Status: blue-sky reconnaissance. Not a settled thesis — a line of thought being stress-tested to see if it holds together. Parent: First Thoughts. This note is the hub for the thread; it holds the substrate claim, and the two child notes take the consequences.
Representation, Not Language
(what the trained object is)
zone, not vector — grown,
not discovered
|
+---------------+---------------+
| |
Map and Territory Map Synchronisation
(is the zone a map OF (two maps, one task —
anything? humans map how do they align, and
territory; LLMs map maps) how does alignment fail?)
| |
tensor = substrate, Darley: fluent, coherent,
zone = shape systematically wrong
| |
+---------------+---------------+
|
Alexandria Quartet as the
worked human-side case• Map and Territory — Humans vs LLMs — whether the map/territory metaphor survives for an LLM, and the tensor-as-substrate distinction.
• Map Synchronisation — how two internal maps are pulled into alignment, why the notes system is a synchronisation protocol, and fluent desynchronisation as the failure mode.
"Language model" is a misnomer for the trained object. What training produces is a shaped representation — encoded in the weights — and language (next-token prediction on text) is the pressure that shaped it, not the substance it's made of. The representation is better understood as a compressed model of whatever structure was present in the training signal, not as "language" itself.
Under this framing, fluency in language is evidence of the representation, not the representation itself. Bolting on vision or audio encoders and getting coherent cross-modal reasoning is expected, not surprising — you're attaching new sensors to an existing representational structure, not teaching language to see.
Rejected framing: "vector space", because it implies a point — precise, singular, arithmetic — and implies a neutral, indifferent container that meanings merely sit inside (classical vector spaces don't care about basis, origin, rotation).
Working framing: a concept is a zone — a region with extent, fuzzy edges, and a density gradient, activated to different degrees by different contexts. And critically, the space itself, as a whole, is also a zone — not a neutral backdrop that meaning is plotted against. The container is not separate from the content. There is no neutral coordinate system meaning is placed into; the geometry of the whole space is itself shaped, bounded, and specific to what produced it (architecture, training corpus, objective).
Consequence: two independently-trained models don't share one space with different coordinates — they have different zones, possibly overlapping, possibly not. Comparing them is a translation problem, not a coordinate change. This is a checkable prediction: expect partial, lossy alignment between two models' representations under stitching/rotation, not clean isomorphism — which is roughly the shape of what the embedding-alignment literature finds (rotation gets you a long way, not all the way).
This also quietly drops the Platonism implicit in "vector space" talk — the idea of one ideal semantic space that any good-enough model is discovering. If the whole thing is a zone, it was grown, contingent on training data and objective, not discovered.
Starting intuition pump. The Amplified Bible's convention of bracketing several alternative English words after a translated term is a human doing, by hand, what triangulating a zone from outside looks like: the original word occupies a region no single English word covers, so several words are offered as probes into that region rather than a single "correct" translation.
Fork resolved, tentatively (2026-09-18): plurality, with weights, not a centroid — and there's now a mechanism for it, not just an intuition. See Concept Factorisation: matching pursuit decomposes a note's embedding into 2–3 dictionary atoms plus a salience weight each, without ever averaging them into one point — a centroid would be exactly the wrong move, since it destroys the multiplicity the Amplified Bible is preserving. Read this way, the bracket set is matching pursuit done by hand: a translator facing a Greek word's zone greedily picks a few English words that each cover a facet of it, rather than reducing to a single 'best' gloss. The zone framing still gets the credit — plurality only makes sense if the underlying object is a zone rather than a point — but the mechanism is what turns 'the brackets mark a boundary, they don't average' from an assertion into something with a because.
• Is a zone defined by what's inside it (words/concepts that belong) or by what activates it (contexts/prompts that light it up)? These are different definitions. Amplified-style translation is evidence for the first; steering-vector interventions are evidence for the second. The thesis currently doesn't commit to one.
• "Meaning is the geometry of the zone" risks overreaching once you're below the embedding layer — interpretability work (Anthropic's own SAE/superposition findings) shows individual neurons are often polysemantic and non-orthogonal. The claim is safer stated about the network's representation of a concept as a whole than about any single clean geometric object inside it.
• Needs a falsifiable prediction, not just a reframing. Candidates so far: (a) cross-modal transfer without re-teaching language; (b) partial-not-clean alignment between independently trained models' representations under stitching; (c) coherent, language-independent behaviour change from steering-vector interventions. None of these have been checked against literature yet within this note — flagged as the next step, not yet done.
The Amplified Bible fork is resolved (see above); the live open question it hands off to is concept-factorisation's own unresolved TBDs — dictionary choice (open-extract vs snap-to-canonical) and subtraction grade (plain vs orthogonal matching pursuit) — which is where this thread's next real test now sits.
• Pick one falsifiable prediction and check it properly against the literature (embedding-stitching/model-alignment work is the most tractable starting point).
• Decide scope: is this a claim about embeddings specifically, or about the network's overall representation of a concept? These want different evidence.
• Decide whether "humans map territory, LLMs map maps" (see Map and Territory) is a difference in kind or degree — it is currently the thread's strongest one-line statement of the human/LLM distinction and also its most attackable.