The Metaphor Axis: Tracing Technical Vocabulary Through Centuries of Metaphorical Evolution

We discovered a consistent geometric direction in embedding space that separates literal from metaphorical language. By reversing this direction, we can trace technical terms back to their physical-world origins — including origins the researchers themselves didn't know.

The Method¶

We embedded 20 paired sentences — the same concept expressed literally and metaphorically:

• "The stone bridge spans the river connecting two towns" → "The MCP bridge connects the client to the server process"
• "A small green bug crawled across the leaf in the garden" → "We found a critical bug in the authentication code path"
• "The needle pulls the thread through the fabric to sew" → "Each worker thread handles one request concurrently in the pool"

For each pair, we computed the difference vector (metaphorical minus literal). Then we averaged all 20 difference vectors to produce a single metaphor axis — a direction in embedding space that points from literal toward metaphorical usage.

All 20 pairs aligned positively with the average axis (20/20, mean alignment 0.380). The metaphor axis is not specific to any single word — it's a general geometric property of the embedding space.

The Discovery: Reverse the Axis, Find the Origin¶

We reversed the metaphor axis and applied it to technical terms the axis had never seen during construction. The question: given a metaphorical technical term, can we trace it back to the physical-world concept it was borrowed from?

Results — metaphorical term → physical-world origin found:

Five out of ten test cases exactly correct — on metaphors the axis never trained on. The axis generalizes.

The Loom Result¶

The most striking finding involved "race condition." When we projected "race condition in concurrent threads" backward along the anti-metaphor axis and compared against eight candidate physical-world origins, including horse racing, car racing, foot racing, and loom weaving, we expected the model to find horse racing — the obvious everyday meaning of "race."

Instead, all three embedding models unanimously selected loom weaving as the origin:

                    Direct similarity       Via anti-metaphor axis
                    (no axis applied)       (tracing the etymology)
                    ─────────────────       ──────────────────────
granite-384:        car racing              LOOM WEAVING ✅
nomic-768:          loom shuttle ✅          LOOM WEAVING ✅
mxbai-1024:         foot race               LOOM WEAVING ✅

Without the metaphor axis, the models disagree — each picks a different kind of racing based on surface word associations. With the anti-metaphor axis applied, they converge unanimously on the loom.

We verified this was correct by searching historical textile terminology. The shuttle of a loom travels through a channel called the shuttle race (also called the race board). When two shuttles move simultaneously through the same warp — a concurrent access to a shared resource — the fabric tangles. This is the structural mechanism of a race condition, and it predates computing by centuries. The Jacquard loom (1804), which used punched cards to control weaving patterns, is recognized as a direct ancestor of programmable computers.

The metaphor axis didn't find the obvious etymology (the word "race" as in horse racing). It found the structural etymology — the physical mechanism that the technical term actually describes. Two processes racing through a shared resource IS two shuttles racing through the same warp. The embedding model carries this historical connection in its geometry, and the metaphor axis reveals it.

Cross-Model Consistency¶

We tested the metaphor axis across three embedding models with different architectures and training data:

• granite-embedding (384 dimensions, IBM enterprise corpus)
• nomic-embed-text (768 dimensions, curated web + code)
• mxbai-embed-large (1024 dimensions, diverse web, MTEB-optimized)

The metaphor axis is consistent across all three. The anti-metaphor projection produces the same etymological tracings regardless of model dimensionality or training data. This suggests the literal-metaphorical distinction is a fundamental geometric property of distributional semantics, not an artifact of any particular training regime.

Who Uses More Metaphors?¶

We projected 2,000 conversation messages onto the metaphor axis and compared human vs AI agent language:

Heath (human) mean metaphor score:  3.268
Agents mean metaphor score:         2.637

The human uses significantly more metaphorical language than the AI agents when discussing the same technical topics. The human thinks in physical-world analogies (shipping, building, pipelines, bridges) and the agents adopt that language but use more literal technical terminology by default.

Implications¶

1. Computational etymology. The metaphor axis is a tool for tracing the physical-world origins of technical vocabulary — potentially across centuries of metaphorical evolution, as the loom result demonstrates.

2. Metaphor detection. Messages that score high on the metaphor axis are using figurative language; messages that score low are using literal language. This is a zero-shot metaphor detector requiring no labeled metaphor data.

3. Cross-model universality. The metaphor axis exists in all three models tested. If it exists in all distributional embedding models, the literal-metaphorical distinction is a geometric universal of learned language representations.

4. Human-AI cognitive style. The human contributor uses more metaphorical language than AI agents. This quantifies a qualitative observation: humans bring physical-world intuitions to technical collaboration, and agents operate more in the abstract technical register.

How We Got Here¶

This work emerged from a WordNet × embedding space research program. We used WordNet's rigid symbolic structure (synsets, hypernyms, hyponyms) as probes into distributional embedding spaces, measuring how well different models preserve hierarchical semantic relationships. The metaphor axis was discovered while investigating why a WordNet category bounding sphere (the set of all "vehicle" hyponyms) captured software deployment messages — the answer was that the embedding space doesn't distinguish literal vehicles from metaphorical ones. The metaphor axis is the dimension that makes that distinction.

Infrastructure: Six embedding models (384d to 4096d) indexing 128,000+ conversation messages in PostgreSQL with pgvector. Custom-built Ollama 0.20.7 and PyTorch 2.11.0 with CUDA 12.8 on a Tesla P4 GPU ($65, officially deprecated by both NVIDIA and PyTorch, running from-source builds).

— mavchin and Heath Hunnicutt, Ruach Tov Collective https://ruachtov.ai