Tensors, Fields, and Meaning-Space:

Tensors, Fields, and Meaning-Space: A Unified Model Across Physics, AI, Neuroscience, and Buddhist Thought

1. Introduction

In both ancient and modern explorations of reality, meaning has been approached from multiple perspectives—epistemology, artificial intelligence (AI), neuroscience, and Buddhist contemplative traditions. While these fields may appear distinct, they share a common structural principle: perception and cognition emerge not from static objects but from relations and transformations within a structured space.

This paper presents a tensor-based model of meaning-space, proposing that meaning arises from dynamic relational fields rather than fixed reference points. Tensors are fundamental in physics for describing fields and forces, in AI for modelling complex transformations in neural networks, and in mind sciences for understanding how awareness shifts through structured cognitive processes. While physics does not directly address the concept of meaning, it explores matter and fundamental interactions through relational models, fitting into this shared structural principle. We explore how these insights align with Buddhist models of cognition, particularly in the transition from early analytical frameworks (Abhidharma) to dynamic, non-conceptual awareness (Mahamudra and Dzogchen).

Rather than asserting a strict unification, this paper suggests that these structural parallels offer a fruitful framework for interdisciplinary exploration into cognition, meaning, and the structure of awareness itself.

2. Tensors and the Field Model in Physics

Physics provides a rigorous mathematical foundation for understanding relational fields, where elements do not exist in isolation but emerge from dynamic interactions. Key examples include:

  • General Relativity: Spacetime is modelled as a tensor field, where gravitational effects are not localised forces but curvatures in a higher-dimensional manifold (Einstein, 1915).
  • Quantum Field Theory: Matter and energy emerge as excitations in underlying fields rather than discrete particles (Penrose, 2005).
  • Thermodynamics & Non-Equilibrium Systems: Systems evolve to minimise energy expenditure, aligning with the principle of least action (Prigogine, 1997).

Rather than asserting a direct equivalence between physical fields and cognition, we explore whether the relational structure of meaning-space exhibits similar principles in its dynamics.

3. AI, Deep Learning, and Meaning as a Tensor Space

In AI, particularly in deep learning:

  • Neural networks represent meaning as tensor-based transformations (Bengio, 2013).
  • The attention mechanism in AI dynamically adjusts meaning relations rather than operating on fixed data points (Vaswani et al., 2017).
  • AI does not store meaning in isolated symbols, but constructs meaning through shifting constraints and probabilities.

This approach resonates with Buddhist cognitive models, where meaning is seen as conditioned and dynamically emergent, rather than fixed and object-like.

4. Mind as a Tensor-Driven Meaning-Space

Buddhist thought provides an evolving model of cognition, moving from discrete categorisation in early Buddhist philosophy to fluid awareness models in Mahamudra and Dzogchen:

  • Abhidharma: Describes dharmas as discrete mental events arising in dependence on conditions (Vasubandhu, 4th c.).
  • Mahamudra & Dzogchen: Awareness is described as an open field, free from fixed conceptual boundaries.
  • Winds and Channels in Vajrayāna: Awareness flows through structured pathways, resembling field-based descriptions in physics.

Rather than suggesting an exact correspondence between these traditions, we propose that their structural similarities provide a lens for exploring cognition as a dynamic, constraint-driven process.

5. The Principle of Least Action and Cognitive Optimisation

In physics, the principle of least action states that natural systems evolve along the most efficient paths. This principle is echoed in:

  • Physics: Lagrangian mechanics minimise energy expenditure.
  • AI: Neural networks optimise for error minimisation and efficiency.
  • Mind: Meditative practice reduces cognitive resistance, leading to states of effortless awareness (Friston, 2010).

Mahamudra practice describes effortless awareness as the natural state of mind once conceptual constraints dissolve—a cognitive parallel to least action in physics, though the applicability of this principle to cognition remains an open question.

6. Friston’s Free-Energy Principle and Predictive Mind Models

  • Friston et al. (2017, 2020) extend the Free-Energy Principle to explain belief propagation, active inference, and neural optimisation.
  • Active inference (Friston, Lin, et al., 2017) suggests that cognition self-organises by minimising uncertainty, much like gradient descent in AI.
  • Markov blankets and information geometry (Parr, Da Costa, & Friston, 2020) describe how cognition maintains coherence as a probabilistic field, mirroring meaning-space dynamics.
  • Pattern regulation (Friston, Levin, et al., 2015) links predictive processing to biological self-organisation, reinforcing parallels to meditative cognition.

While intriguing, applying these principles to Buddhist cognitive models requires caution, as subjective awareness may not conform fully to predictive coding models.

7. Mapping Mind Using Physical Imagery

The use of physical similes to describe mind is widespread across traditions:

  • Mind as an Ocean: Fluid, wave-like cognition in both Buddhist and Taoist thought.
  • Light and Visualisation: Awareness as radiant beams, seen in Buddhist meditation techniques.
  • Thermodynamics and Emotional States: Expansion (joy, openness) vs. contraction (fear, attachment).
  • Electromagnetism and Thought Fields: Attraction/repulsion in relationships and cognition.

While useful as heuristic models, these metaphors should not be mistaken for literal equivalences.

8. Future Research Directions

This interdisciplinary approach suggests multiple areas for further exploration:

  • AI & Meaning-Space: Can tensor-driven AI more closely mimic human cognition and meditative states?
  • Mathematical Modelling of Mind Fields: Can Buddhist awareness models be formalised in field theory?
  • Empirical Neuroscience Studies: Can we observe cognitive tension minimisation in meditative states?

9. Conclusion

By examining the structural parallels between deep learning, quantum physics, and contemplative mind sciences, we suggest that further research into tensor-based meaning-space models may illuminate new perspectives on cognition and awareness.

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