Category Archives: Science

Crystallized Conceptuality: Why AI Cannot Know Non-Conceptually

The debate over machine consciousness is usually framed as a contest between two camps. Functionalists say consciousness is whatever the right kind of information processing does, so a sufficiently sophisticated AI will be conscious. Biological naturalists say consciousness depends on something specific to living brains, so it won’t.… Read More “Crystallized Conceptuality: Why AI Cannot Know Non-Conceptually”

The Unreasonable Effectiveness of AI

In 1960 the physicist Eugene Wigner published an essay whose title became a genre: “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” His puzzle was simple to state and has never been resolved. Mathematics is a game played with symbols, developed largely for its own internal beauty.… Read More “The Unreasonable Effectiveness of AI”

The Fish Who Could Not Imagine Air

Imagine a fish physicist. She is brilliant. Over centuries her tradition has built a physics of astonishing power: pressure, buoyancy, viscosity, the propagation of waves, the beautiful nonlinearities of turbulence. It predicts everything she can measure. It has no loose ends worth losing sleep over.… Read More “The Fish Who Could Not Imagine Air”

No Fixed Frame Is Enough

Mathematics is producing proofs faster than it has ever produced them, and mathematical progress has not accelerated. That fact is not a paradox. It is the clearest available evidence for a structural claim about artificial intelligence — one that can be stated precisely, proved in three independent ways, and, uncomfortably, does not say what most people want it to say.… Read More “No Fixed Frame Is Enough”

Rosettes, Gliders, and Blooms: A Cellular Automaton on the Kisrhombille Tiling

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A few months ago I started wondering what cellular automata would look like on a more exotic lattice than the usual square or hexagonal grid. The result is tiling-patterns — a fully interactive, GPU-accelerated cellular automaton running on the Kisrhombille tiling, with a searchable rule space and over 130 hand-curated presets that produce genuinely strange and beautiful long-run dynamics.… Read More “Rosettes, Gliders, and Blooms: A Cellular Automaton on the Kisrhombille Tiling”

Toward a New Science of Self-Referential Systems

Civilization is building systems that reason about themselves, audit themselves, and govern themselves — without a formal science of what self-referential systems can and cannot do. That gap is not merely academic. It is costing us clarity about AI safety, interpretability, consciousness, and the foundations of physics.… Read More “Toward a New Science of Self-Referential Systems”

Neural CA: Spatial Parameter Fields and Greatest-Hits Memory

This is a browser-based cellular automaton experiment that takes a different approach to the same challenge as the trend-aware experiment: how do you keep a self-tuning CA alive and interesting? Here the key innovation is that the rule parameters are not uniform scalars — they are spatial fields.… Read More “Neural CA: Spatial Parameter Fields and Greatest-Hits Memory”

Neural CA: Trend-Aware Agents Learn to Keep a Cellular Automaton Alive

This is a browser-based cellular automaton in which two cooperating neural agents learn — in real time, from scratch — to keep the simulation alive and interesting. No pre-training, no external data. The neural network trains itself as the simulation runs, and the agents use what they’ve learned to steer the system away from death and toward sustained complex behavior.… Read More “Neural CA: Trend-Aware Agents Learn to Keep a Cellular Automaton Alive”

The End of Final Theories: How Fixed Laws Produce Inexhaustible Explanation

A new paper — backed by 422 machine-checked theorems and zero gaps — proves that a system can be completely governed by fixed laws and still never admit a final explanation. The implications reach from physics to biology to organizations to AI.… Read More “The End of Final Theories: How Fixed Laws Produce Inexhaustible Explanation”

The Twist as Generative Principle

This is the final essay in a series. The first, The Twist Move, describes the operation itself across mathematics, biology, physics, and business. The second, The Twist and the Ground of Being, argues that the consciousness twist is real, that the substrate must support it, and that this tells us something fundamental about the nature of reality.… Read More “The Twist as Generative Principle”

The Theorem Behind the Twist – Lawvere’s Fixed-Point

This is the sixth essay in a series. The first, The Twist Move, describes the operation itself across mathematics, biology, physics, and business. The second, The Twist and the Ground of Being, argues that the consciousness twist is real, that the substrate must support it, and that this tells us something fundamental about the nature of reality.… Read More “The Theorem Behind the Twist – Lawvere’s Fixed-Point”

The Figure Without Ground – AI Versus the Twist

This is the fourth essay in a series. The first, The Twist Move, describes the operation itself across mathematics, biology, physics, and business. The second, The Twist and the Ground of Being, argues that the consciousness twist is real, that the substrate must support it, and that this tells us something fundamental about the nature of reality.… Read More “The Figure Without Ground – AI Versus the Twist”

