1. Through natural language, in human being, occurred the electrical signal by eye or ear. These complex situations are beyond this paper’s limits.

2. Language is a physical object as signal and its transmission. At this circumstances, language must be recognised to be the existence that has finite time.

3. An apple on the desk gradually becomes rotten by passing the time very after the crop in the orchard. #0

4. Like an apple, language has passing physical time in oneself.

5. Language is metamorphosed  by the time progressing.  #1

6. Language includes the outer world from human being to universe. At this declaration, I recall Blaise Pascal’s Pensées. XXXIII. PROOFS OF JESUS CHRIST 308 The infinite distance between body and mind symbolizes the infinitely more infinite distance between mind and charity, for charity is supernatural.(Translated by A.J. Krailsheimer, 1966) #2

7. Language’s time goes freely from the present to the future or the present to the past. #3

8. Language symbolises the time from finiteness to infinity. #4

9. Human being recognises this vast language world perfectly. #5

 

References

 

 

Source: https://atbankofdam.wiki.zoho.com/Macro-Time-and-Micro-Time.html

To be continued.

Author. 

My poor study was restricted in a narrow field of Chinese classical linguistics mainly developed in the late Qing dynasty the latter half of the 19th century,represented by DUAN Yucai, WANG Niansun, WANG Yingzhi, my favourite WANG Guowei and so forth.

So I determined that my approach to language was only in it and it was the most intimate for me at that time and probably herein after considering my tiny accumulation of study.

Next essay shortly showed the situation in 2002.


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Read more: https://srfl-lab.webnode.com/news/quantum-group-language-word-indexed-and-word-synthesized/
 

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Chinese belongs to the isolated language.

In Chinese one character has one meaning and becomes a word in classical usage. Modern Chinese has many words that contain two or over two characters for one meaning, but basically almost all the characters have still classical one-character-one-meaning usage at the root of language.

Shuowenjezi Zhu written by DUAN Yucai typically shows some 2,000 year history of characters and their meanings.

Modern Chinese precisely said by Hanyu is one language of the over 50 languages officially recognized at the research, and I only know several language's grammars by the field work by linguists.

 

National Minority Languages in China   2004

 

 Xixiayu is a very interesting for me resembling the Hanyu and in the late 20th century the language was deciphered by Japanese linguist NISHIDA Tatsuo.

 

The Days of Decipherment

TANAKA Akio

On 20 July 2016 I went Tokyo National Museum, Ueno Park, Tokyo to see the exhibition A JOURNEY TO THE IMMORTALS: TREASURES OF ANCIENT GREECE, where I saw the linear A and B. It reminds me the youth days, so to say, the days of decipherment.

1960s -1970s is the age of decipherment in a sense. I was age 20 in 1967 and was learning language and literature at university. In 1958 John Chadwick's THE DECIPHERMENT OF LINEAR B was published from Cambridge University Press. At the preface of the book he wrote that the decipherment of linear B was told  at Documents in Mycenaean Greek (Cambridge University Press, 1956) and Michael Ventris that deciphered the Linear B.

In the same age in Japan, Xixia wenzi (Xixia characters) in China was deciphered by NISHIDA Tatsuo (1928-2012) who wrote the analysis and grammar of Xixia characters through the paper Seikamoji no bunseki narabini Seikago bunpou no kenkyuu in 1962.
In almost the same time, Inca characters were studying to decipher. I frequently heard that Russian team developed largely.

In early 1970s I frequently went to Kanda, Tokyo where old bookshops were selling vast Oriental books at the Hakusan street and Yasukuni Street. I bought Chinese classics, especially linguistic classics written in the Qing dynasty and I read them almost every day containing the comparison with the western linguistic results. The Qing dynasty's heritage were DUAN Yucai, WANG Niansun, WANG Yingzhi and WANG Guowei and so forth. DUAN Yucai's Showenjezi zhu and WANG Guowei's Guantang jilin  were the most important for me.

In France, 1960s was the days of Bourbaki that was one of the decipher of geometry by algebra, at least I thought so at that time. I sought and bought several Bourbaki's books at the old bookshops in Kanda, Tokyo,which is the largest old bookshop streets in Japan. But from my ability to mathematics Bourbaki was too much difficult to read on. From the days the long and winding road began to mathematics and its applicable study for language universals.

At the exhibition of ancient Greece I confirmed in particular that the stability of language was  kept by letters and characters from the Linear A and Linear B. 

 

These language or character's situation especially of ideogram has become my study's foundation.

 

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7.

