This short paper would finally write on signal through the relation between language and nerve, for which using mathematical method at the way.
This paper's one of kernels is energy which is naturally accepted at the side of nerve, but at the side of language, it may be not accepted widely till now.
In this paper, I probably do not refer to the language's energy, that has been written several times in the papers before.
Around 2008, I was thinking on energy in language related with distance in language. Distance is one of the kernel themes of my study of language universals in those days. In simply saying, distance is the result of movement and for movement there must inevitably needs energy. So I had thought that if language have distance, there must be energy or its alike in language that is supposed in mathematical models. But in my ability in 2008, I could not develop the deep and wide range of language from the theme, energy and distance. So Energy Distance Theory was still now unfinished.
On language and human sense, I ever wrote simply at the next paper.
Macro Time and Micro time
TANAKA Akio
24 July 2013
atbankofdam
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
#0 For WITTGENSTEIN Ludwig Position of Language / December 10, 2005 – August 3, 2012 / Sekinan Research Field of Language
#1 Time of Word / Complex Manifold Deformation Theory / January 1, 2009 / sekinanlogos
#2 PASCAL PENSÉES. Translated with an introduction by A.J. Krailsheimer. PENGUIN BOOKS 1966.
#3 Escalator language and Time For SHINRAN’s Idea and BOHDISATTVA / Escalator Language Theory / December 16, 2006 / Sekinan Research Field of Language
#4 From Finiteness to Infinity on Language / Topological Group Theory / February 1, 2009 / sekinanlogos
#5 Understandability of Language / Complex Manifold Deformation Theory /January 9, 2009 / sekinanlogos
hospital by pneumonia half a month in October 2002, when I always saw the river and the mountains west end of Tokyo. I was the very reviewing life time for my research work.
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.
1970s' dream, writing clear description on language universals by mathematics
From The Days of Ideogram
4. Time property in characters
In Autumn 2002 I got pneumonia and was hospitalized about 2 weeks, where I thought of 1970s' dream, writing clear description on language universals by mathematics. The theme was as hard as ever. So, at the bed I thought the basis of language from the side of Chinese character’s classical approach which had vast heritage till Qing dynasty. I directed my attention to the character's figure which had compound meanings containing time elements continuing from Yin dynasty's hieroglyphic characters left on bones and tortoise carapaces some 2400 years ago. I thought that Chinese characters had containing time and its structure could be written by geometric approach once I had abandoned for difficulty. After leaving hospital, I wrote a paper titled On Time Property Inherent in Characters*3-1.
Word Indexed is the word that has index in a word, by which meanings are separated in a word at waiting situation. In a word meanings are combined by algebraic axioms and theorems starting from group theory.
Word Indexed seems to be more simply structure than Word Synthesized.
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.
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.
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.
1 Quantum of language is the smallest unit of language.
2 Quantum of language moves linearly on the floor of language.
3 Linear movement is the properties of quantum.
4 Floor of language is on the space of language.
5 The space of language is two dimensions.
6 Two dimensions are horizontal and vertical.
7 Horizontal movement makes word, #1
8 Vertical movement makes sentence. #1
9 The space of language is electrical digitized place.
10 Chinese /jiao shi/ means classroom in English.
11 /Jiao/ is a quantum of language.
12 /Shi/ is a quantum of language.
13 /Jiao shi/ is a word.
14 /Jiao/ sends a quantum to /shi/ quantum.
15 /Shi/ quantum receives a quantum from /jiao/ quantum.
16 What sends quantum is called positive.
17 What receives quantum is called negative.
18 Quantum has positive energy in original condition.
19 Quantum changes negative in the situation of quanta set.
20 Quantum change occurs in two situations in general.
21 One situation is what quanta stand side by side on a floor and neighboring quanta connect well. #2
22 The other situation is what quanta change oneself by the non-use of quanta meaning in language history progress. #2
23 Word has a positive- negative construction.
24 Positive-negative construction occurs on a floor.
25 Sentence has a positive-positive construction.
26 Positive-positive construction occurs on different floors.
27 The latter quantum transfers on a different floor. This transfer is called .†
28 Quantum has electrical energy which flows to the electrical zero level.
29 Electrical zero level is a sentence end where quantum of language ideally accord with the real world. #3
30 A floor of language is a non-branches electrical circuit.
31 Word is a non-branch circuit.
32 Sentence is a branch circuit.
33 The meaning of word and sentence is a compound system of electrical signals.
#1 Definition of word and sentence can be seen in the paper “Method of Linguistics” and other papers on the site of Sekinan Research Field of Language /www.sekinan.org/.
At the end of paper 2017, I wrote as the following, where I showed the early intuitive papers related with symmetry or mirror. This concept has succeeded till now and a little developed a new direction towards mathematical based concept especially of quantum group.
The concept called symmetry is very important to describe the complex situation of natural language.
Symmetry contains undifferentiated factors in itself, for example mirror, distance,ant-world and so forth.
I ever tried to cultivate this fantastic field to resolve the hardship on language universals one more step up.
Language based on quantum emerged from thinking the simplest model for containing the finite essential elements of language in summer 2003 at Hakuba, Nagano, Japan at the skirts of Japan Alps. Details are the next.
In August 2003, I went to Hakuba in Nagano prefecture for the summer vacation with my family. At that time I had been thinking on the form of language for which I wrote the paper, that connects with time inherent in characters, in March 2003 also at Hakuba.
At night of August 23 in cottage, I casually saw the advertising paper of electric dictionary. The paper was brought from the convenience store near the cottage in the evening. The dictionary on the paper was Seiko’s English-Japanese dictionary that has additionally consultation for Chinese or French language with large scale. I vaguely considered that after this dictionaries are necessarily taken these multi-lingual way.
At the time I suddenly realized that the form of language may be spherical style in which language contains all the information in itself.That was rather satisfied solution for the tough problem of language that I had been carrying in my life from my twenties.
I wrote the sketch-like paper of the theoretical approach after returning home of Tokyo. The paper was read at the international symposium of UNESCO opened in winter 2003 at Nara. In the paper, the spherical substance of language is seemed to be quantum in DELBRUCK’s image-like physical world. After 5 years from the inspiration at summer of Hakuba, now I consider that spherical essence is manifold in infinite dimensional world.
Now I also realize that the toughest problem of language is minutely solvable in mathematical approach that has structurally definable terms.
Distance is one of the most important elements of my language model of language universals. For this element algebraic approach seems to be clearer description to the model. Refer to the next paper.
Distance theory is considered for the purpose of the guarantee to language.
4
What quanta of language propel to the end of the sentence is for the purpose of the guarantee to language, in which quanta of language finally unite the real world in the end of propelling.
5
The guarantee to the inherent signification of indicator in quantum of language is quantified by the distance which starts from the real world to the quantum of language.
6
A quantum consists of indicators.
An indicator has a signification and a period inherently.
An inherent signification is an element in a quantum.
An inherent time is an element in a quantum.
There are two types of elements, significant and periodical.
Element is defined.
8
A significant element gets a signification from the real world.
A periodical element gets a time from the real world.
9
An indicator gets a meaning and a period from elements.
10
An element emerges from the real world to the language world.
An indicator gets power from the elements in the language world.
A quantum moves in the language world by the power of indicators.
11
An element emerges to the language world, because each element has immanent perceptible area which works upon visual sensation and auditory sensation of the human beings.
12
An indicator gets energy in the language world, because each indicator has a tendency which will approach and finally coincide with the real world.
This continuous tendency guarantees the trust in language for the human beings.
13
A quantum moves in the language world toward the real world.
A quantum is not guaranteed in the situation of cessation.
A quantum is guaranteed by the connection to the real world.
Therefore a quantum propels to the real world.
14
Indicators make meaning and connection rule in a quantum, both are derived from significant and periodical elements in an indicator.
15
Meaning is guaranteed by the tendency of coincidence with the real world.
Guarantee of the meaning is reduced by the remoteness of distance from the real world.
16
Connection rule is decided by periodical elements in indicators.
Signification in an indicator and meaning in a quantum once emerged are occasionally transformed or expanded in the language world.
This alteration is called multiplication.
Multiplication is defined.
18
Multiplication generally occurs by the addition of signification in an indicator.
But multiplication in meaning of a quantum sometimes occurs without any addition oneself.
19
Multiplication in a quantum without addition occurs by situational transition in the language world.
20
Situational transition in a quantum is caused by difference of distance from the real world.
Difference of distance at a quantum is a proceeding of abstract thinking in human beings.
21
A quantum of language itself becomes in the language world.
Word is defined.
Therefore each word has a distance toward the real world.
A distance immanent in a word does not emerge itself.
Distance emerges in the linear situation of words gathering.
This situation is called .
Sentence is defined.
Therefore sentence is an emergence of distance in words gathering.
Words form a line, thereafter one arrangement is determined.
Sentence is realized in our world.
22
In Chinese language, /lai/ come has a larger distance than /liao/completion.
Words are arranged from the end of a sentence, according to the own- possessing- distance.
Therefore /lai le/ having come is realized.
On symmetry I wrote Symmetry Flow Language and Symmetry Flow language 2 in 2007.
Contents are the next.
Symmetry Flow Language
On Symmetry of Language and Time
1 Premise for Symmetry Flow in Language
2 Riemannian Metric, Flow and Entropy
3 Leaf of Language Pourparlers>
4 Homology on Language
5 Simplex, Simplicial Complex and Polyhedron
6 Meaning Variation and Time Shift in Word As Homotopy
Symmetry Flow Language 2
On Symmetry of Language and Time 2
1 Boundary, Deformation and Torus as Language
2 Time Shift of Meaning in Moduli Space
2 Space that is deformed successively is described by parameter that is called moduli.
3 Set M consists of all of moduli.
4 Moduli space M (M) is presented for variation of word’s meaning.
5 Parameter t is presented for time shift of meaning in word.
6 Calabi-Yau manifold Khas two moduli that are deformation of complex structure and Kähler manifold. Moduli have symmetry that is called Mirror symmetry.
7 K’s Ricci tensor is the following.
Rij¯ = 0 i is regular coordinate. j¯ is non-regular coordinate.
Commutative von Neumann Algebra N is generated by only one self-adjoint operator.
