Language between Sergej Karcevskij and string theory, one century's trace
1.
1-1 Language, physical and abstract
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.
1-2 Set theory
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.
1-3 Bourbaki
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.
1-4 Decipherment
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.
- The Days of Decipherment / 2016
- Glitter of youth through philosophy and mathematics in 1970s / 2015
- The Time of WANG Guowei / 2011
1-5 Linguisitic Circle of Prague
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.
- Prague in 1920s / 2015
- The Time of Wittgenstein / 2012
- For WITTGENSTEIN Ludwig Revised / 2005 - 2012
2.
2-1 Quantum Theory for Language
2-1 Quantum Theory for Language
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.
2-2 von Neumann algebra
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.
2-3 Category
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.
2-4 Deformation of complex structure
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.
2-5 Symplectic geometry
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.
3.
3-1 Amalgamation of mathematics and physics
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.
- Language, Amalgamation Mathematics and Physics / 2015
- Perhaps return to physics / 2014
- Half farewell to Sergej Karcevskij and the Linguistic Circle of Prague / 2013
3-2 Derived category
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.
- Bridge across mathematics and physics / Revised / 2016
- Derived Category Language 1, Category theoretic mirror symmetry conjecture
3-3 Ambiguity of language
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.
- Thanks to physics through which I ever dreamt in my future / 2016
- Clifford Algebra Note 5 TOMONAGA’s Super Multi-time Theory
3-4 Distance
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.
- Distance Theory / 2004
- Distance Theory Algebraically Supplemented Brane Simplified Model 1 Bend / 2007
- Distance Theory Algebraically Supplemented Brane Simplified Model 2 Distance / 2007
Overview on distance is the next.
3-5 Seiberg-Witten equation
At the second, Clifford algebra opened the stiff combination between physics and algebra containing Dirac operator and Seiberg-Witten equation.
3-6 Derived Category Language
At the third stage and now, derived category has shown me the new bridge between language, physics and mathematics.
- Derived Category Language 1, Category theoretic mirror symmetry conjecture / 2016
- Karcevskij conjecture 1928 and Kawamata conjecture 2002 / 2016
- Derived Category Language 2 Kawamata Conjecture / 2016
Derived Category Language's contents are the next.
4.
4-1 Material
Physics' logic is not thorough in comparison with mathematics' theoretical way. But physics has at last verification by material.Language is also material as speak, hear, write and letter. In high school days I liked physics, probably through which I thought that the essence of material could be seen. Alike many other natural materials, language has enough wide diversity in it. I finally select language as my study way to nature.
4-2 Conjecture and evidence
TODA Yukinobu's book taught me the precious paper on the correlation between physics and mathematics.
- Black hole attractors and the topological string Hirosi Ooguri, Andrew Strominger, and Cumrun Vafa Phys. Rev. D 70, 106007 – Published 19 November 2004. arXiv:hep-th/0405146.
This paper's abstract at the head is the following.
Abstract
A simple relationship of the form ZBH = |Ztop| 2 is conjectured, where ZBH is a supersymmetric partition function for a four-dimensional BPS black hole in a Calabi-Yau compactification of Type II superstring theory and Ztop is a second-quantized topological string partition function evaluated at the attractor point in moduli space associated to the black hole charges. Evidence for the conjecture in a perturbation expansion about large graviphoton charge is given. The microcanonical ensemble of BPS black holes can be viewed as the Wigner function associated to the wavefunction defined by the topological string partition function.
At this abstract, authors conjectured the relationship ZBH=|Ztop|2 and also wrote evidence for the conjecture. This is the way of physics. I would like to write these style paper , which cannot be written forever for my talent.
4-3 True-false problem
A simple relationship of the form ZBH = |Ztop| 2 is conjectured, where ZBH is a supersymmetric partition function for a four-dimensional BPS black hole in a Calabi-Yau compactification of Type II superstring theory and Ztop is a second-quantized topological string partition function evaluated at the attractor point in moduli space associated to the black hole charges. Evidence for the conjecture in a perturbation expansion about large graviphoton charge is given. The microcanonical ensemble of BPS black holes can be viewed as the Wigner function associated to the wavefunction defined by the topological string partition function.
At this abstract, authors conjectured the relationship ZBH=|Ztop|2 and also wrote evidence for the conjecture. This is the way of physics. I would like to write these style paper , which cannot be written forever for my talent.
4-3 True-false problem
Natural language has several knotty problem by which we are puzzled, for example true-false problem, infinite division problem, stability of word, word order and so on.
1) True-false problem is very famous by True-false circulation of the Crete. This problem is related with dimension.
2) Infinite division problem is also famous by rabbit-tortoise race.
3) Stability of word was presented by Sergej Karcevskij's conjecture at Linguistic Circle of Prague.
4) Word order has many approaches, typically by Noam Chomsky.
For the upper problems my basic attitude has been consistently kept by Roger Penrose's next saying.
4-4 Bridge
Repeatedly say, language has two phases, one is substance and the other is abstract. The two are owed by physics and mathematics.
Bridge across physics and mathematics is trially shown at the next paper.
This bridge is all according from TODA Yukinori's book.
# This essay is unfinished
