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April 19, 20260 citationsOpen Access

Chunking at the Rate Bound: The Hick–Hyman Law as an Instance of the MICP Time Law

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DDDavid Dudaš

Key Points

  • This work aims to relate the Hick–Hyman law in psychology with the decoherence time in quantum physics through Shannon's principles.
  • Identified common derivation of Hick–Hyman law and decoherence time from Shannon's source coding theorem.
  • Analyzed how information acquisition rates differ across domains, especially between quantum systems and human cognitive processes.
  • Derived upper bounds for information acquisition rates at physical temperature based on the Minimum Information Cost Principle.
  • Validated that the formula τ ∝ H(p) is universal across domains like quantum mechanics and psychology.
  • Proposed that the human mind operates significantly below maximum theoretical efficiency for information acquisition.
  • Suggested that experimental confirmation could align quantum measurement and human reaction time behavior in the same framework.

Abstract

Paper VI of the Complexity Binding Theory (CBT) program — the Minimum Information Cost Principle, or MICP — predicts that the decoherence time of a quantum superposition with outcome distribution p scales linearly with its Shannon entropy: τₘeas (p) = H (p) / (γ₀ ln 2). Independently, and for seventy years, experimental psychology has documented the Hick–Hyman law for human choice reaction time: RT (p) = a + b·H (p). This note observes that these two laws share a common derivation from Shannon's source coding theorem: any system that acquires information at a bounded rate R and resolves outcomes drawn from distribution p has resolution time of at least H (p) /R. The functional form τ ∝ H (p) is therefore universal; only the rate R differs between domains, by approximately eight orders of magnitude. The identification does not imply that quantum measurement and neural categorization share a mechanism. It does, however, yield a first-principles upper bound on the information acquisition rate of any physical system at temperature T: Rₘax (T) = kT / (ℏ ln 2). The human conscious mind operates approximately thirteen orders of magnitude below this bound, a statement about the inefficiency of biological computation rather than about consciousness. If MICP's T₂ (p) ∝ H (p) prediction is confirmed experimentally on a qubit platform operating near the Landauer floor, the confirmation would place quantum measurement and human choice reaction on the same formal curve with vastly different slopes.

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Cite This Study

David Dudaš (2026) studied this question.

synapsesocial.com/papers/69e4745f010ef96374d90283https://doi.org/10.5281/zenodo.19625451
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