[Proof outline]
N is generated by countable {An}.
An = *An
Spectrum deconstruction An = ∫1-1λdEλ(n)
C*algebra that is generated by set { Eλ(n) ; λ∈Q∩[-1, 1], n∈N} A
A’’ = N
A is commutative.
I∈A
Existence of compact Hausdorff space Ω = Sp(A )
A = C(Ω)
Element corresponded with f∈C(Ω) A∈A
N is generated by A.
[Index of Terms]
|A|Ⅲ7-5
|| . ||Ⅱ2-2
||x||Ⅱ2-2
Ⅱ2-1
*algebraⅡ3-4
*homomorphismⅡ3-4
*isomorphismⅡ3-4
*subalgebraⅡ3-4
adjoint spaceⅠ12
algebraⅠ8
axiom of infinityⅠ1-8
axiom of power setⅠ1-4
axiom of regularityⅠ1-10
axiom of separationⅠ1-6
axiom of sumⅠ1-5
B ( H )Ⅱ3-3
Banach algebraⅡ2-6
Banach spaceⅡ2-3
Banach* algebraⅡ2-6
Banach-Alaoglu theoremⅡ5
basis of neighbor hoodsⅠ4
bicommutantⅡ6-2
bijectiveⅡ7-1
binary relationⅡ7-2
boundedⅡ3-3
bounded linear operatorⅡ3-3
bounded linear operator, B ( H )Ⅱ3-3
C* algebraⅡ2-8
cardinal numberⅡ7-3
cardinality, |A|Ⅱ7-5
characterⅡ3-6
character space (spectrum space), Sp( )Ⅱ3-6
closed setⅠ2-2
commutantⅡ6-2
compactⅠ3-2
complementⅠ1-3
completeⅡ2-3
countable setⅡ7-6
countable infinite setⅡ7-6
coveringⅠ3-1
commutantⅡ6-2
D ( )Ⅱ3-2
denseⅠ9
dom( )Ⅱ3-2
domain, D ( ), dom( )Ⅱ3-2
empty setⅠ1-9
equal distance operatorⅡ4-1
equipotentⅢ7-1
faithfulⅡ3-4
Gerfand representationⅡ3-7
Gerfand-Naimark theoremⅡ4
HⅡ3-1
Hausdorff spaceⅠ5
Hilbert spaceⅡ3-1
homomorphismⅡ3-4
idempotent elementⅡ9-1
identity elementⅡ9-1
identity operatorⅡ6-1
injectiveⅢ7-1
inner productⅡ2-1
inner spaceⅠ6
involution*Ⅰ10
linear functionalⅡ5-2
linear operatorⅡ3-2
linear spaceⅠ6
linear topological spaceⅠ11
locally compactⅠ3-2
locally vertexⅠ11
NⅢ3-8
N1Ⅲ3-8
neighborhoodⅠ4
normⅡ2-2
normⅡ3-3
norm algebraⅡ5
norm spaceⅡ2-2
normalⅡ2-4
normalⅡ3-4
open coveringⅠ3-2
open setⅠ2-2
operatorⅡ3-2
ordinal numberⅡ7-3
productⅠ8
product setⅡ7-2
r( )Ⅱ2
R ( )Ⅱ3-2
ran( )Ⅱ3-2
range, R ( ), ran( )Ⅱ3-2
reflectiveⅠ12
relationⅢ7-2
representationⅡ3-5
ringⅠ7
Schwarz’s inequalityⅡ2-2
self-adjointⅡ3-4
separableⅡ7-7
setⅠ7
spectrum radius r( )Ⅱ2
Stone-Weierstrass theoremⅡ1
subalgebraⅠ8
subcoveringⅠ3-1
subringⅠ7
subsetⅠ1-3
subspaceⅠ2-3
subtopological spaceⅠ2-3
surjectiveⅢ7-1
system of neighborhoodsⅠ4
τs topologyⅡ7-9
τw topologyⅡ7-9
the second adjoint spaceⅠ12
topological spaceⅠ2-2
topologyⅠ2-1
total order in strict senseⅡ7-3
ultra-weak topologyⅢ6-4
unit sphereⅡ5-1
unitaryⅡ3-4
vertex setⅡ3-3
von Neumann algebraⅡ6-3
weak topologyⅡ5-3
weak * topologyⅡ5-3
zero elementⅡ9-1
[Explanation of indispensable theorems for main theorem]
ⅠPreparation
<0 Formula>
0-1 Quantifier
(i) Logic quantifier ┐ ⋀ ⋁ → ∀ ∃
(ii) Equality quantifier =
(iii) Variant term quantifier
(iiii) Bracket [ ]
(v) Constant term quantifier
(vi) Functional quantifier
(vii) Predicate quantifier
(viii) Bracket ( )
(viiii) Comma ,
0-2 Term defined by induction
0-3 Formula defined by induction
<1 Set>
1-1 Axiom of extensionality ∀x∀y[∀z∈x↔z∈y]→x=y.
1-2 Seta, b
1-3 a is subset of b. ∀x[x∈a→x∈b].Notation is a⊂b. b-a = {x∈b ; x∉a} is complement of a.
1-4 Axiom ofpower set ∀x∃y∀z[z∈y↔z⊂x]. Notation is P (a).
1-5 Axiom of sum ∀x∃y∀z[z∈y↔∃w[z∈w∧w∈x]]. Notation is ∪a.
1-6 Axiom of separationx, t= (t1, …, tn), formula φ(x, t) ∀x∀t∃y∀z[z∈y↔z∈x∧φ(x, t)].
1-7 Proposition of intersection {x∈a ; x∈b} = {x∈b; x∈a} is set by axiom of separation. Notation is a∩b.
1-8 Axiom of infinity ∃x[0∈x∧∀y[y∈x→y∪{y}∈x]].
1-9 Proposition of empty set Existence of set a is permitted by axiom of infinity. {x∈a; x≠x} is set and has not element. Notation of empty set is 0 or Ø.
1-10 Axiom of regularity ∀x[x≠0→∃y[y∈x∧y∩x=0].
<2 Topology>
2-1
Set X
Subset of power set P(X) T
T that satisfies next conditions is called topology.
(i) Family of X’s subset that is not empty set <Ai;i∈I>, Ai∈T→∪i∈I Ai is belonged to T.
(ii) A, B ∈T→ A∩B∈T
(iii) Ø∈T, X∈T.
2-2
Set having T, (X, T), is called topological space, abbreviated to X, being logically not confused.
Element of T is called open set.
Complement of Element of T is called closed set.
2-3
Topological space (X, T)
Subset of XY
S ={A∩Y ; A∈T}
Subtopological space (Y, S)
Topological space is abbreviated to subspace.
<3 Compact>
3-1
Set X
Subset of XY
Family of X’s subset that is not empty set U = <Ui; i∈I>
U is covering of Y. ∪U = ∪i∈I ⊃Y
Subfamily of UV = <Ui; i∈J > (J⊂I)
V is subcovering of U.
3-2
Topological space X
Elements of U Open set of X
U is called open covering of Y.
When finite subcovering is selected from arbitrary open covering of X, X is called compact.
When topological space has neighborhood that is compact at arbitrary point, it is called locally compact.
<4 Neighborhood>
Topological space X
Point of Xa
Subset of X A
Open set B
a∈B⊂A
A is called neighborhood of a.
All of point a’s neighborhoods is called system of neighborhoods.
System of neighborhoods of point aV(a)
Subset of V(a) U
Element of U B
Arbitrary element of V(a) A
When B⊂A, U is called basis of neighborhoods of point a.
<5 Hausdorff space>
Topological space X that satisfies next condition is called Hausdorff space.
Distinct points of X a, b
Neighborhood of aU
Neighborhood of bV
U∩V = Ø
<6 Linear space>
Compact Hausdorff space Ω
Linear space that is consisted of all complex valued continuous functions over Ω C(Ω)
When Ω is locally compact, all complex valued continuous functions over Ω, that is 0 at infinite point is expressed by C0(Ω).
<7 Ring>
Set R
When R is module on addition and has associative law and distributive law on product, R is called ring.
When ring in which subset S is not φ satisfies next condition, S is called subring.
a, b∈S
ab∈S
<8 Algebra>
C(Ω) and C0(Ω) satisfy the condition of algebra at product between points.
Subspace A ⊂C(Ω) or A ⊂C0(Ω)
When A is subring, A is called subalgebra.
<9 Dense>
Topological space X
Subset of X Y
Arbitrary open set that is not Ø in X A
When A∩Y≠Ø, Y is dense in X.
<10 Involution>
Involution* over algebra A over C is map * that satisfies next condition.
Map * : A∈A ↦ A*∈A
Arbitrary A, B∈A, λ∈C
(i) (A*)* = A
(ii) (A+B)* = A*+B*
(iii) (λA)* =λ-A*
(iiii) (AB)* = B*A*
<11 Linear topological space>
Number field K
Linear space over KX
When X satisfies next condition, X is called linear topological space.
(i) X is topological space
(ii) Next maps are continuous.
(x, y)∈X×X ↦ x+y∈X
(λ, x)∈K×X ↦λx∈X
Basis of neighborhoods of X’ zero element 0 V
When V⊂V is vertex set, X is called locally vertex.
<12 Adjoint space>
Norm space X
Distance d(x, y) = ||x-y|| (x, y∈X )
X is locally vertex linear topological space.
All of bounded linear functional over X X*
Norm of f ∈X* ||f||
X* is Banach space and is called adjoint space of X.
Adjoint space of X* is Banach space and is called the second adjoint space.
When X = X*, X is called reflective.
ⅡIndispensable theorems for proof
<1Stone-Weierstrass Theorem>
Compact Hausdorff space Ω
Subalgebra A ⊂C(Ω)
When A ⊂C(Ω) satisfies next condition, A is dense at C(Ω).
(i) A separates points of Ω.
(ii) f∈A →f－∈A
(iii) 1∈A
Locally compact Hausdorff space Ω
Subalgebra A⊂C0(Ω)
When A⊂C0(Ω) satisfies next condition, A is dense at C0(Ω).
(i) A separates points of Ω.
