FATE & CHANCEFATE & CHANCE

Usually, discussions about fate and chance, as Usually, discussions about fate and chance, as well as order and chaos, oscillate between two well as order and chaos, oscillate between two extremes – a complete order (fate, etc.) or a extremes – a complete order (fate, etc.) or a complete disorder (chaos, chance). complete disorder (chaos, chance).

SCHOLARS ON CHAOS SCHOLARS ON CHAOS

““One of the most interesting One of the most interesting issues in the study of chaotic issues in the study of chaotic systems is whether or not the systems is whether or not the presence of chaos may actually presence of chaos may actually produce ordered structures and produce ordered structures and patterns on a larger scale.” patterns on a larger scale.”

ORDER & CHAOSORDER & CHAOS

The scholars deal only with the extremes – The scholars deal only with the extremes – order and the lack of order - without discussing order and the lack of order - without discussing the DEGREE of order. the DEGREE of order.

At this point, they skip a very important stage in At this point, they skip a very important stage in system’s development that Aron system’s development that Aron Katsenelinboigen called aKatsenelinboigen called a

“ “PREDISPOSITION.”PREDISPOSITION.”

WRITERS ON THE DEGREEWRITERS ON THE DEGREE

Between ‘there is God’ and ‘there is no God’ Between ‘there is God’ and ‘there is no God’ there exists a huge space that even a great there exists a huge space that even a great thinker overcomes only with much diffi culty. thinker overcomes only with much diffi culty. The Russian knows only one of the two The Russian knows only one of the two extremes, the middle ground between them is extremes, the middle ground between them is not interesting to him; that is why he usually not interesting to him; that is why he usually knows either nothing or too little.knows either nothing or too little.

Anton ChekhovAnton Chekhov

THE GOAL THE GOAL

The goal of this class is to analyze this The goal of this class is to analyze this missing stage based on missing stage based on Katsenelinboigen’s concept of Katsenelinboigen’s concept of predispositioning. predispositioning.

This concept was developed for disjointed This concept was developed for disjointed protracted systems with semi-complete and protracted systems with semi-complete and semi-consistent linkages between its parts.semi-consistent linkages between its parts.

STAGES OF SYSTEM’S STAGES OF SYSTEM’S DEVELOPMENT DEVELOPMENT

mishmash mishmash mess mess chaos chaos predisposition predisposition orderorder

THE STRUCTURE OF THE THE STRUCTURE OF THE SYSTEM SYSTEM

From the structural point of view, the system From the structural point of view, the system consists of material, relational, and positional consists of material, relational, and positional parameters and their valuations.parameters and their valuations.

THE STRUCTURE OF THE THE STRUCTURE OF THE SYSTEMSYSTEM

Material parameters constitute the skeleton of Material parameters constitute the skeleton of the object.the object.

Positional parameters structure the spatial Positional parameters structure the spatial relations between the objects and their parts, relations between the objects and their parts, such as left, right, close, remote, centered, etc.such as left, right, close, remote, centered, etc.

Relational parameters are inherent in Relational parameters are inherent in biological systems. They indicate relationships biological systems. They indicate relationships between the entities, such as kinship, feelings between the entities, such as kinship, feelings (love, hate), and emotions (anger, fear).(love, hate), and emotions (anger, fear).

DESCRIPTION OF THE STAGES DESCRIPTION OF THE STAGES

MishmashMishmash – all elements exist like a cluster. We – all elements exist like a cluster. We cannot distinguish between the material and cannot distinguish between the material and positional/relational parameters.positional/relational parameters.

MessMess – appearance of singular elements. Relations – appearance of singular elements. Relations between them are unclear. between them are unclear.

ChaosChaos – appearance of first relational parameters. – appearance of first relational parameters. They are limited, not sophisticated, the degree is not They are limited, not sophisticated, the degree is not elaborated, and their relations are mostly local since elaborated, and their relations are mostly local since no global field is formed on this stage. Thus, the no global field is formed on this stage. Thus, the linkages between the elements in chaos are linkages between the elements in chaos are incompleteincomplete and and inconsistentinconsistent..

DESCRIPTION OF THE STAGESDESCRIPTION OF THE STAGES

PredispositionPredisposition – a formation of the global – a formation of the global field. An increase of a number of material, field. An increase of a number of material, positional, and relational parameters, positional, and relational parameters, sophisticated and more defined, is observed. A sophisticated and more defined, is observed. A formation of the degree and a global field. formation of the degree and a global field. Linkages are semi-complete and semi-Linkages are semi-complete and semi-consistent. consistent.

