Autografo

Write a program whose output is its own source code. The obvious attempt fails: to print the program you must write it inside itself, in quotes, and then that copy must contain a copy, and so on without end. The way out is to split the program in two: some text, and some code that prints the text twice, once in quotes and once as it is. The text describes the code; the code, reading the description, reproduces both. Douglas Hofstadter named such programs quines in Gödel, Escher, Bach (1979), after the logician W. V. O. Quine, who studied sentences that talk about themselves; Kleene’s recursion theorem (1938) had already shown that every programming language has them.

Autografo’s tape becomes one: the panel above writes a program that carries your text and prints itself, character for character, and the page checks it by running it in a sealed worker and comparing. The Quine rule plays the same idea on the grid: each generation, the text writes itself again.

A program that can print itself can also write itself somewhere else: into a file, into another program. That is all a computer virus is. Fred Cohen gave them that name, and their first theory, in 1984; the same year Ken Thompson’s Turing Award lecture, “Reflections on Trusting Trust”, showed a compiler that reproduces a hidden back door in every compiler it compiles, using the quine’s trick. The Virus rule is the harmless version: a phrase that copies itself, letter by letter, over the text in its way, and now and then jumps to start again elsewhere, until the text is mostly the virus, and the song with it.

In the late 1940s John von Neumann asked whether a machine could build a copy of itself. It seems it cannot: a machine that builds something must contain its description, and the description of the machine would have to describe the description, forever. His answer, published by Arthur Burks in Theory of Self-Reproducing Automata (1966), was the quine’s: a universal constructor A that builds whatever a tape describes, a copier B that copies any tape, a controllerC, and a tape φ describing A, B and C. A builds the machine from the tape; B copies the tape and gives it to the new machine. The description is used twice, once as instructions and once as data, years before DNA was found to work the same way.

Here the tape is your text; the constructor reads it and makes sound; the copier makes the next generation; the controller is the clock. They light up as they act. The Replicator rule is Edward Fredkin’s much simpler self-reproduction: each cell becomes the exclusive or of itself and its four neighbours. The rule is linear, so after 2, 4, 8, 16 generations any pattern is there five times, itself and a copy at that distance in each direction. The letters are numbers of five bits, and each bit follows the rule on its own, so the copies are the same words, letter for letter, with a babble in between until the next power of two.

Von Neumann built his machine, with Stanisław Ulam’s suggestion, on a grid of cells, each in one of 29 states, each changing by looking at its neighbours. John Conway looked for the simplest such world where interesting things still happen, and found it in 1970: two states, and two rules. A live cell with two or three live neighbours survives; an empty cell with exactly three is born. Martin Gardner published it in Scientific American that October. Life has gliders, guns that fire them, and, it was later shown, everything needed for a computer.

In Life, the letters are the cells: a letter survives among two or three others, and one is born among three, inheriting the letter most of its parents share, or one of theirs, sometimes miscopied, a copying error, coloured amber.HighLife, Nathan Thompson’s variant (1994), lets cells be born among six too, and has a small replicator of its own.

Nothing in Life’s two rules mentions gliders; nobody designed them. That is emergent complexity: order at one scale that the rules at the scale below do not contain. Autografo looks for its own: as the letters live and die, the rows are read for words, and a word that was not in your text, that nobody wrote, is listed, underlined in green, and sung above the rest.

A vowel is the buzz of the vocal folds shaped by the mouth, which resonates at a few frequencies, the formants; the first two are enough to tell the vowels apart. Gordon Peterson and Harold Barney measured them for American English speakers in 1952, and their numbers are the ones used here: a sawtooth for the buzz, three band-pass filters for the mouth. Consonants are noise, bursts and hums. Reading the grid by columns makes chords of letters, the row giving the pitch; letter by letter, it is closer to speech.

Listening runs the other way, the way a phonetician reads a spectrogram: the two strongest resonances become the nearest vowel, noise a fricative, a sudden onset a plosive, silence a space. It is crude, and that is the point: music is written as a babble of letters, which the rules then turn into words, which are sung.