During World War 2, it was very important that signals from the various governments involved in the war to the various armies, navies and air forces be kept secret. Signals, or messages, had to be in code or cipher to make them difficult for the opposition to read.

A ‘code’ and a ‘cipher’ are not the same thing: a cipher changes a message on a letter-by-letter basis, while a code converts whole plaintext words or phrases into other words or numbers. Typically, a code with the words “delta eagle draw on the parrot” could mean “bring tanks up to the south-east front”, whereas the signal “bring tanks up to the south-east front” could be enciphered “eulqj wdqnv xs wr wkh vrxwk hdvw iurqw” using the ‘caesar shift’ cipher, whereby, with a key of three, each letter in the signal is replaced in the alphabet by the letter three further along. Thus, ‘b’ becomes ‘e’, ‘r’ becomes ‘u’, and so on.

It is not hard to crack such ciphers using letter frequency analysis: even in our short sample, we can see that there are quite a few occurrences of the letter ‘w’. In English, the letter ‘e’ is the most common occurring letter, followed by ‘t’. Replacing the letter ‘w’ with the letter ‘e’ in the cipher will give “eulqj edqnv xs er ekh vrxek hdve iurqe”, which is meaningless. Replacing the ‘w’ with the letter ‘t’ is more rewarding: “eulqj tdqnv xs tr tkh vrxtk hdvt iurqt”. We can guess that ‘tr’ and ‘tkh’ may mean “to the”, which gives ‘r’ as ‘o’ and ‘k’ as ‘h’. The rest of the cipher is easily solved.

To send messages by code required that all parts of an army, air force or navy had to have code books and keep them secure. This is very inflexible. The Germans developed a cipher machine, now know as Enigma, which enciphered signals and deciphered them with great security.

Watching the film Enigma, one gets the impression that the cipher was solved by a few university graduates living in a country mansion and headed by Benedict Cumberbatch. Anyway. The British let the US know they had deciphered the Enigma signals. Two effects resulted: the US refined its own cipher-breaking systems and the US investigated what alternative ciphers could be unbreakable.

With regard to the latter, an obvious candidate would be the enciphering of signals that had been reduced to a bit stream of digital information. But then the question arose: Could all messages – being text, pictures and/sound – be reduced to digital format and then reproduced with complete accuracy? If so, unbreakable ciphers were possible.

A mathematician in Bell Laboratories, Claude Shannon, calculated that this was possible and thus laid the foundation, the DNA, for modern communications. He wrote a paper titled ‘The Mathematical Theory of Communication’, which is fundamental in understanding the theory of communication. This theory is not about wires and fibre, but about philosophy; for example, the information content of a system (say my friend Johnny) is the probability that he will receive a message he has not received before – if a 100% probability, then his information content is zero, and vice versa.

Shannon, together with Ralph Hartley, created the Shannon-Hartley law of information transmission: Shannon-Hartley theorem tells the maximum rate at which information can be transmitted over a communication channel of a specified bandwidth in the presence of noise. This may not float your boat, but it does mean there is still a limit to which TV signals can be real-life or how fast the Internet can ever get. Shannon also invented the motorised pogo stick, a chess-playing computer used to juggle while riding a unicycle. And if that does not impress . . . nothing will.