Notes from the Grey Tower

Edgar was always using me as a basis for his human sketches. One day when I was flipping through his practice works, I found a sketch of a disheveled young man whose face was strewn with exhaustion. I lamented to Edgar. “Has your art worsened? This sketch looks nothing like me.”

Edgar told me that that was how I looked during the last semester of my third year to the first semester of my fourth year at Cambridge. I was skipping classes, wholly unbothered with doing my hair, and sat in the activity room of the mathematics society every day decrypting codes. My lunch and dinner would usually consist of only toast and black coffee. 

Lindon came twice every week. We would lock the door to the activity room at midnight, and he’d begin to transcribe the week’s unsolved codes onto paper from memory and hand the sheet of paper to me. I would then hand him last week’s deciphered texts and methods of decryption. Afterwards, we would both burn each of our papers.

I singlehandedly deciphered most of these codes. A small portion of them Lindon found his way through on his own. The remaining portion was undecipherable, and could only be destroyed untouched.

We would turn off the lights, and exchange our ideas in the darkness that Lindon loved so much.

Lindon idolized Andemund. He told me Andemund had independently deciphered numerous high-level foreign codes, and that his way of thinking was extremely unique. His presence to him was equal to that of a god’s— “The learning materials for the newcomers were even written by him!”

The darkness sharpened our thoughts. Realizing the decryption method then was like finding a sliver of light in the dark, and was endlessly exhilarating. 

The codes Lindon brought weren’t too difficult, and were often even easier than Code S which I’d deciphered in the past. As a newcomer whose work was consistently unsatisfactory, he wasn’t allowed access to the codes of high-level security. The codes I used my terrible German to decipher were mostly messages about unimportant things such as the coordination of personnel and the salaries of spies working overseas. Some of the messages mentioned ‘Eaglet’, whom had initially appeared in the text Andemund made me decipher when we first met. He seemed to have been positioned near a figure of importance, and the German military had agreed to give him a bonus. 

One day, Lindon suddenly came up to me, excited, and told me that he had to treat me to dinner; he had come first in his division. 

The things I did for him weren’t favours that could be returned by a meal or two. If I went hungry, I could always borrow money from Edgar. I never had much issue when it came to food and money. The reason why I helped Lindon was to prove to Andemund of my ability and my loyalty towards England. 

Andemund, I am worthy of your trust, although you still do not trust me. 

Lindon brought me to a nearby fancy restaurant. In the middle of the meal he asked me with piece of bread clamped between his teeth, “Alan, your last name is Caster, right?”

“No shit,” I replied.

He thought about it. “During evaluation this week, Mr. Garcia praised me saying that my decryption methods were particularly similar to a certain Jean Caster’s… Do you know her, the famous cryptologist Mrs. Caster? I realized that you have her last name, too.”

“That was my mother. She used to be a cryptographer.” I said in my calmest voice possible. “She passed away when I was five, but nobody told me… that she was this well-known.”

Most of my knowledge on cryptology came from the notes and books left behind by my parents. It was unavoidable that my way of thinking was similar to that of my mother’s. 

The hand Lindon used to lift his fork froze. 

“I’m sorry,” he apologized. 

“It’s no problem.” I said.

“Mr. Garcia’s going to assign me to Room One*. Looks like the work’s going to be much harder from now on.” He told me apologetically. “Alan, thank you for helping me.”

There were a number of cryptography divisions at Bletchley Park, arranged according to importance counting up from number one, and were led individually by different cryptologists. The team at Room One was directly led by Andemund, and was responsible for the decryption of the highest-level codes. 

“You’ll be decrypting the Enigma, then.” I said casually.

The expression that flashed across Lindon’s face was as if he’d just seen a waitress naked. 

“I saw it on the news some time ago.” I couldn’t tell him that Andemund had told me this. “The Germans have been using commercial encryption machines of its kind in the military. They say that it’s unbreakable.”

Some said that the more perfect the cipher, the less afraid you were of publicizing it. Even if the encryption machine were somehow retrieved, and the ciphertexts of a certain day obtained, the complexity of the cipher would still render you, the decipherer, helpless. Germany had always had strong faith in the ability of the Enigma, and thus never truly attempted to hides its existence from the general public. 

He relaxed. “Yes, the Enigma. We’ve been trying to decipher it for a while now.”

The restaurant was spacious and brightly lit, but the patrons were few and far between. We sat in an inconspicuous corner, and Lindon began to quietly explain to me how the Enigma machine ciphered its messages, much against the rules of the organization. The Polish intelligence had managed to procure a replica of the Enigma machine from the Germans, so the machine we were using now was a replica of the replica. 

Its appearance was similar to that of a typewriter. It consisted of three rotors etched with letters, a reflector, six plugs and two keyboards. The positions of the six plugs decided six pairs of letters which would be swapped with each other. When you pressed the key for the letter ‘A’ on the keyboard, it would be ciphered 4-7 times through the rotors and the reflector, and return the letter ‘B’ on the other keyboard, forming ciphertext.

