The Great x=cape

As the new academic term has begun, I have recently started back at my job as a note taker at Plymouth University.

The main student that I help is taking the first-year Mathematics and Statistics course. I’ve always loved Maths, which I imagine is a minority position. So to try to convince you that Maths isn’t just about crusty old professors scribbling indecipherable squiggles on a whiteboard, but also about exciting tales of derring-do, I want to share something taught in one of the lectures.

To set the scene, think of all those World War II Prisoner of War (POW) films you’ve seen. Probably The Great Escape* comes to mind.

The Great Escape

These escapes didn’t occur spontaneously. They were planned, with outside help from Military Intelligence**.

The communication between POWs and Military Intelligence was carried on through the letters the POWs were allowed to send home. Since all letters were censored, the messages had to be encoded.

How this was done was a mystery, until Plymouth University lecturer, David McMullan, cracked the codes hidden in POW John Pryor’s letters home to his parents in Cornwall. The video below gives some background:

I won’t go into all details, as the steps, while not overly complicated, would take ages to explain. I will explain the spelling rule, that allowed important messages to be hidden in innocuous sentences.

The first step is to add an extra letter to our alphabet, a full stop ‘.’. Now there are 27 letters in the alphabet, and 27 = 3 × 3 × 3. We can create a grid, with each box described by a 3-number combination of 1’s, 2’s, and 3’s. We then fill this grid alphabetically, starting with the ‘key’, which was ‘S’ in John Pryor’s case:

John Pryor Grid

I hope that after a couple of minutes of looking at the grid, you can see the pattern in the numbers and the letters. Poor John Pryor had to keep this in his head when he was encoding his messages – you don’t want to leave any incriminating proof that you’ve been working out codes for the guards to find!

Now, we can use this grid to decipher a sentence in a letter. Let’s use as our example:

A few weeks ago we arranged a rather useful scheme, so men could get lager

I personally would never guess this contained a secret message. And it’s lucky for us (and the escapees) the German guards didn’t either.

The first step is to group the words into 3, and take the first letter of each:

ohn Pryor Words to Letters

Now, we convert these 3 letters to 3 numbers. Take the first row, A F W. Looking back at our grid, we notice that A is in column 1F is in column  3, and W is in column 2. So A F W becomes 1 3 2.

If we look again at our grid, though, we see that 1 3 2 corresponds to the letter M.

We can then convert each of our 3-letter combinations into a single letter using the grid:

John Pryor Letters to Letter

The code has converted “A few weeks ago we arranged a rather useful scheme, so men could get lager” into MAPS. – and no one suspected until recently.

The letters were used to pass German secrets to the British government, and to request things such as maps, passports, guns and so forth so the men could escape from the camp.

It may not be as impressive as the work of Alan Turing and Bletchley Park, but it shows what amazing things can be achieved using a little bit of Maths!

.

* Let’s pass over the fact that in the real escape that inspired the film, the escapees were from the British, Commonwealth or Polish armed forces (although sometimes of other nationalities) – there were no Americans, but then Hollywood has always rewritten history.

** Groucho Marx once quipped that “Military Intelligence is a contradiction in terms” . I think once you’ve read about this story, you’ll realise that this is just a very good, but inaccurate, gag.

To be more precise about which intelligence service was involved, it was MI9 that communicated with the POWs. Not to be confused with James Bond‘s MI6.

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