Mathematician and engineer Claude Shannon single-handedly invented the field of "information theory" with his seminal paper "A Mathematical Theory of Communication". Shannon spent the Second World War working on anti-aircraft weaponry and codemaking (his trans-Atlantic colleague Alan Turing had worked more as a codebreaker); after the war, he worked as a researcher for Bell Labs, and it was while engaged in this more prosaic pursuit that he made the conceptual leap that will mean that scientists two hundred years from now will know his name even if his wonderful toys, scientific juggling, and computer chess are forgotten. While working on the problem of noisy phone lines, Shannon proved that it was possible to reduce the possibility of errors in the transmission to arbitrarily small numbers, simply by using well-designed error checking algorithms. (Designing these algorithms then occupied very smart people in the telecommunications industry the next fifty years.) Showing this required Shannon to invent the idea of a communication’s "entropy", thus providing a measurement of the padding built in. Language is fragile where it is not redundant; a missed digit in a binary number could be disastrous, but every English reader can figure out who "Wm Shksper" is meant to be. From Shannon forward, information theorists looked at language as hovering somewhere between redundancy and noise. Information was surprise. People have been trying to keep secrets from each other for a long time; the simple form of cryptography known as the "Caeser cipher" didn’t get its name from the salad. But as Alan Turing showed when he broke the German’s unbreakable Enigma encryption, what smart people can create, smart people can undo. With computer cycles becoming cheaper and cheaper, decent tools available to amateurs can break encryption techniques that were state of the art just a few decades ago, often literally in a matter of minutes. There is only one form of encryption that is and will remain unbreakable, no matter how advanced the tools used for cryptanalysis grow. The one-time pad, also known as the Vernam cipher, after its World War I-era invetor, draws its strength from its size; where a simple Caeser cipher might use a single letter as its key and a modern message encrypted using triple DES might use three fifty-digit numbers, the key for a message encrypted using a one-time pad is the length of the message. Basically, a message is transformed into binary, then the key, a binary number of equal length is applied to it. A plainttext of "10100" and a key of "01101" produces a ciphertext of "11001". But a plaintext of "11111" and a key of "00110" also produces a ciphertext of "11001". (The same applies using keys and texts of letters instead of numbers.) An encrypted message is undecipherable simple because any plaintext, given the right key, might encrypt to the same ciphertext; with the right keys, "ATTACK NOW", "SURRENDER", and "LOLLIPOPS" might all come out as "GKROQPSXI", and a codebreaker faced with "GKROQPSXI" would have absolutely no way of telling.

The sort of attack that solved the mystery of the Beale cipher and cracked century-old Edgar Allen Poe puzzles simply wouldn’t apply; the same message could decode as a map to buried treasure, a shopping list, Poe’s last will and testament, or the secret recipe of Coca-Cola and there would simply be no way to distinguish. This requires the key to be used only once; repeated messages encrypted using the same key will eventually yield up some information for attackers. The Vernam cipher is called the one-time pad for precisely this reason; keys were once issued as a physical pad containing thousands of letters. One copy would be given to a spy and one copy retained by the home office; when all the letters of the key had been used up, when all hundred thousand letters of text had been encrypted, the pad was to be destroyed. Failure to keep this operational protocol and occasional captured pads or pads obtained from defectors led the joint US/UK VENONA project to eventually decode a number of Soviet ciphertexts, including ones apparently proving that Alger Hiss was a Soviet agent.

The cryptographic need for random numbers (in much larger quantities than those found in the RAND Corporation’s classic A Million Random Digits led mathematicians to come up with dozens of pseudo-random number generators, means of cranking out random numbers without using a physical source of randomness like a Geiger counter or a lava lamp. If the numbers used had a recognizable pattern — if, in Shannon’s terms, they were low-entropy, if the each number wasn’t a perfect surprise given the previous — patterns could be found. But if they were, they could form the basis for encryption so perfect that the coded messages could be handed out to all and sundry. You could give them out on the street and they’d be perfectly incomprehensible forever. Or you could put them on the radio.

For years, the numbers stations of Europe and the Americas have been intriguing radio buffs and amateur codebreakers. The format is simple: a tone, a tune, or a phrase, followed by meaningless strings of letters or numbers repeated over and over. Educated speculation suggests that these are messages encrypted using one-time pads (or the conceptually similar "dictionary" method, in which numbers indicated the page and count for letters in a pre-selected book) being transmitted. The messages are incomprehensible to anyone without the key, so why rely on dangerous spycraft to get them to agents in the field when they can do the job with a store-bought shortwave? And like faces in the cloud or "brown noise", the repeated random noise of the numbers stations often comes to seem meaningful in itself, sometimes even hauntingly beautiful. Jeff Tweedy’s celebrated Yankee Hotel Foxtrot took its name from a numbers station recording, eventually sparking a legal battle with Akin Fernandez, who had poured years of his life into his Conet Project, a four-CD set of the weird and affectless voices adding entropy to the airwaves. (Fernandez makes low-fidelity MP3s of the Conet recordings available for free on the Internet but objected to the band using a sample from his CD without authorization; his ownership of something recorded off of shortwave radio is an open question, but the real copyright owners of the numbers transmissions aren’t likely to complain and Wilco settled out of court.) Jim Sanborn’s sculpture created for CIA headquarters in Langley, Virginia, Kryptos, is an attempt to make art for and about America’s cloak and dagger community; it contains a puzzle that Elonka Dunin believes has yet to be solved. (Perhaps Sanborn should have placed it in the NSA’s Fort Meade headquarters in Maryland.)

Claude Shannon once built a remarkable device that Arthur C. Clarke later described:

Nothing could be simpler. It is merely a small wooden casket, the size and shape of a cigar box, with a single switch on one face. When you throw the switch, there is an angry, purposeful buzzing. The lid slowly rises, and from beneath it emerges a hand. The hand reaches down, turns the switch off and retreats into the box. With the finality of a closing coffin, the lid snaps shut, the buzzing ceases and peace reigns once more. The psychological effect, if you do not know what to expect, is devastating. There is something unspeakably sinister about a machine that does nothing — absolutely nothing — except switch itself off.’

Shannon drew the equations. Information is surprise. What happens to the instruments of communication when surprise is all that’s left? What is there to be found in a message that communicates nothing — absolutely nothing — except that it is there?

And the radio counting wasn’t just new to Fernandez, it was beautiful. He’s a disciple of an Italian named Luigi Russolo, who argued in a 1913 manifesto called "The Art of Noises" that the bustle of city life and industrial machinery ought to be included in our musical language, alongside chords and harmonies, violins and oboes. This proved a tough sell. In 1914, Russolo held his first concert with noise-making machines he called Intoners and the show ended in a melee: performers against the audience.

"I understand that shortwave noise is a kind of music," Fernandez says, sounding Russolovian. "And to me the numbers brought another level of beauty to the music."

[Update: Akin Fernandez himself wrote in with some clarifications on the legal issues involved with the Tweedy suit. He also notes that Irdial places no restrictions on MP3 distribution of its works, so download with a clear conscience.]