The Complete Ruby Redfort Collection

by Lauren Child

  Dakota Lyme became so enraged when she lost out to eleven-year-old Ward Partial that she began hurling protractors, set squares and other geometry-based tools at him. Ward, though shaken, did not sustain any critical injuries.

  STOP PRESS: MIRROR READERS PRAISE NEW LOOK

  The Twinford Mirror launched its exciting new-look format to rave reviews. ‘I’ve never seen anything like it in Twinford before,’ exclaimed one regular reader, adding, ‘Come to think of it, it’s identical to the Twinford Echo.’

  Shopping cart

  Despite being back in everyone’s good books, Ruby Redfort still had one last task to complete. She had requested that her final stint of community service should be spent clearing the trash from the vacant lot where the Sacred Heart Cathedral had once stood.

  Sabina for one applauded her daughter’s efforts to keep Twinford tidy and thought it might be nice if the Twinford Garden Committee planted some roses. ‘Red ones, like hearts,’ said Sabina.

  Brant Redfort said he would speak to the Twinford Historical Society to see if it might be possible to open the crypt to the public. ‘I’m sure Dora Shoering would enjoy taking tour groups down there.’

  Mrs Digby said she was happy for the Sacred Heart’s dead to be remembered, but there was no way in a month of Sundays that anyone was getting her to visit them.

  Ruby shivered at the very thought, but didn’t say anything.

  It was after she had completed her task, eight and a half hours later, and was wondering what should be done with the Dime a Dozen shopping cart she had found, that an idea hit her.

  She walked it all the way from College Town back to Amster, stopping only to buy a tin of cat food. This done, she continued on her way to Cedarwood Drive. When she reached Mrs Beesman’s house, she parked the cart in front of her gate and placed the cat food in the basket. Then she went on home to Green-Wood house, where she was looking forward to taking a long, hot soak in the tub.

  The apple

  The apple was sitting on Ruby’s desk, the bruise deepening and the rot spreading. She looked at it for a long while, wondering what it meant, if indeed it meant anything.

  Finally she took her penknife and plunged it deep into the fruit. And a strange thing happened: the knife sliced the apple in two, and out fell a piece of folded white paper.

  Taking it up in her hand she opened it and read it.

  There was only one word, a name.

  She thought about the very last thing the Count had said: the question is: who pulled the trigger?

  She looked back down at the paper and read the name out loud.

  What it said was:

  LB.

  THINGS I KNOW:

  ..................

  The Australian is working for the Count.

  The Count is working for someone.

  The Count has betrayed this someone.

  This someone has a grand plan.

  This someone wants to kill me.

  Lorelei wants to kill me.

  LB killed Bradley Baker.

  THINGS I DON’T KNOW:

  ..................

  WHY to all of the above.

  Where my mom’s snake earrings are.

  Ruby Redfort.

  How to see in four dimensions

  by Marcus du Sautoy, supergeek consultant to Ruby Redfort

  Ruby discovers that the key to decoding the Taste Twister code is the geometry of a 4-dimensional cube. But what on earth is a 4-dimensional cube? We live in a 3-dimensional universe – seeing the objects around us in terms of their height, width and depth – so it’s impossible to see something that lives in four dimensions. Instead we must use some mathematics to conjure up this shape in our mind.

  The key to creating a 4-dimensional cube is the discovery that you can change geometry into numbers, and numbers into geometry. For example, every position on the surface of the earth can be located by two numbers. Ruby uses this fact to find out that the Taste Twister poster points to the Little Seven Grocers. She takes the two numbers written on the Taste Twister billboard and changes these numbers into a location.

  Called latitude and longitude, these two numbers are like a code to locate any place on the earth. For example, the Little Seven Grocers is located at the position given by the two numbers:

  (32.7410, -117.1705)

  These are known as the GPS coordinates of this location. The first number tells you how many units north or south you must go from the equator. The second number tells you how many units east or west you should travel from the line of longitude running through Greenwich in London. (From the equator to each pole consists of 90 units, corresponding to the 90 degree angle between the equator, the centre of the earth and each pole.)

