Ten Year Cryptocurrency Journey: Enlightenment on Bitcoin and GEB System Paradigm 1、 Introduction: A leap in understanding from Bitcoin to GEB After more than ten years of deep participation and observation in the encrypted world, a core understanding has gradually formed: Individual autonomous distributed systems are the basic units of trust, security, and evolution. Bitcoin is the prototype of such a system. This article attempts to construct a quaternary paradigm for explaining the deep logic of the Bitcoin system, the GEB system model, starting from Turing's oracle Turing machine theory. It not only reveals the engineering success of Bitcoin, but also provides a paradigm for the future architecture of complex adaptive systems. Important background: In the past, the entire computer industry (including the later blockchain industry) was mainly based on the Turing machine model proposed by Turing in 1936's "computable numbers", staying at the paradigm of "computable problems". This is a deterministic reductionist logic that can only handle deductive problems and cannot penetrate the closed nature of formal systems. Turing proposed the oracle Turing machine (O-machine) in his doctoral thesis "Ordinal Logic Systems" in 1938, which showed how to surpass the closed path of formal systems through "decidable problems" (an uncomputable type) and open up the possibility of interacting with a perceptible world and constructing complex adaptive systems. This is the logical starting point of the GEB system paradigm. 2、 The Distributed Philosophy Structure of Bitcoin 1. Core issue: How to ensure the distributed trust security of individuals? 2. Solution: Individual Autonomy+Distributed Emergence Bitcoin does not provide a traditional intelligent system, but rather a structure of non intelligent emerging intelligence. 3. System function expression Turing machine function (formerly known as "trading function"): f(compute)=TX(Input(Individual),Output(Individual))f(\text{compute}) = \text{TX}(\text{Input(Individual)}, \text{Output(Individual)}) O-machine function (formerly known as "consensus function"): f(consensus)=Consensus(hash,difficulty)f(\text{consensus}) = \text{Consensus}(\text{hash}, \text{difficulty}) Ultra poor iterative judgment function (formerly known as "system perception function"): f(Transfinite⇔ Bitcoin)=F(f(Compute),f(Consensus))f(\text{Transfinite} \Leftrightarrow \text{Bitcoin}) = F(f(\text{Compute}), f(\text{Consensus})) =f(Consensus Mechanism,External Energy Input,Energy Conversion)=Value Output= f(\text{Consensus Mechanism}, \text{External Energy Input}, \text{Energy Conversion}) = \text{Value Output} 3、 The Oracle Machine Thought in Turing's Doctoral Dissertation Turing proposed a model to extend the Turing machine in 1938 in his book "Ordinal Logic Systems": Oracle Machine（O-machine）， The oracle Turing machine. The purpose is to attempt to break through the formal system closure limitation of G ö del's incompleteness theorem. Turing hoped to introduce the "oracle" as a non internal formal judgment mechanism to expand the expressive power and processing scope of the system. The logical form of the system is: (∀x)(∃y)R(x,y)(\forall x)(\exists y) R(x, y) Xx: Turing machine can formalize computing objects (such as transactions) Yy: Objects that need to be judged by the "Oracle" (such as blocks) RR: Recursive decidable relationship (such as longest chain ownership) This provides a structural logic model for understanding the dynamic consensus and unpredictability of Bitcoin. 4、 Q ₂ Mapping of Bitcoin Consensus Mechanism We can formalize the transaction verification and chain selection process of Bitcoin as follows: (∀tx)(∃block) R(tx,block)(\forall \text{tx})(\exists \text{block})\, R(\text{tx}, \text{block}) That is, every transaction has a certain block as its' oracle ', proving its validity. X=txx=\ text {tx}: Transaction Y=blocky=\ text {block}: block RR: Recursive Confirmation Mechanism Based on Longest Chain Miners act as' relativistic oracle Turing machines' in it: The perspective from which each miner judges the longest chain is asymmetric But the entire system converges to the public chain state through proof of work This is an engineered 'super poor induction' structure 5、 GEB Quaternion Model: Architecture for Building Complex Adaptive Systems 1. Individual Model: Individual Sovereign Account Structure Decentralized Account Model Mapping UTXO model to Bitcoin 2. Lambda Calculus: The computable paradigm of Turing machines Mapping to Bitcoin Script System Realize conditional transactions and logical expressions between individuals 3. f (consensus): O-machine judgment paradigm Corresponding to Turing's oracle machine model Mapping miner behavior to Bitcoin (relative consensus) 4. f (Transfinite \ Lefterrightarrow Bitcoin): Hyperpoor Recursive Inductive Logic The longest chain principle mapped to Bitcoin Realize dynamic consistency and entropy reduction evolution of the system GEB = (Individual Model, λ\lambda-Calculus, f(consensus), f(Transfinite \Leftrightarrow Bitcoin)) This is a structural modeling of the possibilities of intelligent systems in a decentralized environment. 6、 Philosophical foundation: finite approaching infinite 1. Approximation Logic in Natural Phenomena Light, water, and physical path selection - all optimal approximations under finite causal conditions 2. Kantian aesthetics: perception of "purposiveness" Aesthetics is not a rational definition of results, but a limited perception of "overall harmony" 3. The Common Logic of Technology and Art The longest chain of Bitcoin is: Discrete computation approaching continuous truth Feynman path integration: selecting the natural evolution direction from all paths Violin Aesthetics: Constructing Infinite Expression Space with Limited Operations 7、 Summary: Systematic unity from logic to aesthetics Bitcoin is not only a financial revolution, but also a combination of philosophy and engineering: Using limited computing power to achieve infinite trust. The GEB quaternary model reveals a core idea: Evolve in finite, approximate reality in recursion, and emerge intelligence in non intelligence This is the necessary path for us to reach future complex adaptive systems.