(ii) f∈A → f－∈A
(iii) Arbitrary ω∈A , f∈A , f(ω) ≠0
<2Norm algebra>
C* algebra A
Arbitrary element of A A
When A is normal, limn→∞||An||1/n= ||A||
limn→∞||An||1/nis called spectrum radius of A. Notation is r(A).
[Note for norm algebra]
<2-1>
Number field K = R or C
Linear space over KX
Arbitrary elements of Xx, y
< x, y>∈K satisfies next 3 conditions is called inner product of x and y.
Arbitrary x, y, z∈X,λ∈K
(i) <x, x> ≧0, <x, x> = 0 ⇔x = 0
(ii) =
(iii) , λy+z> = λ, y> + , z>
Linear space that has inner product is called inner space.
<2-2>
||x|| = <x, x>1/2
Schwarz’s inequality
Inner space X
|<x, y>|≦||x|| + ||y||
Equality consists of what x and y are linearly dependent.
||・|| defines norm over X by Schwarz’s inequality.
Linear space that has norm || ・|| is called norm space.
<2-3>
Norm space that satisfies next condition is called complete.
un∈X (n = 1, 2,…), limn, m→∞||un – um|| = 0
u∈X limn→∞||un – u|| = 0
Complete norm space is called Banach space.
<2-4>
Topological space X that is Hausdorff space satisfies next condition is called normal.
Closed set of XF, G
Open set of XU, V
F⊂U, G⊂V, U∩V = Ø
<2-5>
When A satisfies next condition, A is norm algebra.
A is norm space.
∀A, B∈A
||AB||≦||A|| ||B||
<2-6>
When A is complete norm algebra on || ・ ||, A is Banach algebra.
<2-7>
When A is Banach algebra that has involution * and || A*|| = ||A|| (∀A∈A), A is Banach * algebra.
<2-8>
When A is Banach * algebra and ||A*A|| = ||A||2(∀A∈A) , A is C*algebra.
<3 Commutative Banach algebra>
Commutative Banach algebra A
Arbitrary A∈A
Character X
|X(A)|≦r(A)≦||A||
[Note for commutative Banach algebra] ( ) is referential section on this paper.
<3-1 Hilbert space>
Hilbert space inner space that is complete on norm ||x|| Notation is H.
<3-2 Linear operator>
Norm space V
Subset of VD
Element of Dx
Map T : x → Tx∈V
The map is called operator.
D is called domain of T. Notation is D ( T ) or dom T.
Set A⊂D
Set TA {Tx : x∈A}
TD is called range of T. Notation is R (T) or ran T.
α , β∈C, x, y∈D ( T )
T(αx+βy) = αTx+βTy
T is called linear operator.
<3-3 Bounded linear operator>
Norm space V
Subset of VD
sup{||x|| ; x∈D} < ∞
D is called bounded.
Linear operator from norm space V to norm space V1 T
In Autumn 2002 I was hospitalized by pneumonia for two weeks, when I thought to put the linguistic research on old Chinese characters so far in order. The result was arranged as a paper titled On Time Property Inherent in Charactersalso at Hakuba in March 2003.
4.
Quantum Theory for Language was added proviso, Synopsis, because the paper was thought at that time as a role of a rather long mathematical paper's preface on quantum theory on language.
In 1970s at my age 20s, while I had read WANG Guowei, also read Ludwig Wittgenstein, from whom I narrowly learnt writing style that was maintained through early papers. On Wittgenstein I wrote The Time of Wittgenstein in January 2012. Especially written essayFor WITTGENSTEIN Ludwig Position of Languageintermittently wrote from December 2005 to August 2012.
13.
WANG Guowei taught me the micro phase of language and Edward Sapir taught me the macro phase of language. His book, Language 1921 shows us the conception of language's change system, Drift. I ever wrote
some essays on him and his book titled Flow of Language in September 2014.
In 1970s, I also learnt mathematics for applying to describe language's minute situation. I had thought that language had to be written clear understanding form for free and precise verification going over philosophical insight. When set theory led by Kurt Godel was raised its head to logical basis, I was also deeply charmed by it. But even if fully using it, language's minute situation seemed to be not enough to write over clearly by my poor talent. The circumstance was written titled Glitter of youth through philosophy and mathematics in 1970s in March 2015. .
17.
One day when I found and bought Bourbaki's series Japanese-translated editions, which were seemed to be possibility to apply my aim to describe language's situation. But keeping to read them were not acquired at that time. So I was engrossed in Chinese classical linguistics achieved in Qing dynasty, typically DUAN Yucai, WANG Niansun, WANG Yinzhi and so forth. The days were written as The Time of Language Ode to The Early Bourbaki To Grothendieck.
After 2008 at Zoho sites, mathematics based language papers were successively written aiming clearer definition. Zoho's annual papers are shown at Sekinan Zoho's Zoho by year from 2008 to 2013. While I continued writing papers, my aim was gradually changed to confirm language's basis through mathematical, especially algebraic geometrical description by language models a little parting from natural language. The circumstances behind confirmation was written at Half farewell to Sergej Karcevskij and the Linguistic Circle of Prague in October 2013 and 40 years passed from I read WANG Guowei in November 2013.
Signal needs energy for dispatching messages to the world by hand power of flag semaphore, hand power and electricity of Mores code and light and electricity of lighthouse.
Language also needs energy for dispatching by human voice and hand of speaking and writing. But there is not human energy, there is not language.
Signal's energy is more diverse than language's.
There is energy's diversity at the root of distinction between signal and language.
The question, what is signal is also meant what is energy.
Now I cannot describe accurate explanation to this question clearly.
Little by little it may be able to writing using mathematics hereafter.
Now I would show several trial papers on the relation between language and energy.
The energy of language seems to be one of the most fundamental theme for the further step-up study on language at the present for me. But the theme was hard to put on the mathematical description. Now I present some preparatory papers written so far.
Section curvature of (N, h) everywhere non-positive
Arbitrary C∞ map f : M → N
Equation
Solution of the equation exists at .
When there exists , is convergent to harmonic map and is free homotopic with .
1
(Harmonic map)
Arbitrary variation of { }
2
(Section of )
3
(Levi-Civita connection)
Levi-Civita connection of (M, g) and (N, h)
[Impression]
1
From Eells-Sampson Theorem, if language is supposed to be expressed by the equation and word is supposed to be expressed by , language is understandable in finite time.The situation contributes guarantee of language.
2
In infinite time, Language still can be understood by word's generation system .
The necessary and sufficient condition for what von Neumann algebra N is purely infinite ( Ⅲtype) is what semi-finite normal trace that is not 0 does not exist over N.
[Explanation]
<1 Trace>
<1-1>
Trace over von Neumann algebra Nτ : N+→ [0, ∞] 0∞ := 0
τ is the map that has next condition.
(i) τ ( A+B ) =τA +τB, ∀A,B∈N
(ii) τ (λA ) = λτ ( A ) ∀A∈N+,∀λ∈[0, ∞)
(iii) τ ( A*A ) = τ ( AA* ) ∀A∈N
<1-2>
Trace over von Neumann algebra Nτ
(1) τ is faithful. A∈N, τ (A) = 0 →A = 0
(2) τ is normal. Increase net {An} ⊂N+τ (supα Aα) = supατ (Aα)
(3) τis definite. τ (I ) < ∞
(4) τis semi-definite. When A(≠0)∈N+, there exist B(≠0)∈N+ while B≦A and τ (B) ≠0.
At this paper, signal is belonged to human world not belonged to outer world or universe.But Signal itself exists to go abroad to the widely opened worlds or universe.
Understanding signal may be able to possess if there be energy which dispatch to the outer.
Decipherment of the all the signals maybe a dream but the routes to decipher areternally remained by the very human ourselves.
On 20 July 2016 I went Tokyo National Museum, Ueno Park, Tokyo to see the exhibition AJOURNEY TO THE IMMORTALS: TREASURES OF ANCIENT GREECE, whereI 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 byNISHIDA 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.
Exhibition Catalogue numbers are the next.
The numbers 39 and 40 are Linear A. 41 and 77 are Linear B.
39. Clay juglet c. 1800 B.C. ~ c. 1700 B.C.
40. Clay bar c. 1700 B.C. ~ c. 1650 B.C.
41. Clay tablet c. 1375 B.C. ~ c. 1350 B.C.
77. Linear B bar and tablet c. the 13th century B.C.
For my part the stability has been one of the biggest themes on language phenomena since I was taught from CHINO Eiichi through the results of the Linguistic Circle of Prague, especially of Sergej Karcevskij.
The exhibition catalogue and Chadwick's book Japanese translated edition.
以下に示す「言語の量子理論」は、英文で書かれたQuantum Theory for Language の草稿となるもので、２００３年３月に長野県白馬の白馬アルプスホテルで書かれたものである。発表するのは今回が初めてである。いままで発表しなかったのは、この草稿がまったく資料のないホテルの部屋できわめて短時間のうちに書かれたものであり、そのためその内容が非常に直感的で、通常の論考とは異なる、私にとってはかなり先鋭的なものであったためである。しかも論考は途中で終わり未完のままである。２００３年１２月に或るシンポジウムで発表するためにこの草稿をもとに書き上げたQuantum Theory for Languageでは、論考の趣旨はほぼ一貫しながらもその表現をより穏やかなものにした記憶がいまもはっきりと残っている。しかし現在この草稿を読み返してみると、私が２００３年当時気にした直感性や先鋭さは、やはり私の言語論の本質に深く根ざしたものであり、ほぼ十年におよぶ言語に関する数学的な記述を経て振り返ると、私が今なお書き残しているもっとも重要ないくつかの主題は、ほぼこの草稿に記されたものであることを私はあらためて確認するに至っている。言語の量子化、量子の出現と消滅、量子の接合と階層、量子集合体、量子群の進行と階層、陽性量子と陰性量子、量子の意味とエネルギー。いずれも私にとって、依然として未知であり魅惑的であり続ける。今後私はふたたびこの草稿の位置にもどり、あらためてみずからの思考を紡いてゆくことになるであろう。老年の今となっては、本質は形態に先行し、もっとも表現したいものを、私にとってそれにもっともふさわしい方法で記述してゆくこととなるであろう。いくばくかの時間がなお残されているのであればだが。二十歳のころ恩師が教えてくれた句は今もそのまま生きている。いざゆかん雪見にころぶところまで。
２０１５年３月２３日、東京にて記す。
This manuscript was written at a hotel of Hakuba, Nagano, Japan in March 2003, where my family stayed for hot spring and ski. In autumn 2002, I thought of relationship between time and characters inspired by WANG Guowei's paper written on old Chinese character's studies, one of which he declared that character heng 亙 was imaged from a ship coming and going the banks. This character contained the notation of the continuous time of ship operation between the banks.
