Complexity Theory Fundamentals
Common Properties
Simple components or agents (simple relatively to whole system)
Nonlinear interactions among components
No central control
Emergent behaviors
hierarchical organization
information processing
collective outcomes of the system, need to be evaluated at the system level
bilogical organisms, organs, body, societies
system as a whole gaining info about the info, using the info to make decisions as a whole, components don't get info nor take decision, they work only on the system as awhole, collectively.
dynamics
how the systems change in time, complex dynamics
evolution and learning
darwinian sense, adaptation, systems improve themselves
Disciplines
Information: the study of represenation, sysmbols, and communication
Computation: the study of how systems process information an act on the results
Dynamics: the study of continually changing structure and behavior of systems
Evolution: the study of how systems adapt to constantly changing environments
Core Goals
Development of mathematical and computational tools that lead to cross-disciplinary insights into complex systems
Example: study of ants, to explain city behavior
Methodologies
General Theory
Experimental work
Theoretical work
Computer simulation
Definitions
Diference definitions to different analysis and systems
Shannon Information
Fractal Dimensions
See PDF with 42 definitions
Measures of Complexity
a non--exhaustive list
Seth Lloyd
See PDF
WEAVER1947
Problems of Simplicity: a few variables
Pressure and Tempearature
Current, Resistanc, and Voltage
Population vs. Time
Problems of Disorganized Complexity: billions or trillions of variables
Laws of temperature and pressure as emerging from trillions of disorganized air molecules, Science of avrages, Statistical Mechanics, Assumes little interaction among variables
Problems of organized complexity: moderate number of variables
Strong, nonlinear interactions among variables
"Problems which involve dealing simultaneously with sizable number of factors which are interrelated into an organic whole" Notion of emergence behavior