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Nathan M. Thornhill - Independent researcher in complexity science, information theory, and computational physics

Nathan M. Thornhill

Author and consciousness researcher. Founder of ICSAC, owner of 3Rivers WebTech. Builder of AI systems, websites, and code. Stereotypical dad.

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"To exist is to continually overcome loss"
6 Publications
4 US Patents
12 Journal Appearances

About

I'm an independent researcher. Complexity science, information theory, computational physics. No university affiliation, no grant funding, no committee telling me what to work on. Nobody handed me any of this.

I came to it from healthcare, nursing assistant up through nursing home administration and ICU admissions. Years on the floor watching people cross the line between conscious and unconscious, watching what holds together and what comes apart. I'd been asking what keeps a pattern alive long before I had the math for it. That's still the engine.

My most recent paper is the Recursive Existence Threshold, and it starts with something that should bother people more than it does. A photograph, a screen of static, and the word "TRUE" can score identical on the single number people keep floating as a measure of consciousness. One's a face. One's noise. One's a fact. The number can't tell them apart, because it was never built to. So I ran a pre-registered test across three substrates — a large language model, the anaesthetized brain, and sleep — to find where the information that number throws away lives. The answer, every time: in the structure, not the scalar. Whatever consciousness turns out to be, it doesn't fit inside one number.

It grew out of the Dynamic Existence Threshold, which put a number on that boundary I'd watched on the ICU floor: an integration–differentiation balance that tells a conscious brain from an unconscious one with 91% accuracy across 136,394 EEG recordings. Under it sit three foundational papers — the Existence Threshold defined what pattern persistence requires, the 86% Scaling Law measured how much information survives a dimensional boundary, and the Dimensional Loss Theorem proved why that number is 86% and not some other.

The implication most people miss is the AI one. That same metric works on neural networks and large language models, giving you a substrate-independent test for whether a system has real organizational coherence or just a convincing impression of it. I hold a US provisional patent on it.

I publish through the Institute for Complexity Science and Advanced Computing because I founded it. No PhD, no advisor, no journal willing to take an outsider's stack of papers seriously, so I built the venue. It's the canonical record; every paper also gets a permanent DOI on Zenodo (CERN), and the work's been picked up by complexity-science communities at UABC in México and the Kapodistrian Academy in Greece. Outsider doesn't mean wrong.

When I'm not doing this, I run 3Rivers WebTech out of Fort Wayne, Indiana, which keeps the lights on. Off the clock: family, the lawn, the house. The to-do list always wins.

What is Complexity Science?

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Complexity science studies how simple parts create surprisingly complex behavior through their interactions. A single bird follows basic rules about speed and spacing, but a flock of thousands produces mesmerizing, coordinated patterns that no individual bird is directing. The same principle appears everywhere: neurons firing in a brain give rise to consciousness, traders making individual decisions create stock market crashes, and water molecules interacting produce weather systems that span continents.

At its heart, complexity science is about emergence—the idea that the whole is more than the sum of its parts. A few key concepts tie the field together: self-organization, where order arises without a central controller; phase transitions, the tipping points where systems suddenly shift from one state to another; and feedback loops, where a system's outputs circle back to shape its future behavior. These aren't metaphors—they're measurable, mathematical patterns that repeat across biology, economics, physics, and computing.

Why does it matter? Because the same mathematics that describes how ice melts into water can describe how a healthy brain transitions into a seizure, or how a stable economy tips into a recession. Complexity science is the shared language for these critical transitions. My research uses that language to build tools that can detect them before they happen.

What is Information Theory?

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Information theory began in 1948 when Claude Shannon published "A Mathematical Theory of Communication," laying out the mathematics of how information can be measured, transmitted, and stored. His core insight was deceptively simple: information can be quantified in bits, and there are fundamental limits on how much information any channel can carry or any process can preserve. Shannon's framework gave engineers the tools to build everything from efficient phone networks to the compression algorithms in your smartphone.

A central concept in information theory is entropy—a measure of uncertainty or surprise in a message. High entropy means high unpredictability (and therefore high information content); low entropy means redundancy and predictability. This same mathematical framework now reaches far beyond telecommunications: biologists use it to analyze DNA sequences, physicists apply it to black hole thermodynamics, and neuroscientists use it to measure the complexity of brain activity.

I use information theory to ask how patterns persist across dimensional boundaries and how systems maintain organizational coherence. The 86% scaling law measures exactly how much information survives when a system crosses from one dimension to another. The Dynamic Existence Threshold uses information-theoretic metrics to detect when a system is losing its internal organization, whether that system is a human brain, a financial market, or the sun's magnetic field.

