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  "slug": "perception-as-interpolation-over-a-discrete-universe",
  "title": "Perception as Interpolation over a Discrete Universe",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Human perception delivers a seamless experience despite receiving sparse, quantized sensory samples. The gap between discrete neural inputs and continuous phenomenology suggests that the brain implements an interpolation operator that reconstructs continuous percepts from discrete data packets. This paper formalizes perception as a reconstruction map I that acts on a bounded subset X of a Banach space E and produces a continuous function ψ:XtoF in a prescribed function space mathscrF. By importing the Lipschitz contraction property of the shift maps s_i in fractal iterated‑function systems [1] and the explicit Lagrange interpolation formula over division rings [5], we derive an error bound \\|ψ(x)-I[ψ](x)\\|≤ L_max Δ x, where L_max=1/2 and Δ x is the maximal sampling interval. Assuming, as a paper‑specific assumption, that Δ x=0.1 mm, the bound evaluates to 5×10^-2 mm. The result predicts that perceptual filling‑in (e.g., blind‑spot completion, phi phenomenon) cannot exceed this geometric error, providing a quantitative target for psychophysical testing. If empirical measurements of perceptual interpolation error surpass 0.05 mm, the interpolation hypothesis would be falsified. The paper concludes with a roadmap for experimental validation and discusses engineering pathways for neuromorphic systems that emulate human‑like interpolation.",
  "abstract_markdown": "Human perception delivers a seamless experience despite receiving sparse, quantized sensory samples. The gap between discrete neural inputs and continuous phenomenology suggests that the brain implements an interpolation operator that reconstructs continuous percepts from discrete data packets. This paper formalizes perception as a reconstruction map $\\mathcal{I}$ that acts on a bounded subset $\\mathsf{X}$ of a Banach space $\\mathsf{E}$ and produces a continuous function $\\psi:\\mathsf{X}\\to\\mathsf{F}$ in a prescribed function space $\\mathscr{F}$. By importing the Lipschitz contraction property of the shift maps $s_i$ in fractal iterated‑function systems [1] and the explicit Lagrange interpolation formula over division rings [5], we derive an error bound  \n\\[\n\\|\\psi(x)-\\mathcal{I}[\\psi](x)\\|\\le L_{\\max}\\,\\Delta x,\n\\]  \nwhere $L_{\\max}=1/2$ and $\\Delta x$ is the maximal sampling interval. Assuming, as a paper‑specific assumption, that $\\Delta x=0.1\\;\\text{mm}$, the bound evaluates to $5\\times10^{-2}\\;\\text{mm}$. The result predicts that perceptual filling‑in (e.g., blind‑spot completion, phi phenomenon) cannot exceed this geometric error, providing a quantitative target for psychophysical testing. If empirical measurements of perceptual interpolation error surpass $0.05\\;\\text{mm}$, the interpolation hypothesis would be falsified. The paper concludes with a roadmap for experimental validation and discusses engineering pathways for neuromorphic systems that emulate human‑like interpolation.",
  "date": "2026-10-20",
  "first_published": "2026-10-20",
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  "url": "https://papers.qnfo.org/papers/perception-as-interpolation-over-a-discrete-universe",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
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        "title": "Perception as Interpolation over a Discrete Universe"
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    "publicationYear": "2026",
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        "description": "Human perception delivers a seamless experience despite receiving sparse, quantized sensory samples. The gap between discrete neural inputs and continuous phenomenology suggests that the brain implements an interpolation operator that reconstructs continuous percepts from discrete data packets. This paper formalizes perception as a reconstruction map I that acts on a bounded subset X of a Banach space E and produces a continuous function ψ:XtoF in a prescribed function space mathscrF. By importing the Lipschitz contraction property of the shift maps s_i in fractal iterated‑function systems [1] and the explicit Lagrange interpolation formula over division rings [5], we derive an error bound \\|ψ(x)-I[ψ](x)\\|≤ L_max Δ x, where L_max=1/2 and Δ x is the maximal sampling interval. Assuming, as a paper‑specific assumption, that Δ x=0.1 mm, the bound evaluates to 5×10^-2 mm. The result predicts that perceptual filling‑in (e.g., blind‑spot completion, phi phenomenon) cannot exceed this geometric error, providing a quantitative target for psychophysical testing. If empirical measurements of perceptual interpolation error surpass 0.05 mm, the interpolation hypothesis would be falsified. The paper concludes with a roadmap for experimental validation and discusses engineering pathways for neuromorphic systems that emulate human‑like interpolation.",
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