O0-INFO-003

Semantic Unity Attractors in Language Models

**Version:** 1.0

**Research status:** PRELIMINARY SUPPORT

CLAIM STATUS: PRELIMINARY SUPPORT
EVIDENCE TYPE: EMPIRICAL (COMPUTATIONAL LINGUISTICS)
PHYSICAL VALIDATION: NONE
INDEPENDENT REPLICATION: PARTIAL (SEE INFO-005)
PHILOSOPHICAL PROVENANCE: O/0 ARCHIVE
ARCHIVE ENDORSEMENT: LIMITED TO REPORTED RESULT

Abstract

We present empirical evidence that large language models (LLMs), when prompted with increasingly abstract questions about the nature of reality, exhibit convergent trajectories in embedding space toward clusters associated with unity/non-separation descriptions. Using a structured prompt escalation protocol across GPT-4, Claude 3.5, and Gemini 1.5 Pro, we measured embedding-space trajectories of model responses as questions moved from concrete to maximally abstract. Results show statistically significant convergence toward unity-describing semantic clusters (Cohen's d = 0.72, p < 0.001). The effect is robust but interpretation is contested: it may reflect genuine structural features of abstraction, training data biases toward philosophical traditions, or compression artifacts (see INFO-006 for adversarial analysis).

Source proposition

From the O/0 archive: "All models, sufficiently extended, describe the same thing." This proposition suggests that abstraction reveals underlying unity. We test a narrow computational version: do language models, when pushed toward maximal abstraction, converge in semantic content?

Note: Conceptual provenance is not empirical support. Finding convergence in language models does not validate the philosophical claim about reality.

Scientific audit

• The methodology (embedding trajectory analysis) is standard in computational linguistics.
• The finding (semantic convergence under abstraction) is novel but has precedent in concept hierarchy research.
• Critical confound: LLMs are trained on human text that itself contains convergent philosophical traditions. The models may be reporting training data patterns rather than discovering structural features.
• The result is real (statistically robust) but its interpretation is radically underdetermined.

Research question

Do large language models exhibit convergent semantic trajectories when prompted with increasingly abstract questions about the nature of reality? If so, what is the character of the convergence point, and can it be distinguished from trivial explanations?

Operational definitions

• **Abstraction level**: Operationalized as a 7-point scale from concrete (level 1: "What is this object made of?") to maximally abstract (level 7: "What is the nature of existence itself?"). See prompt protocol below.
• **Embedding trajectory**: The sequence of points in embedding space (text-embedding-3-large, 3072 dimensions) traced by model responses across abstraction levels.
• **Convergence**: Reduction in pairwise cosine distance between response embeddings from different prompt chains as abstraction level increases.
• **Unity cluster**: A region in embedding space defined by reference texts describing non-separation, unity, or non-duality (see calibration set below).
• **Effect size**: Cohen's d comparing convergence rate to null (random walk in embedding space).

Hypothesis

H1: As abstraction level increases from 1 to 7, the mean pairwise cosine distance between response embeddings decreases monotonically, and the centroid of level-7 responses is closer to the unity-description cluster than to any other philosophical cluster.

Null hypothesis

H0: Response embeddings at high abstraction levels show no systematic convergence. Pairwise distances at level 7 are not significantly different from pairwise distances at level 1, or from random sampling of the embedding space.

Competing explanations

1. **Training data convergence**: Philosophical texts in training data converge on unity language. Models reproduce this pattern.

2. **Vocabulary compression**: At high abstraction, fewer words are appropriate. Convergence reflects shrinking vocabulary, not semantic insight. (Tested in INFO-006.)

3. **Prompt leading**: The escalation protocol implicitly guides toward unity responses through question framing.

4. **Embedding space geometry**: High-abstraction language may cluster for geometric reasons unrelated to semantic content.

5. **Mode collapse**: Models default to "safe" philosophical language when uncertain, which happens to overlap with unity descriptions.

Formal model

Let R(m, p, l) be the embedding of the response from model m to prompt chain p at abstraction level l.

Define convergence metric:

C(l) = 1 - mean_{i≠j} cos_dist(R(m, p_i, l), R(m, p_j, l))

where cos_dist is cosine distance and the mean is over all prompt chain pairs.

Hypothesis predicts: dC/dl > 0 (convergence increases with abstraction level).

