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Inability to calculate everything from the beginning to the end

Inability to calculate everything from the beginning to the end.

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Inability to calculate everything from the beginning to the end

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  1. Inability to calculate everything from the beginning to the end • In short, potentially chess is a deterministic system. However, it is not clear whether this feature of the game can be operationalized. In view of the as­tronomical number of possible variations (of the order of 10120), chess does not yield to an exhaustive search even if the search is conducted by the most power­ful computers.

  2. Inability to calculate everything from the beginning to the end • Numbers like this give any computer the willies -- parallel processor, gallium arsenide, we don't care. Working at 200 million positions per second, Deep Blue would still require a while (an eternity?) to evaluate all possible games: 10100 years. If that doesn't sound longer than the ads in the last quarter of a Super Bowl, remember that the universe is only about 1010 years old.

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

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

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

  6. INDTERMINISTIC SYSTEMS • Chess is the finite game. Life presents an open system. Changes, appearance of new forms makes it impossible to calculate moves. • Another important question concerns the structure of values. How to evaluate an entity if the future is unknown? • What is the role of subjectivity?

  7. Subjectivity of Evaluation • The roots of one's subjective evaluation lie in the fact that the executor cannot be separated from the evaluator, who evaluates the system in accordance with his own particular ability to develop it.

  8. STYLES IN THE GAME OF CHESS

  9. STYLES AND METHODS • Styles: positional and combinational. • Methods: reactive and selective. • Sub-methods: randomization, predispositioning programming

  10. The Combinational Style • First, the combinational style is characterized by a very narrow, clear, mostly material goal. • Secondly, it is distinguished by a program that links the initial position with the final outcome.

  11. The Positional Style • The positional style is distinguished by a positional goal and a formation of semi-complete linkages between the initial step and final outcome. • It serves to create a predisposition to the future development of the position.

  12. The Positional Style • The positional style serves to induce the environment in a certain way; • Second, it serves to absorb an unexpected outcome in your favor; • Third, it helps avoid the negative aspects of unexpected outcomes.

  13. The Positional Style • The positional style gives the player the opportunity to develop a position until it becomes pregnant with a combination. • The positional style of chess does not eliminate the combinational one with its attempt to see the entire program of action in advance. The positional style merely prepares the transformation to a combination when the latter becomes feasible. (Aron Katsenelinboigen, Selected Topics in Indeterministic Systems 21)

  14. POSITIONAL STYLE

  15. Material & Positional Parameters • Positional style in chess deals with material and positional parameters as independent variables. • Material parameters are given in the game of chess (pieces on the chess board). • Positional parameters are created by the chess players.

  16. THE STRUCTURE OF THE SYSTEM From the structural point of view, the system consists of material, relational, and positional parameters and their valuations.

  17. THE STRUCTURE OF THE SYSTEM • Material parameters constitute the skeleton of the object. • Positional parameters structure the spatial relations between the objects and their parts, such as left, right, close, remote, centered, etc. • Relational parameters are inherent in biological systems. They indicate relationships between the entities, such as kinship, feelings (love, hate), and emotions (anger, fear).

  18. PREDISPOSITIONING VS. PROBABILITY • The probabilistic method is grounded in statistics and frequencies of events. • Predispositioning – approaching a system from the point of view of its predisposition – is used when no statistics is available. • Predispositioning is used for unique situations.

  19. Predispositioning Vs. Probability • A much more challenging problem arises when there are no statistics, stochastic programming or sequential analysis to generate probabilities, considering especially that sequential analysis starts with some a priori probability distribution and may take an incredible amount of time or resources to produce an optimal solution. Additionally, there may be unique situations that by definition preclude any reliance on frequency of events whatsoever. In this case, rather than observe a highly uncertain behavior of individual objects, we look at the behavior of the total ensemble formed by these objects, since the latter, generally speaking, are more amenable to statistical patterns; in other words, we reduce a unique situation to some previously known one by stripping the former of its specific unique features. This, however, is a pretty risky procedure since the specific features of a unique event could be quite significant, and eliminating them might result in a drastically distorted estimate of the likelihood of the situation occurring. (Katsenelinboigen Concept of Indeterminism 27–28)

