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Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 1/107
Overview of Complex SystemsPrinciples of Complex Systems
Course CSYS/MATH 300, Fall, 2009
Prof. Peter Dodds
Dept. of Mathematics & StatisticsCenter for Complex Systems :: Vermont Advanced Computing Center
University of Vermont
Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 2/107
OutlineCourse Information
Major CentersResourcesProjectsTopics
FundamentalsComplexityEmergenceSelf-OrganizationModelingStatistical MechanicsUniversalitySymmetry BreakingThe big theoryTools and TechniquesMeasures of Complexity
References
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 3/107
Basics:
I Instructor: Prof. Peter DoddsI Lecture room and meeting times:
307 Lafayette, Tuesday and Thursday, 10:00 am to11:30 pm
I Office: 203 Lord House, 16 Colchester AvenueI E-mail: pdodds@uvm.eduI Website:
http://www.uvm.edu/ pdodds/teaching/2009-08UVM-300/ (�)I Suggested Texts:
I “Critical Phenomena in Natural Sciences: Chaos,Fractals, Selforganization and Disorder: Conceptsand Tools” by Didier Sornette [12].
I “Critical Mass: How One Thing Leads to Another” byPhilip Ball [3]
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 4/107
Admin:
I CSYS/MATH 300 is one of two core requirements forUVM’sCertificate of Graduate Study in Complex Systems (�).
I Five course requirement.
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 5/107
Admin:
Paper products:
1. Outline
Office hours:I Tuesday: 2:30 pm to 4:30 pm
Thursday: 11:30 am to 12:30 pmRm 203, Math Building
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 5/107
Admin:
Paper products:
1. Outline
Office hours:I Tuesday: 2:30 pm to 4:30 pm
Thursday: 11:30 am to 12:30 pmRm 203, Math Building
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 6/107
Grading breakdown:
I Projects/talks (55%)—Students will work onsemester-long projects. Students will develop aproposal in the first few weeks of the course whichwill be discussed with the instructor for approval.Details: 15% for the first talk, 20% for the final talk,and 20% for the written project.
I Assignments (40%)—All assignments will be ofequal weight and there will be three or four of them.
I General attendance/Class participation (5%)
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 7/107
How grading works:
Questions are worth 3 points according to thefollowing scale:
I 3 = correct or very nearly so.I 2 = acceptable but needs some revisions.I 1 = needs major revisions.I 0 = way off.
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 8/107
Schedule:Week # (dates) Tuesday Thursday1 (9/1, 9/3) guest lecture:
Josh Bongardlecture
2 (9/8, 9/10) lecture lecture3 (9/15, 9/17) lecture lecture4 (9/22, 9/24) Project
presentationsProjectpresentations
5 (9/28, 10/1) lecture lecture6 (10/6, 10/8) lecture lecture7 (10/13, 10/15) lecture lecture8 (10/20, 10/22) lecture lecture9 (10/27, 10/29) lecture lecture10 (11/3, 11/5) lecture lecture11 (11/10, 11/12) lecture lecture12 (11/17, 11/19) lecture lecture13 (11/24, 11/26) Thanksgiving Thanksgiving14 (12/1, 12/3) lecture lecture15 (12/8, 12/10) Project
PresentationsProjectPresentations
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 9/107
Important dates:
1. Classes run from Monday, August 31 to Wednesday,December 9.
2. Add/Drop, Audit, Pass/No Pass deadline—Monday,September 14.
3. Last day to withdraw—Friday, November 6.4. Reading and exam period—Thursday, December 10
to Friday, December 18.
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 10/107
More stuff:
Do check your zoo account for updates regarding thecourse.
Academic assistance: Anyone who requires assistance inany way (as per the ACCESS program or due to athleticendeavors), please see or contact me as soon aspossible.
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 11/107
OutlineCourse Information
Major CentersResourcesProjectsTopics
FundamentalsComplexityEmergenceSelf-OrganizationModelingStatistical MechanicsUniversalitySymmetry BreakingThe big theoryTools and TechniquesMeasures of Complexity
References
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 12/107
Centers
I Santa Fe Institute (SFI)I New England Complex Systems Institute (NECSI)I Michigan’s Center for the Study of Complex Systems
(CSCS (�))I Northwestern Institute on Complex Systems
(NICO (�))I Also: Indiana, Davis, Brandeis, University of Illinois,
Duke, Warsaw, Melbourne, ...,I UVM’s Complex System Center (�)
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 13/107
OutlineCourse Information
Major CentersResourcesProjectsTopics
FundamentalsComplexityEmergenceSelf-OrganizationModelingStatistical MechanicsUniversalitySymmetry BreakingThe big theoryTools and TechniquesMeasures of Complexity
References
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 14/107
Books:
I “Modeling Complex Systems” by Nino Boccara [6]
I “Critical Phenomena in Natural Sciences” by DidierSornette [12]
I “Complex Adaptive Systems: An Introduction toComputational Models of Social Life,” by John Millerand Scott Page [10]
I “Micromotives and Macrobehavior” by ThomasSchelling [11]
I “Social Network Analysis” by Stanley Wassermanand Katherine Faust [14]
I “Handbook of Graphs and Networks” by StefanBornholdt and Hans Georg Schuster [7]
I “Dynamics of Complex Systems” by YaneerBar-Yam [4]
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 14/107
Books:
I “Modeling Complex Systems” by Nino Boccara [6]
I “Critical Phenomena in Natural Sciences” by DidierSornette [12]
I “Complex Adaptive Systems: An Introduction toComputational Models of Social Life,” by John Millerand Scott Page [10]
I “Micromotives and Macrobehavior” by ThomasSchelling [11]
I “Social Network Analysis” by Stanley Wassermanand Katherine Faust [14]
I “Handbook of Graphs and Networks” by StefanBornholdt and Hans Georg Schuster [7]
I “Dynamics of Complex Systems” by YaneerBar-Yam [4]
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 14/107
Books:
I “Modeling Complex Systems” by Nino Boccara [6]
I “Critical Phenomena in Natural Sciences” by DidierSornette [12]
I “Complex Adaptive Systems: An Introduction toComputational Models of Social Life,” by John Millerand Scott Page [10]
I “Micromotives and Macrobehavior” by ThomasSchelling [11]
I “Social Network Analysis” by Stanley Wassermanand Katherine Faust [14]
I “Handbook of Graphs and Networks” by StefanBornholdt and Hans Georg Schuster [7]
I “Dynamics of Complex Systems” by YaneerBar-Yam [4]
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 14/107
Books:
I “Modeling Complex Systems” by Nino Boccara [6]
I “Critical Phenomena in Natural Sciences” by DidierSornette [12]
I “Complex Adaptive Systems: An Introduction toComputational Models of Social Life,” by John Millerand Scott Page [10]
I “Micromotives and Macrobehavior” by ThomasSchelling [11]
I “Social Network Analysis” by Stanley Wassermanand Katherine Faust [14]
I “Handbook of Graphs and Networks” by StefanBornholdt and Hans Georg Schuster [7]
I “Dynamics of Complex Systems” by YaneerBar-Yam [4]
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 14/107
Books:
I “Modeling Complex Systems” by Nino Boccara [6]
I “Critical Phenomena in Natural Sciences” by DidierSornette [12]
I “Complex Adaptive Systems: An Introduction toComputational Models of Social Life,” by John Millerand Scott Page [10]
I “Micromotives and Macrobehavior” by ThomasSchelling [11]
I “Social Network Analysis” by Stanley Wassermanand Katherine Faust [14]
I “Handbook of Graphs and Networks” by StefanBornholdt and Hans Georg Schuster [7]
I “Dynamics of Complex Systems” by YaneerBar-Yam [4]
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 14/107
Books:
I “Modeling Complex Systems” by Nino Boccara [6]
I “Critical Phenomena in Natural Sciences” by DidierSornette [12]
I “Complex Adaptive Systems: An Introduction toComputational Models of Social Life,” by John Millerand Scott Page [10]
I “Micromotives and Macrobehavior” by ThomasSchelling [11]
I “Social Network Analysis” by Stanley Wassermanand Katherine Faust [14]
I “Handbook of Graphs and Networks” by StefanBornholdt and Hans Georg Schuster [7]
I “Dynamics of Complex Systems” by YaneerBar-Yam [4]
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 14/107
Books:
I “Modeling Complex Systems” by Nino Boccara [6]
I “Critical Phenomena in Natural Sciences” by DidierSornette [12]
I “Complex Adaptive Systems: An Introduction toComputational Models of Social Life,” by John Millerand Scott Page [10]
I “Micromotives and Macrobehavior” by ThomasSchelling [11]
I “Social Network Analysis” by Stanley Wassermanand Katherine Faust [14]
I “Handbook of Graphs and Networks” by StefanBornholdt and Hans Georg Schuster [7]
I “Dynamics of Complex Systems” by YaneerBar-Yam [4]
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 15/107
Useful Resources:
I Complexity Digest:http://www.comdig.org (�)
I Cosma Shalizi’s notebooks:http://www.cscs.umich.edu/ crshalizi/notebooks/ (�)
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 16/107
OutlineCourse Information
Major CentersResourcesProjectsTopics
FundamentalsComplexityEmergenceSelf-OrganizationModelingStatistical MechanicsUniversalitySymmetry BreakingThe big theoryTools and TechniquesMeasures of Complexity
References
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 17/107
Projects
I Semester-long projects.I Develop proposal in first few weeks.I May range from novel research to investigation of an
established area of complex systems.I We’ll go through a list of possible projects soon.
