Arethusa cipher
From the Quicksilver Metaweb.
When Lawrence first shows the original Arethusa pages (p. 345) to Alan his jaw drops open and Lawrence thinks Alan has, "in some Olympian burst of genius, deciphered the messages in an instant". Instead his astonishment is caused by unexpectedly recognizing the handwriting of the cipher as belonging to Rudy.
Arethusa seems to work as an algorithmic means of generating one-time pads for encryption: In other words, there is some calculation, some equation that Rudy has dreamed up. You give it a valueprobably the date, and possibly some other information as well, such as an arbitrary key phrase or number. You crank through the steps of the calculation, and the result is a number, some nine hundred digits long, which is three thousand binary digits, which gives you six hundred letters (enough to cover one sheet of paper) when you convert it using the Baudot code. The nine-hundred-digit decimal number, the three-thousand-digit binary number, and the six hundred letters are all the same abstract, pure number, encoded differently.
Rudy is using the Zeta function to generate these pseudo-random streams which still imparts some faint patterns to Lawrence. This image evokes the nymph Arethusa commingled and seemingly lost in the noisy stream that was her escape from Alpheus. Yet Alpheus was keen enough to still find her pattern amidst the noise, like a palimpsest. This theme of water as a literal stream of encrypted information is pondered by Lawrence as he stands on the California shoreline before heading out to Australia. He imagines the ocean as a Turing machine, the sand its tape, and the smallest disturbance caused by his footprints betrays information which propogates through the ocean machine to Japan. Sort of a butterfly effect.