  20. LORENZ • One of the most important discoveries was made in 1963, by the meteorologist Edward Lorenz, who wrote a basic mathematical software program to study a simplified model of the weather. Specifically Lorenz studied a primitive model of how an air current would rise and fall while being heated by the sun. Lorenz's computer code contained the mathematical equations which governed the flow the air currents. Since computer code is truly deterministic, Lorentz expected that by inputing the same initial values, he would get exactly the same result when he ran the program. Lorenz was surprised to find, however, that when he input what he believed were the same initial values, he got a drastically different result each time.

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

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

  23. ORDER & CHAOS • The scholars deal only with the extremes – order and the lack of order - without discussing the DEGREE of order. • At this point, they skip a very important stage in system’s development that Aron Katsenelinboigen called a “PREDISPOSITION.”

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

  25. THE GOAL • The goal of this class is to analyze this missing stage based on Katsenelinboigen’s concept of predispositioning. • This concept was developed for disjointed protracted systems with semi-complete and semi-consistent linkages between its parts.

  26. STAGES OF SYSTEM’S DEVELOPMENT • mishmash • mess • chaos • predisposition • order

  27. DESCRIPTION OF THE STAGES • Mishmash – all elements exist like a cluster. We cannot distinguish between the material and positional/relational parameters. • Mess – appearance of singular elements. Relations between them are unclear. • Chaos – appearance of first relational parameters. They are limited, not sophisticated, the degree is not elaborated, and their relations are mostly local since no global field is formed on this stage. Thus, the linkages between the elements in chaos are incomplete and inconsistent.

  28. DESCRIPTION OF THE STAGES • Predisposition – a formation of the global field. An increase of a number of material and relational parameters, sophisticated and more defined, is observed. A formation of the degree and a global field. Linkages are semi-complete and semi-consistent. • Order – all parameters are linked in a complete and consistent way.

  29. STAGES OF THE CREATION OF THE WORLD IN THE TORAH • In the beginning God created the heavens and the earth. • 1:2 Now the earth was formless and empty. Darkness was on the surface of the deep. God's Spirit was hovering over the surface of the waters. • 1:3 God said, "Let there be light," and there was light.

  30. STAGES OF THE CREATION OF THE WORLD IN THE TORAH • 1:4 God saw the light, and saw that it was good. God divided the light from the darkness. • 1:5 God called the light Day, and the darkness he called Night. There was evening and there was morning, one day. • 1:6 God said, "Let there be an expanse in the midst of the waters, and let it divide the waters from the waters."

  31. STAGES OF THE CREATION OF THE 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 evening and there was morning, a second day.

  32. STAGES OF THE CREATION OF THE WORLD IN THE TORAH • 1:9 God said, "Let the waters under the sky be gathered together to one place, and let the dry land appear," and it was so. • 1:10 God called the dry land Earth, and the gathering together of the waters he called Seas. God saw that it was good. • 1:11 God said, "Let the earth put forth grass, herbs yielding seed, and fruit trees bearing fruit after their kind, with its seed in it, on the earth," and it was so.

  33. GOD AS A DECISION-MAKER WHAT KIND OF STYLE OF DECISION-MAKING DID GOD USE?

  34. ELABORATION OF THE SKIES • 1:14 God said, "Let there be lights in the expanse of sky to divide the day from the night; and let them be for signs, and for seasons, and for days and years; • 1:15 and let them be for lights in the expanse of sky to give light on the earth," and it was so. • 1:16 God made the two great lights: the greater light to rule the day, and the lesser light to rule the night. He also made the stars. 1:17 God set them in the expanse of sky to give light to the earth, 1:18 and to rule over the day and over the night, and to divide the light from the darkness. God saw that it was good. 1:19 There was evening and there was morning, a fourth day.

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