AI Agents, Mathematics, and Making Sense of Chaos

From Artificiality This Week

• Our Gathering: Our Artificiality Summit 2025 will be held on October 23-25 in Bend, Oregon. The Summit will focus on the human experience of “The Artificiality”: the emerging paradigm where the boundaries between organic and synthetic systems blur, driven by the fundamental role of information and computation in complex systems. Our 2024 Summit was described as "a perfectly curated weekend of building connections, sharing ideas and having genuine conversations across science, design, art and the innovations that are expanding our future and imagining what can be next in AI."
  • Don't miss our Super Early Bird Fee of $1,495 available through January 31. Sign up here or simply reply to this email.
• Our Ideas: What’s Happening Now in AI Agent Software and Why It Matters. We like to map out the shifts in AI in a way that’s clear and practical. The landscape is complex, and no framework captures everything, but we’ve found it helpful to think about AI software in terms of layers. This is a simplified view—real-world boundaries are fuzzy—but we think it’s a useful lens for understanding where things are today and where they could be headed within a timeline you can plan around. AI software is evolving rapidly as models transform into agents and systems, powered by a critical new layer of coordination software that has recently been termed the orchestration layer. It's a new form of middleware—positioned between foundation models and applications, serving as the coordination layer between them. In this sense, it functions as the operating system for agents.
  • Read more here.
• Our Ideas: The Rise of AI Agents and What We May Never Understand. When the Flash Crash hit in 2010, wiping nearly a trillion dollars from the stock market in minutes before restoring it almost as quickly, something weird happened. Not just the near-catastrophic market event, but a foreshadowing of a future where our mathematical models—often our highest fidelity tools for thinking about systems—break down completely. The crash wasn't caused by a single rogue AI or brilliant hacker, but by the emergent behavior of simple trading algorithms interacting in ways that go beyond our ability to model mathematically. Over a decade later, we still can't write equations that fully explain what happened. This kind of mathematical inadequacy isn't just a temporary limitation—it might be fundamental to how we think about artificial intelligence and its future. While public attention focuses on individual AI models like GPT-4 or Google's Gemini becoming superintelligent, physicist David Wolpert argues we're missing something deeper. Our focus on singular, powerful AI systems is, in his words, "retro, so twentieth century." The real transformation will emerge from networks of AI systems interacting in ways that don't just exceed our predictions, but go beyond what we can actually understand or calculate using math.
  • Read more here.
• Conversations: Doyne Farmer: Making Sense of Chaos. We’re excited to welcome Doyne Farmer to the podcast. Doyne is a pioneering complexity scientist and a leading thinker on economic systems, technological change, and the future of society. Doyne is a Professor of Complex Systems at the University of Oxford, an external professor at the Santa Fe Institute, and Chief Scientist at Macrocosm. Doyne’s work spans an extraordinary range of topics, from agent-based modeling of financial markets to exploring how innovation shapes the long-term trajectory of human progress. At the heart of Doyne’s thinking is a focus on prediction—not in the narrow sense of forecasting next week’s market trends, but in understanding the deep, generative forces that shape the evolution of technology and society. His new book, Making Sense of Chaos: A Better Economics for a Better World, is a reflection on the limitations of traditional economics and a call to embrace the tools of complexity science. In it, Doyne argues that today’s economic models often fall short because they assume simplicity where there is none. What’s especially compelling about Doyne’s perspective is how he uses complexity science to challenge conventional economic assumptions. While traditional economics often treats markets as rational and efficient, Doyne reveals the messy, adaptive, and unpredictable nature of real-world economies. His ideas offer a powerful framework for rethinking how we approach systemic risk, innovation policy, and the role of AI-driven technologies in shaping our future. We believe Doyne’s ideas are essential for anyone trying to understand the uncertainties we face today. He doesn’t just highlight the complexity—he shows how to navigate it. By tracking the hidden currents that drive change, he helps us see the bigger picture of where we might be headed.
  • Listen to our conversation with Doyne here.