SRFL News: Language between Sergej Karcevskij and string theory, one century's trace / 27 August 2016 Edition

Language between Sergej Karcevskij and string theory, one century's trace

TANAKA Akio

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About 2005 I had been seeking and groping the very methodology of describing the model of language. Manifestation of language is always physical by speaking or writing. And the being carried by language is abstract or concept in the thinking of human being. I could not deal adequately this estrangement of utterly contrary.

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Long ago in my age 20s when I met with set theory being typical by Kurt Godel, I dreamt that someday in the near future language could be written clearly by set theory because for example true-false situation became sharply distinct using set theory. Godel's Completeness theorem and Incompleteness theorem were shining above the night sky, which was full of the hardest problems on meaning kept from the Linguistic Circle of Prague for me. In those days I always referred to TAKEUCHI Gaishi's shorter and readable articles.

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But in my ability, the questions could not be solved for even the first elementary steps. The hardest barrier was at the complex situation that language was physical and at the same time was abstract. Say in another simple way physical phase was belonged to physics and abstract phase was belonged to mathematics. But my poor ability could not be endured at this complex combination or chaotic conditions. Surely meaning was far more vast, deep and sophisticated than my shallow thinking. Even so I had not stop learning beginner's mathematics through Japanese translated edition of Bourbaki sought at the old bookshops at Kanda, Tokyo where I was frequently roaming about for thinking of the next step I could adopt.

The Days of Language / 2012

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Going back to my age early 20s, 1970s my every day main work was to read Chinese Qing dynasty's linguistic books that were annotated for Chinese Classics almost written till Zhou period before 256 B.C. The most charming theme was Jagu wenzi that were old Chinese characters written on the tortoise' shells. WANG Guowei wrote vast impressive works at this field. I read his papers one by one from the shorter pieces. I also read DUAN Yucai who was the most respected linguist in Qing dynasty by WANG Guowei. His masterpiece was Shuowenjiezi that were written for characters' form and meaning. Michael Ventris' decipherment of Linear B in 1950s at UK was very interesting and encouraged for researching Oriental ideogram.

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I was born in 1947 and now 2016 I am 69 years old. My age 30s and 40s were passed by reading Chinese and Japanese classics mainly written by Chinese characters for understanding two country's ideogram history. In those days I never abandoned my main theme on understanding the essence of language through clear description using mathematical tools, which gradually declined to geometry for easier approach and more applicable to ideogram. And at last my teacher CHINO Eiichi gave me the decisive theme on language in my career. It was a Sergej Karcevskij's conjecture that were written for the Linguistic Circle of Prague, "Du dualisme asymetrique du signe linguistique", Travaux du Cercle Linguistique de Prague 1. Karcevskij's paper perfectly determined my doubt on language research, that how the description could be realised from the sharp premise like mathematics' theorem. Karcevskij showed us the clear distinction between stable and unstable in a word's meaning. I felt that the direction pointed Karcevskij was to easy to enter against the high cliff of language study till when I could not possibly come through philosophical thinking affected by Ludwig Wittgenstein in my youth.

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In 2003 I wrote Quantum Theory for Language, that is the mixture of classical grammar and intuitive philosophical approach mainly focusing the combination between two words. The paper was adopted the oral presentation at the International Conference of Silk Road 2003 held at Nara, Japan. But I did not satisfied the contents of the paper. The principal reason was that the way of proceeding the theme depended on the over weight of philosophy that was could never deny the theme from anyone who had the questions to my paper. I felt that it was not my way.

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After the paper, Quantum Theory for Language, I successively wrote several papers aiming to make the models for language universals, but almost all were intuitive and not satisfied though some were rather good from the points of view. And another reason not so contented was at the not-clarified elements between physical and mathematical, so to say, the two world, material and abstractness. I had felt long time that I could not find any bridge across the two. Language is physical at phenomenon and also abstractness at thinking. I had been swaying at philosophy , physics and mathematics. The exit could not be found in my age 40s. There were some buddings in the daily work. The big one was at geometry that was very intimate form the start of mathematics and often became the effective tool for solution. Geometry is abstract and at the same time realistic in daily life. Circle is closed at image but circumference is infinite at the movement. I gradually came near to algebraic geometry for its clarity and intimates. In the work, von Neumann Algebra became the most important tool for my aim.

The Day of von Neumann Algebra / 2015

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And yet the bridge across physics and mathematics was the difficult problem to confronting along the way. In those days I met one method to describe the bridge possibly. It was Category, probably in 2005. Saunders Mac Lane's Category for the Working Mathematician, 1998. I trial wrote 3 papers along with Mac Lane's theoretical basis. The first impression to category was alike set theory for me.

There existed a sort of free and flexibility which open a new world of interdisciplinary field of mathematics and physics. But at that time I felt that category was not enough mature to span the two field, mathematics and physics with a bridge. So I once retreated from this new fascinating approach. It depended solely on my lack of researching talent. The date was in 2006 - 2007.

For MAC LANE Saunders Categorical Approach toward Language / 2006-2007

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von Neumann Algebra showed me the decisive direction for describing my image of language universals. But my accumulation on mathematics was so poor to describe over only one small subject of my desire. I had to learn mathematical basis from the beginning point day by day while I had decided to keep on reading the new way and results of contemporary mathematics. In 2008 I wrote several papers on complex structure's deformation being assisted the fine book, Complex structure's deformation and period, SHIMIZU Yuji and UENO Kenji, 2008. Details are shown next. These tiny papers gave me the concrete way to language universals decisively.

The days between von Neumann Algebra and Complex Manifold Deformation Theory / 2015

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After Complex Manifold Deformation Theory, I wrote several papers through fascinating approach by algebraic geometry, among which symplectic geometry was the most pleasant way for making the model of language universals.

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Symplectic geometry seemed to be nearly embodied the ideal model for language universals, but to which I felt somewhat over-separated from natural language at that time. Once more I had to return the basic situation which connect more closely between nature and abstractness. I wanted to contain physical elements in the mathematical abstractness. Energy, boundary and distance were the typical factors for the new models of amalgamation of mathematics and physics. The new fields for language changed the the themes of language universals up to now. That is to say, the heritage of Sergej Karcevskij and the linguistic circle of Prague were still important but at the time apparently become one of the researching themes for language universals, which was probably wider and deeper than 1920s' study awareness. It was so natural thinking of one century's development of mathematics and science.

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In May 2016 I read TODA Yukinobu's Several problems on derived category of coherent sheaf , Sugaku Shobo, Tokyo, 2016, which was let me confirmed the connection between mathematics and physics from the clear theorem- based mathematical standpoint. I have kept a little distance from physical-based approach of contemporary themes, especially on string theory. But TODA's book shows me the descriptive clarified connection between mathematics and physics from the update theorem results of symplectic geometry and derived category. I wrote trial papers being assisted by TODA's book. Details refer to the next.

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My start of study went back to high school days's physics. Mathematics seemed to be the important basis for physic in those days. Nobel Prize winner in physics TOMONAGA Shin-ichiro was the admiration of students, who got the prize by the renormalization theory using the Super-multi-time theory. From the days of school, I maybe have gone through the winding road till now, when string theory has emerged with my interest for the ambiguity spreading of materials's minimum element which is assembling with language's ambiguity through digital processing by computer.

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At first, language and string theory were connected by the concept on distance in word, which contains meanings accumulated from old to new. Distance is one of the most fundamental elements in nature, where various materials including language are coexisted. In my part, early time's intuitive distance has gradually developed to be worth of describing by mathematical or physical way.

Overview on distance is the next.