  So, for example, the coordinates of my college in Oxford, New College, are (51.7542, -1.2520). So you can get to New College by going 51.7542 units north of the equator and 1.2520 steps west. If you want to find out the coordinates of your house then try putting your address into: http://www.gps-coordinates.net/

  It was the great French mathematician and philosopher René Descartes, born in 1596, who came up with this clever way of changing a geometrical location into numbers. Called Cartesian coordinates, they can be used to plot all kinds of things – not just locations on earth. You can describe any geometric shape using these coordinates. If you take a piece of graph paper with a shape drawn on it then we can change the shape into the numbers that tell us the location of the points making up that shape.

  For example, how can I change a square into numbers? What I do is tell you the location of all four corners of the square.

  The corners of the 2D square are located at the positions (0,0), (1,0), (0,1) and (1,1). The geometry of the square has been translated into these four pairs of numbers. (When describing shapes using Cartesian coordinates, the first number, called the x-coordinate, tells you how many units to move left or right, the second coordinate, called the y-coordinate, tells you how many units to move up or down. Beware: it is the opposite order to GPS coordinates.)

  But we don’t just have to stick to using two numbers. Ruby could also have added a third coordinate to the location of the Little Seven Grocers, telling us how high up from sea level the shop is. Using these three coordinates we can then describe the location of any point in our 3-dimensional universe.

  We can also use the same idea to change 3D shapes into numbers. If we want to describe a 3-dimensional cube in coordinates, instead of a square, then we can add a third direction which describes the height of the point above the 2-dimensional graph paper.

  The corners of the 3D cube are located at the positions (0, 0, 0), (1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1, 0), (1, 0, 1), (0, 1, 1) and finally the point furthest from the first corner, located at (1, 1, 1). So the geometry of the cube has been translated into these eight triples of numbers.

  Descartes’ idea of changing geometry into coordinates is a bit like a dictionary changing words from English into French. But this dictionary changes shapes into numbers. On the shapes side of the dictionary, we have seen 2D shapes and 3D shapes, but then the dictionary runs out because we can’t draw a shape in 4D. But the exciting thing is that the numbers side of the dictionary doesn’t run out. It was the great German mathematician Bernhard Riemann, born in 1826, who discovered that you could carry on building shapes out of numbers, even if you couldn’t see them.

  What Riemann realised is that you could use the numbers to describe what a shape was made of, despite being unable to physically build it. All you needed to do was add more coordinates. So to describe a 4-dimensional object, we just add a fourth coordinate that will keep track of how far we are moving in this new imaginary direction. So although I can never physically build a 4-dimensional cube, by using numbers I can still describe it precisely.

  It has 16 vertices, starting at (0,0,0,0), with edges extending to 4 points at (1,0,0,0), (0,1,0,0), (0,0,1,0) and (0,0,0,1) and then continuing along the edges we hit points at (1,1,0,0), (1,0,1,
0), (1,0,0,1), (0,1,1,0), (0,1,0,1), (0,0,1,1), (1,1,1,0), (1,1,0,1), (1,0,1,1), (0,1,1,1) until we reach the farthest point, at (1,1,1,1). This 4D cube is sometimes known as a Tesseract.

  The numbers are a code to describe the shape, and we can use this code to explore the shape without ever having to physically see it. So, using the numbers, we can actually work out that, in addition to the 16 corners, this 4D cube has 32 edges, 24 square faces, and is made by putting together 8 cubes.

  Sometimes people talk about time being the fourth dimension, but actually these dimensions can be used to keep track of anything. For example, suppose you wanted to keep track of the temperature at every location on the earth. You could use three coordinates to locate the position and the fourth coordinate to tell you the temperature at that point.

  In the Taste Twister code, the four different directions keep track of the four different tastes we can detect with our tongues: BITTER, SOUR, SALT, SWEET. Every taste turns into a point located somewhere on this 4-dimensional cube.