OrderOrder – all parameters are linked in a – all parameters are linked in a complete and consistent way.complete and consistent way.

STAGES OF THE CREATION OF STAGES OF THE CREATION OF THE WORLD IN THE TORAH THE WORLD IN THE TORAH

In the beginning God created the heavens and In the beginning God created the heavens and the earth. the earth.

1:2 Now the earth was formless and empty. 1:2 Now the earth was formless and empty. Darkness was on the surface of the deep. God's Darkness was on the surface of the deep. God's Spirit was hovering over the surface of the Spirit was hovering over the surface of the waters. waters.

1:3 God said, "Let there be light," and there 1:3 God said, "Let there be light," and there was light. was light.

STAGES OF THE CREATION OF STAGES OF THE CREATION OF THE WORLD IN THE TORAHTHE WORLD IN THE TORAH

1:4 God saw the light, and saw that it was 1:4 God saw the light, and saw that it was good. God divided the light from the darkness.good. God divided the light from the darkness.

1:5 God called the light Day, and the darkness 1:5 God called the light Day, and the darkness he called Night. There was evening and there he called Night. There was evening and there was morning, one day. was morning, one day.

1:6 God said, "Let there be an expanse in the 1:6 God said, "Let there be an expanse in the midst of the waters, and let it divide the waters midst of the waters, and let it divide the waters from the waters." from the waters."

STAGES OF THE CREATION OF STAGES OF THE CREATION OF THE WORLD IN THE TORAHTHE WORLD IN THE TORAH

1:7 God made the expanse, and divided the waters which were under the expanse from the waters which were above the expanse, and it

was so. 1:8 God called the expanse sky. There was 1:8 God called the expanse sky. There was

evening and there was morning, a second day. evening and there was morning, a second day.

STAGES OF THE CREATION OF STAGES OF THE CREATION OF THE WORLD IN THE TORAHTHE WORLD IN THE TORAH

1:9 God said, "Let the waters under the sky be 1:9 God said, "Let the waters under the sky be gathered together to one place, and let the dry land gathered together to one place, and let the dry land appear," and it was so. appear," and it was so.

1:10 God called the dry land Earth, and the gathering 1:10 God called the dry land Earth, and the gathering together of the waters he called Seas. God saw that it together of the waters he called Seas. God saw that it was good. was good.

1:11 God said, "Let the earth put forth grass, herbs 1:11 God said, "Let the earth put forth grass, herbs yielding seed, and fruit trees bearing fruit after their yielding seed, and fruit trees bearing fruit after their kind, with its seed in it, on the earth," and it was so.kind, with its seed in it, on the earth," and it was so.

GOD AS A DECISION-MAKERGOD AS A DECISION-MAKER

WHAT KIND OF STYLE OF DECISION-MAKING DID GOD USE? WHAT KIND OF STYLE OF DECISION-MAKING DID GOD USE?

WHY GOD COULDN”Y USE PROBABILISTIC METHOD?WHY GOD COULDN”Y USE PROBABILISTIC METHOD?

PREDISPOSITIONING VS. PREDISPOSITIONING VS. PROBABILITYPROBABILITY

The probabilistic method is grounded in The probabilistic method is grounded in statistics and frequencies of events. statistics and frequencies of events.

Predispositioning – approaching a system from Predispositioning – approaching a system from the point of view of its predisposition – is used the point of view of its predisposition – is used when no statistics is available. when no statistics is available.

Predispositioning is used for unique situations.Predispositioning is used for unique situations.

Predispositioning Vs. ProbabilityPredispositioning Vs. Probability A much more challenging problem arises when there are no statistics, A much more challenging problem arises when there are no statistics,

stochastic programming or sequential analysis to generate probabilities, stochastic programming or sequential analysis to generate probabilities, considering especially that sequential analysis starts with some a priori considering especially that sequential analysis starts with some a priori probability distribution and may take an incredible amount of time or probability distribution and may take an incredible amount of time or resources to produce an optimal solution. Additionally, there may be resources to produce an optimal solution. Additionally, there may be unique situations that by definition preclude any reliance on frequency of unique situations that by definition preclude any reliance on frequency of events whatsoever. In this case, rather than observe a highly uncertain events whatsoever. In this case, rather than observe a highly uncertain behavior of individual objects, we look at the behavior of the total behavior of individual objects, we look at the behavior of the total ensemble formed by these objects, since the latter, generally speaking, are ensemble formed by these objects, since the latter, generally speaking, are more amenable to statistical patterns; in other words, we reduce a unique more amenable to statistical patterns; in other words, we reduce a unique situation to some previously known one by stripping the former of its situation to some previously known one by stripping the former of its specific unique features. This, however, is a pretty risky procedure since specific unique features. This, however, is a pretty risky procedure since the specific features of a unique event could be quite significant, and the specific features of a unique event could be quite significant, and eliminating them might result in a drastically distorted estimate of the eliminating them might result in a drastically distorted estimate of the likelihood of the situation occurring. likelihood of the situation occurring.

