
Lux(λ) |光尘|空灵|GEB|Jul 29, 2025 13:30
🧵 Bitcoin is not a system that operates in time, but a structure that constructs "irreversible time" to arbitrate undecidable problems. It consists of three systems: formal system, ordinal logic system, and dissipative time system. This article will gradually reveal this triple structure. 👇
1/
The transaction layer (TX) of Bitcoin is a formal system.
It can process all computable business logic with 100% accuracy - signatures, balances, scripts, etc.
But it encountered the only 'undecidable problem':
👉 Double Spending
2/
Shuanghua is a self referential problem:
The system needs to determine whether a transaction has been used, but this determination itself depends on the overall state of the system, which is asynchronous and local in propagation.
This is precisely the projection of G ö del's incompleteness in reality.
3/
Bitcoin does not attempt to solve double spending at the transaction layer.
It adopts a structural translation strategy:
👉 Transform the double flower problem into a chain fork selection problem.
Different miners package different transactions to generate legitimate but conflicting blockchain branches.
4/
This is where the second system appears:
👉 Turing's ordinal logic system
This is the structure in Turing's doctoral thesis, used to deal with undecidable problems within formal systems.
Core technique:
Introduction of Oracle
Continuous Axiomization through Ultra poor Iteration
5/
In Bitcoin, the corresponding structure is as follows:
Oracle Machine → The current longest chain is regarded as truth
Ultra poor iteration → difficulty adjustment+chain growth
Turing degree → mining difficulty represents the evolution of system judgment power
Bitcoin approaches determinism through structured evolution, rather than being completed in one go.
6/
The question is: How does the oracle (longest chain) itself have credibility?
Relying solely on 'longer chain' is a probabilistic description.
Bitcoin has introduced a third system for this purpose:
👉 Axiomatic time system
7/
This is not abstract time, but physical time constructed by dissipative structures:
Each block generation requires an irreversible SHA256 double hash operation.
This process is random, monotonous, and cannot be traced back, forming a chain like "timestamp" structure.
8/
These three layers of system form a closed loop:
Formal system: computable business (Turing machine)
Ordinal logic system: undecidable problem (oracle+super poor iteration)
Dissipative time system: Axiomatic time as the physical anchor of oracles
Ultimately forming a self-sustaining structure that resolves disagreements.
9/
Key Terminology Comparison Table 👇:
Bitcoin mechanism Turing logic corresponds to TX script system Turing machine (formal system) Chain fork problem undecidable problem Longest chain rule Oracle selection difficulty adjustment Ultra poor iteration Computing power evolution Turing degree improvement Timestamp axiomatic product
10/
📌 Summary:
Bitcoin is not a Turing complete 'language system',
But rather a Turing ordinal logic driven 'time generation system':
It solves undecidable problems through continuous computing power input, axiomatic evolution, and the real time of dissipative structures.
⏳ Time is the ultimate judge of Bitcoin.
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