Until quite recently, our principal image of behaviour that is so complex as to be unstable and aperiodic was the

image of a crowd.

GE-NE-RAL FEE-LING

?!?

THEORY OF CHAOS AND COMPLEXITY

©Prof. Dr. Sándor György FeketeDoctor of the Hungarian Academy of Sciences

SZIU FVM Budapest Institute of Animal Breeding, Nutrition and Laboratory Animal Science, dietvet@yahoo.com;

www.dietvet.hu

„Thus being and non-being produce each other, Difficultand easy bring about each other.” (Lao-Tzu: Tao Te Ching)

WHERE DOES CHAOS COME FROM:IRREGULAR PHENOMENA, COMPUTING POWER

EXAMPLES-weather-spread of edpidemics-cell metabolism-changing animal

populations-rise and fall of civilizations

(Spengler, Toynbee)-flowing streas

(TURBULENCE)-evolution, biodiversity-cell division, apoptosis

CHAOS NAME MISLEADING, BECAUSEApparently random recurrent behavior in a simple deterministic system,That may carrry stability.The best example: the human brain(see later)

NUMBER of Feigerbaum (4.669) and the UNIVERSALITY

„Chaos is not a quirk of mathematics but a universal property of nonlinear feedback systems.

Numerical functions expresse natural laws about systems at the pont of transition between order and turbulence.

Universality: does exists one answer to many more difficult problem. Patterns in numbers implied pattern of turbulence.

The Dragonrepresents the principle of order, Yang, which emerges from chaos, and a Ray of pure light, Yin, emerges out of the chaos and builds the sky.

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HESIOD: THEOGONY(cosmological poem, 8th century B.C.„First of all Chaos came to be and the Earth (the wide-bosomed Gaia) and Eros.…From Chaos derive the beauteous Erebus (lustreless darkness) and Nyx, the Night. Nyx gave birth to Aither, the brightness of heaven and Hemeat, the daily light, falling in love with Erebos (b×s crossing). In turn, Gaia gave birth first to the starry sky, Uranos (parthenogenesis) for fully surrounding herself…” (Kerényi K.: Greek mythology. Gondolat. Budapest, 1977. p. 21.

DETERMINISTIC SYSTEMS: predictable, stable and completely knowableEuclides, René Descartes, Thomas Hobbes, Hume, Bacon, Bronowszki:Post hoc, ergo propter hoc ?!? With the acceptance ofIF after„A” comes „B”, THEN „B” is owing to „A”; but

Csiao Pu-csi: Lao-ce(604-517 B.C.) on water-buffalo (5.

A.D.):

In Taoism there is no inherent order. The

universe is vaste, amorphous and ever

changing. You can never nail it down.

NEW FIELD OF SCIENCE

Antecedents: GÖDEL (1931)In any formal system do exist undemonstable (cannot to be decided) statements:Epimenides-paradoxThis is the so-called not entirely completeness proposition is in relation to the complexity-degree of complexity of the ptoblems that cannot be dicided-proposition is complex at a subjective level, too

IT MEANS THAT THE TRUTH AND THE DEMONSTRABILITY ARE NOTUNCONDITIONALLY THE SAME THING

DEFINITION OF CHAOSA kind of order without periodicity:

- variable, unstable, dynamical- aperiodic and nonlinear

So: simply put, chaos is the occurrence of aperiodic, apparently random (non-predictable) events in a deterministic systemChasos (Greek): „gaping emptiness”

The Signature of Chaos and The Prank of the Little Devil

SENSITIVE DEPENDENCE on initial conditionsInfinitesimally small changes at the start – LEAD TO BIGGER CHANGES LATER. - This is a basic of biodiversity. E.g. home and office PC, explanation of EVOLUTION,

Lorenz and the PC („Deterministic Nonperiodic Flow, 1963”) in the J. Atmospheric Science

Edward LORENZ a meteorologistVery small changes in the initial conditions (memory of PC) produced widely varying and unpredictable response even in a simple three-equation model (temperature, pressure and winf speed)

The Butterfly Effect

(Lorenz, 1972):„Does the Flap of a Butterfly’s Wings in Brazil Set off a Tornado in Texas?”

Escher: Relativity

STRANGE ATTRAKTORS

The point at which the marble settles attrects the marble. E.g. EEG, ECG

POPULATION DYNAMICS

Robert MAY AND THE Animal POPULATIONS: do not behave chaotically, but

POPULATIONDYNAMICS IV

MODEL STILL DOES NOT COVER ALL REAL-LIFE EVENTS, because-species interact with each other (l. ants)-we can never know all the factors affecting one group of animals.

Robert MAY: „There is, unfortunately no punch line to this part of the story.”

Phil Thompson

REPRESENTATION OF CHAOS

Fractal GeometryPhase SpaceMusicEscher’s CompositionsMother Nature

Feedback and its representation: x2+c=result, which is continuously fed back into the changing number (iteration) gives chaotic pattern like fractals

Feedback (loop): the output, or result, affects the input of the system,

thus altering its operation

E.g. population growth,microphone,trade market,

enzyme copies itself(RNA polymerase)

Benoit MANDELBROT: fractal= a broken up and irregular (stone). Fractals are geometrical shapes that are not regular at all.

Self-similarity implies that any subsystem of a fractal system is equivalent to the whole system (e.g. trachea, cauliflower).The fractal geometry is the geometry of special types of irregular shapes

Mandelbrot Equations and Set:an+1=anan-bnbn+c; bn+1=+2bnan+c’

Ink drops; medusa; bacterial growth

Fractal: system of broken dimension

fractus= desribes a broken stone (Latin)Self-similarity: some fractals are only statistically self-similar. If magnifying the small pieces, they do not superimpose on the entire system.But they have the same general type of appearance.

