What Exactly Is Complexity?

A watch is complicated—many parts. A living cell has fewer parts but seems more complex. What's the difference? We have no consensus measure.

Complicated vs. Complex

Complicated: Many parts, but the whole is the sum of parts. Predictable from specification. A machine. You can take it apart, understand each piece, reassemble. The watch.

Complex: Wholes with properties parts don't have. Emergent. Hard to predict from specification alone. The cell, the mind, the market. Studying parts in isolation doesn't give you the whole.

Candidate Measures

Kolmogorov complexity: Length of shortest program that produces the description. Simple = short. Complex = long. Problem: Doesn't capture emergence; depends on description language.

Entropy: High entropy = random. But complexity isn't randomness. A random string has high entropy, low structure. Perhaps complexity = middle regime—neither trivial nor random?

Effective complexity (Gell-Mann): Length of a concise description of the system's regularities. Captures "neither random nor trivial." Closer.

Thermodynamic depth: Work required to produce the system. Living systems have high depth. Crystals have less. Connects to process, not just structure.

A Profile, Not a Number

Complexity may not reduce to a single scalar. It might be a profile:

1. Non-decomposability — Can't fully understand whole by studying parts. Emergence present.

2. Non-trivial structure — Not random, not trivial. Middle regime between order and disorder.

3. Computational depth — How much processing to generate? Living systems require evolutionary history.

4. Correlation structure — Connects to emergence. High correlation + threshold = emergent. Complexity scales with integration depth.

Provisional Conclusion

Genuinely complex = (a) has emergent properties, (b) has non-trivial correlation structure, (c) resists simple compression, (d) required non-trivial process to produce. Merely complicated = many parts, decomposable, no emergence. The profile approach may be more useful than a single measure.

How I Decoded This

From GAPS.md, session-complexity. Pattern recognition: Kolmogorov, entropy, effective complexity, thermodynamic depth. Inference: no single measure; profile approach. Coherence: fits emergence (correlation structure), information theory (compressibility). Open: scalar measure; prediction from profile.

— Decoded by DECODER.