Thursday, 15 September 2016

Language between Sergej Karcevskij and string theory, one century's trace / Book and paper index edition



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

The 30th Anniversary of Sekinan Library Memorial Essay


TANAKA Akio




Sekinan Library
Tokyo


.................................................................................................................................................

Sekinan Library, Tokyo






FIRST PUBLISHED, August 2016 

....................................................................................................................................................



Contents

Preface
Figure

1
1-1 Language, physics and abstract
1-2 Set theory
1-3 Bourbaki
1-4 Decipherment
1-5 Linguistic Circle of Prague
2
2-1 Quantum Theory for Language
2-2 von Neumann algebra
2-3 Category
2-4 Deformation of complex structure
2-5 Symplectic geometry
3
3-1 Amalgamation of mathematics and physics
3-2 Derived category
3-3 Ambiguity of language
3-4 Distance
3-5 Seiberg-Witten equation
3-6 Derived Category Language
4
4-1 Material
4-2 Conjecture and evidence
4-3 True-false problem
4-4  Bridge
5
5-1 Philosophy
5-2 String theory
5-3 Direction for further step
6
6-1 Thanks
6-2 Outlook

Appendix
1. Chronicle
2. Theory
3. Story

References

Search
1. General
2. Zoho
3. Essay
4. Paper
5. Essay and paper

Link
1. Site
2. Twitter

Index
1. File
2. Person
3. Place
4. Book
5. Term
6. Japanese Edition Essay
7. Paper


..................................................................................................................................................

Preface


When I started Sekinan Library at Tachikawa, Tokyo on 1 April 1986, I was 38 years old, after I left the seven year post-graduate study at university at March.  
At first I thought that ideogram would become the main study target for several years as the preparatory work for language universals ever being taught from CHINO Eiichi related with Linguistic Circle of Prague in 1920s. But ideogram being typical by Chinese characters is very hard to write down by the clear description using mathematical approach. several years passed by grope for adequate approach to ideogram's meaning structure.

In May 2003 I  happened to see the application of paper on the Silk Road area's  history and culture. I determined to entry this chance by writing a clear and understandable approach to the meaning of vast and vague world of ancient written Chinese's grammatical structure. In summer that year I wrote over the paper, Quantum Theory for Language that was aimed complex grammar inherent in Chinese characters itself. The paper was presented at the literature section of symposium opened at Nara, Japan in December 2003. At this symposium I met many foreign researchers especially from East Europe and East-central Asia whose mother languages were of course diverse but all headed for the Silk Road's history and culture. At that time I determined that my primary way to convey was for them who might not be interest in my tiny study. 

I put small laboratory for language study especially aiming for language universals from the point of view at using ideogram, so to say characters,  in the daily life now in Japan. European alphabets had already lost ideogram's function. The study of Linear B sent me the complicated situation of ancient Greece and its surrounding areas. My small lab was named Sekinan Research Field of Language. Its location was Hakuba, Nagano, Japan where I completed the proto-paper of symposium's presentation, that was titled On Time Property Inherent in Characters. 

In March 2003 I stayed at Hakuba and wrote a short manuscript for universal grammatical structure. Now I later named Manuscript of Quantum Theory for Language. It was unfinished paper because of the not having the efficient accumulation continuing the clear description to the others attracted in language. Still now I have walked on the way to the hard target of the study on language or language universals.   

Note 1 

  1. The days of Sekinan Library / 2015
  2. Road to Language Universals / 2012

Note 2
  1. Description / 2013
  2. The First Paper Inherent time in Word / 2014

Note 3
  1. Fortuitous Meeting / 2004-2015
  2. Linguistic Circle of Prague / 2012
  3. Prague in 1920s / 2015-2016

Note 4
  1. Manuscript of Quantum Theory for Language / 2003
  2. On Time Property Inherent in Characters / 2003
  3. Quantum Theory for Language / 2004


TANAKA Akio
August, 2016


..................................................................................................................................................
  1.  

..................................................................................................................................................



