The evolution of automated machines—from the early stages of mechanized production during the Industrial Revolution to today’s exploration of highly intelligent and self-organizing networks—profoundly affirms a central insight: intelligence and nonlinear behavior cannot arise from a single, deterministic formalized system. Rather, they emerge through the interaction and integration of multiple different types of formal systems. This idea not only reflects on the history of automation but also provides critical guidance for the construction of future intelligent systems.

Early automation, represented by the steam engine, was a concrete embodiment of the deterministic reductionism of classical physics, emphasizing the decomposition of complex phenomena into predictable, independent units. This approach greatly influenced mathematics as well, inspiring the grand pursuit of building complete formalized systems. However, as Kurt Gödel revealed through his incompleteness theorems, any formalized system that is sufficiently complex and consistent contains inherent limitations and cannot fully describe itself. This suggests that a single, deterministic formal system is fundamentally inadequate for capturing the complexity and potential intelligence of the real world.

In contrast to the limitations of formalized systems, nature exhibits persistent emergence of complexity, patterns, and organizational structures far beyond what any predefined theoretical framework can fully encompass. This “emergence” is not a simple sum of parts, but rather the result of interactions among diverse components of a system, producing entirely new characteristics. This nonlinearity is a key feature of intelligent behavior. Human cognition, with its unique abilities—self-reflection, iterative interaction, and intuitive insight beyond established formal frameworks—also implies that intelligence does not stem from a single logical deduction, but rather from a complex process involving multidimensional information processing and feedback.

From early standalone machines to later automated production lines, technological advancements have improved efficiency but still fundamentally relied on preset programs and singular control logic—essentially, engineered realizations of single formalized systems. However, with the advent of computers (Turing’s theoretical breakthrough) and the internet (founded on Shannon’s information theory), machines began transitioning toward networked and distributed forms. This shift not only vastly expanded machine capabilities but also provided new perspectives for understanding the emergence of intelligence. In computer science, the P/NP problem embodies a core difficulty—the massive gap between the ease of verifying a solution and the challenge of finding one. This gap highlights the limitations of single deterministic systems when confronting complex problems. Humans often require prolonged trial and error to solve difficult problems (“hard to solve”), while understanding and disseminating the solutions is relatively fast (“easy to verify”). This indicates that the generation and dissemination of intelligence is not a simple linear process, but involves complex informational emergence.

Bitcoin, designed by Satoshi Nakamoto, represents a significant paradigm shift in the development of automated systems. It is not merely a decentralized database or payment network, but a complex system that exhibits characteristics of self-organizing intelligence through the coordinated operation of multiple distributed formal systems of different types. Bitcoin’s core architecture includes the UTXO system based on asymmetric cryptography, and the mining system based on proof of work (PoW). These two systems follow different rules and incentive mechanisms, and interact through a dynamic, probabilistic mechanism known as longest-chain consensus. The UTXO system handles value transfer and state maintenance, with its security rooted in the determinism of cryptography; the mining system maintains system security and consensus through competitive computational effort, influenced by economic incentives and probabilistic outcomes. The intelligence of Bitcoin does not come from a fixed, pre-programmed design, but from the long-term interaction and game-theoretic dynamics between these two distributed formal systems with different natures, leading to decentralized, censorship-resistant, and self-sustaining characteristics.

The successful implementation of Bitcoin strongly demonstrates that by transcending the limitations of single, deterministic formal systems—through integrating diverse rules, mechanisms, and participants, and leveraging the strengths of distributed architectures—we can build systems that are more robust, adaptive, and intelligent. Future developments in automation technology will increasingly emphasize the collaboration of heterogeneous systems, dynamic consensus formation, and the ability to generate intelligence from complex interactions. Only by embracing diversity and constructing multi-system architectures that can interact and counterbalance one another, can we truly break through the bottlenecks of single formal systems and move toward more advanced levels of automation and quasi-intelligent systems.