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Physics, Topology, Logic and Computation: A Rosetta Stone

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arxiv 0903.0340 v3 pith:TF75FDHQ submitted 2009-03-02 quant-ph math.CT

John C. Baez , Mike Stay This is my paper · ORCID
classification quant-phmath.CT
keywords computationphysicsquantumdiagramslogictopologyanalogiesbecame
verification ladder T0 review T1 audit T2 compute T3 formal

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In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology: namely, a linear operator behaves very much like a "cobordism". Similar diagrams can be used to reason about logic, where they represent proofs, and computation, where they represent programs. With the rise of interest in quantum cryptography and quantum computation, it became clear that there is extensive network of analogies between physics, topology, logic and computation. In this expository paper, we make some of these analogies precise using the concept of "closed symmetric monoidal category". We assume no prior knowledge of category theory, proof theory or computer science.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Syllepses from 3-shifted Poisson structures and second-order integration of infinitesimal 2-braidings

    math.QA 2025-05 conditional novelty 7.0 of 10

    A coherent totally symmetric strict infinitesimal 2-braiding gives a second-order deformation quantization to a braided monoidal cochain 2-category, and 3-shifted Poisson structures induce syllepses.

  2. Involutive Weak Cubical $\omega$-categories

    math.CT 2025-05 conditional novelty 6.0 of 10

    The authors introduce involutive weak cubical omega-categories as monad algebras and prove the free constructions needed for that definition exist.

  3. A Graphical Interface for Category Theory Proofs in Coq

    cs.LO 2025-05 conditional novelty 6.0 of 10

    This paper presents an interactive Coq plugin, CommutativeDiagrams, that visualizes categorical proofs as commutative diagrams and lets users progress proofs through graph matching and pushout-based lemma application.

  4. Double Categories of Open Systems: the Cospan Approach

    math.CT 2025-09 conditional novelty 4.0 of 10

    Structured and decorated cospan double categories for open systems have an exoskeleton/outer shell structure, and every object in them is a special symmetric Frobenius pseudomonoid.

  5. Accelerating Machine Learning Systems via Category Theory: Applications to Spherical Attention for Gene Regulatory Networks

    math.CT 2025-05 conditional novelty 4.0 of 10

    Spherical attention, an L2-normalized attention variant derived from neural circuit diagrams, is streamable and runs at up to 200 TFLOP/s on an A100, matching FlashAttention-2.

  6. The far side of the cube

    cs.LO 2019-08 conditional novelty 4.0 of 10

    An elementary presentation of the unrestricted (far-side) game model, where strategies are saturated and the usual constraints of innocence, bracketing, alternation, and determinism are all relaxed.

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