But if character contain the time going, character seemed to have any existence of inherent energy in it.
Note 2
29 June 2018
Definition of quantum in this manuscript was intuitive while in my mind there was rather precise image that was not able to write by mathematical approach in the days of 2003.
Now the situation has been changed drastically through the development of quantum group. Particularly from the Drinfeld's speech at the international mathematician conference in 1984.
I wrote a simple trial paper on quantum group in 2008. Kac-Moody Lie Algebra Note 2 Quantum Group 2008
Papers related to the pre-thought on quantum group is seen at SRFL Lab. SRFL Lab's Preparatory paper
Inherent energy in language has been become a little updated after writing in 2003.
Now arranged at the next.
I frequently talked with CHINO Eiichi at the coffee shop near the station we used to get on. The shop was at the second floor and the steps upstairs always sounded squeaking. Under the dim light the topics of conversation was on language or linguistics after all. He was already a university professor but I was a poor research student. But he was always showing me the general tenderness.
The subject he gave me was impressive and useful for me, in which the most important is the history of The Linguistic Circle of Prague and the excellent pioneers of language study. He had of course the unique approach to the study but I had never any conspicuous one except boundless interest on the study.
In his wide and precious telling for me I gradually determined my course to proceed. It was the making of basic and radical foundation on natural language by searching the structure of language through simple and clear description. For keeping this difficult aim I had a decision that there was only way to use mathematics that I had abandoned at the past for its hardness.
In my age 20s, I had read Ludwig Wittgenstein and Nicolas Bourbaki in concentrating. I did not clearly understand Wittgenstein's approach. But I borrowed his writing style that was simple and clear. So my early work’s descriptions were nearly at him. But I decided that I never adopted strongly-intuitive thinking.
I always considered mathematical basis or analogy. My aim was the independence from the intuitive description. Keeping on this course, there was seen the mathematical basis that I must adopt the model in which language universals are clearly described. I entered to the mathematical description of study that was confirmed premises of my way.
Language will become the urgent agenda of this century. Language will be recognised as the amalgamation of mathematics and physics. Because language is a mathematically designed physical transmission system in human being. This transmission is finite and compact within a human body but infinite and eternal connected with the outer worlds in the universe.
Sekinan Library has researched on language from 1986 and successively at SRFL from 2003.
Papers and essays that have been written at Sekinan Library and SRFL Sekinan Research Field of Language
are shown and searched at SRFL Essay and SRFL Paper.
Sekinan Library's main theme is now at language universals that has been a hard target and researched since 1920s at Linguistic Circle of Prague, but the theme had been always put aside from the centre of the study.
In Japan. on Prague School CHINO Eiichi probably first introduced systematically through his direct study experience at Prague between 1958 and 1964.
I first met with him in 1969 at Tokyo, from whom received Russian language lesson at the beginner's small class. And after some 10 years I again met him in 1979 at his lecture on structural linguistics, to which I listen till till March 1986 when I get apart from the university.
In 1986 I also started to study my own object on language, in which the main theme was language universals by mathematical description, surging from Nicolas Bourbaki, that were already applied to wide and deep approach even at human studies at that time.
In 2003 I narrowly wrote up the trial paper on language's characters, at that time not for total language, but I got the steady way to approach the hard target of language's basis mainly on meaning, through which I faintly could see the final target, language universals.
Journey through the Afterlife Ancient Egyptian Book of the Dead by The British Museum 2012
TANAKA Akio
The British Museum has exhibited The ancient Egypt at Tokyo, titled Journey through the Afterlife Ancient Egyptian Book of the Dead.
The exhibition is excellent, especially total length 37 meters' Greenfield Papyrus is the highlight of the exhibit.
I feel over again that the letters on the papyrus is almost everlasting and my usual thought that the letters are superior than the spoken language which is thought important by Ferdinand Saussure.
Of course I have respected Saussure so much and have read COURS DE LINGUISTIQUE GENERALE time to time.
But the Occidental linguistics has not enough tradition on the ideogram as usual at Chinese characters.
Japan has also succeeded the Chinese tradition and culture. So we have much felt the importance on characters and letters.
Each ideogram has its unique molding technique and coinage ability.
I have very satisfied with the hieroglyph's figures comparison to Chinese characters.
20 July 2016 I went to see the exhibition A JOURNEY TO THE IMMORTALS: TREASURES OF ANCIENT GREECE being opened at Tokyo National Museum, Ueno,Tokyo.
At the exhibition I first saw Linear A and Linear B.
Exhibition Catalogue numbers are the next.
The numbers 39 and 40 are Linear A. 41 and 77 are Linear B.
39. Clay juglet
40. Clay bar
41. Clay tablet
77. Linear B bar and tablet
About the two Linear I knew the brief information from the book, THE DECIPHERMENT OF LINEAR B by John Chadwick, Cambridge University Press, 1960.
From the exhibition I also knew still now not to decipher the Linear A.
My simple impression is the next.
If the stability of language exist in the structure, the essence of language is appeared at the letters and characters. So I think. The core of this view contains the view for structure of language, which I would be able to write clearly using mathematics.
For more details, refer to the reference 2.
References
A JOURNEY TO THE IMMORTALS: TREASURES OF ANCIENT GREECE [Exhibition Catalogue]. Tokyo National Museum et al. 2016.
THE DECIPHERMENT OF LINEAR B by John Chadwick, Cambridge University Press, 1960.
Ars longa Seeing Masterpieces of French Landscape Paintings from the Pushkin State Museum of Fine Arts, Moscow TANAKA Akio
On 25 May 2018 I went to Tokyo Metropolitan Museum, Ueno, Tokyo to see the exhibition titled French Landscape Paintings from the Pushkin State Museum of Fine Arts, Moscow.
I have frequently see the modern French paintings represented by the Post-impressionists at the National Western Art Museum,Ueno. But the impression after seeing was pretty different.
The paintings are ranged widely from the 17th to 20th century.
I felt that the The Russian eyes were effected to collect the paintings. For example, Arcadia and the relevant concepts of it were not so popular in Japan but at Russian collectors paid enough attention to them like the Europeans.
One of the most fantastic works for me was Luigi Loir's Smoke on the Paris Circuit Line ( Paris Suburb). Floating smoke, Cloudy sky, Two horses and people chatting or coming and going.
At the moment to see the painting I recalled the famous quotation, Vita brevis, ars longa.
The painting was drawn in 1885, over 130 years ago. But all the landscapes were vivid like the present and probably in future.
When I saw Luigi Loir's Smoke on the Paris Circuit Line ( Paris Suburb), I felt a fresh awareness of time, which was probably came from the vivid smoke floating in the air or the road partly glistered by the rain immediately before. This landscape was filled with time feeling which was coming on and stopped and was going to the future till now. All paintings may contain such a feeling on time. Now I faced a large canvas of Luir, I freshly got the greatness of painting which has a moment and eternity from the 2 dimensional space.
Does this greatness is only in my mind and not out in the outer world? Do I only feel the eternity in my mind? Almost maybe so, but partly maybe not. Time is real and time feeling floating in the panting is also real. Where is the difference between the two ? Time is direct and time in the painting is in direct, which floats via my eyes and mind. The painting gives me the start of time floating. In that case, what is the painting's giving moment? The moment is made from form and colour on the canvas. Thus, direct time has no tool for going on and indirect time has tools, now canvas, paints and brushes. Direct time and indirect time both enters in my body especially in my mind. The two times both floats in my body. I cannot analyse direct time. But indirect time can be analysed using several methods, form analysis, colour analysis and so forth. Language's letter, character and voice also maybe contain moments for making indirect time. Luigi Loir's Smoke on the Paris Circuit Line ( Paris Suburb) gave reconfirmation of a fresh awareness of indirect time's existence.
[Note 2]
6 June 2018
Research of indirect time TANAKA Akio
For the research of indirect time now the several tools are prepared for at mine.
Mains are the next.
Overview of the importance and application in the new future is given at the letter to Y., 2018.
This letter is written in Japanese, now not has English version.
For details of research two sites are presented now at SRFL site.
One is from geometrization conjecture started from W.P. Thurston and succeeded by G. Perelman.
The other is from quantum group started from V. G. Drinfel'd.
1.
Around 2008, I was thinking on energy in language related with distance in language. Distance is one of the kernel themes of my study of language universals in those days. In simply saying, distance is the result of movement and for movement there must inevitably needs energy. So I had thought that if language have distance, there must be energy or its alike in language that is supposed in mathematical models. But in my ability in 2008, I could not develop the deep and wide range of language from the theme, energy and distance. So Energy Distance Theory was still now unfinished.
2.
In another approach of my study on language universals, Edward Sapir's Language, 1921 was one of my favourite books between 1970s and early 1980s. In his book, the most fantastic concept for me was Drift, that indicated the vast movement of language system itself. I ever gave brief account on it.
Edward Sapir's Language, 1921 showed me the dynamism of language proposing the concept, drift.
Drift shows us the macro phase of natural language and I was hinted by Sapir's this concept and proposed the micro phase of natural language. The paper "Quantum Theory for Language" is my first total proposal paper describing the natural language's model.
3.
My language study started from the reading of Old China's Qing dynasty's huge linguistic inheritance, "Xiaoxue", in English Small Study , that is contrary to the name, the most basic and difficult study of classical texts of old China. I particularly loved the books written by WANG Guowei and WANG Yinzhi and DUAN Yucai.
The main book list to which I referred in those days between the age 20s and 40s are shown at the next.
