‍Introduction

Many people approach understanding Bitcoin from the perspectives of cryptography, economics, or computer science. But if we examine it from the deeper structures of logic and game theory, we find that Bitcoin is not only a payment network, but also the first logical system in human history to achieve unique convergence within “infinite dynamics.”

Its foundation can be succinctly expressed as: Bitcoin = (Peer-to-Peer, Consensus Mechanism).

I. Peer-to-Peer: The Carrier of Information

Bitcoin is a peer-to-peer network.

• For an individual node, it can only perceive the interactive information with its neighbors.
• But when the interactions of all nodes are combined, they form the most comprehensive global knowledge of the Bitcoin system.
  

Therefore, the “information layer” of Bitcoin is the peer-to-peer network itself. It is the perceptual foundation of the system, like the neural network of humans, carrying all internal data and connections.

II. Ordinal Logic and Infinity

In his doctoral thesis, Turing proposed the ordinal logic system:

[O = (F, Ord, Oracle)]

• (F): Formal system
• (Ord): Ordinal iteration
• (Oracle): Oracle
  

This system attempted to bring “infinity” into formal reasoning. But it had a fundamental problem: it could not converge to a unique solution. In other words, the system could only remain in an endlessly unfolding dynamic process.

III. Nash’s Revision: Game-Theoretic Equilibrium

Within the framework of game theory, Nash modified this system. He introduced the concept of equilibrium in non-cooperative games. His aim was not merely to remain in non-converging dynamic stability, but to make the system ultimately converge to a unique solution.

Thus, the problem of ordinal logic was corrected:

• Turing showed how infinity could be formally captured;
• Nash, through game-theoretic equilibrium, made this infinite dynamic process approach and converge to a unique solution.

IV. Bitcoin’s Consensus Mechanism

Bitcoin’s consensus mechanism is the concrete realization of this logic:

[C = Nash(OrdinalLogic)]

It is not a predetermined deterministic algorithm, but a convergent mechanism operating within peer-to-peer games. Each node, through peer-to-peer interaction, selects what it recognizes as the longest chain. Eventually, the entire network converges, within infinite dynamics, to a unique ledger.

V. The Essence of Bitcoin

Thus, the essence of Bitcoin can be characterized as:

• Peer-to-peer network: Bitcoin’s information layer, carrying the system’s global knowledge.
• Game-theoretic ordinal logic: Bitcoin’s logical layer, ensuring the system ultimately converges to a unique solution.
  

The combination of the two makes Bitcoin the first peer-to-peer game network in human history to converge to unique consensus within infinite dynamics.

Conclusion

If Turing defined the boundaries of formal systems, and Nash provided the logic of game-theoretic convergence, then Bitcoin is the fusion and realization of both their ideas in reality.

It is not merely a currency, but a super-formal system: Within peer-to-peer relations, through game-theoretic mechanisms, it transforms the non-converging infinite into a unique and stable order.