In depth interpretation: Why did Satoshi Nakamoto design a "Turing incomplete" Bitcoin with "super poor iteration" approaching infinite certainty? abstract The difference between Bitcoin and Ethereum is not only in their consensus mechanisms and performance, but also in their fundamentally different philosophical approaches to "trust" and "certainty". Bitcoin pushes the decision problem onto time and computing power through deliberate Turing incompleteness and a "super poor iteration" that relies on physical time advancement, thus achieving near infinite finality logically. This article will focus on core concepts such as Turing completeness, decision problems, and super poor iterations to explain why Bitcoin is a system structure that is closer to "irretrievable trust". 1、 Turing completeness and the "decidable boundary" of systems 1. Turing completeness: the limit of functionality, the starting point of risk Turing completeness "is a core concept in computational theory, which refers to the ability of a computing system (such as a programming language or virtual machine) to simulate any Turing machine. Simply put, it can perform any computational task that can be described by an algorithm. This infinite expressive power is a breeding ground for innovation, but it also introduces risks from the logical roots: the Halting Problem. This is a fundamental 'undecidable problem', where we cannot create a universal algorithm to determine whether any program will ultimately stop running under a given input. This is a concrete manifestation of "self referential" and "incompleteness" in computational science. **Ethereum's EVM (Ethereum Virtual Machine) is Turing complete. Its Turing completeness leads to the inherent "judgment problem" of all smart contract businesses deployed on it ultimately relying only on the human judgment and rule setting of business designers. This further leads to the fact that the value anchor and trust foundation of the tokens issued based on these contracts are also completely determined by "people" - which leads to the centralization of the token. The meaning of the token is just more transparent than that of the Internet game currency, Q-coin. **The scripting language (Script) of Bitcoin, on the other hand, is deliberately designed to be Turing incomplete. It does not support complex control flow structures such as loops and recursion. This seemingly 'functionally weak' design brings a huge advantage: the execution path and results of all Bitcoin scripts are completely predictable and determinable. It eliminates the risk of 'contract downtime' at the protocol level. Business can only be done internally within the system, and then the undecidable issue of the existence of self business can be thrown out and handed over to the super poor iteration. in short: Turing completeness=powerful functionality+difficult judgment Turing incompleteness=limited functionality+simple judgment 2. Determine if the problem is a breakpoint in system trust In a decentralized consensus system, "decidability" is not only a technical issue, but also the cornerstone of trust. If the underlying logical behavior of a system, such as contract execution, is unpredictable, then the "finality" of its consensus will be challenged. Users and nodes need to trust that the contract will not lose control, and this trust comes from auditing the code and trusting the developers, rather than the native guarantees of the protocol itself. 2、 The design philosophy of Bitcoin: from "finite form" to "physical infinity" Satoshi Nakamoto's design is not a technical compromise, but a profound philosophical insight into safety and certainty. He created a "hyper formal system" structure that goes beyond pure formal systems by combining Turing incompleteness, Proof of Work (PoW), and the longest chain principle. 1. Turing incompleteness="logical certainty" within the system The strict limitations of the Bitcoin scripting language ensure absolute certainty within its' formal system '. The legitimacy verification logic of each transaction (TX) is clear, limited, and can be independently determined by all nodes in the network. This means: There is no infinite loop: the script has an upper limit on the number of execution steps. No state explosion: The possible outcomes of a transaction are limited. No complex external dependencies: Validation relies only on the current transaction and its referenced UTXO state. This layer is a rock solid deterministic structure constructed by Bitcoin within the system. 