Discovering the discovery of the hierarchy of formal languages
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ORIGINAL ARTICLE
Discovering the discovery of the hierarchy of formal languages Boris Stilman
Received: 13 September 2012 / Accepted: 18 December 2012 Springer-Verlag Berlin Heidelberg 2013
Abstract The hierarchy of formal languages is a mathematical representation of linguistic geometry (LG). LG is a type of game theory for a class of extensive discrete games called abstract board games (ABG), scalable to the level of real life defense systems. LG is a formal model of human reasoning about armed conflict, a mental reality ‘‘hardwired’’ in the human brain. LG, an evolutionary product of millions of years of human warfare, must be a component of the primary language of the human brain (as introduced by Von Neumann). Experiences of development of LG must be instructive for solving another major puzzle, discovering the algorithm of discovery, yet another ancient component of the primary language. This paper reports results on discovering mental processes involved in the development of the hierarchy of formal languages. Those mental processes manifesting execution of the algorithm of discovery are called visual streams. This paper reveals the visual streams that were involved in the thought experiments led to the development of the formal theory of LG. Specifically, it demonstrates the streams involved in choosing the formal-linguistic representation of LG; the type of formal languages and grammars, the so-called controlled grammars; the construction of the grammars of shortest trajectories and the grammar of zones. This paper introduces a hypothesis of how we construct and focus visual streams.
B. Stilman (&) STILMAN Advanced Strategies, Denver, CO, USA e-mail: [email protected] B. Stilman University of Colorado Denver, Denver, CO, USA
Keywords Linguistic geometry Primary language Artificial intelligence Algorithm of discovery Game theory Formal language Formal grammar Visual stream
1 Introduction A highly intriguing and difficult issue is an algorithm of discovery, i.e., an algorithm of inventing new algorithms and new models. I suggested [36–38] that all the human discoveries from mastering fire more than a million years ago to revealing the structure of DNA and constructing a nuclear reactor in the twentieth century utilized this algorithm. The algorithm of discovery should be a major ancient item ‘‘recorded’’ in the primary language of the human brain (suggested by von Neumann [47]) due to its key role in the development of humanity. This is a line of research that I have been pursuing in [36–38]. It involves investigating past discoveries and experiences of construction of various new algorithms, especially, those I have been involved in. In my opinion, this research would allow me to make a step towards understanding this major puzzle of making discoveries. I investigated several processes that I was involved in while developing important algorithms and representations at different times in the 1980s and 1990s [37, 38]. I also compared my investigations with published introspecti
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