I. Introduction
There are a number of purely mathematical approaches to the theory of games and to the matter of deciding the value of a position in a given game at a given time in that game. In this paper I will not repeat the wisdom of the conventional theory of games, but rather I will explore the concept of positional evaluation on its own grounds with respect to a collection of sample games, some mathematical in nature, and some more epistemological or experiential. Each section of the paper can be read on its own grounds.
The contents of this paper are as listen below.
Introduction
The Game
MetaGame
The Game of Nine - Perfect Representation
Endless?
Marked or Unmarked?
Knots
Go
Appendix 1 - Comments on the game of Go
Appendix 2 - Principles of Quantum Mechanics
Appendix 3 - On Gödel's Theorem, Self-Reproducing Machines and the
Lambda Calculu
Appendix 4 - On Knots
The Common theme that ties these vignettes together is the dilemma faced by the player who needs to select a next move. The player is an observer of the system (the game) of which he/she is a part (participant).
This is an essay on second order cybernetics. The observer is included in the system. To what end is that observer in the system? To influence to course of events. To make the system possible as an observed system. And who is the observer? In a game these issues come to a head. The observer is playing the game and it is through the playing of the game that the observer comes into being.
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