The GEB team proposes a structural model of an "Organic Computer", which is essentially an integration of three computational systems. Each system processes a different type of information and together they form a computational whole capable of self-evolution, meaningful expression, and experiential memory.

I. Turing Machine: Formal Systems and Shannon Information

• ‍Functional Role: Processes 100% computable and unambiguous logical propositions; belongs to deductive reasoning within formal systems.‍
• Type of Information: Shannon Information – bit sequences that are "meaningless but restorable".‍
• Storage Method: Can be fully restored and reconstructed using binary encoding; forms the foundation of modern computers.‍
• Human Equivalent: The rational system – handles problems with clear structure like language, logic, and mathematics.

II. Oracle Machine: Dissipative Structures and Gödelian Information

• ‍Functional Role: Handles "undecidable problems" that Turing Machines cannot solve (e.g., double-spending, paradoxes, self-reference) by offering "judgments" via external intuitive choices or environmental evaluations.‍
• Type of Information: Gödelian Information – judgments that are "meaningful but cannot be formally restored".‍
• Storage Method: Not stored within the system but jointly recorded by the environment and experience in an irreversible trajectory of time evolution.‍
• Human Equivalent: The intuitive system – often manifested as “inspiration”, “epiphany”, or “situational resonance”.‍
• Key Mechanism: Dissipative Structures provide a way to embed the Oracle Machine into the physical evolution of time, granting it maximum trustworthiness.

III. Transfinite Iterative Ordinal Logic System: The Bridge and Translator

• ‍Functional Role: Coordinates information exchange and trust transfer between the Turing Machine and the Oracle Machine, serving as the translator and logical recursor between formal and non-formal judgment systems.‍
• Role Explanation:
  
  • At the logical level: Constructs ordinal transfinite iterative structures, gradually introducing higher levels of judgment standards, bringing the system closer to completeness.‍
  • At the storage and reasoning level: Establishes mechanisms for the transformation and labeling between Shannon Information (repeatable) and Gödelian Information (one-time events).

• ‍Key Value: Provides a layered, extensible temporal structure for uncertain intuitive judgments (Oracle Machine), allowing partial formalization and cooperation with Turing Machines.

Mapping Structures of the Human Mind

Illustrative Analogies

• Turing Machine is like keyboard input: each keystroke is clear, definite, and reproducible.
• Oracle Machine is like a flash of inspiration: emotionally triggered, internally emergent, and non-repeatable.
• Transfinite Iteration System is like the long-term evolution of memory and thinking patterns: allowing certain inspirations to be “triggered” and “recognized” in the future.

IV. Expression in Mechanical Systems: NP Problems and Asymmetric Interaction

In machine systems, Gödelian Information can be abstractly expressed through the asymmetric structure of NP problems:

• Solution verification is easy (Turing Machine can do it),
• But solution selection originates from undecidable sources (Oracle-like behavior).

If a system can select and continually evolve along one of multiple asymmetric paths, it shows the system has embedded Oracle-like structures into a dissipative history.

The blockchain consensus process in the Bitcoin system—especially Proof of Work (PoW)—is a real-world evolutionary expression of such structures.

Conclusion

An Organic Computer is a “nature-like” system that integrates deterministic Turing reasoning, non-deterministic Oracle judgment, and evolutionary hierarchy constructed through transfinite iteration. It can process formal logical determinism, respond to real-world indeterminism, and build multi-level mechanisms for storing and translating meaning across time. It is not a “mechanical imitation of humans,” but a re-discovery of the formal foundation of the mind within nature.