Quantum group 2

 

In 2008 I wrote on Quantum group at studying Kac-Moody-Lie Algebra.

 

 

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Kac-Moody Lie Algebra

Note 2

Quantum Group

 

TANAKA Akio

 

 

1 <Cartan matrix>

Base field     K

Finite index set     I

Square matrix that has elements by integer     A = ( a_ij )_{i, j ∈ I}

Matrix that satisfies the next is called Cartan matrix.

i, j ∈ I

(1) a_ii = 2

(2) a_ij ≤ 0  ( i ≠j )

(3) a_ij = 0 ⇔ a_ji = 0

2 <Symmetrizable>

Cartan matrix     A = (a_ij)_i, j ∈I

Family of positive rational number    {d_i}_i∈I

Arbitrary i, j∈I    d_ia_ij = d_ja_ji

A is called symmetrizable.

3 <Fundamental root data>

Finite dimension vector space     h

Linearly independent subset of h     {h_i}_i∈I

Dual space of h     h*= Hom_K (h, K )

Linearly independent subset of h*     {α_i} _i∈I

Φ = {h, {h_i}_i∈I, {α_i} _i∈I }

Cartan matrix A = {α_i(h_i)} _{I, j∈I}

Φis called fundamental root data of A that is Cartan matrix.

4 <Standard form>

Symmetrizable Cartan matrix    A = (a_ij)_i, j ∈I

Fundamental root data     {h, {h_i}_i∈I, {α_i} _i∈I }

E = α_i ⊂h*

Family of positive rational number     {d_i}_i∈I

d_ia_ij = d_ja_ji

Symmetry bilinear form over E     ( , ) : E×E → K     ( (α_i ,α_j ) = d_ia_ij )

The form is called standard form.

5 <Lattice>

n-dimensional Euclid space    Rⁿ

Linear independent vector     v₁, …, v_n

Lattice of Rⁿ     m₁v₁+ … +m_nv_n     ( m₁, …, m_n ∈ Z )

Lattice of h     h_Z

6 <Integer fundamental root data>

From the upperv3, 4 and 5, the next three components are defined.

(Φ, ( , ), h_Z )

When the components satisfy the next, they are called integer fundamental root data.

 i ∈ I

(1)  ∈ Z

(2) α_i ( h_z ) ⊂ Z

(3) t_i :=  h_i ∈ h_z

7 <Associative algebra>

Vector space over K     A

Bilinear product over K     A×A → A

When A is ring, it is called associative algebra.

8 <Similarity>

Integer     m

t similarity of m    [m]_t

[m]_t = t^m-t^-m / t- t^-1

Integer   m, n   m≧n≧0

Binomial coefficient     (^m_n)

t similarity of m!     [m]_t! = [m]_t! [m-1]_t!...[1]_t

t similarity of (^m_n)    [^m_n]_t = [m]_t! / [n]_t! [m-n]_t!

[^m₀] = [^m_m]_t = 1

8 <Quantum group>

Integer fundamental root data that has Cartan matrix A = ( a_ij )_{i, j ∈ I}

      Ψ = ((h, {h_i}_i∈I, {α_i} _i∈I ), ( , ), h_z )

Generating set     {K^h}_h∈hz ∪{E_i, F_i}_i∈I

Associative algebra U over K (q), that is defined the next relations, is called quantum group associated with Ψ.

(1) k^hk^h’ = k^h+h’     ( h, h’∈h_Z )

(2) k⁰ = 1

(3) K^hE_iK^-h = q^αi(h)E_i    ( h∈h_Z , i∈I )

(4) K^hF_iK^-h = q^αi(h)F_i   ( h∈h_Z , i∈I )

(5) E_i F_j – F_jE_i = _ij  K_i - K_i^-1 / q_i – q_i^-1     ( i , j∈I )

(6) ^p [^1-aij_p]_qiE_i^1-aij-pE_jE_i^p = 0     ( i , j∈I , i ≠j )

(7) ^p [^1-aij_p]_qiF_i^1-aij-pF_jF_i^p = 0     ( i , j∈I , i ≠j )

 

[Note]

Parameter q in K is thinkable in connection with the concept of <jump> at the paper Place where Quantum of Language exists / 27 /.

Refer to the next.

Place where Quantum of Language exists / Tokyo July 18, 2004

 

Tokyo February 9, 2008

 

Sekinan Research Field of Language

 

www.sekinan.org

Read more: https://srfl-lab.webnode.com/news/kac-moody-lie-algebra-note-2-quantum-group/

 

 

 

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In 2004 I wrote the paper named Place where Quantum of Language exists.