Guantangjilin is the selection of works by WANG Guowei, which contains vast area of history, literature and linguistics. Some people say that his works are a thousand-year peak from the Song era’s philosopher SHU Xi. I bought his book at Haifeng shudian, Kanda, Tokyo in my mid 20s. The date of colophon is February 1973, publisher is Zhonghua shuju Xianggang fenju.
Probably I bought it in 1973 or 1974. In those days I frequently went Haifeng shudian bookshop for buying Chinese classics, mainly Qing Dynasty’s linguistic works that is called ” Xiaoxue”, Small study at China. Guantangjilin is a very difficult book to understand by my poor study result.
His study era is from Yin Dynasty to Qing Dynasty some 2,500 years of Chinese literary history. At his vast works I was especially charmed in Qing Dynasty’s ancient Chinese hieroglyphic characters, Jiaguwenzi by Chinese. After 40 years, in 2003 I wrote a small paper on language universals through this ancient Chinese hieroglyphic characters at the view point of written language.
The title is On Time Property inherent in Characters. From at that time 10 years passed by. Now I am still learning on language universals but its style is far apart from the days 2003 or 1973. Ambiguity of approach by traditional linguistics is not for my part. I dare challenge to a new frontier of description for language study using mathematics or algebraic geometry.
4.
After all,Energy Distance Theory ended in the half-finished situation. But now I am still eager to write and develop the papers on energy and distance. The road is long and winding as ever. I am always accustomed to delay and stagnate. Some rays of light is emitting in the small study room of mine.
In the days of high school, I deeply dreamt that someday physics would perfectly write over this world's phenomena by the clearest descriptions. So I had longed for studying physics in the future. But I selected language's diverse and wide field at the university, from where returning to the clear description like mathematics needed long and winding road for me.
Now in my mind language and physics/mathematics are happily living together for constructing the world's main frame. I wonder why I took so much time to reach here.
Long time ago, at least the days I was strongly influenced by Pascal , philosophy and mathematics were both sides of areas for solving the world's hard problems. It is appropriate that the problems should be solved using all the tools from all the areas, should not be partitioned any artificial walls.
From now on, philosophy so far may be partially solved by mathematics and mathematics might open to the door of complex phenomena in the world never being written clearly. Now they are surely solved one by one by the researchers and we feel the solutions like those are becoming common sense now.
Probably only I reached here being delayed. But at last I am now situated in a tranquil field. Thanks so many pioneers who had cultivated difficult problems to the easier states for applying to the different fields. Especially to mathematicians. Also to physicians through whose worlds I ever dreamt in my future.
In 1970s at Tokyo or in age 20s, there surely exists glitter of youth in my life, now I remember.
In those days, in Japan many fabulous magazines were successively published. Episteme,Toshi（City）、Chugoku（China) and the likes. Especially I loved reading Episteme which had printed many philosophical or philological articles as the form of special issues concentrated important philosopher, thinker and writer. The chief editor of Episteme was NAKANO Mikitaka（1943-2007), probably one of the best editors in the latter half of the 20th century in Japan. The most impressive number was Ludwig Wittgenstein（1889-1951）, probably in 1977. Also influenced from the issue of Kurt Gödel（1906-1978）who gave me the possibility of set theory and its application.
In my life, Wittgenstein gave the big influence for thinking and writing style, never entering or approaching his essential philosophical themes.After millennium year when I started the regular writing on language universals, my writing style was at first rather resembling in his Tractatus Logico-Philosophicus. My paper written in 2003, Quantum Theory for Language shows a very imitative style to him. This tendency kept on for some time till I changed to adopt algebraic method for clearer description to the themes.
1970s was a relatively calm time after those university’s revolution in the late 1960s in which I was also compellingly rolled in. In those days I time to time had wandered between library and old book shops seraching my life-time true themes cowardly avoiding the turmoils of university and towns. Blaise Pascal（1623-1662）’s Pansees was my favourite one. One day at Kanda’s Taiwan Chinese book shop Haifeng Shudian, I bought WANG Guowei（1877-1927）’s Guantangjilin that clearly opened the new frontier for classical Chinese philology along mainly streamed by Small Study, traditional restrict linguistics in China. Influenced WANG Guowei I trlally wrote a paper titled On Time Property Inherent in Characters, 2003 by which I began the later start of language study.
In 1970s, I had cherished a dream in which I wanted to use mathematical description and get the essential of language. But I had not any ability to proceed the study for it while I read at random mathematical books. One day I found and bought the amount Nicolas Bourbaki（1935-）’s text books at old book shop in Kanda, Tokyo. They were hard to continue reading for my talent in those days. After all, the books were put aside the desk. The only remaining in my mind was adoration to Bourbaki and their brilliant achievement. My return to Bourbaki was long after in 1990s when I again tried the pursuit of language having a clear vision to study language universals according to the Linguistic Circle of Prague, especially aiming to resolve the supposition presented by Sergej Karcevskij（1884-1955).
Turning round the past days, my way was always narrow and winding. But it has been kept till now not breaking off in any situations. The way was almost always glittering in my youth days in spite of under the cloudy skies. Probably I have walked happily till now being assisted by many people especially at the field of language, mathematics and the relevant studies.
At random now I remember the dear names, but from whom I never cannot hear their voices. HASEGAWA Hiroshi, CHEN Donghai both Chinese language, KAJIMURA Hideki, CHO Shokichi both Korean language, Natary Muravijowa Russian language, ONO Shinobu Chinese literature, MIIYAZAKI Kenzo, FURUTA Hiromu, KONDO Tadayoshi all three Japanese literature, ANDO Tsuguo French poem, SAEKI Shoichi Haiku, IKEDA Hiroshi Japanese classical drama, SAITO Kohei sculpture, YAMAGISHI Tokuhei bibliography, NISHI Junzo Chinese philosophy, KAWASAKI Tsuneyuki Buddhism, CHINOEiichi Russian language, the Linguistic Circle of Prague. At last dear friend of high school days KANEKO Yutaka mathematics and our youth.
Sergej Karcevskij declared a conjecture for language's asymmetric structure on the TCLP of the Linguistic Circle of Prague in 1928. I briefly wrote about the conjecture as the following.
Prague in 1920s, The Linguistic Circle of Prague and Sergej Karcevskij's paper "Du dualisme asymetrique du signe linguistique"
From Print 2012, Chapter 18
Non-symmetry. It was the very theme that I repeatedly talked on with C. Prague in 1920s. Karcevskij's paper "Du dualisme asymetrique du signe linguistique" that appeared in the magazine TCLP. Absolutely contradicted coexistence between flexibility and solidity, which language keeps on maintaining, by which language continues existing as language. Still now there will exist the everlasting dual contradiction in language. Why can language stay in such solid and such flexible condition like that. Karcevskij proposed the duality that is seemed to be almost absolute contradiction. Sergej Karcevskij's best of papers, for whom C called as the only genius in his last years' book Janua Linguisticae reserata 1994.
[Note, 2 October 2014]
In this Tale, Print 2012, C is CHINO Eiichi who was the very teacher in my life, taught me almost all the heritage of modern linguistics. I first met him in 1969 at university's his Russian class as a student knowing nothing on language study.
Tokyo
23 February 2015 SIL
.....................................................................................................................................
This asymmetric duality of linguistic sign presented by Karcevskij has become the prime mover for my study from the latter half of the 20th century being led by my teacher CHINO Eiichi. But the theme was very hard even to find a clue. The turning point visited after I again learnt mathematics especially algebraic geometry in 1980s. In 2009 I successively wrote the trial papers of the theme assisted by several results of contemporary mathematics. The papers are the following.
Entering in this year 2016, I read TODA Yukinobu's book, Several Problems on Derived Category of Coherent sheaf, Tokyo, 2016. The book shows me the update overview on derived category of coherent sheaf. The essence of my notable points are noted at the following.
When there exists mirror relation between X1 and X2, derived category of X1's coherent sheaf and derived Fukaya category defined from X2's symplectic structure become equivalence.
M. Kontsevich. Homological algebra of mirror symmetry, Vol. 1 of Proceedings of ICM. 1995.
[Note by TANAKA Akio]
In the near future, symplectic geometry may be written by derived category. If so, complex image of symplectic geometry's some theorems will become clearer.
is birational map between smooth objective algebraic manifolds.
And
.
At This condition,
there exists next fully faithful embedding.
.
[Reference]
TODA Yukinobu. Several problems on derived category of coherent sheaf. Tokyo, 2016.Chapter 6, Derived category of coherent sheaf and birational geometry, page 148, Conjecture 6.43.
Kawamata conjecture will hint me the new meaning's entrance in the old meaning at a word.
Notes for KARCEVSKIJ Sergej that I ever wrote will be newly revised through TODA's fine work over viewing the recent 20 year development on derived category that began by Grothendieck.
For TODA's book, refer to the next my short essay.
TODA Yukinobu. Several problems on derived category of coherent sheaf. Tokyo, 2016
TODA Yukinobu's Several problems on derived category of coherent sheaf has built across mathematics and physics. For my part, further more, physics and language seem to be expected to build over from the book.
Chapter 5. Page 116. Conjecture 5.16 shows us the connection between symplectic geometry and algebraic geometry.
I ever wrote several notes on language related with string theory. Now TODA's book newly lights up the relation between physics and language. This relation is really fantastic for me from now on.
1.Language is the most convenient tool for human being.
2.Language has the vast variations in natural language and technical language.
3.Natural language has speech language, written language and their recorded language, for example books, records, CD and so on.
4.Technical language has many computer languages and their related devices.
5.At natural language, there exists many meanings not to confirm clear definitions, for example finite,infinite, discrete, continuity, universal and super.
6.Technical language has naturally defines the meanings by its discrete arithmetical basic using of discreteness.
7.Mathematics is probably belonged to natural language, that uses speech and written language by usual conversations and papers or books.
8.But mathematics can clearly define the meaning through a few axioms and derived theorems. for example boundary, continuity, distance, finite, infinite and space.
9.Mathematics has many strong tools for description, for example mapping, projection and identification.
10.Mathematics has solid structure through long historical verifications from ancient Greece.
TODA Yukinobu. Several problems on derived category of coherent sheaf. Tokyo, 2016
TODA Yukinobu's Several problems on derived category of coherent sheaf has built across mathematics and physics. For my part, further more, physics and language seem to be expected to build over from the book.
