Bits

Complexity

Terms for talking about complexity, with how settled each one is. Other entries build on these.

Computational complexity sorts problems by the time and memory it takes to solve them. Its best-known open question is P versus NP. The field is settled mathematics with famous unsolved problems.
Complex systems studies many interacting parts that produce behavior none of them has alone. It is an interdisciplinary field that borrows tools from physics, biology, mathematics, and the social sciences, not a single theory. The Santa Fe Institute is its best-known home.

Popular writing slides between the two. Check which one a claim means.

Term	Plain meaning	How settled	On this site
Emergence	A whole has properties its parts lack on their own.	Established as a description	The Ouroboros
Self-organization	Order arises from local interactions, with no one in charge.	Established
Complex adaptive system	A network of parts whose whole cannot be predicted from the parts, and which adapts.	Established framework	Four Floors
Chaos	Exact rules, but so sensitive to starting conditions that the future cannot be predicted in practice.	Established mathematics
Edge of chaos	A zone between order and disorder where adaptive complexity may arise.	Hypothesis	The Ouroboros
Self-organized criticality	A system that tunes itself to a tipping point, like a sandpile that slides in avalanches.	Established model, debated reach
Power law	A heavy-tailed pattern in which rare huge events dominate.	Established mathematics, often misclaimed
Network science	The study of nodes and links, from the internet to brains.	Established
Computational irreducibility	Some outcomes cannot be predicted faster than by running them.	A widely cited framing	Computation
Assembly theory	Measures a thing by the fewest steps it takes to build.	Young, contested	The Ouroboros
Functional information	Grows when selection favors what a system does.	A proposed law	The Ouroboros

Calling anything complicated emergent. Emergence names properties the parts lack, not complication.
Reading chaos as disorder. Chaotic systems follow exact rules. They are unpredictable, not random.
Seeing a power law in any straight line on a log plot. Clauset, Shalizi, and Newman tested published claims and found the power law ruled out in some cases. The usual least-squares fit gives inaccurate estimates.
Mixing the two fields. A problem that is hard to compute is not a complex system.
Using the word as an explanation. “Complexity” can do what “quantum” does in pseudoscience: sound like a reason without being one. Detecting Baloney has the checks.