Information Comes in Patterned Spaces.

Information Theory refers to some bullshit from the early 1900s by Claude Shannon et al. He basically formulated communication as such:

Alice's Idea -> Alice's Encoder -> Noise Function -> Bob's Decoder -> Bob's Mind

From this we learn, among other things, how to analyze communication statistically, thanks to the statistically defined noise addition function. This was further used to show (skipping a lot of details) that information is most efficiently transmitted in binary. As applicable as this model may be, the lessons it has to give have already been absorbed into the culture at large, and so I won't waste your time with them.

Instead, I wish to answer perhaps a more provocative question: What is the structure of the unencoded information? What is going on inside Alice's head when she consideres an idea, in the abstract sense?

We know, at least, that such an idea has to at least have some sort of structure, as there is some function (Alice's Encoder) which maps it into a space that is actually mathematically well-defined. The pre-image of that space under the encoder must also be some sort of formally definable superspace, which itself is a subspace of the whole space of the possible idea. That's a lot of words to hand-wavily say that there has to be some formal structure to the space of ideas that Alice can have. Then, in practice, what is an element in a space of ideas?


I now define modality and register. Modality refers to a format of information before it has been encoded for transmission. A register is a more specific type of modality, with emphasis on the style of encoding used.

Some common examples of modalities:

Properties of Modalities

A Proposed Taxonomy.

Now, a question worth asking is: what can modalities look like? Could we taxonomize them? Now that you have hopefully gotten a gist for what they feel like, here is a long list of modalities, rapid-fire:

Now that's great and all, but they won't teach us much in a list. Let's try to organize them. English and English Morse are obviously very similar as they are registers of the same underlying modality. The same can be said of Spanish and Silbo Gomero. Japanese is quite similar and Kenyan Sign Language a bit further off. We can translate between them, and at least for Spanish and English, we can do it with very high fidelity thanks to shared history. We thus have:

Insofar as spoken language is a way of compressing a grammatical parse tree into a linearly-organized sequence of sounds through time, some other "flattened trees" may be the nearest modality-cousins of languages: Programming Languages, Music, Lambda Expressions, and Mathematical Proofs. JSON could be considered in this category too, but it doesn't have such strict and complex grammars as the others in the category.

Slightly more distantly related must be Chinese Characters, insofar as they have a hierarchical structure (although not flattened into a string) along with a clear sense of grammaticality. The same can be said of Nahua Codex Glyphs and Mathematical Formulas.

More distant yet are Organic Compounds and Go Positions, which both feature grammaticality but are not of an obvious hierarchical form. These, along with all of the above, are elements of what I call the "parseable structures," but so are some non-discretized objects like Human Faces, Landscape Paintings, Flavors, and Dance Moves.

Another cluster could be labelled "Dense Mathematical Structures," containing numbers, graphs, rubiks cube scrambles (are all elements of a particular group.)

To Be Continued