Chapter 5. Page 116. Conjecture 5.16 shows us the connection between symplectic geometry and algebraic geometry.
I ever wrote several notes on language related with string theory. Now TODA's book newly lights up the relation between physics and language. This relation is really fantastic for me from now on.
When there exists mirror relation between X1 and X2, derived category of X1's coherent sheaf and derived Fukaya category defined from X2's symplectic structure become equivalence.
M. Kontsevich. Homological algebra of mirror symmetry, Vol. 1 of Proceedings of ICM. 1995.
[Note by TANAKA Akio]
In the near future, symplectic geometry may be written by derived category. If so, complexed image of symplectic geometry's some theorems will become clearer.
Karcevskij conjecture 1928 and Kawamata conjecture 2002
TANAKA Akio
Sergej Karcevskij declared a conjecture for language's asymmetric structure on the TCLP of the Linguistic Circle of Prague in 1928. I briefly wrote about the conjecture as the following.
Prague in 1920s, The Linguistic Circle of Prague and Sergej Karcevskij's paper "Du dualisme asymetrique du signe linguistique"
From Print 2012, Chapter 18
Non-symmetry. It was the very theme that I repeatedly talked on with C. Prague in 1920s. Karcevskij's paper "Du dualisme asymetrique du signe linguistique" that appeared in the magazine TCLP. Absolutely contradicted coexistence between flexibility and solidity, which language keeps on maintaining, by which language continues existing as language. Still now there will exist the everlasting dual contradiction in language. Why can language stay in such solid and such flexible condition like that. Karcevskij proposed the duality that is seemed to be almost absolute contradiction. Sergej Karcevskij's best of papers, for whom C called as the only genius in his last years' book Janua Linguisticae reserata 1994.
[Note, 2 October 2014] In this Tale, Print 2012, C is CHINO Eiichi who was the very teacher in my life, taught me almost all the heritage of modern linguistics. I first met him in 1969 at university's his Russian class as a student knowing nothing on language study.
Tokyo 23 February 2015 SIL .................................................................................................................................... This asymmetric duality of linguistic sign presented by Karcevskij has become the prime mover for my study from the latter half of the 20th century being led by my teacher CHINO Eiichi. But the theme was very hard even to find a clue. The turning point visited after I again learnt mathematics especially algebraic geometry in 1980s. In 2009 I successively wrote the trial papers of the theme assisted by several results of contemporary mathematics. The papers are the following. ......................................................................................................................................
Entering in this year 2016, I read TODA Yukinobu's book, Several Problems on Derived Category of Coherent sheaf, Tokyo, 2016. The book shows me the update overview on derived category of coherent sheaf. The essence of my notable points are noted at the following.
When there exists mirror relation between X1 and X2, derived category of X1's coherent sheaf and derived Fukaya category defined from X2's symplectic structure become equivalence.
M. Kontsevich. Homological algebra of mirror symmetry, Vol. 1 of Proceedings of ICM. 1995.
[Note by TANAKA Akio]
In the near future, symplectic geometry may be written by derived category. If so, complexed image of symplectic geometry's some theorems will become clearer.
In the TODA's book, I received the great hint on Karcevskij's conjecture for language's hard problem. The hint exists at Kawamata conjecture presented in 2002. The details are the following.
is birational map between smooth objective algebraic manifolds.
And
.
At This condition,
there exists next fully faithful embedding.
.
[Reference]
TODA Yukinobu. Several problems on derived category of coherent sheaf. Tokyo, 2016.Chapter 6, Derived category of coherent sheaf and birational geometry, page 148, Conjecture 6.43.
Kawamata conjecture will hint me the new meaning's entrance in the old meaning at a word.
Notes for KARCEVSKIJ Sergej that I ever wrote will be newly revised through TODA's fine work over viewing the recent 20 year development on derived category that began by Grothendieck. For TODA's book, refer to the next my short essay.
TODA Yukinobu. Several problems on derived category of coherent sheaf. Tokyo, 2016
TODA Yukinobu's Several problems on derived category of coherent sheaf has built across mathematics and physics. For my part, further more, physics and language seem to be expected to build over from the book.
Chapter 5. Page 116. Conjecture 5.16 shows us the connection between symplectic geometry and algebraic geometry.
I ever wrote several notes on language related with string theory. Now TODA's book newly lights up the relation between physics and language. This relation is really fantastic for me from now on.
is birational map between smooth objective algebraic manifolds.
And
.
At This condition,
there exists next fully faithful embedding.
.
[Reference]
TODA Yukinobu. Several problems on derived category of coherent sheaf. Tokyo, 2016.Chapter 6, derived category of coherent sheaf and birational geometry page 148 Conjecture 6.43.
T. Bridgeland defined stability conditions on triangulated categories in 2007.
Language's stability presented by Sergej Karcevskij in 1928.
Bridgeland's stability seems to hint for Karcevskij's stability.
T. Bridgeland defined stability conditions on triangulated categories in 2007.
Language's stability presented by Sergej Karcevskij in 1928.
Bridgeland's stability seems to hint for Karcevskij's stability.
Stability conditions on triangulated categories Data ( Z, A ) satisfies the next condition.
is bounded kernel of t-structure. gives stability condition on A .
4. Theorem R. Pandharipande and R.P. Thomas. Pandharipande-Thomas Theorem (1998). K. Behrend. Behrent contructable function (2009). Y. Toda. Curve-counting theories via stable objects (2010). T. Bridgeland. Hall algebras and curve-counting invariants (2011).
5. Definition Mu limit semi-stable object.
6. Space Mu limit semi-stable object's moduli space.
7. Stability of Language In the space(6.) language keeps stability as the set of derived duality.
8. Essence of Language Duality is the essence of language.
2. Theorem R. Pandharipande and R.P. Thomas. Pandharipande-Thomas Theorem (1998). K. Behrend. Behrent contructable function (2009).
Y. Toda. Generating functions of stable pair invariants via wall-crossing in derived categories in algebraic geometry. (2008) Curve-counting theories via stable objects (2010). T. Bridgeland. Hall algebras and curve-counting invariants (2011). D. Joyce and Y.Song. A theory of generalized Donaldson-Thomas invariants. (2012)
3. Definition Generalized DT invariants. ( Joyce and Song. 2012)
4. Isomorphism Isomorphism is induced in the defined moduli spaces.
5. Duality and mirror If language is identified as Calabi-Yau 3 folds, language inevitably induce dual or mirror element.
1.
I have thought of language as a physic existence that has inevitably boundary to the outer world.
My question is simple and primitive. I ever wrote about the change of language - If there be change, there are exactly the situations before change and after change. Just where does changing substance exist? In the essay, rotten apple was used as the symbol of changing language.
1.
Language is variable. If it be true, what is the base of variability?
2.
Language is pronounceable. If it be true, what is emerged by pronounced?
3.
Language is recordable. If it be true, what is emerged by recorded?
4.
Example.
An apple is variable and will be rotten by time proceeding.
An apple is pronounced at a glossary shop and will be bought by a home-maker.
An apple is recordable and will be recorded in a photo.
5.
What distinguishes language from apple? The answer is uncertain. So I make the language models parting from natural language.
Tokyo
22 August 2012
Sekinan Research Field of Language
..................................................................................................................................
2.
Language&s substantiality has been considered since I returned to the mathematical approach for learn language universals from the utterly beginning. In 2005 I wrote a tiny trial paper on the substantiality of language for thinking the study course hereafter.
1 Substance of language is completion which possesses the distance from the real world.
2 The distance is sustained by the fixation for which meaning and time are abstracted.
3 If language has not distance, language appears and disappears following the real world proceeding.
4 Language is substantially unchangeable. Changeability occurs on surrounding.
5 The distance is measured by the longitude from the real world to the substantiality that meaning and time possess.
6 Substantiality is a frame of language.
7 Substantiality is free from the real world.
8 Substantiality is powered by outer energy.
9 Powered substantiality moves complied with possessed command, namely meaning and time.
10 Powered moving substantiality of language is called .
11 The idea of quantum is partially realized by in the supermarket or bookstore.
12 Substantiality is bar code of can or book. Outer energy is bar code reader. Quantum moves in a cash register. Language generates price addition in the real world.
13 Bar code is not language. Bar code is substantiality of language. Bar code does not move by itself. When bar code reader becomes energetic, bar code generates in a cash register. Language, namely, price-additional-work, starts at bookstore of station front in the bustling evening.
Tokyo February 27, 2005
For the Memory of Tanashi Station Front Street February 26, 2005
3.
In 2013, I again wrote on the substantiality of language at the new level containing the determinate essence of language, dimension and time. The title is Macro Time and Micro Time. In this paper I thought that dimension is the essential factor of meaning, especially containing Infinitive meaning.
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 circumstanstances, langauge 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
#0 For WITTGENSTEIN Ludwig Position of Language / December 10, 2005 – August 3, 2012 / Sekinan Research Field of Language
#1 Time of Word / Complex Manifold Deformation Theory / January 1, 2009 / sekinanlogos
#2 PASCAL PENSÉES. Translated with an introduction by A.J. Krailsheimer. PENGUIN BOOKS 1966.
#3 Escalator language and Time For SHINRAN’s Idea and BOHDISATTVA / Escalator Language Theory / December 16, 2006 / Sekinan Research Field of Language
#4 From Finiteness to Infinity on Language / Topological Group Theory / February 1, 2009 / sekinanlogos
#5 Understandability of Language / Complex Manifold Deformation Theory /January 9, 2009 / sekinanlogos
5.
Relation between boundary and synthesis in language is utterly unknown field for me. Study has just started from the entrance position. Recent results are the next.
Synthesis
1 Conjecture for synthesis of meaning in word
29/09/2013 19:25
For synthesis of meaning in word, Conjecture: Condition for synthesis of meaning in word i s proposed by cohomological expression.
2 Conjecture: Condition for synthesis of meaning in word
29/09/2013 18:38
On condition for synthesis of meaning in word, at conjecture is proposed by the next result of etale cohomology.
Result
——————————————————- Canonical natural equivalence
The next two are left exact additional functors. F : A -> A’ G : A’ -> A” A and A’ have enough many injective objects.