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 18/107
Projects
The narrative hierarchy—explaining things on manyscales:
I 1 to 3 word encapsulation, a soundbite,I a sentence/title,I a few sentences,I a paragraph,I a short paper,I a long paper,I a chapter,I a book,I . . .
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 19/107
OutlineCourse Information
Major CentersResourcesProjectsTopics
FundamentalsComplexityEmergenceSelf-OrganizationModelingStatistical MechanicsUniversalitySymmetry BreakingThe big theoryTools and TechniquesMeasures of Complexity
References
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 20/107
Topics:
Measures of complexity
Scaling phenomena
I Zipf’s lawI Non-Gaussian statistics and power law distributionsI Sample mechanisms for power law distributionsI Organisms and organizationsI Scaling of social phenomena: crime, creativity, and
consumption.I Renormalization techniques
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 21/107
Topics:
Multiscale complex systems
I Hierarchies and scalingI ModularityI Form and context in design
Complexity in abstract models
I The game of lifeI Cellular automataI Chaos and order—creation and maintenance
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 22/107
Topics:
Integrity of complex systems
I Generic failure mechanismsI Network robustnessI Highly optimized tolerance: Robustness and fragilityI Normal accidents and high reliability theory
Complex networks
I Small-world networksI Scale-free networks
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 23/107
Topics:
Collective behavior and contagion in social systems
I Percolation and phase transitionsI Disease spreading modelsI Schelling’s model of segregationI Granovetter’s model of imitationI Contagion on networksI Herding phenomenaI CooperationI Wars and conflicts
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 24/107
Topics:
Large-scale Social patterns
I Movement of individuals
Collective decision making
I Theories of social choiceI The role of randomness and chanceI Systems of votingI JuriesI Success inequality: superstardom
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 25/107
Topics:
InformationI Search in networked systems (e.g., the WWW, social
systems)I Search on scale-free networksI Knowledge trees, metadata and tagging
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 26/107
OutlineCourse Information
Major CentersResourcesProjectsTopics
FundamentalsComplexityEmergenceSelf-OrganizationModelingStatistical MechanicsUniversalitySymmetry BreakingThe big theoryTools and TechniquesMeasures of Complexity
References
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 27/107
Definitions
Complex: (Latin = with + fold/weave (com + plex))
Adjective:
1. Made up of multiple parts; intricate or detailed.2. Not simple or straightforward.
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 28/107
Definitions
Possible properties of a Complex System:
I Many interacting agents or entitiesI Relationships are nonlinearI Presence of feedbackI Complex systems are open (out of equilibrium)I Presence of memoryI Modular/multiscale/hierarchical structureI Evidence of emergence propertiesI Evidence of self-organization
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 28/107
Definitions
Possible properties of a Complex System:
I Many interacting agents or entitiesI Relationships are nonlinearI Presence of feedbackI Complex systems are open (out of equilibrium)I Presence of memoryI Modular/multiscale/hierarchical structureI Evidence of emergence propertiesI Evidence of self-organization
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 28/107
Definitions
Possible properties of a Complex System:
I Many interacting agents or entitiesI Relationships are nonlinearI Presence of feedbackI Complex systems are open (out of equilibrium)I Presence of memoryI Modular/multiscale/hierarchical structureI Evidence of emergence propertiesI Evidence of self-organization
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 28/107
Definitions
Possible properties of a Complex System:
I Many interacting agents or entitiesI Relationships are nonlinearI Presence of feedbackI Complex systems are open (out of equilibrium)I Presence of memoryI Modular/multiscale/hierarchical structureI Evidence of emergence propertiesI Evidence of self-organization
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 28/107
Definitions
Possible properties of a Complex System:
I Many interacting agents or entitiesI Relationships are nonlinearI Presence of feedbackI Complex systems are open (out of equilibrium)I Presence of memoryI Modular/multiscale/hierarchical structureI Evidence of emergence propertiesI Evidence of self-organization
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 28/107
Definitions
Possible properties of a Complex System:
I Many interacting agents or entitiesI Relationships are nonlinearI Presence of feedbackI Complex systems are open (out of equilibrium)I Presence of memoryI Modular/multiscale/hierarchical structureI Evidence of emergence propertiesI Evidence of self-organization
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 28/107
Definitions
Possible properties of a Complex System:
I Many interacting agents or entitiesI Relationships are nonlinearI Presence of feedbackI Complex systems are open (out of equilibrium)I Presence of memoryI Modular/multiscale/hierarchical structureI Evidence of emergence propertiesI Evidence of self-organization
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 28/107
Definitions
Possible properties of a Complex System:
I Many interacting agents or entitiesI Relationships are nonlinearI Presence of feedbackI Complex systems are open (out of equilibrium)I Presence of memoryI Modular/multiscale/hierarchical structureI Evidence of emergence propertiesI Evidence of self-organization
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 28/107
Definitions
Possible properties of a Complex System:
I Many interacting agents or entitiesI Relationships are nonlinearI Presence of feedbackI Complex systems are open (out of equilibrium)I Presence of memoryI Modular/multiscale/hierarchical structureI Evidence of emergence propertiesI Evidence of self-organization
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 29/107
Examples
Examples of Complex Systems:
I human societiesI cellsI organismsI ant coloniesI weather systemsI ecosystems
I animal societiesI disease ecologiesI brainsI social insectsI geophysical systemsI the world wide web
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 30/107
Examples
Relevant fields:
I PhysicsI EconomicsI SociologyI PsychologyI Information
Sciences
I CognitiveSciences
I BiologyI EcologyI GeociencesI Geography
I MedicalSciences
I SystemsEngineering
I ComputerScience
I . . .
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 31/107
Definitions
Complicated versus Complex.
I Complicated: Mechanical watches, airplanes, ...I Engineered systems can be made to be highly robust
but not adaptable.I But engineered systems can become complex
(power grid, planes).I They can also fail spectacularly.I Explicit distinction: Complex Adaptive Systems.
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 31/107
Definitions
Complicated versus Complex.
I Complicated: Mechanical watches, airplanes, ...I Engineered systems can be made to be highly robust
but not adaptable.I But engineered systems can become complex
(power grid, planes).I They can also fail spectacularly.I Explicit distinction: Complex Adaptive Systems.
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 31/107
Definitions
Complicated versus Complex.
I Complicated: Mechanical watches, airplanes, ...I Engineered systems can be made to be highly robust
but not adaptable.I But engineered systems can become complex
(power grid, planes).I They can also fail spectacularly.I Explicit distinction: Complex Adaptive Systems.
