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{
    "pk": 49092,
    "title": "A Mathematical Model of Civilizational Dynamics: Quantifying Toynbee’s Challenge–Response Theory with Newtonian Mechanics",
    "subtitle": null,
    "abstract": "<p>This study presents a civilizational dynamics model that applies Newtonian mechanics to Toynbee's challenge-response theory. By defining quantifiable indicators of societal response (α) and challenge (β), the model constructs a civilizational sustainability index S(t)=lnα(t)−lnβ(t). The first, second, and third differences of S(t) are interpreted as civilizational velocity, acceleration, and jerk, respectively, offering dynamic insights into the non-linear changes of civilizational states. Simulations applied to Roman civilization (BC 100 – AD 100) identify critical transitions within this historical period, providing empirical support for Toynbee’s hypothesis that civilizations collapse when challenges are either too weak or overwhelming. The model offers a novel quantitative method to analyze civilizational resilience and decay by capturing structural transformations through mathematical dynamics. While acknowledging the limitations of quantitative modeling in the humanities, this interdisciplinary approach demonstrates significant potential for extension to fields such as economics, politics, and systemic risk analysis.</p>",
    "language": "eng",
    "license": {
        "name": "Creative Commons Attribution 4.0",
        "short_name": "CC BY 4.0",
        "text": "Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.",
        "url": "https://creativecommons.org/licenses/by/4.0"
    },
    "keywords": [
        {
            "word": "Toynbee’s theory"
        },
        {
            "word": " civilizational dynamics"
        },
        {
            "word": " Newtonian mechanics"
        },
        {
            "word": " challenge-response"
        },
        {
            "word": " simulation modeling"
        },
        {
            "word": " historical cycles"
        },
        {
            "word": " S-curve"
        },
        {
            "word": " systemic collapse"
        }
    ],
    "section": "Article",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/58z1j452",
    "frozenauthors": [
        {
            "first_name": "Jung",
            "middle_name": "Won",
            "last_name": "Lee",
            "name_suffix": "",
            "institution": "Lee Institute for Mathematical Science (Informal Research Center)",
            "department": ""
        }
    ],
    "date_submitted": "2025-07-22T20:58:59.467000Z",
    "date_accepted": "2025-11-17T12:38:23.752000Z",
    "date_published": "2025-12-25T12:03:00Z",
    "render_galley": {
        "label": "Final version",
        "type": "pdf",
        "path": "https://journalpub.escholarship.org/cliodynamics/article/49092/galley/48733/download/"
    },
    "galleys": [
        {
            "label": "Final version",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/cliodynamics/article/49092/galley/48733/download/"
        }
    ]
}