If F transfers A’ s injective object to G acyclic object, the next canonical natural equivalence is concluded. R ( G O F ) =~ RG O RF .
——————————————————–
Conjecture Preparation
Word is shown by R . This word is called old word .
Base meaning in word is shown by F .
Word that has base meaning is shown by RF .
Additional meaning to word is shown by G .
Word that has additional meaning is shown by RG . This word is called intermediate word .
Word that has base meaning and additional meaning is shown by R ( G O F ). This word is called new word . Conjecture For completion of new word, old word and intermediate word have the condition shown by the canonical natural equivalence of etale cohomology.
3 Canonical natural equivalence
29/09/2013 18:08 Canonical natural equivalence
The next two are left exact additional functors. F : A -> A’ G : A’ -> A” A and A’ have enough many injective objects.
If F transfers A ‘s injective object to G acyclic object, the next canonical natural equivalence is concluded. R ( G O F ) =~ RG O RF .
6.
Three Conjectures containing Synthesis Conjecture are shown at the next.These conjectures are the latest result of language universals at SRFL Sekinan Research Field of Language.
0 The world spreads around the human being.
1 Language divides the world.
2 Language connects the world.
3 Language bends the world.
4 Language stretches the world.
5 Language shrinks the world.
6 Language extinguishes the world.
7 Language creates the world.
8 Language gives despair.
9 Language gives hope.
10 Language is pasting on spacetime with energy.
Tokyo March 3, 2007
Tokyo November 3, 2008 Added
Postscript
[Referential note / November 29, 2007] For Authentication of Solidity
[Definition added / November 3, 2008]
Definition 10, the part of is newly added.
From KAWAMATA Yujiro, Stab X that consists of the set having all <locally finite> and <numerical>< stability condition> on derived category D(X) has finite dimensional complex manifold’s structure. Stab (X) is conjectured to be connected and simply connected. In derived category, exact sequence is extinct and distinguished triangle is generated.
Refer to the next paper. KAWAMATA Yujiro Daisukikagaku to doraiken Sugaku 58-1 Iwanami Shoten 2006
3
Now blow up and blow down is presented.
φ: QY(M) → M
M is nonsingular variety. Y is M’s submanifold.
QY(M) is blow up along Y.
φis arrow of algebraic variety
φis called QY(M)’s blow down.
4
Also birational mapping that is extension of blow up and blow down is presented.
Birational mapping is what rational mappingφ: V→W has mapping ψ: W→V. Here existsφ∘ψ= idV ψ∘φ=idW .
5
By birational mapping, algebraic variety V, W and X is presented. These three are formed to be new distinguished triangle that is supposed to be equivalent with V, W and X.
6
Word that consists of category makes sentence that consists of distinguished triangle by birational mapping with algebraic method.
10 Here time of word is defined by manifold’s time of Ricci flow’s collapse.
11 By Thurston conjecture, when compact 3 dimensional manifold is cut and separated by 2 dimensional sphere and torus, while generated compact manifold has sphere boundary, sphere is put together there. As the result new generated manifold has locally uniform structure.
12 Peculiar solution of Thurston conjecture is Poincaré conjecture that is what simply connected 3 dimensional compact manifold is homomorphic to 3 dimensional sphere surface S3.
13 According by Thurston conjecture, what put together newly generated 3 dimensional manifold is called connected sum.
Connected sum is expressed by M1#M2. M1and M2 are 3 dimensional manifolds.
14 Here sentence is defined by manifold’s connected sum.
Here I will try to consider on the generation and the function of characters that have been used in Chinese which is classified to isolating language in linguistic typology.
Concerning the early forms of characters, we can verify them by the ancient inscriptions on bone and tortoiseshell that were discovered at /Yinxu/ and so forth. At the first stage that is usually classified to five on the inscriptions, they already displayed the inceptive completion, from where it is very difficult to speculate the beginning shapes of characters. On vocabulary and syntax, inscriptions displayed the almost same inceptive completion. Here what is inceptive completion is meant that comprehension or speculation is practicable by the usage of modern Chinese. Therefore the generation and the function of characters are subsidiary after the inscriptions. On the situation of forming the inscriptions namely explanation to decipher inscriptions, many researches are accumulated. Here, in these researches, I proceed with consideration claiming the works of after 1990 in main.
1 Generation of characters
When we see the inscription of character /yu/ that means bringing up in English, it is impossible to doubt that this inscription shows the situation of childbirth time by woman. In this inscription the situation of childbirth is shown by three stages. First there is a figure in which woman is going to give birth to a baby crossing both arms at the front of her chest. She takes a bent-forward posture, sticks her buttocks out and bend her knees gently. Second the situation of what the waters break is shown by the signs similar to dotted lines. Third at central or under part of the waters, a new born baby is shown in the shape of baby’s head inverted. Through three factors illustrated in the inscription, character /yu/ is clearly expressed the situation of childbirth time and the immediately after the birth time.
When we see the inscription of character /yan/ that means language or speak in English, the form of the inscription is simplified or transformed considerably at the first stage of classification on inscriptions. So the explanation to decipher inscriptions is developed variously. Here I will show one interpretation including the result of Chinese archeology in recent years. A form of character /yan/ is able to see the three parts that are upper, middle and under. According to the result of Chinese archeology, the upper part is regarded as the tongue’s point of a bronze bell used at meeting in /Yin/ period. The central part of character /yan/ is the body of a tongue. The under part of character /yan/ is regarded to be the outside of a bell. In /Yin/ period, at the time to let the meeting begin, the bronze-like bell was ringed loudly to let the people connected to know. When the meeting was opened, the bell was inferred to put up side down on a table. That is to say, the main body of a bell is inferred to be putted up side down and the tongue of a bell is inferred to be putted upward on the form of bell’s setting. This setting of a bell is shaped regarded to become the character’s form of inscription of on bone and tortoiseshell. According to this interpretation of the inscription, /yan/ can be said to show the situation of post-notification of a meeting in /Yin/ period.
Therefore the figuration of the reversed bell was regarded to become the inscription of character /yan/.
When we see the inscription of character /geng/ that means to cross in English, we comprehend that the inscription shows the two parallel lines in which a bow pattern is included. WANG Guowei†0 regarded that this inscription is as same as the character /heng/ that means permanent or lasting in English. Now I follow his interpretation. He wrote in his paper that two up-and-down lines are both banks of a river and inner bow shaped figure is a ship which goes and returns between the banks†1. According to this interpretation, /geng/ or /heng/ shows the operations of crossing a river, that operations are permanently repeated in an identical space†1.
From the inscriptions of three characters of /yu/, /yan/ and /geng/, now we can induce or infer the following.
First, Inscriptions which are original shapes of characters, in some cases, have a proceeding time in characters themselves. That is to say, as for character /yu/, that means the time of childbirth, from beginning to end. As for character /yan/, that means the time of meeting, from announcement to being open. As for character /heng/, that means the proceeding time of crossing the river by ferry.
Second, on the inscriptions, several aspects of the various phenomena which occur on the proceeding time in characters are sometimes shown by the images or implications. As for character /yu/, remarkable aspects’ figures are bending mother’s body, amniotic fluid and new born baby†2. As for character /yan/, the one remarkable is the bell which is set in the upside down condition, which means the announcement of meeting which was already opened a few minutes ago. The other remarkable is the same bell which is set on the table in the upside down condition, which means the meeting is now going†3. As for character /heng/, remarkable aspects are both banks and a ferry boat.
Third, on the inscriptions, several aspects, which are shown by the remarkable figures, transmit the messages. As for character /yu/, babybirth from mother’s body, the situation of birth time and new baby appeared in this world are transmitted simultaneously by the one character /yu/. As for character /yan/, transmitting is announcement of meeting, opening of meeting and contents of being discussed by the meeting. As for character /heng/, work of crossing the river, reach the opposite bank of the river and repetitions of these works, namely, constancy are transmitted for the information.
Therefore from the induction or inference on the generation of character’s meaning above mentioned, the following function of characters is led for us.
2 Function of characters
First, the time-proceeding aspect being inhered in every character has the strong tendency toward the most distinctive information of the real world. As for character /yu/, while woman is giving birth to a baby, the most distinctive information is the figure of mother’s body bending, and after birth, the existence of a new baby becomes the most distinctive information†2. The various grammatical functions of one character are generated from the time proceeding and successive phenomena of distinctive aspects in the real world.
As for character /yu/, at the birth time, verbal aspect of giving birth is emphasized, but after birth nounal aspect of a new born baby oneself is emphasized. As for character /yan/, before the meeting verbal aspect of telling the opening is the most important thing, but while being opened or after the meeting the nounal aspect of speaking content of the meeting is the most valuable thing†3.
Second, when two or over two characters are connected, every character wants to emphasizes selecting one distinctive aspect inherent in oneself, and want to connect to the other character or characters. Because if two or over two aspects is transmitted, there will appear the non-clearness in the information. As for character /yu/, connection with character /sheng/ (which means grow in English), namely /sheng yu/, in this situation /yu/ means give birth to in English. Connection with /cai/ (which means a person of talent in English), namely /yu cai/, in this situation /yu/ means educate in English. That is to say, character /yu/ has two phases of meanings. One is concerned with the situation of child-birth of mother’s body. The other is concerned with the situation of a person that is already growing.
Third, every character has several aspects of inherent time inclination. When there is a connection of two characters, each character has the choosing operation from the several meanings in the character. Two or over two characters generate a new meaning complex by the operations of choosing the most precedent meaning in the each. This complex can maintain the new clearness of information on the connection of characters which have many branches of meanings in total.
For example, from above mentioned characters /yu/, /yan/ and /heng/, when two characters /heng/ and /yan/ are connected to one word /heng yan/, /heng/ chooses the meaning constant in English and /yan/ chooses the meaning utterance in English. New meaning complex is the expression by the stable person. This /heng yan/ appears in the Chinese classic Mengzi by the complex meaning.
Then, when every individual character does selectivity of aspects, what functions does work in the characters? On the other hand, when two or over two characters connect by the choosing the most precedent meaning respectively, what functions does work out of the characters?