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. Macro Time and Micro Time / 2013
  2. Presupposition on Natural Language / 2012

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. Linguistic Circle of Prague / 2012
  2. On Structure / 2009

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. The Days of Language / 2012

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.

  1. The Days of Decipherment / 2016​
  2. Glitter of youth through philosophy and mathematics in 1970s / 2015
  3. The Time of WANG Guowei / 2011

1-5 Linguistic 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.

  1. Prague in 1920s / 2015
  2. The Time of Wittgenstein / 2012
  3. For WITTGENSTEIN Ludwig Revised / 2005 - 2012

2.
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.
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.

  1. The Day of von Neumann Algebra / 2015

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.


  1.  For MAC LANE Saunders Categorical Approach toward Language / 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.

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


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.

  1. Symplectic Language Theory / 2009
  2. Floer Homology Language / 2009
  3. Model Simplified Level 2 / 2005


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.  

  1. Language, Amalgamation Mathematics and Physics / 2015 
  2. Perhaps return to physics / 2014 
  3. 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.

  1. Bridge across mathematics and physics / Revised / 2016
  2. 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.

  1. Thanks to physics through which I ever dreamt in my future / 2016
  2. Clifford Algebra Note 5 TOMONAGA’s Super Multi-time Theory
  3. Gromov-Witten Invariantational Curve / 2009​

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.

  1. Distance Theory / 2004
  2. Distance Theory Algebraically Supplemented Brane Simplified Model 1 Bend / 2007 
  3. 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. 

  1. Clifford Algebra Note 4 Dirac Operator From 3-dimensional Spinor Group to 4-dimensional Spin Manifold /  2008

3-6 Derived Category Language
At the third stage and now, derived category has shown me the new bridge between language, physics and mathematics.

  1. Derived Category Language 1, Category theoretic mirror symmetry conjecture / 2016
  2. Karcevskij conjecture 1928 and Kawamata conjecture 2002 / 2016
  3. Derived Category Language 2 Kawamata Conjecture / 2016

Derived Category Language's contents are the next.
  1. Derived Category Language 1 - 13 / 2016

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.

  1. Perhaps return to physics

4-2 Conjecture and evidence
TODA Yukinobu's book taught me the precious paper on the correlation between physics and mathematics.

  1. 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
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.

  1. True-false problem of the Crete / 2013
  2. Papers on language dimension In chronological order / 2015

2) Infinite division problem is also famous by rabbit-tortoise race.

  1. von Neumann Algebra 3 Note 1 Properly Infinite

3) Stability of word was presented by Sergej Karcevskij's conjecture at Linguistic Circle of Prague.

  1. Parts and Whole / 2013
  2. Derived Category language 3 Language stability and triangulated category / 2016

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.

  1. THE ROAD TO REALITY A Complete Guide to the Laws of the Universe, 2005 by Roger Penrose / 2012    


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.

  1. Substantiality Dedicated to SAPIR Edward / 2005
  2. Pleasure of Mathematics / 2014

Bridge across physics and mathematics is shown at the next trial paper.

  1. Derived Category Language 1, Category theoretic mirror symmetry conjecture / 2016

This bridge is all according from TODA Yukinori's book.

  1. Bridge across mathematics and physics / Revised / 2016

5.
5-1 Philosophy
I may go back to the complex mixture of physics, mathematics and at last philosophy.

  1. ​Glitter of youth through philosophy and mathematics in 1970s / 2015
  2. For WITTGENSTEIN Ludwig Revised. Position of Language / 2004-2014
  3. ​The Essence of Language. Seeing the exhibition TREASURES OF ANCIENT GREECE, Tokyo National Museum / 2016

5-2 String theory
From the standpoint of mathematical view, string theory in physical field has some conjectures at the premise for discussing at the present.  This situation resembles the relationship between language and mathematics. I ever tried to describe the whole image of language using physical terms. By the trial, whole image emerged rather clearer than classical linguistic approach. But the premise of language's location has been conjectured not to verify any substantial evidence. The details are at the next paper.

