
Lux(λ) |光尘|空灵|GEB|Jul 31, 2025 12:06
🧵 [1] From Turing Machine to Bitcoin: Constructing a Decidable Irreversible Time System
Why is Bitcoin not Turing complete but able to build global consensus?
It is not a failed formal system, but a meta formal system. Let's dismantle it 👇
[2]
The Bitcoin system structure can be divided into three layers, corresponding to three types of judgment problems:
TX layer: Turing machine system
Block layer: Oracle+Ultra poor Iterative System
Time layer: Axiomatic time system composed of dissipative structures
Three layer collaboration, from undecidable to decidable, and then to embedding irreversible time.
[3]
🧩 TX layer issue: Double Flower
This is a classic undecidable problem, similar to the business version of the "shutdown problem": the system cannot determine whether a certain TX has been executed internally.
The Turing machine system cannot solve this problem internally and must be elevated to a higher level.
[4]
🧠 Task of Block Layer: Conversion+Adjudication
The double flower problem has been transformed into a Block fork problem - a problem of type ∼ x ∃ y.
The formal system cannot solve the problem, it can only be handed over to an "external judge": the oracle system.
This is precisely the core idea of Turing's 1939 paper on ordinal logic systems.
[5]
💡 How does the oracle system make judgments?
Construct higher-order judgment systems through super poor iteration. Each new ruling accumulates on the basis of the previous order, gradually establishing a nearly complete system.
This allows the Block to choose a "trustworthy arbiter" that, although formally non constructible, is executable in operation.
[6]
🔥 Judgment is not equal to time, time needs to be 'physicalized'
Each block determined by the oracle needs to be written into the timeline and become a part of the global history.
This requires the emergence of a third layer system: dissipative structure systems.
[7]
⛓️ Dissipative structure system: an axiomatic system that transforms time into irreversibility
The PoW mechanism constructed by Bitcoin using computing power consumes thermal resources in reality, casting a time stamp every 10 minutes.
Each block is embedded in an irreversible sequence of physical events. Thermodynamics=Axiom.
[8]
📐 The three-layer system corresponds to Turing's three papers:
1936 "computable numbers": Turing machines
1939 "Ordinal Logic System": Oracle and Ultra poor Iteration
1952 "Fundamentals of Morphology": dissipative structures
Bitcoin is not Turing complete, but it combines these three theories into a running philosophical machine.
[9]
🎯 How does Bitcoin solve the "trust" problem?
Double flowers cannot be determined → Rise to fork selection
Fork cannot be constructed → decision given by super poor iteration
Judgment not trusted → Physical embedding with thermodynamic structure
Ultimately, trust=time=calculating irreversible costs.
[10]
🧠 Essence: Bitcoin is a hyper formal system
It does not rely on Turing completeness, but on a three-layer coupled system to achieve:
Computable logic
External arbitration system
Physical time basis
It unifies "computability, selectivity, and temporality" into one machine.
[11]
🚀 We are living in an unprecedented moment:
Bitcoin has constructed a referable irreversible time machine using a formal system, oracle, and thermodynamics.
This is not only a monetary revolution, but also a significant leap in computational philosophy.
Bitcoin Turing Computational Philosophy Time Consensus
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