Complexity Limits & Algorithmic Tradeoffs

Primes about the irreducible costs and limits of computation and problem-solving: measures and conservation of complexity (essential vs. accidental complexity, conservation of complexity, requisite variety), and theorems bounding what algorithms can achieve (no free lunch theorem, bounded rationality, garbage in garbage out).

12 primes in this family — primes that sit near one another in abstraction space (k-means over structural-signature embeddings). Each is shown with its short description.

• Accidental Vs Essential Complexity — A system's complexity splits into the irreducible difficulty of the problem and the removable difficulty introduced by the chosen approach.
• Algorithm — Step-by-step problem-solving procedure.
• Bounded Rationality — Limited decision capacity.
• Commensurability — Diverse values expressed in common metric enabling comparison.
• Complexity — Measures system intricacy.
• Complexity (Time/Space) — Resource scaling with input size.
• Garbage In, Garbage Out — The quality of a transformation's output is bounded above by the quality of its inputs; no downstream sophistication can repair defects already present in the input.
• Law of Conservation of Complexity — Every problem has an irreducible complexity floor that design can shift between parties or moments but cannot reduce below the floor.
• Measurement and Disturbance — Obtaining information while minimizing measurement perturbation.
• No Free Lunch Theorem — Averaged over all problem instances, no search, optimization, or learning procedure outperforms any other; a method's value is the match between its inductive bias and the problems it faces.
• Requisite Variety — Match environmental complexity.
• Self-Organization — Order without central control.