The most shocking isomorphism in the history of science: from the stopping problem of Turing machines, the Kleene Hierarchy, Hilbert's tenth/second problem, to Bitcoin's heaviest chain consensus. To what extent can we achieve 'absolute certainty'? Reviewing Martin Davis' classic work "computability and unsolvability" on 2/10, one of the core cornerstones of computational theory is the problem of machine stoppage. Turing proved that there is no universal algorithm that can determine whether any program will stop under a given input. The 3/10 shutdown problem is at the $\ Sigma1 ^ 0 $level of the Klein arithmetic hierarchy (recursively enumerable/semi decidable): if the program will shut down, it can be "seen with one's own eyes" within a finite number of steps (existence quantifier $\ exists $); But if trapped in a dead loop, the algorithm will never be able to determine within a finite number of steps. The gap between being able to capture positive examples but unable to have global knowledge is an iron law at the arithmetic level. 4/10 Hilbert's Tenth Problem (Root Determination of Diophantine Equations) is connected to this fate. Through the relay proof of Davis, Putnam, Robinson, and Matiashevich (DPRM theorem), it is proven that every $\ Sigma1 ^ 0 $set is equivalent to having a solution to the Diophantine equation. Since the shutdown problem is unsolvable, there is no universal judgment algorithm for the Diophantine equation. 5/10 Revisit Hilbert's Second Problem and G ö del's Incompleteness Theorem. Can the system internally verify that there are no contradictions? From the perspective of the Kleinian level, this belongs to the universal proposition of $\ Pi_1 ^ 0 $or even higher order. Absolute certainty cannot be self proven within a closed finite form system. 6/10 Pulling the Perspective to Distributed Computing: Bitcoin's "Nakamoto Consensus" is logically perfectly isomorphic to the above theory. In an asynchronous P2P network with network latency, local chain reassembly verification is semi decidable ($\ Sigma1 ^ 0 $), and nodes can iteratively calculate the current heaviest chain at any time. However, pursuing absolute global finality (i.e. proving that 'the heaviest chain at this moment will never be reassembled in the future') is logically equivalent to a universal quantifier proposition ($\ Pi_1 ^ 0 $), which corresponds to the limit in distributed asynchronous networks (such as the FLP impossibility theorem) and is unsolvable in algorithms. 8/10 is like a single Turing machine that cannot 100% predict the life and death of a program, and distributed nodes cannot absolutely determine that a certain block is permanently irreversible at the moment. Absolute finality cannot be achieved in mathematics and distributed computing. The greatness of 9/10 Bitcoin lies in its use of engineering solutions to bypass this theoretical boundary: it introduces proof of work (PoW) and economic games, replacing "absolute finality" with "probabilistic finality". As the depth of the block increases (such as 6 confirmations), the probability of recombination converges exponentially to zero. From the limits of single machine computing power to distributed ledger consensus, humans have always used probability and mechanism design to elegantly cross those insurmountable ultimate theoretical boundaries. ✨ Original link: https://(github.com)/gguoss/My-10-Year-Journey-in-the-Crypto-World/blob/main/%E4%BB%8E%E8%AE%A1%E7%AE%97%E7%90%86%E8%AE%BA%E7%9A%84%E7%AE%97%E6%9C%AF%E5%B1%82%E6%AC%A1%E5%88%B0%E5%88%86%E5%B8%83%E5%BC%8F%E5%85%B1%E8%AF%86%E7%9A%84%E6%9E%81%E9%99%90%EF%BC%9A%E8%AE%BA%E6%AF%94%E7%89%B9%E5%B8%81%E6%9C%80%E9%87%8D%E9%93%BE%E5%88%A4%E5%AE%9A%E4%B8%8E%E5%85%8B%E8%8E%B1%E5%B0%BC%E5%B1%82%E6%AC%A1%E3%80%81%E5%81%9C%E6%9C%BA%E9%97%AE%E9%A2%98%E5%8F%8A%E5%B8%8C%E5%B0%94%E4%BC%AF%E7%89%B9%E9%97%AE%E9%A2%98%E7%9A%84%E5%90%8C%E6%9E%84%E6%80%A7.md