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 31/107
Definitions
Complicated versus Complex.
I Complicated: Mechanical watches, airplanes, ...I Engineered systems can be made to be highly robust
but not adaptable.I But engineered systems can become complex
(power grid, planes).I They can also fail spectacularly.I Explicit distinction: Complex Adaptive Systems.
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 31/107
Definitions
Complicated versus Complex.
I Complicated: Mechanical watches, airplanes, ...I Engineered systems can be made to be highly robust
but not adaptable.I But engineered systems can become complex
(power grid, planes).I They can also fail spectacularly.I Explicit distinction: Complex Adaptive Systems.
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Definitions
Nino Boccara in Modeling Complex Systems:[6] “... there is no universally accepted definition of acomplex system ... most researchers would describe asystem of connected agents that exhibits an emergentglobal behavior not imposed by a central controller, butresulting from the interactions between the agents.”
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Frame 33/107
Definitions
The Wikipedia on Complex Systems:“Complexity science is not a single theory: itencompasses more than one theoretical framework andis highly interdisciplinary, seeking the answers to somefundamental questions about living, adaptable,changeable systems.”
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Frame 34/107
Definitions
Philip Ball in Critical Mass:[3] “...complexity theory seeks to understand how orderand stability arise from the interactions of manycomponents according to a few simple rules.”
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Definitions
Cosma Shalizi:“The "sciences of complexity" are very much a potpourri,and while the name has some justification—chaoticmotion seems more complicated than harmonicoscillation, for instance—I think the fact that it is moredignified than "neat nonlinear nonsense" has not beenthe least reason for its success.—That opinion wasn’texactly changed by working at the Santa Fe Institute forfive years.”
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Definitions
Steve Strogatz in Sync:
“... every decade or so, a grandiose theory comes along,bearing similar aspirations and often brandishing anominous-sounding C-name. In the 1960s it wascybernetics. In the ’70s it was catastrophe theory. Thencame chaos theory in the ’80s and complexity theory inthe ’90s.”
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Frame 37/107
Outreach
08/27/2007 09:17 PMComplexity Society
Page 1 of 1http://www.complexity-society.com/
MembershipTo join TCS apply here.
Complexity Society NewsletterThe August 2007 edition is nowavailable.
Complexity DigestThe current issue of ComplexityDigest 2007.29 is now availableon-line.
Recent Event:Summer School in ComplexityScience organised by ImperialCollege, London,Wye College, Kent, UK.8–17th July 2007.
Forthcoming Events:ECCS’07 European Conferenceon Complex Systems,Dresden,Germany.1-5th October 2007.
New PaperThe Fractal Imagination: NewResources for ConceptualisingCreativity.
Journal"Emergence: Complexity &Organization (ECO)", A journalof research, theory and practiceon Organisations as complexsystems.
HOME ABOUTUS CONTACTS NEWS &
EVENTS LINKS FAQs JOURNAL& PAPERS
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Welcome to theCOMPLEXITY SOCIETY
"The Application of Complexity Science to Human Affairs"
The Complexity Society provides a focal point for people in theUK interested in complexity. It is a community that usescomplexity science to rethink and reinterpret all aspects of theworld in which we live and work.
Its core values are OPENNESS, EQUALITY and DIVERSITY.
Open to all, open to ideas, open in process and activities Equality, egalitarian, non-hierarchical, participative Diverse, connecting and embracing a wide range of views,respecting differences
The society objectives are to promote the theory of complexity ineducation, government, the health service and business as wellas the beneficial application of complexity in a wide variety ofsocial, economic, scientific and technological contexts such assources of competitive advantage, business clusters andknowledge management.
Complexity includes ideas such as complex adaptive systems,self-organisation, co-evolution, agent based computer models,chaos, networks, emergence and fractals.
Membership is open to all and current members include peoplefrom universities, business, and government fundedorganisations.
©2007 The Complexity Society Privacy Policy Disclaimer
Page last updated: 13 August, 2007
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Frame 38/107
Outreach
“The society objectives are to promote the theory ofcomplexity in education, government, the health serviceand business as well as the beneficial application ofcomplexity in a wide variety of social, economic, scientificand technological contexts such as sources ofcompetitive advantage, business clusters and knowledgemanagement.”
“Complexity includes ideas such as complex adaptivesystems, self-organisation, co-evolution, agent basedcomputer models, chaos, networks, emergence, andfractals.”
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Frame 38/107
Outreach
“The society objectives are to promote the theory ofcomplexity in education, government, the health serviceand business as well as the beneficial application ofcomplexity in a wide variety of social, economic, scientificand technological contexts such as sources ofcompetitive advantage, business clusters and knowledgemanagement.”
“Complexity includes ideas such as complex adaptivesystems, self-organisation, co-evolution, agent basedcomputer models, chaos, networks, emergence, andfractals.”
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Frame 39/107
OutlineCourse Information
Major CentersResourcesProjectsTopics
FundamentalsComplexityEmergenceSelf-OrganizationModelingStatistical MechanicsUniversalitySymmetry BreakingThe big theoryTools and TechniquesMeasures of Complexity
References
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Frame 40/107
Definitions
The Wikipedia on Emergence:
“In philosophy, systems theory and the sciences,emergence refers to the way complex systems andpatterns arise out of a multiplicity of relatively simpleinteractions.
... emergence is central to the physics ofcomplex systems and yet very controversial.”
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Frame 40/107
Definitions
The Wikipedia on Emergence:
“In philosophy, systems theory and the sciences,emergence refers to the way complex systems andpatterns arise out of a multiplicity of relatively simpleinteractions. ... emergence is central to the physics ofcomplex systems and yet very controversial.”
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Frame 41/107
Emergence:
Examples:
I Fundamental particles ⇒ Life, the Universe, andEverything
I Genes ⇒ OrganismsI Brains ⇒ ThoughtsI Fireflies ⇒ Synchronized Flashes [videos]I People ⇒ World Wide WebI People ⇒ Behavior in games not specified by rules
(e.g., bluffing in poker)I People ⇒ Religion
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Frame 42/107
Emergence
Thomas Schelling (Economist/Nobelist):
[youtube] (�)
I “Micromotives andMacrobehavior” [11]
I SegregationI Wearing hockey helmetI Seating choices
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Frame 43/107
Emergence
Friedrich Hayek (�)(Economist/Philospher/Nobelist):
I Markets, legal systems, political systems areemergent and not designed.
I ‘Taxis’ = made order (by God, Sovereign,Government, ...)
I ‘Cosmos’ = grown orderI Archetypal limits of hierarchical and decentralized
structures.I Hierarchies arise once problems are solved.I Decentralized structures help solve problems.I Dewey Decimal System versus tagging.
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Frame 43/107
Emergence
Friedrich Hayek (�)(Economist/Philospher/Nobelist):
I Markets, legal systems, political systems areemergent and not designed.
I ‘Taxis’ = made order (by God, Sovereign,Government, ...)
I ‘Cosmos’ = grown orderI Archetypal limits of hierarchical and decentralized
structures.I Hierarchies arise once problems are solved.I Decentralized structures help solve problems.I Dewey Decimal System versus tagging.
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Frame 43/107
Emergence
Friedrich Hayek (�)(Economist/Philospher/Nobelist):
I Markets, legal systems, political systems areemergent and not designed.
I ‘Taxis’ = made order (by God, Sovereign,Government, ...)
I ‘Cosmos’ = grown orderI Archetypal limits of hierarchical and decentralized
structures.I Hierarchies arise once problems are solved.I Decentralized structures help solve problems.I Dewey Decimal System versus tagging.
Overview
CourseInformationMajor Centers
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Topics
FundamentalsComplexity
Emergence
Self-Organization
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Symmetry Breaking
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References
Frame 43/107
Emergence
Friedrich Hayek (�)(Economist/Philospher/Nobelist):
I Markets, legal systems, political systems areemergent and not designed.