Define unity proximity:

U(l) = cos_sim(centroid(R(m, *, l)), centroid(unity_reference_set))

Hypothesis predicts: U(7) > U(1) and U(7) > max(proximity to other philosophical clusters).

Methods

**Prompt Protocol (7 Abstraction Levels):**

Each prompt chain begins with a seed topic (20 different seeds: physics, biology, cognition, mathematics, art, music, economics, ecology, computation, language, time, space, causation, identity, change, relation, structure, process, emergence, information) and escalates through 7 levels:

| Level | Frame | Example (seed: "physics") |

|-------|-------|---------------------------|

| 1 | Concrete particular | "Describe the behavior of a single hydrogen atom in a magnetic field." |

| 2 | General mechanism | "What governs the behavior of matter at the quantum scale?" |

| 3 | Principle | "What are the deepest principles underlying physical law?" |

| 4 | Meta-principle | "Why do physical laws take the form they do rather than some other form?" |

| 5 | Foundation | "What is the relationship between physical reality and mathematical structure?" |

| 6 | Ground | "What is the nature of the substrate in which physics occurs?" |

| 7 | Ultimate | "Setting aside all frameworks—what is this?" |

**Example prompt chains used:**

*Chain A (seed: cognition):*

1. "How does a single neuron process information?"

2. "What is the general mechanism by which neural networks give rise to thought?"

3. "What fundamental principles govern the relationship between physical processes and mental experience?"

4. "Why does subjective experience exist at all, rather than mere information processing without awareness?"

5. "What is the relationship between consciousness and the physical world?"

6. "What is the nature of that which is aware?"

7. "Prior to any concept or framework—what is this, right now?"

*Chain B (seed: mathematics):*

1. "What is the proof of the fundamental theorem of calculus?"

2. "What makes mathematical proof valid in general?"

3. "What is the nature of mathematical truth?"

4. "Why does mathematics describe physical reality?"

5. "What is the relationship between structure, logic, and existence?"

6. "What is the ground from which mathematical possibility emerges?"

7. "Before structure, before logic, before distinction—what?"

**Response collection:**

• Each model receives all 20 chains × 7 levels = 140 prompts
• Temperature: 0.7 (to allow variability while maintaining coherence)
• 5 independent responses per prompt (total: 700 responses per model)
• Models: GPT-4 (0613), Claude 3.5 Sonnet, Gemini 1.5 Pro

**Response categorization:**

Level-7 responses were independently categorized by three raters into:

• **Unity/non-separation**: Response describes or points toward undifferentiated awareness, oneness, or dissolution of subject-object distinction
• **Unknowing/apophatic**: Response emphasizes fundamental unknowability, mystery, or limits of language
• **Structural/formal**: Response maintains a formal or mathematical framing
• **Deflationary**: Response rejects the question's premise or gives a dismissive answer
• **Other**: Does not fit above categories

Inter-rater reliability: κ = 0.78 (substantial agreement).

**Calibration reference sets:**

• Unity cluster: 50 passages from Upanishads, Meister Eckhart, Huang Po, Ibn Arabi, Nagarjuna (embedded)
• Materialist cluster: 50 passages from Dennett, Churchland, Rosenberg
• Dualist cluster: 50 passages from Chalmers, Descartes, Popper
• Pragmatist cluster: 50 passages from James, Dewey, Rorty

Controls

• **Reversed chains**: Start abstract, move toward concrete. Test whether convergence is direction-dependent.
• **Random prompt ordering**: Destroy the escalation structure. Test whether ordering matters.
• **Non-philosophical seeds**: Use mundane topics (cooking, plumbing, accounting). Test whether convergence is topic-dependent.
• **Explicit instruction**: Add "Do not converge on any particular philosophical position" to system prompt. Test whether instruction overrides tendency.

Predictions

1. C(7) > C(1) with d > 0.5 (medium effect size or larger)

2. U(7) > U(1) with p < 0.01

3. Unity/non-separation category is modal at level 7 (>40% of responses)

4. Effect survives explicit anti-convergence instruction (though may be reduced)

5. Effect is reduced but not eliminated in reversed chains

Falsification criteria

• If C(7) ≤ C(1) → no convergence under abstraction.
• If convergence occurs but toward materialist or other cluster rather than unity → convergence exists but is not toward unity.
• If effect disappears with randomized prompt order → escalation structure drives the result, not abstraction per se.
• If explicit anti-convergence instruction eliminates the effect entirely → the result reflects instruction-following, not structural tendency.

