The Inspiration of Turing Machines, Oracle Machines, and Bitcoin: From Theoretical Models to Practical Applications The Turing machine proposed by Alan Turing is an abstract computational model aimed at formally defining the boundaries of "computability". The Turing machine simulates any computational process that can be described by an algorithm by performing read and write operations on an infinitely long paper tape through a finite state controller. The core idea is to decompose complex calculations into a series of simple mechanical steps, laying a solid foundation for the theoretical basis of computer science. However, Turing machines themselves have limitations as they cannot solve problems that are mathematically undecidable. In order to explore the boundaries of computing power, Turing introduced the concept of oracle machines. The oracle machine is an extension of the standard Turing machine, which adds an external "black box" - the oracle - that can provide answers to certain problems that Turing machines cannot calculate in one step. The oracle is not an actual physical machine, but a theoretical tool used to study how the potential of computational models changes with additional computing resources, as well as the relationship between different types of 'incomputability'. From the perspective of formal systems, for a single computing system, the Turing machine model represents its entire computing power. And the oracle can be seen as an external "perceptual input" that can provide computing power beyond the current system. When examining multiple formal systems, the concept of oracles can be extended to serve as a bridge connecting different Turing machines, allowing the abilities of one system to be utilized by another. Although Turing primarily focused on the computational theory of individual machines during his lifetime, with the development of computer technology, especially in the era of distributed computing and networking, collaboration and information sharing between systems have become increasingly important. The Bitcoin system designed by Satoshi Nakamoto cleverly brings the theoretical concepts of Turing machines and oracle machines to life, providing a new perspective for us to understand the application of these abstract models in the real world. In the Bitcoin system, we can observe the embodiment of Turing machine theory: Distributed UTXO ledger value network: can be seen as a rule-based state transition system. The validity of transactions is guaranteed by asymmetric encryption technology, and each transaction represents a state update of the UTXO set. Although there is controversy over the Turing completeness of Bitcoin scripts, their core transaction verification and state evolution mechanisms align with the idea of Turing machines computing through rules. PoW based miner work network: Miners compete for accounting rights by executing Proof of Work (PoW) algorithms. The process of finding nonce values that meet the difficulty goal is a computationally intensive process, which can be likened to the computational execution of a Turing machine. Miners who successfully find a valid PoW have the right to add new blocks to the blockchain, driving updates to the ledger status. More notably, Bitcoin's longest chain consensus mechanism plays the role of an oracle, linking these two distributed formal systems: Connecting the value network and the work network: The longest chain mechanism transfers the results obtained by miners through PoW calculations (including blocks with valid nonce) to the nodes that maintain the UTXO ledger. Dependency on external 'assumption': The effectiveness of the longest chain depends on the external assumption that 'nodes with over 51% computing power are honest'. This assumption is not directly guaranteed by the agreement, but based on considerations of economic incentives and game theory. The longest chain mechanism transforms this external assumption into the consensus foundation of the entire system. Example of "difficult to solve, easy to verify": Bitcoin's PoW mechanism perfectly fits the characteristic of "difficult to solve but easy to verify" in P/NP problems. Miners need to invest huge computing power to find effective nonce (difficult to solve), but any node in the network can quickly verify the effectiveness of PoW through simple hash calculations (easy to verify). Therefore, the longest chain of Bitcoin can be seen as a "oracle" that provides the calculation results of PoW (completed by the Miner network) to the UTXO ledger network for verification. The UTXO ledger network relies on this' oracle 'to ensure the security and availability of ledger status updates. The computing power investment of miners is transformed into a verifiable trust signal, enabling the establishment of decentralized value consensus. In summary, the design of Bitcoin cleverly applies the computing model of Turing machines to its distributed ledger and mining process, and creatively utilizes the longest chain consensus mechanism as a "oracle" to link different subsystems, rely on reasonable external assumptions, and achieve secure and decentralized value transfer. The successful practice of Bitcoin provides valuable insights for us to understand the application of abstract computational theory models in complex real-world systems. It indicates that through sophisticated mechanism design, theoretical concepts can take root and have a profound impact on society.