  Although we can never actually see a 4D cube, there are ways to fake a view, as Ruby showed in her mathlympics competition. For example, the picture I drew of the cube isn’t actually a cube. It’s a 2D picture of the 3D cube. The great breakthrough by artists like Leonardo da Vinci in the fifteenth century was the idea of perspective – a way to draw 3D shapes on a 2D canvas to give you the illusion of seeing a scene in 3D. So for example, one way to draw a 3D cube on a 2D canvas might be to draw a large square with a smaller square inside, then join up the corners. This gives you the illusion of ‘seeing’ a 3D cube.

  Shadows work the same way. If I took a cube made out of wire and shone a light on the shape, then the 2D shadow I would see on the floor might look like the square inside a square.

  Just as you can paint a 3D shape on a 2D canvas or shine a light on a 3D shape and create a 2D shadow, there is a way to create a shadow or picture of a 4D shape in 3 dimensions. A 3D cube when squashed into 2D became a square inside a square. It turns out that the shadow of a 4D cube in 3 dimensions is a small cube inside a larger cube where there are extra edges inserted to join the points of the large cube to the points of the smaller cube. This is the picture that Ruby draws in the final round of the mathlympics competition.

  If you ever go to Paris then you can actually see an example of this 3D shadow of a 4D cube. At La Défense in Paris there is a huge structure called La Grande Arche built by Danish architect Johann Otto von Spreckelsen. It is essentially a large cube with a smaller cube inside with the corners of the cubes joined up. If you visit La Grande Arche and count carefully, you can see the 32 edges that can be described using Descartes’ coordinates.

  But every shape has many different shadows. If I take my 3D wire cube and I alter the position of the torch, I can get different 2D shadows or perspectives. This is the breakthrough Ruby makes with the mandala shape on the back of the labels on the Taste Twister bottles.

  By taking different perspectives on a 4D cube, you can get different 3D viewpoints. (An animation showing these changing shadows of the Tesseract can be seen here: https://commons.wikimedia.org/wiki/File:8-cell.gif.) The mandala shape that is the key to decoding the locations of the taste code is arrived at by turning the 4D shape and getting a new perspective. You can actually see the two cubes still in the mandala shape. One is highlighted in the figure below. The other is obtained by shifting this cube down and right.

  The mandala image is actually a 2D picture of a 3D shape, which is itself a shadow of a shape in four dimensions.

  And if your brain isn’t smoking by now then maybe you could be the next Ruby Redfort or Bernhard Riemann.

  Froghorn decided to protect his office door using the Catalan numbers. If you take a shape like a pentagon, the Catalan number of the pentagon is the number of different ways you can divide it up into triangles by drawing lines between the points of the pentagon. With a pentagon there are five different ways:

  But what about a hexagon? Why not try drawing lines in a hexagon and see how many different ways you can divide the shape into triangles? You should find that there are fourteen different ways.

  The first few Catalan numbers are 1, 2, 5, 14, which was the code for Froghorn’s door.

  To protect his safe Froghorn uses the lazy caterer’s sequence. Take a pizza. How many pieces can you get using three straight cuts without moving the pieces? The maximum number is 7 pieces.

  To cut the pizza again, choose a line that cuts all the previous lines but avoids a point where two lines meet. You will get an extra 4 pieces.

  The first few lazy caterer’s numbers are 2, 4, 7, 11, 16, which are the numbers you need to break into Froghorn’s safe.

  Footnotes

  Chapter 5

  fn1 IF YOU WANT TO IMPROVE YOUR EYESIGHT THEN YOU SHOULD DRINK THIS.

  Chapter 32

  fn1 AS EVER THIS IS A VIGENERE CIPHER. THE KEY WORD IS: A PERSON; FROM PUGLIA.

  Acknowledgments

  Without the following three people, I am not sure this book would have been finished before Christmas. Nick Lake, for his superb editing and inspired additions, Lily Morgan, a fabulous copy-editor who knows Twinford like the back of her hand, and David Mackintosh, for his impeccable design taste and perfect illustrations. I would like to thank them for being so generous with their time and so incredibly nice to boot.

