Complex Systems and Emergence: A Holistic Speech - staff…staff.on.br/jlkm/LectureWarsaw/talk.pdf · Planetary System Galaxy, Clusters, Spiral Arms Kohl-Moreira, J.L. Warsaw Talk,

Complex SystemsEmergence & Complex System

Theory of Information & EntropyConclusions

Complex Systems and Emergence: A HolisticSpeech

João Luiz Kohl-Moreira1

1Coordenadoria de Astronomia e AstrofísicaObservatório Nacional - MCT

Warsaw Talk, 2014

Kohl-Moreira, J.L. Warsaw Talk, 2014



ExamplesWhat they have in common?Reductionism, Final Theory, Everything TheoryEmergentism: Not ExhaustiveExamples

What is a Complex System?

Complex System ≡ Dynamic System





Gas





Oceans





Snow in a Mountain





Ecological System





Social Group





Ant Colony





Planetary SystemGalaxy, Clusters, Spiral Arms





Neural System





Market





Talk Audience





What these things have in common?Besides being complex?





Doing Science

TaxonomyRelationship





Not Reductionism

Since end of 19th Century - success of the Newtonian SystemFeeling that nothing or too few things left to be successfulyexplained by scienceExperiments and new thoughts in the beginning of 20th

Century broke down this feelingNowadays these feelings seem to have returned (particle ofGod, and so on)





Not Reductionism







Not Reductionism







Not Reductionism







Theory of Emergence

Try to describe common characteristics of systems calledcomplexIt does not replace already established theoriesIt aggregates them knowledgeNot a Theory of Everything





Theory of Emergence

Try to describe common characteristics of systems calledcomplexIt does not replace already established theoriesIt aggregates them knowledgeNot a Theory of Everything





Sprout





Tornado





Avalanche





War





Speciation





Boo





The Capitalism





The SubjectPsyche




Same thingHeuristics

Scenario

Complex System ⇐⇒ Emergence ⇐⇒ Complex SystemEmergence ≡ Complex System





Scenario

Complex System ⇐⇒ Emergence ⇐⇒ Complex SystemEmergence ≡ Complex System





Complex System

Formed by elements of same kindSum of the parts is not sufficient to describe the emergenceThe elements forming the new emergence are themselvescomplex systems





Evolution

Every emergence has a beginning, middle and end: it evolves





Understanding Emergence / Complex System

Complex systems involves combinationsMathematics: combinatorial analysis





Understanding Emergence / Complex System

Complex systems involves combinationsMathematics: combinatorial analysis





Intractability

What is the least path for travelling to the 28 brazilian statecapitals?The fastest computer ever should take about 2× the age ofthe universe to find itThis is an intractable problem





Intractability






Intractability






NP=P

This equation means: is there a way to solve a non-polynomialproblem in a time depending on a polynomial function?In other words: may a computer test all the possiblecombinations in system?Since 1960’s there is a debate about and mathematiciansdidn’t answered this questionUS$ 1 million rewards to whom capable to answer it





NP=P






NP=P






NP=P






Neural System

How long to verify all the connections in the brain?





Heuristics

In mathematics one uses to apply the so-called HeuristicMethodsEvolutive algorithms, genetic algorithmsAnealingAnt behaviorSet of metaphores





Heuristics






Heuristics






Heuristics






Heuristics






Force





Oedipus Complex




Entropy

Mechanics of Evolution

Claude Shannon




Entropy

Rudolf Clausius

Entropy (1865)2nd Law of Thermodynamics




Entropy

Robert Fludd’s Watermill

No perpetual motion




Entropy

Ludwig Boltzmann

S = k logW




Entropy

Gibbs

S =−k∑i

pi logpi




Entropy

Shannon: stochastic process

Probability of character “w” being followed by the character“a” forming a word in a languageThen, what the probability of the character, say, “t” comingnext?Then “b”?And so on




Entropy






Entropy






Entropy






Entropy

Opennheimer

H =−∑i

pi log2 pi

S =−k∑i

pi logpi

By calling its function “Entropy” Shannon applied a heuristics




Entropy

Opennheimer

H =−∑i

pi log2 pi

S =−k∑i

pi logpi





Entropy

Opennheimer

H =−∑i

pi log2 pi

S =−k∑i

pi logpi





Entropy

Entropy & Information

By doing so he gives a tip to the physicists:Entropy has a relationship with informationHe gives entropy a meaning




Entropy






Entropy






Entropy

Entropy & Modern Sciences

Today virtually all areas of knowledge use the concept ofentropy out of thermodynamic context




Entropy

Geophysics




Entropy

Anthropology




Entropy

Economy

Inflation?Entropy ≡ System of prices




Entropy

Economy

Inflation?Entropy ≡ System of prices




Entropy

Ecology

Measure of diversity




Entropy

Psychoanalysis

Sonia Alberti’s talkFreud’s “Civilization and its Discontents”Metapsychology




Entropy

Psychoanalysis





Entropy

Psychoanalysis





Entropy

This Audience




Entropy

J. Maynard Smith

In a universe where increasing disorder is a physicallaw, complex organisms (including human beings and,more broadly speaking, social organizations) can persistonly if they behave in a way that tends to increase theirprobability of surviving and reproducing themselves.Thus, an evolutionary-selection argument suggests thatindividuals may tend to maximize the expected value ofsome measure of general survival and reproductive fitnessor sucess.




Entropy

What is Universe?

The universe we live is the realm of the informationInformation ≡ DisturbanceDisturbance ≡ bias (deviation from normal distribution)Nature, following the increasing entropy’s law, tends to destroyinformationIf we want to exist we must disturbBe subversive




Entropy

What is Universe?





Entropy

What is Universe?





Entropy

What is Universe?





Entropy

What is Universe?





Entropy

What is Universe?





Conclusions

Emergence is a self recurrent process that is result ofcombinatorial systems with large number of elements (complexsystems)Heuristics is used to describe emergencesEvery complex system(the emergence issue) has an entropylinked to it, which follows the 2nd Law of ThermodynamicsThe universe is the set of recurrent emergences




Conclusions





Conclusions





Conclusions





The End

“This is Apollo 13, signing off”James Lovell - Cmt


Documents

Complex Systems and Emergence: A Holistic Speech - staff…staff.on.br/jlkm/LectureWarsaw/talk.pdf · Planetary System Galaxy, Clusters, Spiral Arms Kohl-Moreira, J.L. Warsaw Talk,