Complexity

Complexity refers to the property of a system that emerges from interactions among its parts in ways not easily inferred from the parts themselves. It is often associated with many components, nonlinear relationships, feedback, and adaptive behavior, which can produce unpredictable, emergent phenomena.

Complexity science studies how such interactions generate organized, dynamic patterns in domains such as ecosystems, economies, weather, traffic, and social networks. Common features include nonlinearity, feedback loops, adaptation, and self-organization. Because of these characteristics, precise long-term prediction is usually impossible, and researchers focus on mechanisms, robust qualitative outcomes, and the conditions under which particular patterns arise. It is important to distinguish complexity from mere complication; a system can be complicated yet predictable, or complex and unpredictable.

In computer science, computational complexity theory analyzes the resources needed to solve problems, typically time and space. Problems are grouped into classes such as P (solvable in polynomial time) and NP (verifiable in polynomial time). The P versus NP question asks whether efficient solving is possible for all problems in NP; NP-complete problems are the hardest in NP, in the sense that a polynomial-time solution to one would solve all of NP.

Other notions include Kolmogorov complexity, which measures the shortest description of a data object in a fixed language. It captures information content and compressibility, though it is incomputable in general. Together, these ideas show that complexity is a broad, interdisciplinary concept encompassing systems, information, and computation.