  Thank you to Marcus du Sautoy for creating not only a sophisticated code, but also one that I can actually understand. Thank you to Derek Landy for taking my call (even though he was mid-deadline), and chatting me through kung fu and aikido, at breakneck speed.

  Thank you to AD and TC for their support, Folder for inspired ideas, George for facts, Marcia for creating time, Wendy for trouble-shooting, and Phil for making most things possible.

  Special thanks as always to AJM.

  Dedication

  For Lucy G

  Epigraph

  'Close your eyes and see the truth'

  Author anonymous, from the indigo code-breaker's bible.

  Contents

  Cover

  Title Page

  Dedication

  Epigraph

  Maps

  The buried fear

  An ordinary kid

  Chapter 1. A window on the world

  Chapter 2. Long distance

  Chapter 3. Catching up

  Chapter 4. Baby Grim

  Chapter 5. Snakes and mushrooms

  Chapter 6. Larger fish to fry

  Chapter 7. One bad apple or two?

  Chapter 8. Little green men

  Chapter 9. Lucite

  Chapter 10. The stars above

  Chapter 11. Act normal

  Chapter 12. Ghost Files

  Chapter 13. Sprayed and delivered

  Chapter 14. The wrong kind of snow

  Chapter 15. Thirty Minutes of Murder

  Chapter 16. Look under V

  Chapter 17. Evil all around

  Chapter 18. Location unknown

  Chapter 19. Minus 10

  Chapter 20. Hold your breath

  Chapter 21. C.O.L.D.

  Chapter 22. Something remembered

  Chapter 23. A man’s best friend

  Chapter 24. Hypocrea asteroidi

  Chapter 25. Mushrooms from Mars

  Chapter 26. The trolley problem

  Chapter 27. À la mode

  Chapter 28. Nothing but glamour

  Chapter 29. Yellow notebooks

  Chapter 30. A stroke of luck

  Chapter 31. Place of death

  Chapter 32. Hit and run

  Chapter 33. One and the same

  Chapter 34. I remember nothing

  Chapter 35. Who to tell?

  Chapter 36. Loveday

  Chapter 37. A safe house

  Chapter 38. Lost and found

  Chapter 39. Cousin Mo

  Chapter 40. On the cards

  Chapter 41. What we know

  Chapter 42. Chasing a shadow

  Chapter 43. Wh
at to do if You are Caught in an Avalanche

  Chapter 44. Buried alive

  Chapter 45. Cold comfort

  Chapter 46. Run

  Chapter 47. On thin ice

  Chapter 48. Sorrow

  Chapter 49. We wish you a merry Christmas

  Chapter 50. Even the mundane can tell a story

  Chapter 51. The fly barrette

  Chapter 52. Instinct

  Chapter 53. Nothing is completely safe

  Chapter 54. All systems are down

  Chapter 55. Make like bananas

  Chapter 56. The Eye Ball

  Chapter 57. A man about a dog

  Chapter 58. No Rule 81

  Chapter 59. Follow me

  Chapter 60. Hanging on by an eyelash

  Chapter 61. Blink and you die

  Chapter 62. 1974

  Two lucky escapes

  Heroics

  The oak on Amster Green

  A badge of approval

  Team players

  Crime pays

  A note on the Prism Vault codes

  Picture this

  Footnotes

  Acknowledgments

  Special thanks

  The buried fear

  IT HAPPENED ONE BRIGHT APRIL DAY when the child, then barely five weeks old, was sleeping. The world crashed down and the baby opened its eyes, but there was only darkness to see. The walls were packed around it, almost touching, and the doors and the windows all gone. The baby cried out, but no one came. It screamed and clenched its furious fists, trying in vain to push at the tomb of rubble, but nothing happened. Its little mind began to panic, its eyes closed shut and its heart began to hurt.