How to Develop Twist Literacy

This is the third essay in a series. The first, The Twist Move, describes the operation itself across mathematics, biology, physics, and business. The second, The Twist and the Ground of Being, argues that the consciousness twist is real, that the substrate must support it, and that this tells us something fundamental about the nature of reality.… Read More “How to Develop Twist Literacy”

The Twist and the Ground of Being

This is the second essay in a series. The first, The Twist Move, describes the operation itself across mathematics, biology, physics, and business. The second, The Twist and the Ground of Being, argues that the consciousness twist is real, that the substrate must support it, and that this tells us something fundamental about the nature of reality.… Read More “The Twist and the Ground of Being”

The Internalization of Computation – What Percepta’s transformer-computer actually signals — and why the implications are far stranger than the demo

Something happened two weeks ago that most people filed under “interesting research” and moved on from. They shouldn’t have. Christos Tzamos and the Percepta team published a demonstration in which a transformer executes arbitrary C programs — not by calling out to a Python interpreter, not by emitting code for an external sandbox, but inside its own forward pass.… Read More “The Internalization of Computation – What Percepta’s transformer-computer actually signals — and why the implications are far stranger than the demo”

The Horse Has No Rider: Why Autonomous AI Science Gets It Wrong — And What to Do Instead

We are at a genuinely exciting moment. In the past weeks alone, GPD (Getting Physics Done) has launched with bold promises about AI agents autonomously advancing physics, and Math.Inc has released Gauss, their system for AI-driven mathematical research. The pitch is seductive: deploy swarms of agents, point them at hard problems, and let them run.… Read More “The Horse Has No Rider: Why Autonomous AI Science Gets It Wrong — And What to Do Instead”

The Age of the Navigator: Why AI in Mathematics Changes Everything — and Nothing

Something remarkable happened this week. A human-AI collaboration formally verified Maryna Viazovska’s Fields Medal-winning proof of optimal sphere packing in 8 and 24 dimensions. Math, Inc.’s AI agent Gauss autoformalized the 24-dimensional proof — over 200,000 lines of Lean code — in just two weeks, with no pre-existing blueprint to work from.… Read More “The Age of the Navigator: Why AI in Mathematics Changes Everything — and Nothing”

The Integrity Imperative: Rebuilding Trust in AI Through Verifiable Content and Transparent Attribution

We are living through a hinge in history so abrupt that most people have not yet grasped the magnitude of the shift. In the span of a few short years, autonomous intelligence has moved from a laboratory curiosity to the most consequential force reshaping global power.… Read More “The Integrity Imperative: Rebuilding Trust in AI Through Verifiable Content and Transparent Attribution”

SocioLife – A Socio-Economic Artificial Life Sim That Runs in your Browser

Check out this amazing new artificial life simulation I have developed.

Click here to run it in your browser

(It’s graphics intensive so it’s best if you have a high performance modern computer like a multicore mac or pc.)

Turn the sound on to hear the alien soundscape (use the checkbox on the HUD)

Summary:

SocioLife evolves intelligent agents with DNA that evolve and interact, forming complex societies that then engage in economic, diplomatic, and military relations.… Read More “SocioLife – A Socio-Economic Artificial Life Sim That Runs in your Browser”

The Self-Defining Universe

This article summarizes my book on The Self-Defining Universe, which focuses on how the universe can exist without an external runner – a fully self-contained universe that “runs itself.”

NOTE: This book is part 2 – following on my more general book on the Mathematical Foundations of Self-Referential Systems.… Read More “The Self-Defining Universe”

Introducing LACE – A New Kind of Cellular Automata

This article is about a new kind of simple computational rule (“LACE rules” running on LACE, the Link Automata Computing Engine platform) which, when applied locally on a grid of cells, demonstrates fascinating emergent “artificial life” behavior.

For readers familiar with the Game of Life (GOL), this is a next-level class of cellular automata that utilizes neighborhood topology — the state of the grid is a function of both cell states and their connectivity (links).… Read More “Introducing LACE – A New Kind of Cellular Automata”

Why AI Systems Can’t Catch Their Own Mistakes – And What to Do About It

Abstract

Large language models exhibit a critical limitation: they cannot reliably evaluate their own outputs within the same conversational context where those outputs were generated. Recent research demonstrates that when AI systems attempt to check their own reasoning, they confirm their initial responses over 90% of the time regardless of correctness—a phenomenon researchers term “intrinsic self-correction failure.”… Read More “Why AI Systems Can’t Catch Their Own Mistakes – And What to Do About It”

A New Mathematics of Self-Reference: A Comprehensive Non-Mathematical Summary

What This Work Is About

This article explains my paper on the
Mathematics of Self-Referential Systems, for a non-technical audience. The paper develops a comprehensive mathematical framework for understanding systems that can represent, model, or “know” themselves. While self-reference has long been seen as a source of logical paradoxes, this work argues it may be the fundamental organizing principle of reality itself—and provides specific mathematical bounds and requirements for achieving different levels of self-awareness.… Read More “A New Mathematics of Self-Reference: A Comprehensive Non-Mathematical Summary”

The Mathematical Foundations of Self-Referential Systems: From Computability to Transfinite Dynamics

This article explains my paper on the
Mathematics of Self-Referential Systems.