I ‘Taxis’ = made order (by God, Sovereign,Government, ...)
I ‘Cosmos’ = grown orderI Archetypal limits of hierarchical and decentralized
structures.I Hierarchies arise once problems are solved.I Decentralized structures help solve problems.I Dewey Decimal System versus tagging.
Overview
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Topics
FundamentalsComplexity
Emergence
Self-Organization
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Tools and Techniques
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Frame 43/107
Emergence
Friedrich Hayek (�)(Economist/Philospher/Nobelist):
I Markets, legal systems, political systems areemergent and not designed.
I ‘Taxis’ = made order (by God, Sovereign,Government, ...)
I ‘Cosmos’ = grown orderI Archetypal limits of hierarchical and decentralized
structures.I Hierarchies arise once problems are solved.I Decentralized structures help solve problems.I Dewey Decimal System versus tagging.
Overview
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Topics
FundamentalsComplexity
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Measures of Complexity
References
Frame 43/107
Emergence
Friedrich Hayek (�)(Economist/Philospher/Nobelist):
I Markets, legal systems, political systems areemergent and not designed.
I ‘Taxis’ = made order (by God, Sovereign,Government, ...)
I ‘Cosmos’ = grown orderI Archetypal limits of hierarchical and decentralized
structures.I Hierarchies arise once problems are solved.I Decentralized structures help solve problems.I Dewey Decimal System versus tagging.
Overview
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Frame 44/107
Emergence
James Coleman in Foundations of Social Theory :Weber
CapitalismProtestantReligiousDoctrine
EconomicBehavior
Values
Societal level
Individual level
Coleman
I Understand macrophenomena arises frommicrobehavior which in turn depends onmacrophenomena. [8]
I More on Coleman here (�).
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Frame 44/107
Emergence
James Coleman in Foundations of Social Theory :Weber
CapitalismProtestantReligiousDoctrine
EconomicBehavior
Values
Societal level
Individual level
Coleman
I Understand macrophenomena arises frommicrobehavior which in turn depends onmacrophenomena. [8]
I More on Coleman here (�).
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Frame 45/107
Emergence
Higher complexity:
I Many system scales (or levels)that interact with each other.
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Frame 46/107
Emergence
Even mathematics: [9]
Gödel’s Theorem (roughly):we can’t prove every theorem that’s true.
Suggests a strong form of emergence:
Some phenomena cannot be formally deduced fromelementary aspects of a system.
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Frame 46/107
Emergence
Even mathematics: [9]
Gödel’s Theorem (roughly):we can’t prove every theorem that’s true.
Suggests a strong form of emergence:
Some phenomena cannot be formally deduced fromelementary aspects of a system.
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Frame 47/107
Emergence
The idea of emergence is rather old...
“The whole is more than the sum of its parts” –Aristotle
Philosopher G. H. Lewes firstused the word explicity in 1875.
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Frame 47/107
Emergence
The idea of emergence is rather old...
“The whole is more than the sum of its parts” –Aristotle
Philosopher G. H. Lewes firstused the word explicity in 1875.
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Frame 47/107
Emergence
The idea of emergence is rather old...
“The whole is more than the sum of its parts” –Aristotle
Philosopher G. H. Lewes firstused the word explicity in 1875.
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Frame 48/107
Definitions
There appears to be two types of emergence:
Weak emergence:System-level phenomena is different from that of itsconstituent parts yet can be connected theoretically.
Strong emergence:System-level phenomena fundamentally cannot bededuced from how parts interact.
(Strong emergence is what Mark Bedau calls magic...)
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Frame 48/107
Definitions
There appears to be two types of emergence:
Weak emergence:System-level phenomena is different from that of itsconstituent parts yet can be connected theoretically.
Strong emergence:System-level phenomena fundamentally cannot bededuced from how parts interact.
(Strong emergence is what Mark Bedau calls magic...)
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Frame 48/107
Definitions
There appears to be two types of emergence:
Weak emergence:System-level phenomena is different from that of itsconstituent parts yet can be connected theoretically.
Strong emergence:System-level phenomena fundamentally cannot bededuced from how parts interact.
(Strong emergence is what Mark Bedau calls magic...)
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Frame 48/107
Definitions
There appears to be two types of emergence:
Weak emergence:System-level phenomena is different from that of itsconstituent parts yet can be connected theoretically.
Strong emergence:System-level phenomena fundamentally cannot bededuced from how parts interact.(Strong emergence is what Mark Bedau calls magic...)
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Frame 49/107
Definitions
Complex Systems enthusiasts often decry reductionistapproaches . . .
But reductionism seems to be misunderstood.
Reductionist techniques can explain weak emergence(e.g., phase transitions).
‘A Miracle Occurs’ explains strong emergence.
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Frame 49/107
Definitions
Complex Systems enthusiasts often decry reductionistapproaches . . .
But reductionism seems to be misunderstood.
Reductionist techniques can explain weak emergence(e.g., phase transitions).
‘A Miracle Occurs’ explains strong emergence.
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Frame 49/107
Definitions
Complex Systems enthusiasts often decry reductionistapproaches . . .
But reductionism seems to be misunderstood.
Reductionist techniques can explain weak emergence(e.g., phase transitions).
‘A Miracle Occurs’ explains strong emergence.
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Frame 49/107
Definitions
Complex Systems enthusiasts often decry reductionistapproaches . . .
But reductionism seems to be misunderstood.
Reductionist techniques can explain weak emergence(e.g., phase transitions).
‘A Miracle Occurs’ explains strong emergence.
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Frame 50/107
The emergence of taste:
I Molecules ⇒ Ingredients ⇒ TasteI See Michael Pollan’s article on nutritionism (�) in the
New York Times, January 28, 2007.
nytimes.com
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Frame 51/107
Reductionism
Reductionism and food:I Pollan: “even the simplest food is a hopelessly
complex thing to study, a virtual wilderness ofchemical compounds, many of which exist incomplex and dynamic relation to one another...”
I “So ... break the thing down into its component partsand study those one by one, even if that meansignoring complex interactions and contexts, as wellas the fact that the whole may be more than, or justdifferent from, the sum of its parts. This is what wemean by reductionist science.”
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Frame 51/107
Reductionism
Reductionism and food:I Pollan: “even the simplest food is a hopelessly
complex thing to study, a virtual wilderness ofchemical compounds, many of which exist incomplex and dynamic relation to one another...”
I “So ... break the thing down into its component partsand study those one by one, even if that meansignoring complex interactions and contexts, as wellas the fact that the whole may be more than, or justdifferent from, the sum of its parts. This is what wemean by reductionist science.”
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Frame 51/107
Reductionism
Reductionism and food:I Pollan: “even the simplest food is a hopelessly
complex thing to study, a virtual wilderness ofchemical compounds, many of which exist incomplex and dynamic relation to one another...”
I “So ... break the thing down into its component partsand study those one by one, even if that meansignoring complex interactions and contexts, as wellas the fact that the whole may be more than, or justdifferent from, the sum of its parts. This is what wemean by reductionist science.”
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Frame 52/107
Reductionism
I “people don’t eat nutrients, they eat foods, and foodscan behave very differently than the nutrients theycontain.”
I Studies suggest diets high in fruits and vegetableshelp prevent cancer.
I So... find the nutrients responsible and eat more ofthem
I But “in the case of beta carotene ingested as asupplement, scientists have discovered that itactually increases the risk of certain cancers. Bigoops.”
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Frame 52/107
Reductionism
I “people don’t eat nutrients, they eat foods, and foodscan behave very differently than the nutrients theycontain.”
I Studies suggest diets high in fruits and vegetableshelp prevent cancer.
I So... find the nutrients responsible and eat more ofthem
I But “in the case of beta carotene ingested as asupplement, scientists have discovered that itactually increases the risk of certain cancers. Bigoops.”
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Frame 52/107
Reductionism
I “people don’t eat nutrients, they eat foods, and foodscan behave very differently than the nutrients theycontain.”
