complex systems ---> one made up of a large number of parts that interact in a non-simple way

main points of this chapter:

• frequency with which complexity takes the form of hierarchy
• relationship between the structure of a complex system and the time required for it to emerge through evolutionary processes
• compare clues in problem solving to stable intermediate forms (e.g.: the defect safe, reuse in object-oriented systems)
• relationship between complex systems and their descriptions ---> there is no conservation law of complexity

• watches of a 1000 parts - interruptions by phone calls
• Tempus: interruptions lead to restart from scratch
• Hora: subassemblies of ten (at each level) ---> 111 subassemblies
• the evolution of complex forms from simple elements depends critically on the numbers and distribution of potential stable intermediate forms

• problem solving requires selective trial and error
• cues signaling progress (partial results, stepping stones) = stable intermediate forms
• safe with 10 dials, each with 100 possible settings

working: 100¹⁰ settings ---> average: 5 * 10¹¹

defect: 10 * 50 = 500 trials

• Definition: the interactions among the subsystems are weak but not negligible
• hierarchical systems have the property of near decomposability: intracomponent linkages are generally stronger than intercomponent linkages
• examples: the search in computer science for systems architectures which allow to build nearly decomposable systems (further example: structure of learning environments, e.g., "skiing")
• near decomposability and comprehensibility (a "chicken and egg problem"): are we able to understand the world because it is hierarchic -- or does it appear hierarchic because those aspects of it which are not elude our understanding and observation?

if a complex structure is completely unredundant (i.e. if no aspect of its structure can be inferred from any other) then it is its own simplest description

forms of redundancy:

• hierarchic systems are composed of only a few different kind of subsystems (restricted alphabet of elementary terms)
• hierarchic systems are often nearly decomposable
• "recoding" ---> the redundancy that is present but unobvious in the structure of a complex can often be made patent
• the task of science is to make use of the world's redundancy to describe that world simply ---> the descriptions are part of the "Sciences of the Artificial"

• state descriptions:

a circle is the locus of all points equidistant from a given point

examples: pictures, blueprints, diagrams, chemical structural formulas

characterize the world as sensed

• process descriptions:

to construct a circle, rotate a compass with one arm fixed until the other arm has returned to its starting point

examples: recipes, differential equations, equations for chemical reactions

characterize the world as acted upon

• declarative ("what") versus procedural ("how") controversy in Artificial Intelligence

• the individual organism in its development goes through stages that resembles some of its ancestral forms
• one way to solve a complex problem is to reduce it to a problem previously solved
• catalogs, case-based memories
• phylogeny: domain-oriented design environments (e.g., computer network design)
• ontogeny: individual design project (e.g., the computer network here at CU Boulder)