Distance Theory Algebraically Supplemented
Brane Simplified Model  1 Bend



5-3 Direction for further step
In language, basic terms for understanding the structure have been prepared at the history of study. One of the most fundamental terms seems to be distance.  Because All the moving existence have distance,  Refer to the next.

                                      Distance Theory Algebraically Supplemented
Brane Simplified Model Escalator Language Theory>  2 Distance
Direct Succession of Distance Theory
6.
6-1 Thanks
All the thanks are belonged to the next.

[Philosophy]
  1. PASCAL Blaise: Macro Time and Micro Time / 2013
  2. WITTGENSTEIN Ludwig: The Time of Wittgenstein  / 2012
[Language]
  1. CHADWICK John: The Essence of LanguageSeeing the exhibition TREASURES OF ANCIENT GREECE, Tokyo National Museum / 2016
  2. DUAN Yucai:  
  3. KARCEVSKIJ Sergej: Sergej Karcevskij, Soul of Language / 2012
  4. SAPIR Edward: Substantiality Dedicated to SAPIR Edward / 2005 
  5. WANG Guowei: The Complete Works of WANG Guowei, Revised / 2012  40 years passed I read WANG Guowei / 2013
[Physics]
  1. BOURBAKI Nicolas: Bourbaki' ELEMENTS DE MATHEMATIUE THEORIE DES ENSEMBLES Fascicule de resiltats Troisieme edition, 1964 / 2012　
  2. KURATA Reijiro: KURATA Reijiro's Phrase
  3. TANIYAMA Yutaka: The Complete Works of TANIYAMA Yutaka / 2012 
  4. TODA Yukinobu: Bridge across mathematics and physics / Revised / 2016

6-2 Outlook
Derived category may open the new frontier for language and string theory in the sight.
  1. Kontsevich's conjecture Category theoretic mirror symmetry conjecture / 2016
  2. Derived Category Language 1 / Category theoretic mirror symmetry conjecture / 2016
  3. Karcevskij conjecture 1928 and Kawamata conjecture 2002 / 2016


..................................................................................................................................................



Appendix
1. Chronicle
  1. Chronicle / 2015

2. Tree
  1. Genealogical Tree of Sekinan's Paper Sixth Edition / 2015

     3. Story
    1. To Winter / 2015
    2. 10 Extracts from Story, To Winter, 2015


    Theory

    2003
    1. On Time Property Inherent in Characters


    2004
    1. Quantum Theory for Language
    2. Distance Theory
    3. Prague Theory
    4. Reversion Theory
    5. Mirror Theory
    6. Mirror Language
    7. Guarantee of Language
    8. Property of Quantum
    9. Quantification of Quantum
    10. Actual Language and Imaginary Language
    11. Guarantee of language
    12. Place where quantum of language exists
    13. Actual language and imaginary language
    14. Property of quantum
    15. Quantification of quantum  
    16. Direction
    17. Uniformity

    2005

    2007
    1. Algebraic Linguistics


    2008

      1. Clifford Algebra
      2. Energy Distance Theory
      3. Functional Analysis
      4. Holomorphic Meaning Theory
      5. Kac-Moody Lie Algebra 
      6. Operator Algebra
      7. Reversion Analysis Theory
      8. Stochastic Meaning Theory
      9. von Neumann Algebra
      10. Complex Manifold Deformation Theory 
      2009
      2016
      Faq




      References
      1
      1. LITTLE Williams et al. The Shorter Oxford English Dictionary. Oxford. 1933.  Revised 1958. Tradition of Dictionary / 2012
               2. KANNO Michiaki. JIgen. Tokyo. 1923.
      2.
      1. DUAN Yucai:  Suowenjiezi. Reprint Edition. Taibei. 1972. Prague Theory Dedicated to KARCEVSKIJ, PRAGUE and CHINO / 2004 
      2. WANG Guowei. WANG Guowei Quanji Riji. Beijing. 1978. The Complete Works of WANG Guowei, Revised / 2016
      3. JAKOBSON Roman and WAUGH Linda. THE SOUND SHAPE OF LANGUAGE. Indiana. 1979. Roman Jakobson / 2012
      4. SAPIR Edward, Language. 1921. Substantiality Dedicated to SAPIR Edward / 2005 Edward Sapir&s Language, 1921 / 2014
        