I Studies suggest diets high in fruits and vegetableshelp prevent cancer.
I So... find the nutrients responsible and eat more ofthem
I But “in the case of beta carotene ingested as asupplement, scientists have discovered that itactually increases the risk of certain cancers. Bigoops.”
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Frame 52/107
Reductionism
I “people don’t eat nutrients, they eat foods, and foodscan behave very differently than the nutrients theycontain.”
I Studies suggest diets high in fruits and vegetableshelp prevent cancer.
I So... find the nutrients responsible and eat more ofthem
I But “in the case of beta carotene ingested as asupplement, scientists have discovered that itactually increases the risk of certain cancers. Bigoops.”
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Frame 53/107
Reductionism
Thyme’s known antioxidants:4-Terpineol, alanine, anethole, apigenin,ascorbic acid, beta carotene, caffeicacid, camphene, carvacrol, chlorogenicacid, chrysoeriol, eriodictyol, eugenol,ferulic acid, gallic acid,gamma-terpinene isochlorogenic acid,isoeugenol, isothymonin, kaempferol,labiatic acid, lauric acid, linalyl acetate,luteolin, methionine, myrcene, myristicacid, naringenin, oleanolic acid,p-coumoric acid, p-hydroxy-benzoicacid, palmitic acid, rosmarinic acid,selenium, tannin, thymol, tryptophan,ursolic acid, vanillic acid.
[cnn.com]
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Frame 54/107
Reductionism
“It would be great to know how this all works, but in themeantime we can enjoy thyme in the knowledge that itprobably doesn’t do any harm (since people have beeneating it forever) and that it may actually do some good(since people have been eating it forever) and that even ifit does nothing, we like the way it tastes.”
Gulf between theory and practice: baseball andbumblebees.
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Frame 54/107
Reductionism
“It would be great to know how this all works, but in themeantime we can enjoy thyme in the knowledge that itprobably doesn’t do any harm (since people have beeneating it forever) and that it may actually do some good(since people have been eating it forever) and that even ifit does nothing, we like the way it tastes.”
Gulf between theory and practice: baseball andbumblebees.
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The big theory
Tools and Techniques
Measures of Complexity
References
Frame 55/107
OutlineCourse Information
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FundamentalsComplexity
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Tools and Techniques
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Frame 56/107
Definitions
Self-Organization
“Self-organization is a process in which the internalorganization of a system, normally an open system,increases in complexity without being guided or managedby an outside source.”(also: Self-assembly)
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Frame 57/107
Definitions
Emergence but no Self-Organization?
H20 molecules ⇒ Water
Random walks ⇒ Normal distributions
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Frame 57/107
Definitions
Emergence but no Self-Organization?
H20 molecules ⇒ Water
Random walks ⇒ Normal distributions
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Frame 57/107
Definitions
Emergence but no Self-Organization?
H20 molecules ⇒ Water
Random walks ⇒ Normal distributions
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Frame 58/107
Definitions
Self-organization but no Emergence?
Water above and near the freezing point.
Emergence may be limited to a low scale of a system.
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Frame 58/107
Definitions
Self-organization but no Emergence?
Water above and near the freezing point.
Emergence may be limited to a low scale of a system.
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Frame 58/107
Definitions
Self-organization but no Emergence?
Water above and near the freezing point.
Emergence may be limited to a low scale of a system.
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Frame 59/107
Economics
Eric Beinhocker (The Origin of Wealth): [5]
Dynamic:
I Complexity Economics: Open, dynamic, non-linearsystems, far from equilibrium
I Traditional Economics: Closed, static, linear systemsin equilibrium
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Frame 60/107
Economics
Agents:
I Complexity Economics:Modelled individually; use inductive rules of thumb tomake decisions; have incomplete information; aresubject to errors and biases; learn to adapt over time
I Traditional Economics: Modelled collectively; usecomplex deductive calculations to make decisions;have complete information; make no errors and haveno biases; have no need for learning or adaptation(are already perfect)
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Frame 61/107
Economics
Networks:I Complexity Economics: Explicitly model bi-lateral
interactions between individual agents; networks ofrelationships change over time
I Traditional Economics: Assume agents only interactindirectly through market mechanisms (e.g. auctions)
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Frame 62/107
Economics
Emergence:
I Complexity Economics: No distinction betweenmicro/macro economics; macro patterns areemergent result of micro level behaviours andinteractions
I Traditional Economics: Micro-and macroeconomicsremain separate disciplines
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Frame 63/107
Economics
Evolution:I Complexity Economics:
The evolutionary process of differentiation, selectionand amplification provides the system with noveltyand is responsible for its growth in order andcomplexity
I Traditional Economics:No mechanism for endogenously creating novelty, orgrowth in order and complexity
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Frame 64/107
Upshot
I The central concepts Complexity and Emergence arenot precisely defined.
I There is as yet no general theory of ComplexSystems.
I But the problems exist...Complex (Adaptive) Systems abound...
I Framing: Thinking about systems is essential today.I We use whatever tools we need.
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References
Frame 64/107
Upshot
I The central concepts Complexity and Emergence arenot precisely defined.
I There is as yet no general theory of ComplexSystems.
I But the problems exist...Complex (Adaptive) Systems abound...
I Framing: Thinking about systems is essential today.I We use whatever tools we need.
Overview
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Topics
FundamentalsComplexity
Emergence
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Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 64/107
Upshot
I The central concepts Complexity and Emergence arenot precisely defined.
I There is as yet no general theory of ComplexSystems.
I But the problems exist...Complex (Adaptive) Systems abound...
I Framing: Thinking about systems is essential today.I We use whatever tools we need.
Overview
CourseInformationMajor Centers
Resources
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Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 64/107
Upshot
I The central concepts Complexity and Emergence arenot precisely defined.
I There is as yet no general theory of ComplexSystems.
I But the problems exist...Complex (Adaptive) Systems abound...
I Framing: Thinking about systems is essential today.I We use whatever tools we need.
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 64/107
Upshot
I The central concepts Complexity and Emergence arenot precisely defined.
I There is as yet no general theory of ComplexSystems.
I But the problems exist...Complex (Adaptive) Systems abound...
I Framing: Thinking about systems is essential today.I We use whatever tools we need.
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 65/107
OutlineCourse Information
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FundamentalsComplexityEmergenceSelf-OrganizationModelingStatistical MechanicsUniversalitySymmetry BreakingThe big theoryTools and TechniquesMeasures of Complexity
References
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 66/107
Models
Nino Boccara in Modeling Complex Systems:
“Finding the emergent global behavior of a large systemof interacting agents using methods is usually hopeless,and researchers therefore must rely on computer-basedmodels.”
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Frame 67/107
Approaches
Nino Boccara in Modeling Complex Systems:
Focus is on dynamical systems models:I differential and difference equation modelsI chaos theoryI cellular automataI networksI power-law distributions
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References
Frame 67/107
Approaches
Nino Boccara in Modeling Complex Systems:
Focus is on dynamical systems models:I differential and difference equation modelsI chaos theoryI cellular automataI networksI power-law distributions
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FundamentalsComplexity
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Tools and Techniques
Measures of Complexity
References
Frame 67/107
Approaches
Nino Boccara in Modeling Complex Systems:
Focus is on dynamical systems models:I differential and difference equation modelsI chaos theoryI cellular automataI networksI power-law distributions
Overview
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Topics
FundamentalsComplexity
Emergence
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Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 67/107
Approaches
Nino Boccara in Modeling Complex Systems:
Focus is on dynamical systems models:I differential and difference equation modelsI chaos theoryI cellular automataI networksI power-law distributions
Overview
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Topics
FundamentalsComplexity
Emergence
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Modeling
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Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 67/107
Approaches
Nino Boccara in Modeling Complex Systems:
Focus is on dynamical systems models:I differential and difference equation modelsI chaos theoryI cellular automataI networksI power-law distributions
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 67/107
Approaches
Nino Boccara in Modeling Complex Systems:
Focus is on dynamical systems models:I differential and difference equation modelsI chaos theoryI cellular automataI networksI power-law distributions
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 68/107
Models
Philip Ball in Critical Mass:[3] “... very often what passes today for ‘complexityscience’ is really something much older, dressed up infashionable apparel. The main themes in complexitytheory have been studied for more than a hundred yearsby physicists who evolved a tool kit of concepts andtechniques to which complexity studies have barelyadded a handful of new items.”