“There are 6 possible arrangements for the 3 rotors, and each rotor contains 26 letters each.”

“17576 possible permutations for the rotors.” I immediately said.

Lindon nodded. “And the number of permutations for the 6 pairs of swapped letters… 105869…”

“1058 691 676 442 000 possibilities.” I felt like as if my head was going to burst. 

Lindon shrugged. “A lot of people say Mr. Garcia’s trying to decipher the impossible.”

I thought, as far as Andemund was concerned, there was no such thing as an undecipherable code. If you regarded Lindon and I as mathematical geniuses, then he was a mathematical pervert. While we were still trying to find out the patterns within the complicated jumble of numbers, he had already assembled a team of expert mathematicians, linguists, world-class chess players and cryptologists, and became the apparition that gripped the Germans by their throats in the dark. 

Following Lindon’s incorporation into Room One, the time he got to spend with his idol grew. He was very excited about it, so I was forced to listen to countless things about Andemund every time we met— He praised Lindon’s work (most of it was mine) publicly, dined with him at night— he had his coffee black every time, and would stay after dinner to discuss with him about his work. I felt uncomfortable at the last point of mention. I thought I was the only one able to keep Andemund company while he worked, but apparently I was wrong. 

The opinions Lindon had on himself were always terrible. I was very disgruntled by this and directly asked him. “What part does Andemund like about you?”

“He said the way I approached problems was unique, and on some level was quite similar to his.”

In the beginning, Andemund and I were clueless on how to tackle the Enigma. Andemund had obtained the replica of the Enigma machine, retrieved for us numerous code sheets and ciphertexts from the spies he’d deployed in Germany, and had perversely managed to deduce the way the Enigma was encrypted using the resources at hand. But the settings of the Enigma changed each day, and its encryption method was ridiculously complex, so decryption remained far beyond our ability at the moment.

The Enigma wasn’t named the ‘enigma’ for nothing.

Some time later, I recalled what had been written in my mother’s notes. It was the summer of 1938, when I had officially burned the last notebook my mother left behind. I remembered her way of utilizing mathematical formulae to break codes enciphered by machines, and tried to improve on her methods to apply them in breaking the Enigma.

I thought about it for a long time and wrote my conclusions on paper. The proof extended to a whole thirty pages. I handed it to Lindon, who thought of it as a joke. “Converting the way the Enigma machine works into a mathematical formula? Oh, Alan, you must’ve gone mad!”

Upon my furious insistence, he unwillingly handed my proof in. 

I remembered that the summer of 1938 was an idyllic one. The sunlight was always warm, and the weather wasn’t too hot either. Lindon and I, as well as other members of the mathematics society, came out from the activity room and into the blinding sunlight. I saw Andemund and his car steadily parked next to the lawn outside the library.

I never expected that he would have come here. I was stunned to where I stood.

Then I lazily swaggered over to him. “Missed me, darling?”

Andemund glanced over, the ghost of a smile on his face. He went past me and directly walked up to Lindon. “The decryption formula you handed in last time was excellent. There’s an emergency meeting going on at the moment. You’ll have to go back with me.”

Andemund had never praised me while smiling like this before. He had always said to me, Alan, you’re still too young. Alan, this isn’t important. Alan, you cannot join Bletchley Park. 

I had also never seen Lindon smile so brilliantly before. The whiteness of his teeth showed through his grin.

I heard their conversation after they got into the car. Andemund sounded extremely pleased. “Lindon, about how you told me last time that you’d hole up under your bed to think. That is quite intriguing…”

I wouldn’t have felt a thing if not for the comparison between him and I. I realized that Lindon and I had essentially swapped positions. I was holing up in the activity room of the mathematics society every day decrypting codes, essentially becoming the Lindon in the past with his disheveled, messy-as-grass hair, while Lindon, on the other hand, was beginning to dress in shirts and suits in gentlemanly fashion. Before, I would still receive the occasional flirtatious glance from the waitresses at the bars but now I would be looked down upon if I did so much as follow a woman from behind. 

Someone tapped my shoulder. I jumped. 

“How curious, to see Andemund come personally for someone at Cambridgeshire.”

It was the man in gold-rimmed glasses that I saw behind Andemund last time. 

He had come in Andemund’s car, but didn’t return with him. 

“Alan, you look like you’re about to eat someone alive.*” He proffered a hand, smiling as he introduced himself. “We’ve met before. My name is Arnold Visco*, currently working at the Golf, Cheese and Chess Society. I trust that you know where that place is. ”

I shrugged. “You’re not in military uniform.”

The man in rimmed glasses was wearing a casual black vest over a loose shirt. He smiled naturally. “That’s because I’m not here on behalf of Bletchley Park this time. I’m here for a personal task Mr. Garcia sent me on.”

Arnold Visco was a psychologist at the MI6. He was responsible for interpreting intercepted materials at Bletchley Park, and was directly under Andemund’s command.

“Andemund sent you here for a personal task. What does that have to do with me?”