PHASE SPACE: represents the state of an object in a multi-dimensional plane

Trajectory (arrow): path of movement in the phase space or the direction of movementLoops: periodicityTwist: changeEmpty spaces: physical impossibility

PHASE SPACE MAKES A DYNAMIC SYSTEM EASY TO WATCH: system of broken dimension

CHAOS AND THE LIVING BODYConventional model (as a machine): dangerously obsoleteToday: a holistic system full of fractals and chaosChaotic dynamics: feedback loopsAlways remember you’re unique, just like everyone else. E.g. the brain structure of identic twins is not the same!!!!

CLOUD FRACTALS AND BRAIN SURFACE

Charles Baudelaire: Alchemy of pain (The flowers of Depravity) :

Alchimie de la douleur (Les fleurs du mal)

„There are having the Mother Nature in the light of their soul, and are there being in mourning: which for one means the house of death, for the other the life and the light!”

„L’un t’éclaire avec son ardeur,L’autre en soi met son deuil, Nature!Ce qui dit à l’un: Sépulture!Dit à l’autre: Vie et splendeur!”

ADVANTAGES OF FRACTAL STRUCTURE

Makes the body flexible and robustIncrease the surface area (e.g. alveoli, villi, capillary etc.)Because they are self-similar, parts of the body’s fractal structures can easily be replaced (if injured, lost, desquamation etc.)

Body Fractals-circulatory system-lymph system-lungs-muscle tissue-calyx filters in thekidney,-small intestine-folding patterns of the surface of thebrain etc.

CHAOS may hold system and stability, too (e.g. brain), and its edge is the (COMPLEXITY),together:CHAOTICS

Complex system= =spontaneous self-organization+adaptiation

COMPLEXITYNonlinear, complex, dynamic systems have the ability to balance between order and chaos.Balance point between order and chaos: „edge of chaos”Spontaneous self-organization (e.g.. migratory birds, groups of social animals)Active adatation andEmphasizes the interconnection of all things

COMPLEXITY AS THE THEORY OF THE LIFE AT THE EDGE OF CHAOS,

Includes the entire spectrum, from embryological development, evolution, the dynamics of ecosystems, complex societies, right up to Gaia.Examples: space flight,elektronic circuits, rain forests,economy, living systems

GAIA-MODELL: WHITE AND BLACK DAISIES AND WARMING; # OF RABBITS AND FOXES

Escher: Metamorphosis

I. LIFE Itself is an expression of self-organizationThey are open , but yet they can attain an maintain a structureThe flow of energy allows them spontaneously to self-organizeThe system can create novel structuresTheir parts are so numerous that is no way in which a casual relationship between them can be established (e.g. regulation of feed intake)Components are interconnected by a network of feedback loops (e.g. hormones).

II. BRAIN: EEG shows strange attractors

The human brain is a complex, nonlinear feedback system. A healthy brain maintain a low level of chaos (formatio reticularis),which often self-organizes into a simpler order when presented with a familiar stimulus.

EPILEPSY

loss of low chaotic stateabnormale periodic orderseizures

III. POSTGENETICSK.J. Simons: the junk DNA is not a garbigeRNA –interference (pickton, miRNS, siRNS): in the intron (Nobel Prize in 2006)Pellionisz: the inner mathematics of the genom is a fractal geometra (compressed information!!!). Becaouse these special math formations are self-similar.

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IV. HEART: ECG is a „spider-like” strange attractorWhen a group of heart muscle fibres have a refractory time that is longer than the interval between heartbeats, turbulence could set inThis undesirable chaos is recognized by the „inteligent” heart pace-makerek

ECG of healthy and sick heart in phase space

V. CHAOS AND CONSCIOUSNESSEach neuron is considered to represent one variable. In phase space, each neuron is given one dimension: there are therefore 10 billion dimensions.Consciencness is the point moving within this phase space. This point is described as our „ego made tangible”Conclusions. Path is chaotic, but not random, it follows a strange attractor (‘personality’); not predictable or sequential and no limit on the number of states (‘limitless consciousness’)

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EXPECTED BREAKTHROUGHS

Chance + serendipityIt must be dialogueSee: life cycle of a project and prerequisites and prior obligation of the implementationMore and more ethical aspects‘Understand Wilcox’ up for

the Nobel Prize in genetic engineering’

„Wie alles sich zum Ganzen webt,

Eins in dem andern wirkt und lebt.”

„ How one acts in another and gains!”

INDIVIDUAL TREATMENT OF PATIENT-- TECHNICAL ADVICE – POST-NORMAL ANALYSIS

Characteristics of post-normal science:

-QUALITY replaces TRUTH as the organizing

principle.-Scientists or experts assure

the quality control process as the input

-Laymen (e.g. animal right activists, housewife, owner,

consumer etc.) can assess the context of results in the

real-life situation

BRIAN ARTHUR

„If the special civilizations and environments has been insufficiently understood and the elements of holistic context have not been taken into account, thus

the grandly devised deterministic programmes couldnot achieve their projected end (introduction of wild rabbit into Australia, Iraq-Aphganistan waretc.).

„DON’T STOPTO THINK,YOU MAYFORGET TO STARTAGAIN”

Confucius(551 B.C. – 479 B.C.)

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