{
  "abstract": "This chapter reconstructs the McCulloch-Pitts program as a physics of neural computation rather than the familiar cartoon of a binary neuron. The 1943 logical calculus is developed in both directions: given a net, characterize the propositions realized by its activity; given an admissible logical expression, construct a net that realizes it. We recover the original distinction between thresholded excitatory summation and absolute inhibitory veto-one the weighted-threshold form cannot preserve for arbitrarily large excitatory inputs-and read unit-time delay as the physical realization of logical depth. Recurrence is treated exactly: an autonomous, deterministic network of finitely many binary units has a finite state space, so every trajectory eventually enters a periodic orbit-a fact about finite-state dynamics, not unbounded Turing computation. A single threshold element realizes only linearly separable Boolean functions, whereas finite feedforward networks of them synthesize any Boolean function on a finite domain. We then follows McCulloch and Pitts beyond threshold logic. The 1945 heterarchy paper turns cyclic preference into an obstruction to representation by a scalar utility. The 1947 work on universals asks how a physical network can identify inputs related by nuisance transformations, developed here via group averaging and feedback canonicalization. The 1959 frog-retina study makes the adequate-stimulus question experimental, revealing parallel invariant operations before the brain proper. Spike-triggered analysis shows how a nonlinearly driven neuron can have a vanishing first-order average while second-order statistics recover its hidden selectivity: methodological failure can masquerade as physiological absence. Modern mathematical tools are used without projecting their notation onto the historical papers, and limitations of the idealization are stated explicitly.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02183",
  "author_total": 1,
  "authors": [
    {
      "name": "Nima Dehghani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3a553h8mzrj5w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02183",
  "fulltext_url": null,
  "id": "3a553h8mzrj5w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02183",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "cs.FL"
    ],
    [
      "arxiv",
      "cs.NE"
    ],
    [
      "arxiv",
      "physics.bio-ph"
    ],
    [
      "arxiv",
      "q-bio.NC"
    ],
    [
      "openalex",
      "1702|Neural Networks and Applications"
    ]
  ],
  "openalex": "W7207516487",
  "pdf_url": "https://arxiv.org/pdf/2609.02183",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3a553h8mzrj5w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:16Z",
      "native_id": "2609.02183",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02183"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.NC",
      "subfield": "neuroscience"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.bio-ph",
      "subfield": "biological-medical"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Neural Logic, Invariance, and the Retina---McCulloch and Pitts",
  "title_text": "Neural Logic, Invariance, and the Retina---McCulloch and Pitts",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:21Z",
  "url": "https://research.draconitic.com/paper/3a553h8mzrj5w",
  "venue": "arXiv",
  "versions": []
}