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Turing's Machine 213

Thanks to Turing's insight into coding schemes and the machines
he designed, the British were soon able to read almost every coded
message the Germans sent during the war, giving the Allies an enormous
advantage. The D-Day invasion involved convincing Hitler that the Allies
had a huge army of nearly 400,000 men, massed around Dover preparing
an attack on Calais head on, with a second army in Scotland poised to
attack Norway. In truth, they had only 150,000 men planning an assault
on the Normandy Beaches in the South. Just before the landings messages
were decoded showing Hitler had fallen for the Allied subterfuge. Even
as the Normandy landings began, Hitler still thought this a bluff and
kept his 28 divisions at Calais waiting for the imagined attack. Without
this intelligence advantage, the Allies would have needed a much larger
invasion force, and Churchill believed Turing's work shortened the war
by as much as two years.

The cracking of Enigma remained a secret after the war and
Turing's story remained untold for many years. When Churchill wrote
his history, The Second World War, a massive work in six volumes, all
sorts of sensitive information featured, but Turing's work was omitted.
One sentence hints that Churchill might write something about it in the
future, but he never did. Churchill considered the work at Bletchley Park
so sensitive he had it put in the highest classification – extending the
30-year secrecy rule. We must presume the decoding schemes were still
being deployed during the Cold War. The papers were finally released in
2010.

In one of those sad turns in history Turing was found guilty of gross
indecency for homosexuality in 1954, a criminal act at the time, and was
prescribed hormone treatment. This affected his mental state and he took
his life by eating an apple laced with cyanide. He was eventually honored
posthumously as a war hero and one of the most significant thinkers of
the 20th Century. A Turing Award is the equivalent of the Nobel Prize for
Computing. He was given a royal pardon in 2013.

To see how Turing came up with the idea for the Turing machine
and solved the decision problem, we need to get a feel for theoretical
mathematics. That might sound a little heavy going but don't worry, I will
use a simple piece of mathematics to explain, one we have all played with
as children, secret codes.

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