Principle of Computational Equivalence

The Principle of Computational Equivalence states that all processes following definite rules can be viewed as computations.

This applies to:

• Human-designed algorithms
• Natural phenomena
• Physical processes
• Biological systems

Computational Ceiling

Almost all processes that are not obviously simple achieve the same maximum level of computational sophistication. This means there’s essentially just one “highest level” of computation, and nearly everything complex reaches it.

This upper limit of computational sophistication in our universe acts as a law of nature limiting what computations are possible.

The Paradox

While we can know systems are computationally equivalent, we often can’t predict their behavior without running them step by step. This explains why computational irreducibility exists: when observer and system have equivalent computational power, there’s no shortcut to prediction. The observer must essentially “keep pace” with the system’s evolution.

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Sources

• What if We Had Bigger Brains Imagining Minds Beyond Ours