compartments for isolating elements from each other. It was, of course, a professional machine, as far removed from a normal fridge as a spaceship is from a paper aeroplane. That was one of the things George loved about Annie’s house: it was full of unexpected gadgets and scientific oddities which Eric had bought or acquired or been given in the course of his many years of work. George looked at the fridge enviously; it glowed with a strange blue light. The most technologically advanced item in his whole house probably contained less processing power than Annie’s refrigerator.
George was just musing on that depressing fact when he realized that there were voices coming from the sitting room.
‘Annie! George!’ Annie’s dad, Eric, stuck his head round the kitchen door. He was smiling broadly, his eyes sparkling behind his thick glasses, his tie loosened and his shirt sleeves rolled up. He came in carrying two crystal glasses.
‘I’ve come to get a fill-up,’ he explained, reaching for a dusty old bottle and pulling the cork out with a loud thop. He poured out a sticky brown fluid and turned to go back to the sitting room.
‘Come and say hello to my guest.’ His face was creased into long laughter lines. ‘I think she has something that might interest you.’
George and Annie immediately forgot their brief argument and followed Eric into the sitting room, which was packed from floor to ceiling with rows and rows of books. It was a beautiful room, full of interesting objects like Eric’s old brass telescope. The cutting-edge technology that ruled the rest of the house was less overwhelming here; it was cosy and inviting rather than cool and futuristic. On the squashy sofa, which Eric had owned since his student days, sat a very ancient lady.
‘Annie, George,’ said Eric, handing the old lady her glass of sherry. ‘This is Beryl Wilde.’
Beryl accepted the drink gratefully and started slurping it straight away. ‘How d’you do!’ She waved a cheery hand at them.
‘Beryl is one of the greatest mathematicians of our times,’ said Eric seriously.
Beryl burst out laughing. ‘Oh! Don’t be absurd!’
‘It’s true!’ he insisted. ‘Without Beryl’s mathematical genius, millions more people would have died.’
‘What people?’ asked George.
Annie had whipped out her smartphone and was trying to pull up a Wikipedia entry for Beryl Wilde.
‘How do you spell your last name?’ she asked.
‘You won’t find it,’ said Beryl, guessing what Annie was trying to do, her pale blue eyes twinkling. ‘I’m completely covered by the Official Secrets Act. Still, even after all these years. You won’t find me anywhere.’
Eric gestured to an object on the coffee table in front of the sofa. ‘This,’ he said dramatically as he pointed to what looked like an old-fashioned typewriter, ‘is an Enigma machine – one of the ones used during the Second World War to encode messages. It meant that messages could be sent that were impossible for interceptors to understand. But Beryl was one of the mathematicians who broke the Enigma code. Which meant that the war ended much sooner than it might have done, and fewer people on both sides lost their lives.’
‘OMG!’ said Annie, looking up from her phone. ‘So you could read the secret messages without the other people realizing you knew what they were planning? Like, if someone read all my emails now . . .? Except, obviously,’ she added, ‘I’m not fighting a war with anyone. Except Karla Pinchnose, who made everyone laugh at me when I spelled something wrong on the smartboard . . .’
‘Exactly.’ Beryl nodded. ‘We could intercept their messages and decrypt the content so we knew what they were planning to do. That gave us a huge advantage.’
Our everyday numbering system – the decimal system – is based on a factor of 10. We number from 1 to 9, and then go to a new column for the number of ‘10’s.
36 = 3 × 10, plus 6 × 1
48 = 4 × 10, plus 8 × 1
148 = 1 × 100, plus 4 × 10, plus 8 × 1
And so on.
With early computer systems, a binary numbering system was used. This is because binary is based on a factor of 2, so the only digits used are 0 and 1.
10 = 1 × 2, plus 0 × 1 i.e. the number 2 in the decimal system
11 = 1 × 2, plus 1 × 1, i.e. the number 3
111 = 1 × 4, plus 1 × 2, plus 1 × 1 i.e. the number 7
The 0/1 choice could be linked to switches in the computer circuits so that 0 = ‘off’ and 1 = ‘on’ and code written in binary could then make the circuits turn themselves on and off as needed to make calculations.
Nowadays, computers are much more sophisticated and codes are often written using a hexadecimal numbering system, based on a factor of 16. This counts figures from 0 to 9 but then also uses A for ten, B for eleven and so on up to F for fifteen.
C therefore represents 12 in the decimal system
10 is the hexadecimal way of writing the number 16
11 = seventeen
1F = 1 × 16, plus F × 1 (15) = 31
20 = 2 × 16 = 32
F7 = F × 16 (15 × 16 = 240), plus 7 × 1 = 247
100 = 256