From mechanization to self-organization: the emergence of complexity beyond a single formal system The development process of automated machines, from the single mechanized production in the early stages of the Industrial Revolution (about 300 years ago, roughly in the Newtonian era) to the current move towards highly intelligent and self-organizing networked systems, deeply reflects the evolution of scientific thinking. Early automation machines, represented by steam engines, were concrete manifestations of the scientific idea of reductionism, emphasizing the decomposition of complex phenomena into predictable independent parts. This kind of thinking has also deeply influenced the field of mathematics, giving rise to the grand goal of building a complete formal system. However, in the early 20th century, Kurt G ö del revealed through his incompleteness theorem that any sufficiently complex and compatible formal system cannot fully describe itself, and there must be propositions within the system that cannot be proven or falsified. This theorem not only shakes the foundation of mathematical research, but also implies the inherent limitations of a single formal system in capturing the complexity of the real world. In contrast to the limitations of formal systems, our natural reality exhibits an emerging 'completeness'. The term 'completeness' here does not refer to mathematical completeness, but rather to the ability of nature to continuously generate new phenomena, laws, and organizational structures beyond any predetermined theoretical framework. This' completeness' may be related to the unique ability of human cognition, namely self reflection, iterative interaction, and intuitive insight beyond existing formal frameworks. Through introspective thinking (as advocated by Socrates) and debate and communication with others, individuals can continuously revise and expand their cognitive models, breaking free from the constraints of a single logical system. From early independent machines to later automated production lines, the development of technology, while improving efficiency, essentially still relies on pre-set programs and a single control logic, which can be seen as the engineering implementation of a single formal system. However, with the emergence of computers (Turing's theoretical breakthrough) and the Internet (Shannon's foundation of information theory), machines began to move towards networking and distribution. This transformation not only greatly expands the functionality of machines, but also provides a new perspective for us to understand the significance of G ö del's incompleteness theorem in the field of computation. For example, the P/NP problem in computer science explores the boundaries of computational complexity, and its core challenge may have deep connections with the undecidability of certain propositions within formal systems. The Bitcoin designed by Satoshi Nakamoto represents an important leap in the development of automation systems. It is not just a decentralized database or payment network, but a complex system that can be understood as a collaborative operation of multiple different types of distributed formal systems and exhibits self-organizing characteristics. The core architecture of Bitcoin includes two key types of distributed formal systems: Distributed UTXO (Unscented Transaction Output) system based on asymmetric encryption: This system utilizes cryptographic principles to ensure the security of transactions and the uniqueness of asset ownership. The complexity of its transaction verification process can be compared to the difficulty of verifying solutions in P/NP problems. Each UTXO can be viewed as an independent state, and the overall state of the system is the set of all unused outputs. A distributed miner system based on Proof of Work (PoW): Miners compete for the accounting rights of new blocks by performing a large number of hash operations. This competitive computing power investment is a key mechanism for maintaining blockchain security and preventing double payments. The behavior of miners follows a clear set of mining rules and reward mechanisms. The core mechanism for connecting and coordinating these two distributed formal systems is the longest chain consensus. The longest chain is not a theorem derived entirely from mathematical logic, but rather an intuitive assumption based on probability and economic incentives, where the longest proof of work chain represents the most widely recognized and trusted transaction history in the system. The longest chain is not only the fundamental support for the value of UTXO system, but also the result of distributed competition and maintenance among miners. The innovation of Bitcoin lies in its lack of reliance on a single centralized control or pre-set complete set of rules, but rather the emergence of a decentralized, censorship resistant, and self-sustaining feature through dynamic interactions and games between multiple distributed formal systems with different properties. The state evolution of UTXO systems is constrained by cryptographic rules, while the behavior of miner systems is driven by economic incentives and consensus rules. The two interact and constrain each other through the dynamic, historical based "consensus anchor" of the longest chain. The concept of constructing complex systems through multiple types of distributed formal systems provides important insights for the future development of automation technology. It indicates that beyond the limitations of a single formal system, by integrating different types of rules, mechanisms, and participants, and leveraging the advantages of distributed architecture, we can build more robust, adaptive, and intelligent systems. The practice of Bitcoin has proven the feasibility of this approach and indicates that future automation systems will place greater emphasis on the collaboration of heterogeneous systems, dynamic consensus formation, and the ability to emerge intelligent from complex interactions.