How can humans tame 'infinity'? This is an epic story spanning thousands of years! From the Zeno paradox in ancient Greece to today's Bitcoin, we have been struggling with this concept. This is not just mathematics, but also a leap in human thought. Infinite Mathematics Philosophy Bitcoin First stop: Capture 'infinitesimal'. The birth of calculus resolved the Zeno paradox with the magic spell of "limits". When Δ x approaches 0, we can accurately capture the instantaneous changes. Planck's energy quantum also set the lower limit of "infinitesimal" for the physical world. We have learned to find finite answers in infinite segmentation. ✨ Calculus quantum mechanics limit Second stop: taming 'infinity'. Cantor's set theory reveals that infinity is different from infinity! He used "cardinality" to stratify and "ordinal" to sort, constructing a ladder of super poor iterations. Turing's "ordinal logic" attempted to climb the Tower of Babel of truth with this tool, but the path seemed endless as the system continued to diverge .. Set theory Cantor Turing ordinal logic Third stop: Let infinity converge. When mathematicians were lost on the infinite ladder, John Nash brought crucial insight! His "Nash equilibrium" proved that in multi-party games, the system will converge to a stable state - no one can unilaterally change the strategy for profit. This' anchor point 'ends the dilemma of infinite divergence! The Beauty of Nash Equilibrium Game Theory in Mathematics Core idea connection: Our capture of infinity is a metaphysical language evolution from geometry to mathematical logic, and then to computational science. Infinitesimal: Limits and Quantization (Convergence to 0) Infinity: Set Theory and Ordinal Logic (Constructing Superfast Structures) Infinite convergence: Nash equilibrium (end divergence) is the ladder of thought! Ultimate Leap: Bitcoin! This numerical miracle is the engineering implementation of the "gamified ordinal logic" in reality. It has a three-layer structure: Turing Machine Layer: Transaction Verification (Deterministic) Oracle Machine Layer: Block Generation after Longest Chain Selection (Uncertainty, PoW) Ordinal Logic Layer: Global Consistency (Longest Chain Consensus) See how it uses Nash equilibrium to ensure trust! Bitcoin and Nash Equilibrium: In the Bitcoin network, each miner's decision is based on maximizing profits. The most rational choice is to follow the rules and mine on the longest chain. Any attempt to do evil will suffer huge losses. Therefore, the entire system automatically converges to a unique and honest equilibrium state. Nash equilibrium is the cornerstone of decentralized trust in Bitcoin! Decentralized blockchain Bitcoin is the first system in human history to engineer "infinite games" and "ordinal logic" on a large scale. It keeps iterating (generating blocks) while maintaining convergence (longest chain) through game mechanisms. This is a world of trust running on 'infinity'. Future challenges and prospects: How to use this framework to model more complex adaptive systems? Can the combination of AI and blockchain expand computing boundaries? Is our capture of infinity touching upon some kind of 'computational realism'? Endless thinking! Future Technology AI Web3