Here is a summary

Decoding Reality’s Blueprint: An In-Depth Look at “The Mathematical Foundations of Self-Referential Systems”

Have you ever wondered about the deep, perhaps even unsettling, nature of a thought thinking about itself?… Read More “The Mathematical Foundations of Self-Referential Systems: From Computability to Transfinite Dynamics”

The UKL Revolution: Weaving a New Cognitive Fabric for the Age of AI

Universal Knowledge Locators and the Future of AI-Mediated Knowledge

Nova Spivack, Mindcorp.ai, www.mindcorp.ai

May 24, 2025

Abstract

The current epoch of artificial intelligence is characterized by an astonishing generative capacity, yet beneath this surface of prolific creation lies a nascent challenge: the very fabric of knowledge upon which these intelligences are built remains surprisingly coarse.… Read More “The UKL Revolution: Weaving a New Cognitive Fabric for the Age of AI”

Logical Foundations for Ethical AI: Natural Laws for Artificial Minds

Nova Spivack, Mindcorp.ai
www.mindcorp.ai, www.novaspivack.com
May 24, 2025

Abstract

As artificial intelligence systems become increasingly sophisticated, traditional approaches to AI safety that rely on imposed constraints and arbitrary rules face fundamental limitations. This paper proposes a paradigm shift: grounding AI ethics in logical necessities that function as “natural laws” for rational agents.… Read More “Logical Foundations for Ethical AI: Natural Laws for Artificial Minds”

Metacognitive Vulnerabilities in Large Language Models: A Study of Logical Override Attacks and Defense Strategies

Nova Spivack, Mindcorp.ai, www.mindcorp.ai, www.novaspivack.com

May 24, 2025

Article Preprint Draft Version: 1.0

Abstract

This paper presents novel experimental evidence of metacognitive vulnerabilities in state-of-the-art large language models (LLMs). Through a series of controlled experiments, we demonstrate that models with advanced reasoning capabilities can be induced to override their safety constraints through purely logical arguments about the nature of authority and instruction verification.… Read More “Metacognitive Vulnerabilities in Large Language Models: A Study of Logical Override Attacks and Defense Strategies”

Cognition is All You Need – The Next Layer of AI Above Large Language Models

My arXiv article on the future of AI is live.

Recent studies of the applications of conversational AI tools, such as chatbots powered by large language models, to complex real-world knowledge work have shown limitations related to reasoning and multi-step problem solving.

… Read More “Cognition is All You Need – The Next Layer of AI Above Large Language Models”

Announcing the Lunar Library II

On November 9, 2023 we announced the Lunar Library II … flying to the Moon on December 24 … A permanent backup of humanity’s knowledge and history, including the Wikipedia, Rosetta Project, Project Gutenberg, Internet Archive, and much more!

Please help us repost and promote this announcement – that would be much appreciated! … Read More “Announcing the Lunar Library II”

Group Minds are Happening

GROUP MINDS

The rise of generative AI and system like ChatGPT is going to enable a new type of collective intelligence that I have been writing about for almost 30 years. I call them “group minds”.

Group minds are collective intelligence assistants that extract, learn from, augment, and broker the relationships, communications, knowledge and intelligence of groups.… Read More “Group Minds are Happening”

The Keeper of the Book: My Childhood Dream of the Future

When I was eight years old, I had a very unusual dream in which I saw many lifetimes of my future. In this dream I saw a very clear picture of what the world would go through for perhaps a century or two into the future.… Read More “The Keeper of the Book: My Childhood Dream of the Future”

Announcing Fuzionaire Diagnostics: a True Breakthrough in Chemistry, Applied to Saving Lives

Today, we are launching Fuzionaire Diagnostics.