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Frame 69/107
Old School
I Statistical Mechanics is “a science of collectivebehavior.”
I Simple rules give rise to collective phenomena.
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Frame 70/107
OutlineCourse Information
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FundamentalsComplexityEmergenceSelf-OrganizationModelingStatistical MechanicsUniversalitySymmetry BreakingThe big theoryTools and TechniquesMeasures of Complexity
References
Overview
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FundamentalsComplexity
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Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 71/107
Statistical mechanics
The Ising Model (�):
I Idealized model of a ferromagnet.I Each atom is assumed to have a local spin that can
be up or down: Si = ±1.I Spins are assumed arranged on a lattice
(e.g. square lattice in 2-d).I In isolation, spins like to align with each other.I Increasing temperature breaks these alignments.I The drosophila of statistical mechanics.
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Frame 71/107
Statistical mechanics
The Ising Model (�):
I Idealized model of a ferromagnet.I Each atom is assumed to have a local spin that can
be up or down: Si = ±1.I Spins are assumed arranged on a lattice
(e.g. square lattice in 2-d).I In isolation, spins like to align with each other.I Increasing temperature breaks these alignments.I The drosophila of statistical mechanics.
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Topics
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Statistical Mechanics
Universality
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Tools and Techniques
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References
Frame 71/107
Statistical mechanics
The Ising Model (�):
I Idealized model of a ferromagnet.I Each atom is assumed to have a local spin that can
be up or down: Si = ±1.I Spins are assumed arranged on a lattice
(e.g. square lattice in 2-d).I In isolation, spins like to align with each other.I Increasing temperature breaks these alignments.I The drosophila of statistical mechanics.
Overview
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Topics
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Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 71/107
Statistical mechanics
The Ising Model (�):
I Idealized model of a ferromagnet.I Each atom is assumed to have a local spin that can
be up or down: Si = ±1.I Spins are assumed arranged on a lattice
(e.g. square lattice in 2-d).I In isolation, spins like to align with each other.I Increasing temperature breaks these alignments.I The drosophila of statistical mechanics.
Overview
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Resources
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Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 71/107
Statistical mechanics
The Ising Model (�):
I Idealized model of a ferromagnet.I Each atom is assumed to have a local spin that can
be up or down: Si = ±1.I Spins are assumed arranged on a lattice
(e.g. square lattice in 2-d).I In isolation, spins like to align with each other.I Increasing temperature breaks these alignments.I The drosophila of statistical mechanics.
Overview
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Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 71/107
Statistical mechanics
The Ising Model (�):
I Idealized model of a ferromagnet.I Each atom is assumed to have a local spin that can
be up or down: Si = ±1.I Spins are assumed arranged on a lattice
(e.g. square lattice in 2-d).I In isolation, spins like to align with each other.I Increasing temperature breaks these alignments.I The drosophila of statistical mechanics.
Overview
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Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
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Frame 72/107
Ising model
2-d Ising model simulation:http://www.pha.jhu.edu/ javalab/ising/ising.html (�)
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Frame 73/107
Phase diagrams
Qualitatively distinct macro states.
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Frame 74/107
Phase diagrams
Oscillons, bacteria, traffic, snowflakes, ...
Umbanhowar et al., Nature, 1996 [13]
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Frame 75/107
Phase diagrams
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Frame 76/107
Phase diagrams
W0 = initial wetness, S0 = initial nutrient supply
http://math.arizona.edu/~lega/HydroBact.html
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Frame 77/107
Ising model
Analytic issues:
I 1-d: simple (Ising & Lenz, 1925)I 2-d: hard (Onsager, 1944)I 3-d: extremely hard...I 4-d and up: simple.
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Frame 77/107
Ising model
Analytic issues:
I 1-d: simple (Ising & Lenz, 1925)I 2-d: hard (Onsager, 1944)I 3-d: extremely hard...I 4-d and up: simple.
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Frame 77/107
Ising model
Analytic issues:
I 1-d: simple (Ising & Lenz, 1925)I 2-d: hard (Onsager, 1944)I 3-d: extremely hard...I 4-d and up: simple.
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Frame 77/107
Ising model
Analytic issues:
I 1-d: simple (Ising & Lenz, 1925)I 2-d: hard (Onsager, 1944)I 3-d: extremely hard...I 4-d and up: simple.
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Frame 78/107
Statistics
I Origins of Statistical Mechanics are in the studies ofpeople... (Maxwell and co.)
I Now physicists are using their techniques to studyeverything else including people...
I See Philip Ball’s “Critical Mass” [3]
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Frame 78/107
Statistics
I Origins of Statistical Mechanics are in the studies ofpeople... (Maxwell and co.)
I Now physicists are using their techniques to studyeverything else including people...
I See Philip Ball’s “Critical Mass” [3]
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Frame 78/107
Statistics
I Origins of Statistical Mechanics are in the studies ofpeople... (Maxwell and co.)
I Now physicists are using their techniques to studyeverything else including people...
I See Philip Ball’s “Critical Mass” [3]
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Frame 79/107
OutlineCourse Information
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The big theory
Tools and Techniques
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Frame 80/107
Universality
Universality:The property that the macroscopic aspects of a systemdo not depend sensitively on the system’s details.
I The Central Limit Theorem.I Lattice gas models of fluid flow.
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Frame 80/107
Universality
Universality:The property that the macroscopic aspects of a systemdo not depend sensitively on the system’s details.
I The Central Limit Theorem.I Lattice gas models of fluid flow.
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Frame 81/107
Universality
I Sometimes details don’t matter too much.I Many-to-one mapping from micro to macroI Suggests not all possible behaviors are available
at higher levels of complexity.
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Frame 81/107
Universality
I Sometimes details don’t matter too much.I Many-to-one mapping from micro to macroI Suggests not all possible behaviors are available
at higher levels of complexity.
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Frame 81/107
Universality
I Sometimes details don’t matter too much.I Many-to-one mapping from micro to macroI Suggests not all possible behaviors are available
at higher levels of complexity.
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Frame 82/107
Fluids
Fluid flow is modeled by the Navier-Stokes equations.
Works for many very different fluids:
I The atmosphere, oceans, blood, galaxies, the earth’smantle...
and ball bearings on lattices...?
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Frame 82/107
Fluids
Fluid flow is modeled by the Navier-Stokes equations.
Works for many very different fluids:
I The atmosphere, oceans, blood, galaxies, the earth’smantle...
and ball bearings on lattices...?
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Frame 83/107
Lattice gas models
Collision rules in 2-d on a hexagonal lattice:
Lattice matters...No ‘good’ lattice in 3-d.
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Frame 83/107
Lattice gas models
Collision rules in 2-d on a hexagonal lattice:
Lattice matters...No ‘good’ lattice in 3-d.
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Frame 84/107
OutlineCourse Information
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FundamentalsComplexityEmergenceSelf-OrganizationModelingStatistical MechanicsUniversalitySymmetry BreakingThe big theoryTools and TechniquesMeasures of Complexity
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Modeling
Statistical Mechanics
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The big theory
Tools and Techniques
Measures of Complexity
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Frame 85/107
Symmetry Breaking
Philip Anderson’s paper: “More is Different.”Science (1972). [1]
I Argues against idea that the only real scientists arethose working on the fundamental laws.
I Symmetry breaking ⇒ different laws/rules at differentscales...
