Discovering the discovery of Linguistic Geometry
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ORIGINAL ARTICLE
Discovering the discovery of Linguistic Geometry Boris Stilman
Received: 12 April 2012 / Accepted: 8 June 2012 Springer-Verlag 2012
Abstract Linguistic Geometry (LG) is a type of game theory for extensive discrete games scalable to the level of real life defense systems. This scalability is based on changing the paradigm for game solving—from search to construction. LG was developed by generalizing experiences of the advanced chess players. LG is a formal model of human reasoning about armed conflict, a mental reality ‘‘hard-wired’’ in the human brain. It appears that this algorithm, an evolutionary product of millions of years of human warfare, served in its turn as the principle mover for evolution of human intelligence. Its special role in human history and its relationship to the Primary Language of the human brain (as introduced by J. Von Neumann) suggest that the experiences of development of LG must be instructive for solving another major puzzle, discovering the Algorithm of Discovery. This algorithm should be an ancient component of the Primary Language as well. This paper refining our experiences of discovering LG reports the first results of this research. Keywords Linguistic Geometry Primary Language Artificial intelligence Algorithm of discovery Game theory Visual stream
B. Stilman University of Colorado Denver, Denver, CO, USA B. Stilman (&) STILMAN Advanced Strategies, Denver, CO, USA e-mail: [email protected]
1 Introduction Linguistic Geometry (LG) [26] is a game-theoretic approach that has demonstrated a significant increase in size of problems solvable in real time (or near real time). This paper continues a series of papers [35, 36, 27, 28] intended to investigate role of LG in human culture. In here, I will make the next step by utilizing vast experiences of developing LG for discovering the algorithm of discovery. In this paper I will focus on the processes that led to major advances in LG. I will show that they resulted from the interplay of the socalled mental visual streams and only later were wrapped into the formal mathematics and computer programs. Even this wrapping was rooted in those visual streams. Note that this approach is different from the typical algorithms of ‘‘discovery’’ in data mining, e.g., [45, 46]. Here, I attempt to model human algorithm for making discoveries, a major product of evolution of human intelligence. The word Linguistic refers to the model of strategies formalized as a hierarchy of formal languages. These languages and their translations are the constructs that permit us describe strategies leading the game from state to state. These languages utilize a powerful class of generating grammars, the controlled grammars [26], which employ formal semantics of the game to control generation of a string of symbols using mutual influence of the substring generated so far and the grammar’s environment. The word Geometry refers to the geometry of the game state space, SPACE (Sect. 3), which is a set of all the states resulting
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