(Katsenelinboigen Concept of Indeterminism 27–(Katsenelinboigen Concept of Indeterminism 27–28)28)

LORENZLORENZ One of the most important discoveries was made in 1963, by One of the most important discoveries was made in 1963, by

the meteorologist Edward Lorenz, who wrote a basic the meteorologist Edward Lorenz, who wrote a basic mathematical software program to study a simplified model of mathematical software program to study a simplified model of the weather. Specifically Lorenz studied a primitive model of the weather. Specifically Lorenz studied a primitive model of how an air current would rise and fall while being heated by how an air current would rise and fall while being heated by the sun. Lorenz's computer code contained the mathematical the sun. Lorenz's computer code contained the mathematical equations which governed the flow the air currents. Since equations which governed the flow the air currents. Since computer code is truly deterministic, Lorentz expected that by computer code is truly deterministic, Lorentz expected that by inputing the same initial values, he would get exactly the same inputing the same initial values, he would get exactly the same result when he ran the program. Lorenz was surprised to find, result when he ran the program. Lorenz was surprised to find, however, that when he input what he believed were the same however, that when he input what he believed were the same initial values, he got a drastically different result each time. initial values, he got a drastically different result each time.

LORENZLORENZ By examining more closely, he realized that he was not By examining more closely, he realized that he was not

actually inputing the same initial values each time, but ones actually inputing the same initial values each time, but ones which were slightly different from each other. He did not which were slightly different from each other. He did not notice the initial values for each run were different because the notice the initial values for each run were different because the difference was incredibly small, so small as to be considered difference was incredibly small, so small as to be considered microscopic and insignificant by usual standards. The microscopic and insignificant by usual standards. The mathematics inside Lorenz's model of atmospheric currents mathematics inside Lorenz's model of atmospheric currents was widely studied in the 1970's. Gradually it came to be was widely studied in the 1970's. Gradually it came to be known that even the smallest imaginable discrepancy between known that even the smallest imaginable discrepancy between two sets of initial conditions would always result in a huge two sets of initial conditions would always result in a huge discrepancy at later or earlier times, the hallmark of a chaotic discrepancy at later or earlier times, the hallmark of a chaotic system, of course.system, of course.

Inability to calculate everything Inability to calculate everything from the beginning to the end from the beginning to the end

In short, In short, potentiallypotentially chess is a deterministic chess is a deterministic system. However, it is not clear whether this system. However, it is not clear whether this feature of the game can be feature of the game can be operationalizedoperationalized. In . In view of the astronomical number of possible view of the astronomical number of possible variations (10 to the 120variations (10 to the 120 thth power), chess does power), chess does not yield to an not yield to an exhaustive searchexhaustive search even if the even if the search is conducted by the most powerful search is conducted by the most powerful computers. computers.

Inability to calculate everything Inability to calculate everything from the beginning to the endfrom the beginning to the end

Numbers like this give any computer the Numbers like this give any computer the willies -- parallel processor, gallium arsenide, willies -- parallel processor, gallium arsenide, we don't care. Working at 200 million we don't care. Working at 200 million positions per second, Deep Blue would still positions per second, Deep Blue would still require a while (an eternity?) to evaluate all require a while (an eternity?) to evaluate all possible games: 10 to the100th power years. If possible games: 10 to the100th power years. If thatthat doesn't sound longer than the ads in the doesn't sound longer than the ads in the last quarter of a Super Bowl, remember that last quarter of a Super Bowl, remember that the universe is only about 10 to the10th power the universe is only about 10 to the10th power years old. years old.

