Overview of Complex Systemspdodds/teaching/courses/2009-08UVM... · Complexity in abstract models I The game of life I Cellular automata I 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 1/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 2/108

OutlineCourse Information

Major CentersResourcesProjectsTopics

FundamentalsComplexityEmergenceSelf-OrganizationModelingStatistical MechanicsUniversalitySymmetry BreakingThe big theoryTools and TechniquesMeasures of Complexity

References

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 3/108

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: [email protected] 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]

http://www.uvm.edu/~pdodds/teaching/2009-08UVM-300/

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 4/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 5/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 6/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 7/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 8/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 9/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 11/108

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, ..., UVM (CSC)

http://www.cscs.umich.edu/

http://www.northwestern.edu/nico/

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 13/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 14/108

Useful Resources:

I Complexity Digest:http://www.comdig.org (�)

I Cosma Shalizi’s notebooks:http://www.cscs.umich.edu/ crshalizi/notebooks/ (�)

http://www.comdig.org

http://www.cscs.umich.edu/~crshalizi/notebooks/

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 16/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 17/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 19/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 20/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 21/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 22/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 23/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 24/108

Topics:

InformationI Search in networked systems (e.g., the WWW, social

systems)I Search on scale-free networksI Knowledge trees, metadata and tagging

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 26/108

Definitions

Complex: (Latin = with + fold/weave (com + plex))

Adjective:

1. Made up of multiple parts; intricate or detailed.2. Not simple or straightforward.

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 27/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 28/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 29/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 30/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 31/108

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.”

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 32/108

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.”

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 33/108

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.”

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 34/108

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.”

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 35/108

Definitions

Nonlinear (OED)1. a. Math. and Physics. Not linear; ... involving orpossessing the property that the magnitude of an effector output is not linearly or proportionally related to that ofthe cause or input. First cited use 1844.

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 36/108

Definitions

Nonlinear (OED)b. colloq. to go non-linear: to lose one’s head; to rave,esp. about a particular obsession. First cited use 1985.

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 37/108

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.”

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 38/108

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

SITEMAP

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

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 39/108

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,wombats, and fractals.”

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 41/108

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.”

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 42/108

Emergence:

Examples:

I Fundamental particles ⇒ Life, the Universe, andEverything

I Genes ⇒ OrganismsI Brains ⇒ ThoughtsI Fireflies ⇒ Synchronized FlashesI People ⇒ World Wide WebI People ⇒ Behavior in games not specified by rules

(e.g., bluffing in poker)I People ⇒ Religion

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 43/108

Emergence

Thomas Schelling (Economist/Nobelist):

[youtube] (�)

I “Micromotives andMacrobehavior” [11]

I SegregationI Wearing hockey helmetI Seating choices

http://www.youtube.com/watch?v=JjfihtGefxk

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 44/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 45/108

Emergence

Thomas Schelling (Economist/Nobelist):

I “Micromotives and Macrobehavior” [11]

I Segregation, wearing hockey helmet, seating choices

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 46/108

Emergence

James Coleman in Foundations of Social Theory :Weber

CapitalismProtestantReligiousDoctrine

EconomicBehavior

Values

Societal level

Individual level

Coleman

Understand macrophenomena arises from microbehaviorwhich in turn depends on macrophenomena. [8]

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 47/108

Emergence

Higher complexity:

I Many system scales (or levels)that interact with each other.

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 48/108

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.

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 49/108

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.

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 50/108

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...)

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 51/108

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.

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 52/108

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

http://www.nytimes.com/2007/01/28/magazine/28nutritionism.t.html

nytimes.com

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 53/108

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.”

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 54/108

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.”

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 55/108

Reductionism

Thyme’s known antioxidants:4-Terpineol, alanine, anethole, apigenin, ascorbic acid,beta carotene, caffeic acid, camphene, carvacrol,chlorogenic acid, chrysoeriol, eriodictyol, eugenol, ferulicacid, gallic acid, gamma-terpinene isochlorogenic acid,isoeugenol, isothymonin, kaempferol, labiatic acid, lauricacid, linalyl acetate, luteolin, methionine, myrcene,myristic acid, naringenin, oleanolic acid, p-coumoric acid,p-hydroxy-benzoic acid, palmitic acid, rosmarinic acid,selenium, tannin, thymol, tryptophan, ursolic acid, vanillicacid.

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 56/108

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.

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 58/108

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)

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 59/108

Definitions

Emergence but no Self-Organization?

H20 molecules ⇒ Water

Random walks ⇒ Normal distributions

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 60/108

Definitions

Self-organization but no Emergence?

Water above and near the freezing point.

Emergence may be limited to a low scale of a system.

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 61/108

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

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 62/108

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)

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 63/108

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)

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 64/108

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

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 65/108

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

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 66/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 68/108

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.”

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 69/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 70/108

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.”

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 71/108

Old School

I Statistical Mechanics is “a science of collectivebehavior.”

I Simple rules give rise to collective phenomena.

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 73/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 74/108

Ising model

2-d Ising model simulation:http://www.pha.jhu.edu/ javalab/ising/ising.html (�)

http://www.pha.jhu.edu/~javalab/ising/ising.html

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 75/108

Phase diagrams

Qualitatively distinct macro states.

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 76/108

Phase diagrams

Oscillons, bacteria, traffic, snowflakes, ...

Umbanhowar et al., Nature, 1996 [13]

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 77/108

Phase diagrams

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 78/108

Phase diagrams

W0 = initial wetness, S0 = initial nutrient supply

http://math.arizona.edu/~lega/HydroBact.html

http://math.arizona.edu/~lega/HydroBact.html

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 79/108

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.

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 80/108

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]

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 82/108

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.

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 83/108

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.

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 84/108

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...?

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 85/108

Lattice gas models

Collision rules in 2-d on a hexagonal lattice:

Lattice matters...No ‘good’ lattice in 3-d.

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 87/108

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...

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 88/108

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

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 89/108

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.

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 90/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 91/108

More is different:

from http://www.xkcd.com

http://www.xkcd.com

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 93/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 95/108

Tools

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 97/108


How do we measure the complexity of a system?

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 98/108


(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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 99/108

Hmmm

(Aside)

What about entropy and self-organization?

Isn’t entropy supposed to always increase?

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 100/108

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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 101/108


(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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 102/108


(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.

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 103/108


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


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 104/108


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.”

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 105/108

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.

http://www.uvm.edu/~pdodds/research/papers/others/1972/anderson1972a.pdf

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 106/108

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.

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 107/108

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.

http://www.uvm.edu/~pdodds/research/papers/others/2007/foote2007a.pdf

Overview


Resources

Projects

Topics


Emergence

Self-Organization

Modeling


Universality

Symmetry Breaking

The big theory



References

Frame 108/108

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.

http://www.uvm.edu/~pdodds/research/papers/others/1996/umbanhowar1996a.pdf

Documents

Overview of Complex Systemspdodds/teaching/courses/2009-08UVM... · Complexity in abstract models I The game of life I Cellular automata I Chaos and order—creation and maintenance