Preface

Understanding Bitcoin’s core is not just about computing power and hash values. Hidden behind it is a chain of reasoning in computational philosophy: Time storage vs. space storage → Consistency vs. completeness → Individual/collective resonance → Dissipative structure → Longest chain irreversibility.

Today, let’s try to break this chain apart.

I. Time Storage ≠ Space Storage

Information storage can generally be divided into two categories:

• Space storage: Static snapshots, emphasizing consistency and determinacy
• Time storage: Dynamic sequences, pursuing completeness, even if contradictions are included
  

In simple terms:

• Space storage is like a frozen photo
• Time storage is more like a complete video

II. Consistency and Completeness: Two Extremes That Cannot Coexist

In a closed system, consistency and completeness cannot both be achieved.

• Space storage → Has consistency but can only reflect one slice of time storage, lacking the full picture
• Time storage → Has completeness but inevitably contains conflicting information
  

This is not only a conclusion from information theory but also a norm in distributed systems.

III. When Multiple Free Individuals Resonate Simultaneously

In a distributed environment, if multiple free and independent individuals compute the same problem at the same time, they are likely to arrive at opposite results (A and Not-A).

• In space, this appears as “inconsistency”
• In time, it means “completeness expansion”
  

Similar phenomena in physics include the three-body problem, resonance problems, and non-integrable systems—unpredictable, yet real.

IV. Dissipative Structures and the Irreversibility of Time

Dissipative structures tell us that time has a unidirectional nature, and this irreversibility comes from:

• Free individuals resonating in parallel → Branches spreading that cannot be traced back
• Once a branch is established → An unchangeable snapshot is formed in space storage
• In terms of information theory, this is the accumulation of entropy and Gödel information

V. PoW: Writing Irreversibility into the Blockchain

Bitcoin’s Proof-of-Work (PoW) mechanism solidifies the irreversibility of time as an on-chain fact.

• Miners (individuals) search for a nonce in parallel (resonance process)
• Finding a valid nonce → Forms a block (space storage snapshot)
• Block joins the longest chain → Advances the global time sequence
  

This process relies not only on computational difficulty but also on the irreversible evolution of distributed resonance and dissipative structures.

VI. Core Conclusion

Distributed resonance of free individuals ⇒ Time irreversibility of dissipative structures ⇒ Security of the longest chain

This is the physical and information-theoretical foundation of Bitcoin’s security, as well as the key to understanding the intertwining of time and space in complex systems.

VII. Closing

The irreversibility of Bitcoin’s longest chain is not merely a mathematical problem but the intersection of information theory, distributed computing, and statistical physics. Time and space were originally two separate worlds. The longest chain is the stitching that sews them together.