INDTERMINISTIC SYSTEMSINDTERMINISTIC SYSTEMS

The only approach that will make chess The only approach that will make chess operationally deterministic is an optimality operationally deterministic is an optimality ((max-minmax-min) algorithm that generates an optimal ) algorithm that generates an optimal move for each side at each stage of the game. move for each side at each stage of the game. What this approach implies is that in terms of What this approach implies is that in terms of the final outcome no better move than the one the final outcome no better move than the one selected by the algorithm exists. So far, no selected by the algorithm exists. So far, no such algorithm has been devised; in fact, its such algorithm has been devised; in fact, its existenceexistence has not been proved, to say nothing has not been proved, to say nothing of constructive implementation.of constructive implementation.

INDTERMINISTIC SYSTEMSINDTERMINISTIC SYSTEMS That means that it is impossible to approach such system That means that it is impossible to approach such system from from

the endthe end. The one distinguishing mark of a changing system is . The one distinguishing mark of a changing system is the presence of the presence of two-ended source of development two-ended source of development. Aron . Aron Katsenelinboigen calls itKatsenelinboigen calls it Janus processes Janus processes following the image following the image of the Romans’ god Janus. In accordance with the Roman of the Romans’ god Janus. In accordance with the Roman mythology, Janus, as the patron of beginnings and endings, mythology, Janus, as the patron of beginnings and endings, has two faces looking in opposite directions: one in front, the has two faces looking in opposite directions: one in front, the other at the back of his head (other at the back of his head (Webster New World Dictionary, Webster New World Dictionary, 1980). The features of 1980). The features of Janus processesJanus processes require a new require a new methodological approach, which leaves room for the classical methodological approach, which leaves room for the classical methods, but now these methods must be integrated into the methods, but now these methods must be integrated into the new scheme (and new methods) that is adequate for the study new scheme (and new methods) that is adequate for the study of changing systems. of changing systems.

INDTERMINISTIC SYSTEMSINDTERMINISTIC SYSTEMS

Especially, this new methodological approach Especially, this new methodological approach is required when one deals with an is required when one deals with an incomplete incomplete Janus processJanus process. It denotes a process where the . It denotes a process where the changes in the system are triggered both at the changes in the system are triggered both at the endend and at the and at the beginning beginning but the beginnings but the beginnings and the ends are not fixed forever and the way and the ends are not fixed forever and the way between them is not complete, that is, it can between them is not complete, that is, it can have gaps.have gaps.

INDTERMINISTIC SYSTEMSINDTERMINISTIC SYSTEMS

Chess is the finite game. Life presents an open Chess is the finite game. Life presents an open system. Changes, appearance of new forms system. Changes, appearance of new forms makes it impossible to calculate moves. makes it impossible to calculate moves.

STYLES IN THE GAME OF STYLES IN THE GAME OF CHESSCHESS

STYLES AND METHODSSTYLES AND METHODS

Styles: positional and combinational Styles: positional and combinational Methods: reactive and selectiveMethods: reactive and selective Sub-methods: randomization, Sub-methods: randomization,

predispositioning, programming predispositioning, programming

The Combinational StyleThe Combinational Style

First, the combinational style is characterized First, the combinational style is characterized by a very narrow, clear, mostly material goal.by a very narrow, clear, mostly material goal.

Secondly, it is distinguished by a program that Secondly, it is distinguished by a program that links the initial position with the final links the initial position with the final outcome.outcome.

The Positional StyleThe Positional Style

The positional style is distinguished by a The positional style is distinguished by a positional goal and a formation of semi-positional goal and a formation of semi-complete linkages between the initial step and complete linkages between the initial step and final outcome. final outcome.

It serves to create a predisposition to the future It serves to create a predisposition to the future development of the position.development of the position.

The Positional StyleThe Positional Style

The positional style serves to induce the The positional style serves to induce the environment in a certain way;environment in a certain way;

Second, it serves to absorb an unexpected Second, it serves to absorb an unexpected outcome in your favor;outcome in your favor;

Third, it helps avoid the negative aspects of Third, it helps avoid the negative aspects of unexpected outcomes.unexpected outcomes.

The Positional StyleThe Positional Style The positional style gives the player the opportunity to The positional style gives the player the opportunity to

develop a position until it becomes pregnant with a develop a position until it becomes pregnant with a combination.combination.

The positional style of chess does not eliminate the The positional style of chess does not eliminate the combinational one with its attempt to see the entire program of combinational one with its attempt to see the entire program of action in advance. The positional style merely prepares the action in advance. The positional style merely prepares the transformation to a combination when the latter becomes transformation to a combination when the latter becomes feasible. feasible.

((Aron KatsenelinboigenAron Katsenelinboigen, , Selected Topics in Selected Topics in Indeterministic SystemsIndeterministic Systems 21) 21)