Some of the primary aims of Connection Theory include:
- Current: To capture and express known ontological concepts that are presently essential to mathematical activity: sets, ordinals, functions, mappings, categories...
- Posthuman: To lay the groundwork for a (posthuman), noun-less, proto-language.
- Ontological: To rigorously define the conceptual equivalent of a ‘set’ to Set Theory or a ‘category’ to Category Theory. To define a fundamental “building block” (as it were) of a new way of viewing existing and novel mathematical theories.
The idea here is create a language system that is capable of sensibly and meaningfully communicating all known/existing topics in mathematics whilst introducing one's that:
Don't yet exist in mathematics.
Can't exist within the edifice of Set Theory, Category Theory, etc.
Such a language system would be a 1-way mapping between two languages (since translation from the target language is not possible back into Natural Language).
Clarifying Language Concepts
I've already written a bit about this topic and it's worth exploring more here:
Encryption Languages - to encode a meaning into a gesture, table, stomping, knocking on a table, other word, etc. - e.g. "One if by land, two if by sea" (Paul Revere using lanterns to represent military movements). This forms the basis of cryptography, Pig Latin, the Signal Corps, Morse Code, etc. Essentially, to represent something in one language using something else (password encryption, salting, hashing).
Body Languages - there are fully recognized Natural Languages (like American Sign Language) that are predominantly gesture based. Most people mean "body language" to indicate the informal meaning (gestures like an open hand - indicating "you go first"), short-hand, or to assist with implicature. These exist to indicate meaning, stand for a sentence/expression/word, to simplify communication, coordinate activities, etc.
Artificial Languages - mathematical languages that are fully defined, lack ambiguity, obey axiomatic construction rules, etc. Programming languages. These are sub-fragments of a larger meta-language (FOL is a subset of Natural English, Ruby is written in C, etc.).
Machine Language/Code is often called "human unfriendly" or "human unreadable" code. This is, strictly speaking, because it's a formal edifice lacking many useful heuristics (found in, say, the Domain Name System which associates IP addresses with natural language monnikers) and not because it's a "posthuman" language. Future artificial languages (that govern the equivalent of modern Central Processing Units) are likely prime candidates for posthuman languages that don't yet exist. To be sure, the extreme difficulty in translating or reading Machine Code will be comparable to an actual posthuman language (at least one that can be transcribed per some of the possible ways below).
What Would Posthuman Languages Be Like
A few ideas:
- Inaudible but noise-emissive signals (telecommunications fall under this category since they vastly augment natural human communication in just such a way).
- Lacking the ontological underpinnings of natural human language - predicates, objects, subjects, nouns, sentences, propositions - nor their referents.
- Exceeding two-dimensions in reading/writing (top-bottom, left-right), breaking the three-dimensional nature of books (multiple two-dimensional pages arrayed in a sequence).
- Not falling into the standard cryptographic classification patterns: translation, salt, hash, substitution, etc. (Pig Latin, stomping to mean something, using various flags of different colors in the signal corps, Paul Revere’s lanterns, Morse code, etc.)
- Not conforming to Syntax Tree generative grammars, lacking classification within known phonemic patterns.
- Language that cannot be translated into human languages but which has some meaning - e.g. - meaning that cannot be transcribed into human languages although it has semantic content.
- Language that is not-static (the meaning of a human word can change in use but any occasion of utterance is permanently fixed/transient), non-procedural.
- Language that obeys animal language patterns like bird-songs and symmetry groups (strictly speaking this is not “beyond” human language since it’s reasonable to maintain that it can be parsed).
- Language that exceeds the five human senses in grounding descriptions: smells, sight, sound, etc. all of which have served as human language substrates (though smell rarely).
- That which is not “body language” (which conveys meaning transcribable into natural human language).
- All natural language is spatial (involving sound transmitted through space, gestures illuminated by sight/light/photons traveling, symbols on a page, etc.) - either a system that's non-spatial (at all) or that breaks these spatial constraints down in some way.
- Is a semantically-closed, diagrammatic, generative grammar, supporting optionally uniform substitution across lambda operators.
- It eliminates subjects and objects from its base vocabulary and constructs entities that can’t be reduced to objects, relations, and functions (although each of these entities can be constructed by it).
- All basic math theories can be recaptured within it - category theory, set theory.
So, it is itself a basic, new, math theory and language and one that formalizes both diagramming itself along with the other existing math theories.
In this regard, it meets some of the more limited objectives above.