2. "Ultra poor iteration"="physical certainty" outside the system However, the Bitcoin system still faces an ultimate 'undecidable problem': which chain is the only real and final chain in the event of a fork? Satoshi Nakamoto did not attempt to "determine" this problem through algorithms within the formal system, but cleverly handed it over to the physical world, approaching determinism infinitely through an endless "super poor iteration" process. This process is driven by two core components: Proof of Work (PoW): Anchoring accounting rights closely to real-world energy consumption (computing power) and time. Falsifying history requires significant and irreversible physical costs to be reinvested. The principle of longest chain: All nodes always follow and acknowledge the chain that has accumulated the most workload (i.e. longest). This process is like the hyperfine iteration in mathematical set theory: The birth of each new block is an iteration based on the previous state. This iterative process takes physical time as an ordinal, approximately every 10 minutes, and theoretically never stops. The difficulty of overturning old blocks increases exponentially with each new block added (one iteration). Therefore, the ultimate nature of Bitcoin is not "judged" at a certain point in time, but rather its history is "infinitely approaching and determined" over time. A block that is covered by 6 new blocks is considered 'safe', which is not an absolute judgment, but a probability threshold widely accepted in practice. Its true security and certainty continue to strengthen over time, approaching 100%. 3、 Comparison of Ethereum: From computability to limited trust 1. Complexity of EVM: computable ≠ decidable The Turing completeness of Ethereum makes it a powerful 'world computer', but it also means a shift in the trust model: Any business logic: can build complex applications such as DeFi, DAO, etc. Unpredictable state: Contract behavior may result in unforeseen outcomes for developers (such as The DAO event). Transfer of trust: Due to the undecidability of contracts, trust is partially transferred from the protocol itself to the "contract writers," "code auditors," and "artificial economic mechanisms (Gas). 2. The Limited Trust Structure of PoS At the consensus level, Ethereum has shifted towards proof of stake (PoS) mechanism, and its trust model is fundamentally different from Bitcoin. The finality of PoS depends on a finite set of validators confirming it through voting. Economic incentives: using pledged tokens as a reward and punishment mechanism to incentivize honest behavior among validators. Limited governance entity: The achievement of consensus relies on a finite, countable set of validators (e.g., reaching 2/3 of the voting weight). Reversible risk: In theory, if more than a certain proportion of validators (such as 1/3 or 2/3, depending on the specific mechanism) collectively commit wrongdoing or disconnect, the consensus of the system may be reversed or stalled. This means that the ultimate nature of Ethereum is determined within its formal system through a limited governing entity. The ultimate nature of Bitcoin lies outside the system, approaching through an infinite process of physical evolution. 4、 Why is the certainty of Bitcoin more ontological? The core of this comparison lies in the understanding of the source of "trust", which has entered the realm of ontology (philosophical exploration of the essence of existence). PoS is an internal decision-making mechanism within formal systems, while Bitcoin is an approximation mechanism outside of formal systems. The philosophical significance behind this is profound: The judges are different: Ethereum's "final confirmation" is determined by a countable group of validators. The 'final confirmation' of Bitcoin is not determined by any specific group, but is jointly 'proven' by the entire universe through irreversible time passing and energy consumption. G ö del incompleteness metaphor: As revealed by G ö del's incompleteness theorem, no sufficiently powerful formal system can prove its own non contradiction internally. Satoshi Nakamoto did not attempt to violate this rule. He did not allow the Bitcoin system to "claim" its correctness internally, but instead handed over the responsibility of proving its "existence and uniqueness" to the physical reality outside the system. The difference in trust foundation: The trust foundation of PoS is based on the assumption of "economic rationality". The foundation of trust in Bitcoin is the "immutability of physical laws". The former is social science, while the latter is natural science. Conclusion: The root of trust lies not in "who judges", but in "who cannot overthrow" Ethereum and other PoS chains, no matter how intricately designed their governance mechanisms, ultimately answer the question: "Who should we trust to determine the final state The architecture of Bitcoin fundamentally avoids this issue. It does not propose who will make the judgment, but provides an objective factual record that can be independently verified by all participants and cannot be overturned by anyone. It pursues not a 'definite truth' bestowed by authority, but an 'evolutionary fact' that constantly consolidates itself in the long river of time. This is why Bitcoin is a meta formal system: it is a complex that tightly integrates a logically consistent formal system (transaction script) with a ruthless and impartial physical reality (proof of work, time iteration). In this system, 'ultimate certainty' is not a one-time judgment behavior, but an infinitely approaching and eternal evolutionary process. **