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Kolmogorov Complexity vs. Computational Irreducibility: Understanding the Distinction
Community Essay James K. Wiles Community Essay James K. Wiles

Kolmogorov Complexity vs. Computational Irreducibility: Understanding the Distinction

James K. Wiles

Kolmogorov complexity and computational irreducibility describe two kinds of limits on simplification, but they apply in different ways. Kolmogorov complexity measures the shortest possible description of an object, such as a string. Computational irreducibility refers to processes that cannot be predicted or accelerated. This paper introduces each concept, explains their theoretical distinction, and illustrates the difference using simple examples.

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What If We Had Bigger Brains? Imagining Minds beyond Ours
Computational Essay Stephen Wolfram Computational Essay Stephen Wolfram

What If We Had Bigger Brains? Imagining Minds beyond Ours

Stephen Wolfram

We humans have perhaps 100 billion neurons in our brains. But what if we had many more? Or what if the AIs we built effectively had many more? What kinds of things might then become possible? At 100 billion neurons, we know, for example, that compositional language of the kind we humans use is possible. At the 100 million or so neurons of a cat, it doesn’t seem to be. But what would become possible with 100 trillion neurons? And is it even something we could imagine understanding? 

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Observer Theory and the Ruliad: An Extension to the Wolfram Model
Community Essay Sam Senchal Community Essay Sam Senchal

Observer Theory and the Ruliad: An Extension to the Wolfram Model

Sam A. Senchal

This paper introduces a rigorous category-theoretic extension to Observer Theory within Wolfram's Ruliad framework, demonstrating how observers and observes like us sample and integrate information across hierarchical domains, addressing consciousness, causation, and the transition from discrete computational processes to continuous perceived reality.

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What Can We Learn about Engineering and Innovation from Half a Century of the Game of Life Cellular Automaton?
Computational Essay Stephen Wolfram Computational Essay Stephen Wolfram

What Can We Learn about Engineering and Innovation from Half a Century of the Game of Life Cellular Automaton?

Stephen Wolfram

Things are invented. Things are discovered. And somehow there’s an arc of progress that’s formed. But are there what amount to “laws of innovation” that govern that arc of progress?

There are some exponential and other laws that purport to at least measure overall quantitative aspects of progress (number of transistors on a chip; number of papers published in a year; etc.). But what about all the disparate innovations that make up the arc of progress? Do we have a systematic way to study those?

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Towards a Computational Formalization for Foundations of Medicine
Computational Essay Stephen Wolfram Computational Essay Stephen Wolfram

Towards a Computational Formalization for Foundations of Medicine

Stephen Wolfram

As it’s practiced today, medicine is almost always about particulars: “this has gone wrong; this is how to fix it”. But might it also be possible to talk about medicine in a more general, more abstract way—and perhaps to create a framework in which one can study its essential features without engaging with all of its details?

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On the Nature of Time
Computational Essay Stephen Wolfram Computational Essay Stephen Wolfram

On the Nature of Time

Stephen Wolfram

Time is a central feature of human experience. But what actually is it? In traditional scientific accounts it’s often represented as some kind of coordinate much like space (though a coordinate that for some reason is always systematically increasing for us). But while this may be a useful mathematical description, it’s not telling us anything about what time in a sense “intrinsically is”.

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Foundations of Biological Evolution: More Results & More Surprises
Computational Essay Stephen Wolfram Computational Essay Stephen Wolfram

Foundations of Biological Evolution: More Results & More Surprises

Stephen Wolfram

A few months ago I introduced an extremely simple “adaptive cellular automaton” model that seems to do remarkably well at capturing the essence of what’s happening in biological evolution. But over the past few months I’ve come to realize that the model is actually even richer and deeper than I’d imagined. And here I’m going to describe some of what I’ve now figured out about the model—and about the often-surprising things it implies for the foundations of biological evolution.

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Hypergraph rewriting and Causal structure of $\lambda$-calculus
Research Paper Utkarsh Bajaj Research Paper Utkarsh Bajaj

Hypergraph rewriting and Causal structure of $\lambda$-calculus

Utkarsh Bajaj

Hypergraph rewriting is studied through categorical frameworks to establish foundational concepts of events and causality in graph rewriting systems. Novel concepts are introduced within double-pushout rewriting in adhesive categories. An algorithm is constructed to determine causal relations between events during λ-calculus evaluation, with extensions developed for arbitrary λ-expressions.

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Quantum Potato Chips
Research Paper Nikolay Murzin Research Paper Nikolay Murzin

Quantum Potato Chips

Nikolay Murzin, Bruno Tenorio, Sebastian Rodriguez, John McNally, Mohammad Bahrami

This study maps qubit states under symmetric informationally-complete measurements to a tetrahedron in 3D space, identifying a "quantum potato chip" region where quantum states reduce to classical binary variables. States in this special region can be fully reconstructed using only two projective measurements, unlike states elsewhere in the quantum state space.

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What’s Really Going On in Machine Learning? Some Minimal Models
Computational Essay Stephen Wolfram Computational Essay Stephen Wolfram

What’s Really Going On in Machine Learning? Some Minimal Models

Stephen Wolfram

It’s surprising how little is known about the foundations of machine learning. Yes, from an engineering point of view, an immense amount has been figured out about how to build neural nets that do all kinds of impressive and sometimes almost magical things. But at a fundamental level we still don’t really know why neural nets “work”—and we don’t have any kind of “scientific big picture” of what’s going on inside them.

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Why Does Biological Evolution Work? A Minimal Model for Biological Evolution and Other Adaptive Processes
Research Paper Stephen Wolfram Research Paper Stephen Wolfram

Why Does Biological Evolution Work? A Minimal Model for Biological Evolution and Other Adaptive Processes

Stephen Wolfram

Why does biological evolution work? And, for that matter, why does machine learning work? Both are examples of adaptive processes that surprise us with what they manage to achieve. So what’s the essence of what’s going on? I’m going to concentrate here on biological evolution, though much of what I’ll discuss is also relevant to machine learning—but I’ll plan to explore that in more detail elsewhere.

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