Abstract

This paper proposes and demonstrates an interdisciplinary formula:

⇒ Distributed resonance of free individuals

⇒ Time irreversibility of dissipative structures

⇒ Security of Bitcoin’s longest chain

The formula establishes a mapping from logical philosophy and physical dissipative structures to cryptocurrency security, revealing the deep computational-philosophy foundation of Bitcoin’s irreversibility.

I. Two Paradigms of Information Storage

The modes of information existence can be divided into two categories:

1. Space Storage
   • Essence: Consistency
   • Logical Basis: Law of the excluded middle (A or Not-A, cannot both hold true)
   • Method: Deduction
   • Computational Model: Turing machine (computable)
   • Mathematical Correspondence: Cantor’s actual infinity (ℵ₀)
2. Time Storage
   • Essence: Completeness, allowing coexistence of contradictions
   • Logical Basis: Does not follow the law of the excluded middle (A and Not-A can both exist within a fuzzy boundary)
   • Method: Induction
   • Computational Model: Beyond Turing machines (non-computable)
   • Mathematical Correspondence: Cantor’s potential infinity (ℵ₁)
     

Conclusion: Time storage contains far more information than space storage, just as the set of non-computable elements is far larger than the set of computable elements.

II. Time Irreversibility and Resonance Mechanism

1. Time Irreversibility
   • Equivalent relation:
   • Past irreversibility ⇔ Future unpredictability
   • If a formal system is fully consistent, it must be reversible; time is irreversible because it cannot be fully formalized.
2. Distributed Resonance of Free Individuals
   • Definition: Parallel action and feedback of independent degrees of freedom at the same moment.
   • Characteristics: Inductive nature, non-computability, sensitivity to chaos (similar to the three-body problem and Poincaré chaos).
3. Dissipative Structure Mapping
   • In an open system, the resonance of free individuals manifests as a dissipative structure:
   • Spontaneous emergence of low-entropy order from high-entropy chaos, with irreversible directionality.

III. Computational Philosophy of Bitcoin’s Longest Chain

1. Miners as Free Individuals
   • Each miner is an independent computational degree of freedom.
   • Competing simultaneously to solve a new block forms a distributed resonance.
2. Collapse from Time Storage to Space Storage
   • Global parallel computation (time storage, the non-computable possibility space)
   • → One miner finds a block and broadcasts it (instantaneous collapse into consistent space storage).
3. Irreversibility of the Longest Chain Rule
   • Repeated “resonance → collapse” produces an ordered sequence of blocks.
   • Once a block enters the longest chain, it embeds the irreversible history of the entire network’s resonance.

IV. Unified Formula and Interdisciplinary Mapping

⇒ Distributed resonance of free individuals

⇒ Time irreversibility of dissipative structures

⇒ Security of the longest chain

• Left End (Driving Force): Distributed resonance of free individuals provides computational entropy and unpredictability.
• Middle (Evolutionary Law): Dissipative structures convert chaotic energy into directional time flow.
• Right End (Result): Security of the longest chain — the irreversible history of Bitcoin.

Conclusion

Bitcoin’s irreversibility does not stem solely from cryptographic puzzles but harnesses a deeper physical-philosophical mechanism: It transforms the distributed resonance of free individuals into the time irreversibility of dissipative structures and solidifies it into immutable history through the longest chain rule.

This process is a continuous cycle from chaotic induction (time storage) to deductive solidification (space storage).