We were sitting at a pub I used to frequent some time ago. The afternoon breeze blew comfortably between us. I ordered a plain beer, while he ordered a blue margarita. Arnold’s jaw was sharp, and his eyes beneath his gold-rimmed glasses were always narrowed into slits, giving an inexplicable air about him. 

Though he was rather direct about what he was going to do. “As you know, I work as a psychologist. Your feelings towards Mr. Garcia have troubled him rather deeply. His task for me was… to make you stop liking him.”

*Debated on whether to use ‘Office One’ or ‘Room One’. ’Office One’ is the literal translation, but for aesthetic reasons I decided on ‘Room One’ (mainly because I don’t think Office One sounds right in English, but English isn’t my first language, so I could be wrong). May perhaps be referring to ‘Hut 1’, an additional building (among many other huts) that was built for extra accommodation during the war where more work was done there. I’m leaning towards using ‘room’ or ‘office’ though, since if the author were really referring to the huts then I believe they may have used ‘小屋’ instead (as used by Wikipedia). May make changes on this later; I’m still not very able to find much information about Bletchley Park that’s readily available online yet. 

*Lit. “Your eyes are glowing green.” A Chinese phrase that can mean a person is extremely jealous, filled with malicious intent, or hungry for something. 

*Unsure about the official translation of Arnold Visco. Original text: “阿諾德.維斯科”. His last name may be translated as Vesco, Wiskow, etc. Using Visco because it sounds the nicest. May make changes later if I am able to get my hands on an official translation.

[10/2/2021] Translator’s notes: A little extension on how the Enigma machine works, for those of you interested. I will be explaining the math behind the conversation Alan and Lindon had that briefly described how the Enigma machine worked.

In simple terms, Enigma machine is consisted of 3 parts: the keyboard (input), 3 rotors, a reflector, and a plugboard (for encryption), and a series of 26 lamps arranged in the form of a keyboard, each etched with its corresponding letter (output). When the keyboard is pressed, the letter goes through the plugboard, the rotor, the reflector, then back to the rotor, through the plugboard again, and finally returns a letter on the series of lamps. Since all of this is done via electric circuits, you could understand the pathway of the letter as below:

Input letter ‘A’ —> Plugboard —> 3 Rotors —> Reflector —> 3 Rotors —> Plugboard —> Output letter ‘B’

The encryption of the Enigma machine is done in two parts, by the rotors and by the plugboard. For the rotors, there are 3 rotors in total, each with 26 letters. The 3 rotors are equipped with a stepping component so that the 3 rotors rotate at different speeds, similar to how a clock functions— the fast rotor, rotor and the slow rotor can respectively be understood as the second, minute and hour hands of a clock. Thus, the amount of permutations that can be performed by the 3 rotors is as below:

26 x 26 x 26 = 17576 (permutations)

While I am not qualified to explain how the electric circuits work within the Enigma machine, it should be noted that the 3 rotors in the Enigma machine are distinct. Thus, the amount of arrangements the rotors has is equal to:

3! = 6 (arrangements)

As an extension, during the war, the Germans had 5 sets of rotors to choose and swap from. So, in reality, there were 5 x 4 x 3 = 60 (arrangements) of the rotors, though you don’t need to know that for the calculations done in the novel. 

Secondly, the plugboard. The plugboard consisted of 26 holes each corresponding to a letter that could be plugged in by a plug connecting 2 letters, effectively swapping these two letters during input. For example, if the setting of the plugboard were set to (ab), then an input of ‘a’ would return ‘b’, and an input of ‘b’ would return ‘a’. A setting of (cd) would make ‘c’ become ‘d’, and ‘d’ become ‘c’, and so on. 

Up to 13 plugs could be used in theory to swap 13 pairs of letters, but normally only 10 were used. In the exposition Alan gave, only 6 pairs were used, so the amount of permutations possible by 6 pairs of swapped letters are as below:

26! / (14! x 6! x 2^6) = 100 391 791 500 (permutations)

The amount of ways to arrange 6 pairs of letters (12 letters in total) are 26!/(26-12)! = 26!/14!

As the order of the 6 pairs can be disregarded, the above number can be divided by 6!

And as the order of the letters within the pair of 2 letters can be disregarded, each pair is divided by 2, allowing the whole thing to be divided by 2^6.

Hence the above calculation. 

Thus, the number of permutations the Enigma machine can provide:

<Rotors>        <Plugboard>

(26^3 x 3!) x [26! / (14! x 6! x 2^6)] = 10 586 916 764 424 000 (permutations)

Considering the fact that I only learnt about the existence of factorials only 6 months ago, there is a large chance that I may get this wrong, but hopefully my calculations are correct. I have noticed that the number I calculated differs slightly from the one in the novel by one digit, but I have no idea what went awry in the middle, so please do enlighten me if anyone finds out where. 

Math aside, this chapter was a pain in the ass to translate. I’m not very satisfied with how it flows, and the English sounds very rigid albeit with correct grammar. I’ll do edits after my brain stops overheating from the math, which will probably be tomorrow. If you’ve read this far, then it means you’re either very interested in math or have nothing better to do. Either way, thank you for reading!