Two Ways of Measuring: A Framework for Distance, Memory, and Fault-Tolerant Computation

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Auteur principal: Quni-Gudzinas, Rowan Brad
Format: Recurso digital
Publié: Zenodo 2026
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author Quni-Gudzinas, Rowan Brad
author_facet Quni-Gudzinas, Rowan Brad
contents <p></p> <p>A pebble rests in a shallow depression on a granite outcrop in the Australian outback. It has been there for ten thousand years. Rain has fallen on it. Wind has blown over it. The ground has trembled with distant earthquakes. The pebble has jiggled, rattled, and shifted—but it has never left its depression.</p> <p>Why?</p> <p>Because the depression is a <strong>container</strong>. Its walls rise just high enough that the random jostling of the world—a raindrop’s splash, a gust of wind, the tremor of a far-off quake—cannot lift the pebble over the rim. The pebble is free to move <em>within</em> its container, but it cannot escape without a push that exceeds the rim height. The container remembers the pebble’s rough position across geological time, not because it actively corrects the pebble’s location, but because its geometry passively rejects perturbations below a threshold.</p> <p>The principle the pebble embodies can be generalized and formalized into a framework for building computers whose memories endure through the geometry of their state space rather than through constant vigilance.</p> <p>The principle has a name: the <strong>threshold principle</strong>. The mathematics that underlies it is <strong>ultrametric geometry</strong>.</p>
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id zenodo_https___doi_org_10_5281_zenodo_19976946
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publishDate 2026
publisher Zenodo
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spellingShingle Two Ways of Measuring: A Framework for Distance, Memory, and Fault-Tolerant Computation
Quni-Gudzinas, Rowan Brad
<p></p> <p>A pebble rests in a shallow depression on a granite outcrop in the Australian outback. It has been there for ten thousand years. Rain has fallen on it. Wind has blown over it. The ground has trembled with distant earthquakes. The pebble has jiggled, rattled, and shifted—but it has never left its depression.</p> <p>Why?</p> <p>Because the depression is a <strong>container</strong>. Its walls rise just high enough that the random jostling of the world—a raindrop’s splash, a gust of wind, the tremor of a far-off quake—cannot lift the pebble over the rim. The pebble is free to move <em>within</em> its container, but it cannot escape without a push that exceeds the rim height. The container remembers the pebble’s rough position across geological time, not because it actively corrects the pebble’s location, but because its geometry passively rejects perturbations below a threshold.</p> <p>The principle the pebble embodies can be generalized and formalized into a framework for building computers whose memories endure through the geometry of their state space rather than through constant vigilance.</p> <p>The principle has a name: the <strong>threshold principle</strong>. The mathematics that underlies it is <strong>ultrametric geometry</strong>.</p>
title Two Ways of Measuring: A Framework for Distance, Memory, and Fault-Tolerant Computation
url https://doi.org/10.5281/zenodo.19976946