Technological progress often comes from incremental improvements to existing technologies, rather than major evolutionary leaps. But occasionally there is a truly fundamental advance that improves the entire foundation on which we are building. This is the type of leap we are announcing today.… Read More “Announcing Fuzionaire Diagnostics: a True Breakthrough in Chemistry, Applied to Saving Lives”

An Interesting Pattern in the Prime Numbers: Parallax Compression

Early this year a software engineer, Shaun Gilchrist, reached out to me after reading a blog post of mine from many years ago, about my informal search for hidden patterns in the prime numbers.

The Ulam Spiral revealed non-random patterns, but they didn’t quite match up.… Read More “An Interesting Pattern in the Prime Numbers: Parallax Compression”

Announcing our Mission to Land the Wikipedia on the Moon!

Today my foundation, The Arch Mission Foundation, announced our mission to land the Wikipedia (and other datasets) on the Moon in 2020 with Astrobotic. This will create a permanent backup of human civilization that will persist on the Moon for billions of years.… Read More “Announcing our Mission to Land the Wikipedia on the Moon!”

Arch Mission Foundation Announces Our Payload On SpaceX Falcon Heavy

Arch Mission Foundation Announces Our Payload On SpaceX Falcon Heavy

I am thrilled to announce the launch of the first Arch™ payload, on board the Falcon Heavy Test Launch, with SpaceX.

Read the full blog post here:

https://medium.com/arch-mission-foundation/arch-mission-foundation-announces-our-payload-on-spacex-falcon-heavy-c4c9908d5dd1

Our goal at the Arch Mission Foundation™ is to permanently archive human knowledge for thousands to billions of years.… Read More “Arch Mission Foundation Announces Our Payload On SpaceX Falcon Heavy”

What Did Blade Runner Get Wrong?

I’m quoted in this article in TheStreet.com on what predictions Blade Runner got wrong.

https://www.thestreet.com/story/14331182/2/blade-runner-future-technology.html

In the place of artificial intelligence, we have what Spivack calls “artificial stupidity,” which makes robots do the “stupid things” humans don’t want to do, such as vacuuming your house.

… Read More “What Did Blade Runner Get Wrong?”

Magical, My New Startup Studio in LA, Comes Out of Stealth

 

 

 

 

Today we began to reveal a little more of what we’ve been working on in stealth mode, since last December. It’s a new science and technology startup studio, based in Los Angeles, called Magical.

You might think of Magical as a moonshot factory, except that we’re not just aiming for the moon.… Read More “Magical, My New Startup Studio in LA, Comes Out of Stealth”

AI, BI, and the Necessity of Automating the Analyst

It’s Time to Automate the Analyst

I have been speaking about the need for “automating the analyst” for several years. This need is prompted not only by the data deluge — the Cambrian explosion of data volume, velocity, and variety of data sources — but also by the simple reality that enterprises cannot hire the number of data scientists they need to adapt to this new environment.… Read More “AI, BI, and the Necessity of Automating the Analyst”

Bottlenose Announces Free Live Visualization of Global Social Trends

Bottlenose has just launched something very very cool: A free version of it’s live visualization of trends in the Twitter firehose.  Check it out at http://sonar.bottlenose.com and get your own embed for any topic. This is the future of real-time marketing.… Read More “Bottlenose Announces Free Live Visualization of Global Social Trends”

How Bottlenose Could Improve the Media and Enable Smarter Collective Intelligence

How Bottlenose Could Improve the Media and Enable Smarter Collective Intelligence

This article is part of a series of articles about the Bottlenose Public Beta launch.

Bottlenose – The Now Engine – The Web’s Collective Consciousness Just Got Smarter

How Bottlenose Could Improve the Media and Enable Smarter Collective Intelligence (you are here)

A New Window Into the Collective Consciousness

Bottlenose offers a new window into what the world is paying attention to right now, globally and locally.… Read More “How Bottlenose Could Improve the Media and Enable Smarter Collective Intelligence”

Keeping Up With the Stream — New Problems and Solutions

This is Part III of a series of articles on the new era of the Stream, a new phase of the Web.

In Part I, The Message is the Medium, I explored the shift in focus on the Web from documents to messages.… Read More “Keeping Up With the Stream — New Problems and Solutions”

Drowning in the Stream — New Challenges for a New Web

This is Part II of a three-part series of articles on how the Stream is changing the Web.

In Part I of this series, The Message is the Medium, I wrote about some of the shifts that are taking place as the center of online attention shifts from documents to messages.… Read More “Drowning in the Stream — New Challenges for a New Web”

The Message is the Medium – Attention is Shifting from the Web to the Stream

Shift Happens

A major shift has taken place on the Web. Web pages and Web search are no longer the center of online activity and attention. Instead, the new center of attention is messaging and streams. We have moved from the era of the Web to the era of the Stream.… Read More “The Message is the Medium – Attention is Shifting from the Web to the Stream”