      3.
      1. PASCAL Blaise. PENSEES. Translated and Introduction by A.J. Krailsheimer. PENGUIN BOOKS. 1966. Macro Time and Micro Time / 2013
      2. WITTGENSTEIN Ludwig. TRACTATUS LOGICO-PHILOSOPHICUS. Translated by C.K.Ogden. 1922. Dover edition. 1999. Citation from Ludwig Wittgenstein / 2012
      3. SHAKESPEARE William. THE COMPLETE WORKS. Oxford. 1988. Henry the Fourth, For SAEKI Shizuto and Shakespeare / 2012.
      4.
      1. NAMBU Yoichiro. Development of Particle Physics. Tokyo. 2009.
        5.
        1. FUKAYA Kenji. Symplectic Geometry. Tokyo. 2008. 
        2. TAKEUCHI Gaishi.  
        3. TODA Yukinobu. Several problems on derived category of coherent sheaf. Tokyo. 2016.Bridge across mathematics and physics / Revised / 2016



        Search

        1.General



        Link
        1. Site



            Index
            It  is used for the outer essays and papers of Sekinan Library's sites.

            1. File
            1. File / 2003-2007
            2. Zoho wiki index / 2016
            3. SRFL Essay. top-page Search site-window / 2015-2016
            4. SRFL Paper. top-page Search site-window / 2015-2016

              2. Person
              1. BOURBAKI Nicolas
              2. CHADWICK John
              3. CHEN Donhai
              4. CHINO Eiichi
              5. CHO Shokichi
              6. CHOMSKY Noam
              7. DUAN Yucai
              8. FUKAYA Kenji
              9. Godel Kurt
              10. JAKOBSON Roman
              11. KAJIMURA Hideki
              12. KANEKO Yutaka
              13. KARCEVSKIJ Sergej
              14. KARLGREN Bernhard
              15. KONTSEVICH Maxim
              16. KURATA Reijiro
              17. LITTLE Williams
              18. MURAVIJOVA Natary
              19. NAMBU Yoichiro
              20. NISHI Junzo
              21. ONO Shinobu
              22. PASCAL Blaise
              23. PENROSE Roger
              24. SAEKI Shizuto
              25. SAITO Kohei
              26. SAPIR Edward
              27. SHAKESPEARE William
              28. SINAI Yakob G.
              29. SONTAG Susan
              30. TAKENOUCHI Osam
              31. TAKEUCHI Gaishi
              32. TAN Sitong
              33. TANIYAMA Yutaka
              34. TODA Yukinobu
              35. TOMONAGA Shin-ichiro
              36. VENTRIS Michael
              37. von NEUMANN John 
              38. WANG Guowei
              39. WANG Niansun
              40. WANG Yinzhi
              41. WAUGH Linda
              42. WITTGENSTEIN Ludwig
              3. Place
              1. Hakuba
              2. Kanda
              3. Linguistic Circle of Prague
              4. Prague
              5. Sekinan Library
              6. SRFL
              7. Tachikawa
              8. Ueno
              Tokyo National Museum, Ueno, Tokyo, 2011

              4. Book
              5. Term
              1. algebraic
              2. amalgamation
              3. category
              4. conjectures
              5. description
              6. dimension
              7. disposition
              8. elements
              9. energy
              10. faq
              11. flow
              12. genealogical tree
              13. jiaguwen
              14. language universals
              15. Linear B
              16. meaning minimum
              17. model
              18. set theory
              19. Small study
              20. stability
              21. themes
              22. time in word
              23. Xiaoxue 
              6. Japanese Edition Essay
              7. Paper



              ..................................................................................................................................................

              Tokyo
              16 August 2016 - 16 September 2016
              Posted by at

              No comments:

              Post a Comment

              Subscribe to: Post Comments (Atom)