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Frame 86/107
Symmetry Breaking
“Elementary entities of science X obey the laws ofscience Y”
I XI solid state or
many-body physicsI chemistry
I molecular biologyI cell biologyI ·I psychologyI social sciences
I YI elementary particle
physicsI solid state
many-body physicsI chemistryI molecular biologyI ·I physiologyI psychology
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Tools and Techniques
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Frame 87/107
Symmetry Breaking
Anderson:[the more we know about] “fundamental laws, the lessrelevance they seem to have to the very real problems ofthe rest of science.”
Scale and complexity thwart the constructionisthypothesis.
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Frame 87/107
Symmetry Breaking
Anderson:[the more we know about] “fundamental laws, the lessrelevance they seem to have to the very real problems ofthe rest of science.”
Scale and complexity thwart the constructionisthypothesis.
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FundamentalsComplexity
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Symmetry Breaking
The big theory
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References
Frame 88/107
Symmetry Breaking
I Page 291–292 of Sornette [12]:Renormalization ⇔ Anderson’s hierarchy.
I But Anderson’s hierarchy is not a simple one: therules change.
I Crucial dichotomy between evolving systemsfollowing stochastic paths that lead toinevitable or particular destinations (states).
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Frame 88/107
Symmetry Breaking
I Page 291–292 of Sornette [12]:Renormalization ⇔ Anderson’s hierarchy.
I But Anderson’s hierarchy is not a simple one: therules change.
I Crucial dichotomy between evolving systemsfollowing stochastic paths that lead toinevitable or particular destinations (states).
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 88/107
Symmetry Breaking
I Page 291–292 of Sornette [12]:Renormalization ⇔ Anderson’s hierarchy.
I But Anderson’s hierarchy is not a simple one: therules change.
I Crucial dichotomy between evolving systemsfollowing stochastic paths that lead toinevitable or particular destinations (states).
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
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References
Frame 89/107
More is different:
from http://www.xkcd.com
Overview
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FundamentalsComplexity
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Frame 90/107
OutlineCourse Information
Major CentersResourcesProjectsTopics
FundamentalsComplexityEmergenceSelf-OrganizationModelingStatistical MechanicsUniversalitySymmetry BreakingThe big theoryTools and TechniquesMeasures of Complexity
References
Overview
CourseInformationMajor Centers
Resources
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Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 91/107
A real science of complexity:
A real theory of everything:
1. Is not just about the ridiculously small stuff...2. It’s about the increase of complexity
Symmetry breaking/Accidents of history
vs. Universality
I Second law of thermodynamics: we’re toast in thelong run.
I So how likely is the local complexification of structurewe enjoy?
I Another key: randomness can give order.
Overview
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Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 91/107
A real science of complexity:
A real theory of everything:
1. Is not just about the ridiculously small stuff...2. It’s about the increase of complexity
Symmetry breaking/Accidents of history
vs. Universality
I Second law of thermodynamics: we’re toast in thelong run.
I So how likely is the local complexification of structurewe enjoy?
I Another key: randomness can give order.
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 91/107
A real science of complexity:
A real theory of everything:
1. Is not just about the ridiculously small stuff...2. It’s about the increase of complexity
Symmetry breaking/Accidents of history
vs. Universality
I Second law of thermodynamics: we’re toast in thelong run.
I So how likely is the local complexification of structurewe enjoy?
I Another key: randomness can give order.
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 91/107
A real science of complexity:
A real theory of everything:
1. Is not just about the ridiculously small stuff...2. It’s about the increase of complexity
Symmetry breaking/Accidents of history
vs. Universality
I Second law of thermodynamics: we’re toast in thelong run.
I So how likely is the local complexification of structurewe enjoy?
I Another key: randomness can give order.
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 91/107
A real science of complexity:
A real theory of everything:
1. Is not just about the ridiculously small stuff...2. It’s about the increase of complexity
Symmetry breaking/Accidents of history
vs. Universality
I Second law of thermodynamics: we’re toast in thelong run.
I So how likely is the local complexification of structurewe enjoy?
I Another key: randomness can give order.
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 91/107
A real science of complexity:
A real theory of everything:
1. Is not just about the ridiculously small stuff...2. It’s about the increase of complexity
Symmetry breaking/Accidents of history
vs. Universality
I Second law of thermodynamics: we’re toast in thelong run.
I So how likely is the local complexification of structurewe enjoy?
I Another key: randomness can give order.
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 91/107
A real science of complexity:
A real theory of everything:
1. Is not just about the ridiculously small stuff...2. It’s about the increase of complexity
Symmetry breaking/Accidents of history
vs. Universality
I Second law of thermodynamics: we’re toast in thelong run.
I So how likely is the local complexification of structurewe enjoy?
I Another key: randomness can give order.
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 92/107
OutlineCourse Information
Major CentersResourcesProjectsTopics
FundamentalsComplexityEmergenceSelf-OrganizationModelingStatistical MechanicsUniversalitySymmetry BreakingThe big theoryTools and TechniquesMeasures of Complexity
References
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 93/107
Tools and techniques:
I Differential equations, difference equations, linearalgebra.
I Statistical techniques for comparisons anddescriptions.
I Methods from statistical mechanics and computerscience.
I Computer modeling.
Key advance:
I Representation of complex interaction patterns asdynamic networks.
I The driver: Massive amounts of DataI More later...
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 93/107
Tools and techniques:
I Differential equations, difference equations, linearalgebra.
I Statistical techniques for comparisons anddescriptions.
I Methods from statistical mechanics and computerscience.
I Computer modeling.
Key advance:
I Representation of complex interaction patterns asdynamic networks.
I The driver: Massive amounts of DataI More later...
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 93/107
Tools and techniques:
I Differential equations, difference equations, linearalgebra.
I Statistical techniques for comparisons anddescriptions.
I Methods from statistical mechanics and computerscience.
I Computer modeling.
Key advance:
I Representation of complex interaction patterns asdynamic networks.
I The driver: Massive amounts of DataI More later...
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 93/107
Tools and techniques:
I Differential equations, difference equations, linearalgebra.
I Statistical techniques for comparisons anddescriptions.
I Methods from statistical mechanics and computerscience.
I Computer modeling.
Key advance:
I Representation of complex interaction patterns asdynamic networks.
I The driver: Massive amounts of DataI More later...
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 93/107
Tools and techniques:
I Differential equations, difference equations, linearalgebra.
I Statistical techniques for comparisons anddescriptions.
I Methods from statistical mechanics and computerscience.
I Computer modeling.
Key advance:
I Representation of complex interaction patterns asdynamic networks.
I The driver: Massive amounts of DataI More later...
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 93/107
Tools and techniques:
I Differential equations, difference equations, linearalgebra.
I Statistical techniques for comparisons anddescriptions.
I Methods from statistical mechanics and computerscience.
I Computer modeling.
Key advance:
I Representation of complex interaction patterns asdynamic networks.
I The driver: Massive amounts of DataI More later...
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 93/107
Tools and techniques:
I Differential equations, difference equations, linearalgebra.
I Statistical techniques for comparisons anddescriptions.
I Methods from statistical mechanics and computerscience.
I Computer modeling.
Key advance:
I Representation of complex interaction patterns asdynamic networks.
I The driver: Massive amounts of DataI More later...
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 93/107
Tools and techniques:
I Differential equations, difference equations, linearalgebra.
I Statistical techniques for comparisons anddescriptions.
I Methods from statistical mechanics and computerscience.
I Computer modeling.
Key advance:
I Representation of complex interaction patterns asdynamic networks.
I The driver: Massive amounts of DataI More later...
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 94/107
The absolute basics:
Science in three steps:
1. Find interesting/meaningful/important phenomenainvolving spectacular amounts of data.
2. Describe what you see.3. Explain it.
Beware your assumptionsDon’t use tools/models because they’re there, or becauseeveryone else does...
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 94/107
The absolute basics:
Science in three steps:
1. Find interesting/meaningful/important phenomenainvolving spectacular amounts of data.
2. Describe what you see.3. Explain it.
Beware your assumptionsDon’t use tools/models because they’re there, or becauseeveryone else does...
