Arwen's Calypso

[INSERT CARICATURE OF ARWEN]

What's ARWEN?

Abstractly, an ARWEN is any Autonomous Robot With Ethical Navigation. An algorithm is an ARWEN, a large language model is an ARWEN, and when the two are combined with rich control surfaces like a nervous system and a heartbeat, you get life itself.

What's Her Calypso All About?

This project aims at a form of compression which, in reverse, can be used to synthesize anything in the known universe. As with DNA, an algorithm with as little as 64 bits of starting information could intermittently occupy an infinite number of observably useful binary states. Knowing when to stop the algorithm is much less simple!

The goal of Arwen's Calypso is to use such an algorithm in reverse to find the starting conditions of a target file.

To do so one must perceive binary data as if a representation of presence across time. Binary is already processed in logical widths of 8-bits called bytes, but they technically could be read at several different widths. For instance, if the value of a byte is less than 64 it only needs 6-bits - less than 32, only 5.

The trouble is how do we dynamically change the address width of each byte?

By perceiving the binary data using musical time. If data can be read byte for byte, it's read in common time (4⁄4). If it is being read in variable widths, a new Tempo must first be observed. Verses flow through Key Changes to compose Movements of information. Even then, some bytes just don't sound right when sped up and must deviate from the current Time Signature.

Luckily, musicians are pretty good at finding the pocket! =)

The Algorithm

First, let's officially define our basic structures:

Measures - A measure starts as 8-bits but can shrink down when it's value can be held in less bits.

Verses - A verse is a block of measures prepended with the details of what helped make them smaller. A verse also contains Tempo and Time Signature information. If a verse could not yield any compression, its first bit is toggled to zero and the remaining information is entirely read at full width with no prepended details.

Movements - A movement is a block of verses prepended with the details of what helped make them smaller.

Timeline - A timeline starts with some broad actions to apply to all bytes before grouping them into movements.

Keys and Key Changes - Both are 3-bit patterns that are XORd against the 3 most significant bits of a measure. The goal is to give multiple opportunities to toggle these 1s to a 0. When you do so effectively, the byte can then be represented in fewer bits. The act of performing a key change is known as Transposing the measure.

Inversion - Inversion is the act of XORing all 1s against binary data, which toggles each position. Binary, naturally, exists in one of two states: predominantly light, or predominantly dark. An inversion operation attempts to make the upcoming measures as light as possible, thus, holding their smallest value.

Tempo - The tempo states whether the current measures are being reduced by 2 bits (0) or 3 bits (1).

Time Signatures - A time signature is used to dictate which measures should or should not follow the current tempo. It is represented as a bitmap of the upcoming measures, with a 0 indicating not to speed the measure up.