**Documentary evidence submitted during the trial of Michael Walker.**

*Date: Wed, 04 Apr 2012 04:44 PM*

*From: michaelwalker1260@pimail.com*

*To: yuki_yamamoto@suuji.co.jp*

*Subject: Reading By Numbers*

1 – I met your mother in a number garden in Hokkaido.

2 – When I was 5830 days old I saw a news report about Professor Sujimoto. He had made a virtual number garden for his students.

3 – I vowed I would study in Japan and started learning Japanese.

4 – I was accepted into the University of Sapporo and enrolled in their math department. Professor Sujimoto’s fame had increased after he had discovered what was, at the time, the largest prime number ever found.

5 – Sujimoto conducted all of his lectures online in a VR environment he had created himself.

6 – When I logged in, I was presented with a menu that allowed me to create an avatar to represent myself. I chose the symbol for pi.

7 – An oak tree stood in the center of the garden. It reached unending into the sky and its trunk was alive with an army of marching ants, each of them carrying a glowing neon digit. Together they formed the prime number Sujimoto had discovered — a number more than 42 million digits long.

8 – Twenty-three other students attended that lecture. Their avatars took the forms of anime characters, *kawaii* cats and other fantastic creatures. Sujimoto’s avatar was reminiscent of a monk — wearing brown robes and conical hat.

9 – A text bubble appeared in the air beside the monk. “Welcome to this year’s first class on number theory.”

10 – “Numbers have a purity that words cannot match.”

11 – “They are the building blocks of science. By studying them we can learn about ourselves and our place in the universe. I have created this garden to give you a chance to explore the world of numbers and their hidden beauty.”

12 – He pointed to the garden beds where different colored numbers grew. “There are transcendental numbers, abundant numbers, undulating numbers, pandigital numbers, deficient numbers, surreal numbers, happy numbers, weird numbers and my personal favorites, the

13 – vampire

14 – numbers.” A bed of numbers erupted from the ground in front of Sujimoto. It contained the numbers from 1 to 1000 arranged in orderly rows. The numbers were purple and had pale, green stems. “I want you to pick one integer. This is going to be your special number for the year. Then explore the garden.”

15 – The student avatars crowded around the purple numbers and started plucking them. I wanted to choose 3, 7, 22 or 227 because they are used when estimating pi, but some other students must have had the same idea. I chose 220 instead.

16 – I wandered past a garden of hyperreal numbers and came to a numberfall. A torrent of digits cascaded down shiny, black rocks and emptied into a gleaming, blue lake. I queried the VR interface and discovered the numberfall was displaying part of the infinite sequence of digits that makes up pi. I waded through the water until I stood underneath the numberfall. The digits crashed all about me. I was submerged in infinity.

17 – A unicorn splashed into the lake. It had the purple number 284 wrapped around its horn. When the unicorn saw the number stuck to my side, it started bouncing up and down in excitement. Someone was pressing the jump key too often.

18 – “Look at our numbers!!! We have to be friends. It’s fate!!!”

19 – That was how I met

20 – your mother.

21 – It took me a moment to grasp the significance of what she was saying. 220 and 284 are the smallest pair of *amicable* numbers. The sum of the proper divisors of 220 (1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110) is 284. The sum of the proper divisors of 284 (1, 2, 4, 71, 142) is 220. The numbers are bound together.

22 – Your mother decided we were meant to be together. I had only just arrived in Japan and I didn’t have any friends. So I was happy to meet her after class.

23 – She was also interested in codes and sent me emails with hidden messages. A message with (32) at the end meant I had to read every thirty-second line to find the meaning.

24 – We fell in love.

25 – The next four years were the happiest of my life. I specialized in the process of random number generation. Computers usually only generate pseudorandom numbers. Deterministic algorithms can be recreated, so the numbers aren’t truly random. Eventually a pattern will emerge. To get true random numbers, computers have to rely on external sources, such as devices to measure atmospheric noise.

26 – We got married after we graduated. Some of my friends in Australia warned me about the difficulties of intercultural relationships. I thought our love for numbers would help us bypass that.

27 – Cultural differences sometimes even extend to numbers. In western countries we count in thousands, but in Japan they count in ten thousands. 20,000 is not 20 thousands, it is 2 ten thousands. I also learned other numbers have been polluted by superstition.