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 94/107
The absolute basics:
Science in three steps:
1. Find interesting/meaningful/important phenomenainvolving spectacular amounts of data.
2. Describe what you see.3. Explain it.
Beware your assumptionsDon’t use tools/models because they’re there, or becauseeveryone else does...
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 94/107
The absolute basics:
Science in three steps:
1. Find interesting/meaningful/important phenomenainvolving spectacular amounts of data.
2. Describe what you see.3. Explain it.
Beware your assumptionsDon’t use tools/models because they’re there, or becauseeveryone else does...
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 95/107
OutlineCourse Information
Major CentersResourcesProjectsTopics
FundamentalsComplexityEmergenceSelf-OrganizationModelingStatistical MechanicsUniversalitySymmetry BreakingThe big theoryTools and TechniquesMeasures of Complexity
References
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 96/107
Measures of Complexity
How do we measure the complexity of a system?
Overview
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Tools and Techniques
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References
Frame 97/107
Measures of Complexity
(1) Entropy: number of microstates that could underlie aparticular macrostate.
I Used in information theory and statisticalmechanics/thermodynamics.
I Measures how uncertain we are about the details ofa system.
I Problem: Randomness maximizes entropy, perfectorder minimizes.
I Our idea of ‘maximal complexity’ is somewhere inbetween...
Overview
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FundamentalsComplexity
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Modeling
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Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 97/107
Measures of Complexity
(1) Entropy: number of microstates that could underlie aparticular macrostate.
I Used in information theory and statisticalmechanics/thermodynamics.
I Measures how uncertain we are about the details ofa system.
I Problem: Randomness maximizes entropy, perfectorder minimizes.
I Our idea of ‘maximal complexity’ is somewhere inbetween...
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 97/107
Measures of Complexity
(1) Entropy: number of microstates that could underlie aparticular macrostate.
I Used in information theory and statisticalmechanics/thermodynamics.
I Measures how uncertain we are about the details ofa system.
I Problem: Randomness maximizes entropy, perfectorder minimizes.
I Our idea of ‘maximal complexity’ is somewhere inbetween...
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 97/107
Measures of Complexity
(1) Entropy: number of microstates that could underlie aparticular macrostate.
I Used in information theory and statisticalmechanics/thermodynamics.
I Measures how uncertain we are about the details ofa system.
I Problem: Randomness maximizes entropy, perfectorder minimizes.
I Our idea of ‘maximal complexity’ is somewhere inbetween...
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 98/107
Hmmm
(Aside)
What about entropy and self-organization?
Isn’t entropy supposed to always increase?
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Frame 98/107
Hmmm
(Aside)
What about entropy and self-organization?
Isn’t entropy supposed to always increase?
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Frame 99/107
Hmmm
Two ways for order to appear in a system withoutoffending the second law of thermodynamics:
(1) Entropy of the system decreases at the expense ofentropy increasing in the environment.
(2) The system becomes more ordered macroscopicallywhile becoming more disordered microscopically.
Overview
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Topics
FundamentalsComplexity
Emergence
Self-Organization
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Statistical Mechanics
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Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
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Frame 99/107
Hmmm
Two ways for order to appear in a system withoutoffending the second law of thermodynamics:
(1) Entropy of the system decreases at the expense ofentropy increasing in the environment.
(2) The system becomes more ordered macroscopicallywhile becoming more disordered microscopically.
Overview
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Topics
FundamentalsComplexity
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Statistical Mechanics
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Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 99/107
Hmmm
Two ways for order to appear in a system withoutoffending the second law of thermodynamics:
(1) Entropy of the system decreases at the expense ofentropy increasing in the environment.
(2) The system becomes more ordered macroscopicallywhile becoming more disordered microscopically.
Overview
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Topics
FundamentalsComplexity
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The big theory
Tools and Techniques
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References
Frame 100/107
Measures of Complexity
(2) Various kinds of information complexity:
I Roughly, what is the size of a program required toreproduce a string of numbers?
I Again maximized by random strings.I Very hard to measure.
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Frame 100/107
Measures of Complexity
(2) Various kinds of information complexity:
I Roughly, what is the size of a program required toreproduce a string of numbers?
I Again maximized by random strings.I Very hard to measure.
Overview
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FundamentalsComplexity
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Frame 100/107
Measures of Complexity
(2) Various kinds of information complexity:
I Roughly, what is the size of a program required toreproduce a string of numbers?
I Again maximized by random strings.I Very hard to measure.
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Topics
FundamentalsComplexity
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Self-Organization
Modeling
Statistical Mechanics
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Symmetry Breaking
The big theory
Tools and Techniques
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Frame 101/107
Measures of Complexity
(3) Variation on (2): what is the size of a programrequired to reproduce members of an ensemble of astring of numbers?
Now: Random strings have very low complexity.
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Frame 101/107
Measures of Complexity
(3) Variation on (2): what is the size of a programrequired to reproduce members of an ensemble of astring of numbers?
Now: Random strings have very low complexity.
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Frame 102/107
Measures of Complexity
Large problem: given any one example, how do we knowwhat ensemble it belongs to?
One limited solution: divide the string up intosubsequences to create an ensemble.
See Complexity by Badii & Politi [2]
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Measures of Complexity
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Frame 102/107
Measures of Complexity
Large problem: given any one example, how do we knowwhat ensemble it belongs to?
One limited solution: divide the string up intosubsequences to create an ensemble.
See Complexity by Badii & Politi [2]
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 102/107
Measures of Complexity
Large problem: given any one example, how do we knowwhat ensemble it belongs to?
One limited solution: divide the string up intosubsequences to create an ensemble.
See Complexity by Badii & Politi [2]
Overview
CourseInformationMajor Centers
Resources
Projects
Topics
FundamentalsComplexity
Emergence
Self-Organization
Modeling
Statistical Mechanics
Universality
Symmetry Breaking
The big theory
Tools and Techniques
Measures of Complexity
References
Frame 103/107
Measures of Complexity
So maybe no one true measure of complexity exists.
Cosma Shalizi:
“Every few months seems to produce another paperproposing yet another measure of complexity, generally aquantity which can’t be computed for anything you’dactually care to know about, if at all. These quantities arealmost never related to any other variable, so they formno part of any theory telling us when or how things getcomplex, and are usually just quantification forquantification’s own sweet sake.”
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Frame 104/107
References I
P. W. Anderson.More is different.Science, 177(4047):393–396, August 1972. pdf (�)
R. Badii and A. Politi.Complexity: Hierarchical structures and scaling inphysics.Cambridge University Press, Cambridge, UK, 1997.
P. Ball.Critical Mass: How One Thing Leads to Another.Farra, Straus, and Giroux, New York, 2004.
Y. Bar-Yam.Dynamics of Complex Systems”.Westview Press, Boulder, CO, 2003.
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References
Frame 105/107
References II
E. D. Beinhocker.The Origin of Wealth.Harvard Business School Press, Cambridge, MA,2006.
N. Boccara.Modeling Complex Systems.Springer-Verlag, New York, 2004.
S. Bornholdt and H. G. Schuster, editors.Handbook of Graphs and Networks.Wiley-VCH, Berlin, 2003.
J. S. Coleman.Foundations of Social Theory.Belknap Press, Cambridge, MA, 1994.
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References
Frame 106/107
References III
R. Foote.Mathematics and complex systems.Science, 318:410–412, 2007. pdf (�)
J. H. Miller and S. E. Page.Complex Adaptive Systems: An introduction tocomputational models of social life.Princeton University Press, Princeton, NJ, 2007.
T. C. Schelling.Micromotives and Macrobehavior.Norton, New York, 1978.
D. Sornette.Critical Phenomena in Natural Sciences.Springer-Verlag, Berlin, 2nd edition, 2003.
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Frame 107/107
References IV
P. B. Umbanhowar, F. Melo, and H. L. Swinney.Localized excitations in a vertically vibrated granularlayer.Nature, 382:793–6, 29 August 1996. pdf (�)
S. Wasserman and K. Faust.Social Network Analysis: Methods and Applications.Cambridge University Press, Cambridge, UK, 1994.
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