— On the Essential Relationship Between Time and Space from the Perspective of Information Theory and Computation Theory

1. Time and Space: The Storage Containers of Matter

Time and space are the two fundamental dimensions in which matter exists and unfolds.

Space, as the storage container of matter, preserves definite, consistent, and meaningless Shannon information; time, on the other hand, carries complete, meaningful, yet possibly contradictory Gödel information.

Here, meaning exists within time, while reality exists within space. Space reflects the static form of matter, while time records the dynamic process of matter’s unfolding.

2. The Dual Abstraction and Organic Nature of Information

Shannon information is stored in space, possessing replicability and verifiability—an objective data foundation. By contrast, Gödel information exists in time, carrying complex semantics and dynamic unfolding, difficult to fully restore. It embodies the “organic embedding” of information—embedded within the irreversible flow of time.

This means most information embedded in time has disappeared from the current space and exists only in the historical trajectory of time, while information embedded in space remains complete and easily verifiable.

3. The Division of Labor Between Turing Machines and Transfinite Iteration

Traditional Turing machine theory addresses the processing of definite, restorable Shannon information in space, emphasizing reducibility and computability.

In contrast, ordinal logic systems based on dissipative structures and transfinite iteration break through the limitations of formal systems, handling unpredictable, possibly paradoxical Gödel information in time, reflecting a computational process that is dynamic and not fully restorable.

4. The Time–Space Perspective on NP Problems

In NP problems, the solving process occurs in the time dimension, involving complex, long-sequence computation that cannot be fully reduced to present-space data, requiring intuition and experience. The verification process occurs in the space dimension—results are definite and quickly verifiable, consistent with the Turing machine computational model.

This difference in time–space information storage reveals the fundamental reason why NP problems are hard to solve but easy to verify.

5. The Time–Space Mapping of Bitcoin’s Computational Process

In the Bitcoin system, the process of solving the nonce is stored in the time dimension— a transfinite iteration process of resonating degrees of freedom particles and dissipative structures.

The final determined nonce result, however, is stored in the space dimension, restorable and verifiable through the Turing machine model’s verification mechanism.

Conclusion

Time and space each carry fundamentally different forms of information. The time dimension preserves dynamically unfolding Gödel information, reflecting the complexity and meaning of computational processes; the space dimension preserves definite, restorable Shannon information, reflecting the objectivity and verifiability of computation.

The traditional Turing machine model applies to the processing of space-based information, while transfinite iteration logic based on dissipative structures transcends the limits of time-based information storage.