28 – The end came when I saw a documentary about an autistic savant who could perform astonishing feats of calculation and memory. He recited pi from memory to 22,514 digits. I could not do this.

29 – He said that in his mind numbers have different shapes and colors. I could not see this. The numbers I loved had

30 – betrayed me.

31 – They had shown themselves to others, but not to me.

32 – Kaori told me she was pregnant.

33 – At the time it was an unexpected and unwelcome

34 – addition.

35 – 1 + 1 should not equal 3.

36 – Your grandmother said we had to go to a

37 – fortune teller

38 – to help us choose your name.

39 – A fortune teller had chosen your mother’s name by selecting a kanji with a lucky number of strokes.

40 – Your grandmother poisoned your mother’s thinking with superstition.

41 – We argued.

42 – Then

43 – your grandmother

44 – became ill and was admitted to hospital.

45 – When I arrived at the hospital,

46 – she was asleep.

47 – Kaori sat by her bedside.

48 – She looked pale and tired.

49 – I had brought some flowers,

50 – so I

51 – put them on the table by the bed.

52 – Kaori stared at the flowers. “What are those?” she demanded.

53 – “I bought some flowers for your mother.”

54 – “They’re chrysanthemums!”

55 – The old woman stirred in her sleep.

56 – “What’s the matter? I thought your mother would appreciate them. They are Japan’s national flower.”

57 – “You never give chrysanthemums to someone in hospital! They’re only for funerals.”

58 – “How was I supposed to know that?”

59 – I picked up the flowers. “I will get rid of them. There’s no need to get upset. You’re acting like I

60 – killed

61 – her.”

62 – “That’s because you bought four of them!

63 – I’ve told you before, four is an unlucky number in Japan.

64 – It sounds like death.

65 – You want my mother to die, don’t you! You’ve always hated her.”

66 – “What are you talking about? That’s crazy.”

67 – “Then why did you bring her *four* chrysanthemums?”

68 – “The shop only had four left,” I replied. “They’re just flowers.” I threw the flowers in the bin.

69 – “I was only trying to help

70 – her.”

71 – Kaori stared at me for a long time. Then she reached into her handbag and took out her ATM card.

72 – “What about this?” She flung the card at me. “You changed the PIN on my card yesterday, didn’t you? I had to go into the bank to find out what the new number was. And you know what the new number was, don’t you? 1260!”

73 – “I don’t know what you’re talking about,” I said.

74 – “1260 is a vampire number,” Kaori said.

75 – “I don’t know anything about that. The bank must have given you a new number for some reason. It was probably just chosen randomly.”

76 – “Don’t lie to me, Michael! I know all about your so-called *random* numbers! You chose that because you want to frighten me.”

77 – “Please calm down. Your mother isn’t well, and you’re pregnant. You’re very emotional.”

78 – “I don’t love you any more, Michael.”

79 – “That’s not true.”

80 – “You need to get help.”

81 – In case your mother has neglected your education I should explain about *vampire* numbers. They are numbers with an even number of digits that can be equally divided into two so-called *fangs*. These fangs are factors of the number and contain all of the digits of the original number.

82 – 1260’s fangs are 21 and 60 (21×60=1260).

83 – Your grandmother died that night.

84 – Kaori divorced me.

85 – Now, I sit in my small room and think about my mistakes. I thought numbers had betrayed me. But now I know it was not their fault.

86 – They are always true. It is superstitious people that sully the perfection of numbers.

87 – If someone tells you they love you, how do you prove it’s true? Even if it is true, how do you know it will be true tomorrow?

88 – Numbers are eternally perfect. The square root of 100 will always equal 10.

89 – Japanese law doesn’t recognize the custody rights of foreign parents. I have never even met you. But that will change one day soon.

90 – I will come for you and your mother.

91 – I have begun to make my own simple number garden.

92 – I have marked the walls with some of my favorite numbers.

93 – 220.

94 – 284.

95 – 1260.

96 – Sometimes numbers grow into things they shouldn’t.

97 – I am watching these numbers closely. One day they will grow into something very special.

98 – My health has been poor. To help me relax I perform simple integer divisions.

99 – But I am very careful about what numbers I choose to divide.

100 – I am always happier when there is no remainder.

(10)