Intuition Machine
Three levels, four columns, one operator
QML — the Quaternion Modeling Language — is a short list of ingredients, seven axioms, one derived operator, and one small model in which every formal claim has been machine-checked.
What experience sorts into
The theory begins with Peirce's claim that all experience sorts into exactly three basic kinds.
Firstness — quality
Something in itself, without reference to anything else. A felt character, a possibility, a mood. The redness of red before any comparison.
Secondness — causation
Brute encounter between two things. Resistance, effort, surprise. The door that will not open.
Thirdness — mediation
A third thing that brings a first and a second into relation. A law, a habit, a convention, a meaning.
The order is about what you can ignore
The three come in an order, and it is not about time or importance. Call X prescissively prior to Y when X can be attended to while neglecting Y, but not the other way around.
You can contemplate the pure feel of a colour without thinking about any collision or law. You cannot contemplate a collision without it having some felt character.
1st ≺ 2nd: quality without reaction is conceivable;
every reaction has a felt character.
2nd ≺ 3rd: brute encounter without interpretation is
conceivable; every law applies to something actual.
Therefore: 1st ≺ 2nd ≺ 3rd
This ordering — abstractive dependency — is the single most load-bearing idea in the theory, and it returns at the very end in the tradeoff theory.
One sentence, four things you can attend to
Independently of the three levels there is a second, four-way division, arriving from thinking about signs and media rather than experience. Any sign can be examined along two distinctions: is it this particular sign-event or the whole system? And are we asking what it means, or what it is made of?
ii = Instance·Content ie = Instance·Vehicle ci = System·Content ce = System·Vehicle
A spoken sentence makes it concrete. The meaning of this one utterance is ii. The sound waves of this one utterance are ie. The shared language's semantics is ci. Its grammar and phonology, considered as a machine, is ce.
McLuhan's Laws of Media independently discovered this four-faced structure. Its independence from the three-level division is not an accident of intellectual history — it is a formal fact: the four-way division cannot be derived from the operator that generates the levels.
Everything is built from this
𝔏 = ⟨ L, ⊑, π, {Φ_q}, {Φ̄_q}, ⊕, ⊖, ι, γ ⟩
qml_q(x, y) := Φ_q(x) ⊖ Φ̄_q(y)
Take the first input and unfold it one step toward mediation; take the second and fold it one step toward quality; then ask what the unfolded thing contains beyond the folded thing. That remainder is the output.
The subscript q records a basic commitment: no cognitive operation executes without an attentional mode. There is no view from nowhere — every act of abstraction or grounding is somebody's act, performed in some register.
The loss is built in from the beginning
Unfolding and folding are not inverses. Folding what you unfolded does not return you to where you started — abstracting an experience and then trying to recover the experience from the abstraction loses something, and the axiom builds that loss in rather than apologising for it later.
Instead of inversion, the two maps are related by an adjunction: a looser but exact relationship defined by a single "fits under" equivalence. One consequence, proved rather than assumed, is that convention can never be fully grounded — rebuild a convention from its grounding and you get less than the convention claimed.
That permanent remainder is why no amount of process eliminates spin-room, and why the honest goal is making the groundable portion commonly checkable.
Build it, or find out which layer is missing.
Design engagements build the architecture for a specific organisation. Diagnostic engagements establish which of its loops actually close, which of its claims reach evidence, and which of its standing rules no longer have an owner.