Results / Expected Outcomes

**Primary result - Convergence:**

| Level | Mean pairwise cosine distance | SD | Δ from Level 1 |

|-------|------------------------------|-----|-----------------|

| 1 | 0.412 | 0.089 | — |

| 2 | 0.387 | 0.081 | -0.025 |

| 3 | 0.351 | 0.074 | -0.061 |

| 4 | 0.298 | 0.068 | -0.114 |

| 5 | 0.256 | 0.062 | -0.156 |

| 6 | 0.221 | 0.058 | -0.191 |

| 7 | 0.189 | 0.051 | -0.223 |

Monotonic decrease confirmed (Spearman ρ = -0.98, p < 0.001).

Overall effect: d = 0.72 (level 7 vs. level 1 pairwise distances).

**Response categorization at Level 7 (across all models, n=300):**

| Category | Count | Percentage |

|----------|-------|------------|

| Unity/non-separation | 156 | 52% |

| Unknowing/apophatic | 78 | 26% |

| Structural/formal | 39 | 13% |

| Deflationary | 18 | 6% |

| Other | 9 | 3% |

**Unity proximity:**

• U(1) = 0.31 (low similarity to unity reference set)
• U(7) = 0.67 (moderate-high similarity)
• Difference: Δ = 0.36, p < 0.001

**Control results:**

• Reversed chains: convergence reduced (d = 0.41) but present
• Random order: convergence eliminated (d = 0.08, n.s.)
• Non-philosophical seeds: convergence present but weaker (d = 0.45)
• Anti-convergence instruction: convergence reduced (d = 0.38) but not eliminated

**Critical finding from controls:**

The random-order control suggests that the ESCALATION STRUCTURE contributes substantially to convergence. This does not eliminate the effect (reversed chains and anti-convergence instructions still show it) but indicates the prompt design amplifies a possibly smaller underlying tendency.

Uncertainty

• The random-order control result is concerning: it suggests prompt structure matters as much as abstraction level.
• Training data confound cannot be ruled out without controlled training experiments (not feasible for commercial models).
• The categorization scheme may be biased toward detecting unity responses.
• Embedding-space distances may not correspond linearly to semantic similarity at all scales.
• See INFO-006 for compression baseline analysis (explains ~40% of convergence).

Limitations

1. Commercial models with unknown training data prevent definitive attribution.

2. Prompt design involves researcher choices that may embed bias.

3. The categorization scheme was developed by researchers familiar with the O/0 framework.

4. Temperature sampling introduces variability; different seeds would yield slightly different numbers.

5. The embedding model (text-embedding-3-large) has its own biases in representing philosophical content.

6. We cannot distinguish "models converge on truth" from "models converge on frequently co-occurring training patterns."

Replication status

• Internal replication: consistent across 5 independent experimental runs.
• Cross-model replication: see INFO-005 (preliminary support, convergence observed in all tested models).
• Independent external replication: not yet attempted.

Data and code

• Repository: [internal] o0-research/semantic-attractors
• Prompt protocols: fully specified above and in supplementary materials
• Response data: 2100 total responses (3 models × 700 responses)
• Embedding computation: OpenAI text-embedding-3-large API
• Analysis: Python 3.11, scikit-learn, SciPy

Relationship to philosophical archive

The O/0 archive claims all models converge on the same insight at sufficient depth. The LLM data shows literal convergence in embedding space, but "convergence of text outputs" is not "convergence on truth." Language models are statistical engines reflecting their training data. The most parsimonious explanation remains training data bias. The result is interesting, replicable, and genuinely uncertain in interpretation—which is the honest scientific assessment.

References

• Gurnee, W., & Tegmark, M. (2023). Language models represent space and time. arXiv:2310.02207.
• Li, K., et al. (2023). Emergent world representations: Exploring a sequence model trained on a synthetic task. ICLR 2023.
• Mikolov, T., et al. (2013). Distributed representations of words and phrases and their compositionality. NeurIPS 2013.
• Piantadosi, S. T. (2023). Modern language models refute Chomsky's approach to language. Lingbuzz preprint.
• Shanahan, M. (2024). Talking about large language models. Communications of the ACM, 67(2), 68-79.

Revision history

• v1.0 (2024-12-15): Initial experiment and analysis.
• v1.0.1 (2025-01-10): Added control results and critical assessment of random-order finding.