From Turing Machines to Bitcoin: The Evolutionary Path of Computing Paradigms ——The boundary between linear computability and nonlinear relative computability 1、 Introduction: Two paradigms of computation At the origin of computing history, Alan Turing defined the "Turing machine" in 1936, establishing the basic framework of modern computing theory and fundamentally answering the question of "what is computable". Two years later, Turing introduced the "oracle machine" in his doctoral thesis in 1938- a computing system that could reason with the help of external information sources, relative to the Turing machine, in order to break through the incompleteness of formal logic systems. Today, we re-examine these two computational models and find that they are not only theoretical divisions, but also constitute a watershed between two types of system paradigms in technical practice: Turing machine: a deterministic, linear, top-down reductionist system. Oracle Turing Machine: A Non deterministic, Nonlinear, Bottom Up Evolutionary System. And the most representative manifestation of this paradigm divergence in contemporary times is the emergence of the Bitcoin system. 2、 Turing 1936: Turing machine and linear computability Turing proposed the concept of the "Turing machine" in his masterpiece "On Computable Numbers" in 1936. This is a top-down, deterministic computational model, whose core features include: Computability: emphasizes whether a problem can be solved by a strictly defined algorithm in a finite number of steps. Linear structure: State transitions are sequential and static. Closed logic: The calculation process is completely completed inside the machine, and the environment is not visible. Reductionist thinking: Complex problems can be broken down into combinations of basic components. Traditional computer programming, formal logic proofs, and automatic control systems are all extensions of this paradigm. 3、 Turing 1938: Oracle Turing Machine and Relative Computability However, Turing himself soon realized that not all mathematical truths could be exhausted by the Turing machine. In 1938, he proposed the "Oracle Machine" in his doctoral thesis "Systems of Logic Based on Ordinals": The oracle machine does not break through computational impossibility, but introduces external information sources (oracles) as a relative judgment basis. This model describes a type of relative computability or decidability. It has characteristics such as openness (dependent on external context), nonlinearity (not exhaustible in linear processes), and adaptability (changing structure with input). The corresponding philosophical perspective has shifted from reductionism to evolutionism and complex systems thinking. In short: The Turing machine answered 'What can we calculate?'; The oracle pointed out how to find locally decidable structures in non computable data. 4、 Bitcoin: The Real Emergence of Distributed Oracle Turing Machines Bitcoin is not built on traditional Turing machine style linear computing logic. Its system behavior is closer to a distributed oracle Turing machine network, reflecting the following characteristics: Bottom up consensus formation: Each Miner node acts as a local judgment unit, forming a global state through a Proof of Work mechanism in the absence of central coordination. Nonlinear evolutionary system: The system state continuously reconstructs with changes in participating nodes, hash rate, and time, resulting in a stable but non static overall order. Openness and adaptability: The Bitcoin protocol itself is only the smallest set of rules, and its ecology and behavior patterns have evolved over a long period of time in an open environment. Deterministicity takes priority over computability: the essence of a system is not to solve an algorithmic problem, but to reach a decidable consensus on whether a set of historical records is "recognized by all nodes". Bitcoin has thus become a real-life 'oracle system': it does not rely on a single point of computing power or logical reasoning, but on the dynamic sense of order formed by the entire system's game structure and evolutionary process. 5、 Systematic Comparison: Two Computational Cosmologies Attribute Turing Machine Model (1936) Oracle Turing Machine Model/Bitcoin System (1938) Theoretical Source Turing "Computable Numbers" (1936) Turing "Ordinal Logic Systems" (1938) Computational Type Computability Relative Computability Logical Structure Linear, Closed, Deterministic Nonlinear, Open, Adaptive Control Architecture Top down Bottom up System Characteristics Static, Predictable, Restoring Theory Dynamic, Evolutionary, Complex System Information Acquisition All derived from internal states with the help of external "Oracle" to judge typical representative program logic, imperative computing models Bitcoin, consensus systems, complex network worldviews Metaphorical Newtonian mechanical universe, Darwinian evolutionary universe 6、 Conclusion: Bitcoin is not a program, but a shift in computational perspective We can view Bitcoin as a deep computational revolution: it is not an "algorithmic tool" in the Turing sense, but an "evolutionary mechanism" in the oracle sense. It presents a completely new computational logic that does not rely on centers or pursue deterministic solutions, but achieves determinacy through game theory, emergence, and consensus. This computational model not only surpasses traditional program structures, but also foreshadows the fundamental paradigm of complex system construction in the decentralized era. In this sense, Bitcoin is not only a revolution in monetary form, but also an evolution of computational philosophy.