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Published on: June 8, 2018
Beyond symbolic algebra with quantum picturalism
Selma Dündar-Coecke1,2, Lia Yeh3,4, Emmanuel Pothos5
1Neurossance, Oxford, United Kingdom.
Frontiers in Cognition
|July 9, 2026
Summary
Quantum Picturalism (QPic) offers a diagrammatic alternative to symbolic quantum mechanics, enhancing understanding through visual representations. This approach aligns quantum concepts with human cognition, improving accessibility and educational potential.
Area of Science:
- Quantum mechanics
- Category theory
- Cognitive science
Background:
- Symbolic formalisms in quantum theory can obscure meaning.
- An alternative diagrammatic approach, Quantum Picturalism (QPic), emphasizes structure and relations.
- Formalism choice impacts ontological commitments and accessibility of quantum features.
Purpose of the Study:
- Examine the epistemological, cognitive, and educational significance of non-symbolic thought in quantum mechanics.
- Investigate if quantum processes can be represented in ways more aligned with human cognition.
- Demonstrate how non-symbolic formalism's cognitive aspects can be integrated into pedagogical practice.
Main Methods:
- Utilizing Quantum Picturalism (QPic) as a guiding example of a diagrammatic formalism.
- Examining historical precedents in non-symbolic mathematical thought (e.g., Euclidean geometry, Leibniz's calculus).
- Applying theories of embodied cognition, dual coding, and conceptual metaphor theory.
Main Results:
- Diagrammatic formalisms like QPic privilege structure, relation, and transformation over states and objects.
- QPic supports reasoning through the composition of visually represented quantum processes.
- Non-symbolic formalisms can be integrated into pedagogical practices for enhanced understanding.
Conclusions:
- The choice of formalism (symbolic vs. diagrammatic) is not neutral and influences conceptualization of quantum phenomena.
- Human intuition may align better with relational and visual frameworks for understanding complex ideas.
- QPic offers a more inclusive entry point to quantum mechanics, democratizing access to quantum innovation.
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