Publications

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Books

Cover of Foundations of the Existence Threshold: The Scholarly Collection

Foundations of the Existence Threshold — The Scholarly Collection

Nathan M. Thornhill, · Institute for Complexity Science and Advanced Computing

The collected volume. Four peer-reviewed papers — The Existence Threshold, the 86% Scaling Law, the Dimensional Loss Theorem, and the Dynamic Existence Threshold — joined by three original bridge essays and front matter that trace the framework from binary discrete systems through dimensional embedding to dynamic Phi. 100 pages, 7×10 trade paperback. ISBN 979-8-9958925-0-2 · LCCN 2026941912.

Research Papers

Recursive Existence Threshold — Where Meaning May Live

, · preprint, under review at Consciousness and Cognition

The substrate-neutral scalar that keeps getting proposed as a sufficiency index for consciousness is provably content-blind by construction: a photograph, white noise, and the word “TRUE” can be matched on density, lose the same organization scalar, and keep an identical 4/13 of their connectivity. So where does the information live that the scalar throws away? One pre-registered test, three substrates, three answers. In a transformer, factual truth is linearly decodable from the residual stream (AUC 0.83) while the scalar stays blind across all 29 layers. In the anaesthetized brain, which individual a recording belongs to decodes from leakage-controlled connectivity where the scalar sits at chance. In sleep, a recurrence measure survives residualizing the scalar out across five stage contrasts. A sufficiency predicate for consciousness cannot be a single global scalar — what it leaves out is multiply-realizable relational structure that a transformer’s residual stream and the brain’s thalamocortical loops both carry.

Architecture-Independent Geometric Memory Failure

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Two Parallel Lines of Evidence. A synthesis note recording the chronology of two independent lines of evidence that converge on architecture-independent geometric fixed points as the principal explanatory mechanism for representational memory failure: the 86% Scaling Law (Thornhill 2026b) and the Dimensional Loss Theorem with GPT-2/Gemma-2 validation (Thornhill 2026c) from January 2026, and the Sentra production-embedding study (Barman, Starenky, Bodnar, Narasimhan, Gopinath, March 2026) reporting variance concentration to ~16 effective dimensions via participation-ratio methodology. The two bodies of work use different metrics and report different specific quantities, but converge on the same architecture-independent geometric explanation.

The Dynamic Existence Threshold

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Integration-Differentiation Balance Predicts System State Across Substrates. A universal framework for detecting organizational dissolution across diverse systems. Demonstrates that a structural coupling metric (Integration-Differentiation balance) achieves 91% accuracy across 136,394 EEG recordings and predicts critical transitions 5-30 days in advance across financial markets, space weather, and neural data.

Journal Appearances

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Selected for distribution through the Social Science Research Network ejournal system

June 2026
June 16, 2026

Architecture-Independent Geometric Memory Failure

Selected for distribution in Generative AI

June 3, 2026

Architecture-Independent Geometric Memory Failure

Selected for distribution in Computer Science Education, Vol. 9, Issue 107

June 3, 2026

Architecture-Independent Geometric Memory Failure

Selected for distribution in Information Theory & Research, Vol. 7, Issue 64

May 2026
May 1, 2026

The Dynamic Existence Threshold

Selected for distribution in Information Theory & Research, Vol. 7, No. 51

April 2026
April 17, 2026

The Dimensional Loss Theorem

Selected for distribution in Generative AI, Vol. 4, No. 73

April 13, 2026

The Dimensional Loss Theorem

Selected for distribution in Information Systems, Vol. 9, No. 69

April 10, 2026

The 86% Scaling Law

Selected for distribution in Information Systems, Vol. 9, No. 68

March 2026
March 24, 2026

The Dimensional Loss Theorem

Selected for distribution in Computer Science Education, Vol. 9, No. 55

March 23, 2026

The 86% Scaling Law

Selected for distribution in Computer Science Education, Vol. 9, No. 54

March 13, 2026

The Existence Threshold

Selected for distribution in Information Theory & Research, Vol. 7, No. 29

March 12, 2026

The Existence Threshold

Selected for distribution in Artificial Intelligence, Vol. 9, No. 47

January 2026
January 8, 2026

The Existence Threshold

Selected for distribution in Advanced Theoretical Physics and Mathematics Community — Kapodistrian Academy of Science (Greece)

US Provisional Patents

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US Provisional Patent No. 64/029,658 — Filed April 4, 2026

Methods and Systems for Consciousness Classification and Complex System Monitoring

US Provisional Patent No. 63/964,528

Systems and Methods for Adversarial Geometric Encoding to Preserve Information Across Dimensional Boundaries

US Provisional Patent No. 63/967,821

Systems and Methods for Optimal Dimensional Encoding in Neural Networks

US Provisional Patent No. 63/969,588

Complete Three-Dimensional Geometric Encoding System for Data Preservation and Analysis

Contact

Research inquiries, collaboration, media, or anything else: email me.

[email protected]