Machines, Mathematics And A Monkey – It’s An Enigma

A few days ago my son Paddy came back from school, his eyes shining with excitement. His class had gone on a trip to NUIG where there was a science festival on, and his maths class went to a workshop presented by James Grimes, who travels the world with an original Enigma machine, one of those used by the Nazis to send and receive secret messages during the war. Paddy carefully explained over dinner exactly how the Enigma machine worked. Despite having read Robert Harris’ novel Enigma some six years ago, I still didn’t have the way the machine worked down. It was just beyond my pay grade, but Paddy has a calm and careful way of explaining things that makes learning anything easy. He never patronises or loses patience, whether it’s something to do with phones, computers – or coding machines. Every time his sister Liv interrupted his flow (he can be a bit lengthy) he would wait for her to finish, just a tad testily, then pick up where he left off. By the time he was done, I was like, “Ohhhh…so THAT’S how it worked!”

I remembered the excitement I had felt after reading the Robert Harris book. How it was thanks to Alan Turing, principally, that the Enigma machine’s secrets were exposed. Basically, significant figures in the German army would have an Enigma machine, for all the world like a tricky-looking typewriter. They would hit a key on the front half of the keyboard, which would light up a letter on the back end of the keyboard. In this way, a coded sentence would be generated. This would then be sent to another German officer who also had an Enigma machine, and when he fed the code into that, it would reverse-code it back to the original meaning. Three wheels at the back of the machine, which turned every time a letter was punched, meant the substituted letter was never the same twice. Their starting position controlled the letter chosen to form the code but that starting position was changed every day at midnight. That meant that you could spend all day cracking a message, only to have all your work rendered useless on the stroke of midnight.

Luckily, the Allies knew two things: that a letter could never substitute for itself (an “e” would never be “e” in code) and the Germans always started their nightly broadcasts with a weather report. These, clearly, followed a pattern, and with the help of the giant proto-computers that Alan Turing designed to make calculating the possible letter combinations more achievable, they eventually cracked the code. The Allies had to use their information sparingly: they did not want the enemy to know that their top secret coding machines had been compromised. Imagine knowing that your warships were being targeted by U-Boats, and not being able to issue a warning to take evasive action, for fear of giving the game away. Heartbreaking.

I was enchanted by the story of the Enigma machine, and how Alan Turing and his team shortened the war by at least two years, or perhaps even won the war for the Allies. The way he couldn’t live his life after the war as he may have liked as a gay man is beyond sad, but it’s the combination of his great intellect, how he put it to such invaluable use and how shamefully he was treated afterwards that I find so impossible to resist.

It also piques my interest. I have a latent interest in the world of maths: I am a sort of ignorant enthusiast, with a tragically weak capacity for serious mathematical thought. That doesn’t mean maths doesn’t excite me.

Monkey Maths

Occasionally, I have attempted to help the children with their maths homework. This causes my husband Marcel huge alarm. He is very good at maths in a truly maths-geek way: it’s his job, after all. Eventually, finding me spouting on in a confident but confused way, he could not hold back.
“You can’t help the kids with their maths homework!” he cried. “You have the level of maths of a MONKEY!”
At that, we all fell about laughing…how can you take that seriously?
But the fact of the matter is that I am intrigued by maths. One day many years ago in Belfast, I awoke with a hangover. The house I was in belonged to a statistician named Malachy, and I suppose he was into maths as hobby. There was a book lying around the living room called Mathematics For The Millions and it promised to address all the questions to which I wanted answers: how folk realised you could count up to more than 3, how whoever thought up logarithms did so, how calculus works. But in my compromised state, it was all a bit too much. Luckily, the proprietor of a second hand bookshop in Belfast City Centre, later on that day, was on hand to help me.
“Mathematics for the Millions, by Lancelot Hogben? Yes, I have it,” he said in a charming Northern accent, disappearing into the dark recesses of aisles of dusty tomes, reappearing with an old green book smelling deliciously musty.
It remains one of the books I intend to take with me to a desert island, should the need arise, but not until then.

This is all by way of explanation as to why I was so excited to hear that the Enigma machine was in Galway for a few days. I arranged to sketch it, which time was afforded to me most generously. I spent the most wonderful two hours in the company of James Grimes, sketching the machine, and generally shooting the breeze. It felt like – it was – a huge privilege to have a private audience with the machine, and indeed with James.
“Do you know one of my favourite aspects of the war?” said James. “Gays and Jews [in the form of Turing and the Polish brainboxes who first cracked Enigma] were the ones who beat Hitler, some of the groups he persecuted the most.”
How wonderful.

Two things made me wonder. Why, when the Germans realised someone knew their moves in advance did they assume there was a spy passing on secrets, and not consider that their machine might have been compromised?
“The Germans were waging an offensive war,” said James. “They thought it would be fast – all over by Christmas. The British, on the other hand, were fighting a sneaky war. It was just beyond the ken of the Germans that someone might have cracked their code.”
Okay, I could see how that might have happened. But what about the fact that there were Enigma-type machines, used by banks and the like, freely available before the war? Why not just buy them then, and decipher how they worked?
“The commercial machines were different,” said James. “Those used by the military were far more complicated.”
“Yes,” I said, “but they would have gone a long way towards helping them understand the concept.”
James didn’t have much of an answer for that.

Sketching the Enigma machine will remain one of the high points of my life this year (two of my men friends suggested running off with it; just as well James watched me like a hawk!) – I’m going to re-read Enigma by Robert Harris. Perhaps this time around I might even understand it. What do they say about a roomful of monkeys and an infinite amount of time…?

Congratulations to the Giveaway Winners!

Some of you will remember that I did a giveaway last week for tokens to access articles on my website. There were some really great suggestions for future articles. Here are some of my favourites:

– Illustrated maps to enliven a sketchbook
– Ways to inspire the “art bug” without being overwhelming
– How to simplify detail without losing the essence
– Proportions of people in a public space
– Reflections
– Grass
– Water in puddles
– Twilight
– Using colour to create more depth and the role of warm and cool colours to convey distance.
– Simple people on the go in an urban setting
– How to develop a daily sketching habit – paring down your kit, setting aside specific times?
– Using simple colour palettes
– Gimmicks (my word!) to make sketches look cool!

I will be sending the tokens to all the people who contributed their refreshing ideas. All I have to do now is actually think about how best to explain and develop the topics mentioned. I am very grateful for them as without you, the readers, telling me what you’d like to know. it’s hard to guess…

Until next time!