3 Self selectivity of function on character
Now I examine the situation of what two or over two characters connect and generate the new aspect complex. For instance, I adopt above mentioned characters connection word /heng yan/.
In the first place, /yan heng/, which is a reverse disposition of /heng yan/, is examined. This characters disposition is not notified as the one word generally in the Chinese. This characters set is usually recognized as a sentence. The meaning is <The utterance is eternal.> in English. That is to say, this characters set does not generate new aspect complex and two aspects of every individual character form in a line. Why this divergence, namely generating word or sentence, occurs in the characters disposition?
Here I infer that< time property inherent in characters> is worked. Detailed inference is mentioned below.
3 Here human mind be on Riemann sphere and outer world be on complex plane, regular presentation of words on complex plane makes variable velocity consequence on Riemann sphere.
4 Concentration is in whether human mind has Riemann sphere or not.
Refer to the following paper in early work on characters.
6 In Aurora Theory, word of language is expressed on complex plane, phrase of language is expressed on Riemann sphere and sentence is expressed in Riemann sphere.
5 Now there are 5 s, namely, [ I, meet, he, library, yesterday].
6 There becomes , namely, / I meet he library yesterday. /
7 New returns to .
8 New s are 6, [ I, meet. he. library, yesterday, I meet he library yesterday ].
9 There add 3s. [met, him, at].
10 New is generated, / I met him at library yesterday. / .
11 is static and fixed but is dynamic and changeable.
12 needs energy for its dynamism but does not need dynamic devices.
13 resembles Nintendo’s FAMICON, but differs in the following 14-18.
14 is a source of .
14 is a part of automatic language generating machine.
15 is a figure which is scanned and reproduced easily.
16 ’s inputting devices are various, such as typing, voice inputting, manual writing, pictograph and so forth.
17 can install to language-answering-devices, such as telephone, vending machine, showing-way-machine and so forth. Answer is always individually different for the most adequate purpose.
18 ’s is possible to be written as a sophisticated figure which is transformed to easy-readable style.
19 ’s is enlarged by the adding-from-old-to-new system. See upper No.5-10.
Journey through the Afterlife Ancient Egyptian Book of the Dead by The British Museum 2012
TANAKA Akio
The British Museum has exhibitedThe ancient Egypt at Tokyo, titledJourney through the Afterlife Ancient Egyptian Book of the Dead. The exhibition is excellent, especially total length 37 meters'Greenfield Papyrus is the highlight of the exhibit.
I feel over again that the letters on the papyrus is almost everlasting and my usual thought that the letters are superior than the spoken language which is thought important by Ferdinand Saussure. Of course I have respected Saussure so much and have readCOURS DE LINGUISTIQUE GENERALE time to time. But the Occidental linguistics has not enough tradition on the ideogram as usual at Chinese characters.
Japan has also succeeded the Chinese tradition and culture. So we have much felt the importance on characters and letters. Each ideogram has its unique molding technique and coinage ability. I have very satisfied with hieroglyph's figures comparison to Chinese characters.
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, whereI 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.
Exhibition Catalogue numbers are the next.
The numbers 39 and 40 are Linear A. 41 and 77 are Linear B.
39. Clay juglet c. 1800 B.C. ~ c. 1700 B.C.
40. Clay bar c. 1700 B.C. ~ c. 1650 B.C.
41. Clay tablet c. 1375 B.C. ~ c. 1350 B.C.
77. Linear B bar and tablet c. the 13th century B.C.
For my part the stability has been one of the biggest themes on language phenomena since I was taught from CHINO Eiichi through the results of the Linguistic Circle of Prague, especially of Sergej Karcevskij.
The exhibition catalogue and Chadwick's book Japanese translated edition. Reference
1. Ideogram Ideogram has long history. In the early paper I ever simply defined ideogram*0-1.
I also wrote relative papers on ideogram from the viewpoint of Chinese characters*3-1, 3-2, 3-3.
Especially Manuscript of Quantum Theory for Language 2003 is a starting root of my research on language universals*3-2. The history of ideogram continues from Egyptian hieroglyph to Chinese character and now adds LATEX Symbol List*6-1. The 21st century will necessarily become the century of ideogram. The reasons are below.
Ideogram can contain rich information in small space.
Ideogram can show information at a glance.
Ideogram can sustain information stably in long time*1-7.
Ideogram has fertile capability to superb diversity of languages*8-5.
2. Set theory Probably in summer 1977, I was designing for a paper on the sentence in language. The central part of the paper was connection between words or sentence, in which the logic of language would be shown using the set theory as a simplified model of true and false. I was strongly influenced from Kurt Godel, Gaishi Takeuchi and Bourbaki*1-1. But this design was abandoned for my lack of mathematical basis keeping on.
3. Qing dynasty's linguistics In 1980s and 1990s I was lost in learning Chinese classical character theory, Xiaoxue, especially Qing dynasty for ideogram's fundamental property*2-1. At this period I did not write any paper on language. I solely read WANG Guowei*1-2, WANG Yinzhi, DUAN Yucai and Qing dynasty's linguists.
4. Time property in characters In Autumn 2002 I got pneumonia and was hospitalized about 2 weeks, where I thought of 1970s' dream, writing clear description on language universals by mathematics. The theme was as hard as ever. So, at the bed I thought the basis of language from a side of Chinese character’s classical approach which had vast heritage till Qing dynasty. I directed my attention to the character's figure which had compound meanings containing time elements continuing from Yin dynasty's hieroglyphic characters left on bones and tortoise carapaces some 2400 years ago. I thought that Chinese characters had containing time and its structure could be written by geometric approach once I had abandoned for difficulty. After leaving hospital, I wrote a paper titled On Time Property Inherent in Characters*3-1.
5. Quantum elements In 2003 staying at Hakuba, Nagano, I wrote a rial paper on language universals from the viewpoint of physics. This was remained manuscript till now. The title was Manuscript ofQuantum Theory for Language*3-2 for the time being. Because in summer 2003 I wrote the first paper on language universals from physics titles as Quantum Theory for Language*3-3 which was read at a conference held in winter 2003 of Nara Japan.
6. Finite generative Language probably begins from finite elements and generates.*3-6, 3-7 its world responding to outer world. I learned the concept of finite generative from von Neumann Algebra*4-1 at around 2006 and 2007.
7. Structure and dimension Language probably has structure, which details are unknown now for me. But several phenomena hints me the existence of structure containing dimension. Its example is shown at the Crete's lie, on which I wrote a tiny paper titled as True-false problem of the Crete*3-8in 2013.
More details on mathematical approach to dimension is shown at Algebraic Geometry Language*4-2.
8. Immanent time Chinese character has immanent time in figure *3-1, 3-4. On the theme I wrote several papers between 2003 and 2005. Main papers related with the theme are seen in Early Paper and Early Paper 2*5-1, 5-2.
For the immanent time, I wrote a mathematical paper titles as Word as Infinite Loop Space*3-9.
In comparison with Chinese character, hieroglyph is very fantastic object on ideogram. For more details, hieroglyph is more complex for describing the concept using two functions, logogram expressing things' meaning and phonogram expressing words' pronunciation*0-2, 8-3.
Besides hieroglyph has also definitive element which is put at the end of the word. This element is very similar to Chinese character's meaning element which is called Pang 旁 in Chinese*8-3.
But even for learning hieroglyph's basis, I have not enough time now. I only like to see the relative events on hieroglyph at time to time . The exhibition held at Mori Arts Gallery in 2012, Tokyo titled as The British Museum ANCIENT EGYPTIAN BOOK OF THE DEAD JOURNEY THROUGH THE AFTERLIFE *8-2 was very fantastic, in which The Greenfield Papyrus was overwhelming.
9. Disposition, distance, flow and boundary
For thinking of language, I have been interested in four elements, disposition, distance flow and boundary*3-10,11,12, 13, which seem to become the basis of language.
especially at researching ideogram, disposition is fundamental to construct grammar.
10. Energy, dimension and distance For more further research language , now I suppose at least three elements being based from mathematical description, which are energy, dimension and distance*3-14.
11. Mapping and category Ideogram now has an important part in computer age. Image confirmation is very popular at internet banking system, which can contain vast information in one image, so password decoding is more difficult than phonogram or Arabic numerals.
Generally ideogram has vast information to the others using comparatively easy way. This ideograms situation resembles mapping at category theory in mathematics. For this point I wrote rough sketch to apply category theory to language theory. Sketch name is Derived Category Language 2016*4-3.
1. Language is variable. If it be true, what is the base of variability?
2.
Language is pronounceable. If it be true, what is emerged by pronounced?
3.
Language is recordable. If it be true, what is emerged by recorded?
4.
Example.
An apple is variable and will be rotten by time proceeding.
An apple is pronounced at a glossary shop and will be bought by a homemaker.
An apple is recordable and will be recorded in a photo.
5.
What distinguishes language from apple? The answer is uncertain. So I make the language models parting from natural language.
I was born in 1947 and become 68 years old this summer. My unripeness to language study has come to the declining years. Return to physics or mathematics is almost alike to back to youth age, when almost every day solving rudimentary problems for entire interest to unknown world.
In my mind there still are some hard themes to challenge, one of which is energy in language. The theme is originated from Edward Sapir, who presented the concept "drift" in Language, 1921. It was the macro and intuitive concept that was supposed by his precise thinking and vast field work of America native's language. I think that I would develop the theme from the physics-mathematics field.
In the garden
Peony begins to come out in the cold winter.
If there be change in language, from which to which language changes in its true nature?
---------------------------------------------------------------------------------------------------------
1.
I have thought of language as a physic existence that has inevitably boundary to the outer world.
My question is simple and primitive. I ever wrote about the change of language - If there be change, there are exactly the situations before change and after change. Just where does changing substance exist? In the essay, rotten apple was used as the symbol of changing language.
1.
Language is variable. If it be true, what is the base of variability?
2.
Language is pronounceable. If it be true, what is emerged by pronounced?
3.
Language is recordable. If it be true, what is emerged by recorded?
4.
Example.
An apple is variable and will be rotten by time proceeding.
An apple is pronounced at a glossary shop and will be bought by a home-maker.
An apple is recordable and will be recorded in a photo.
5.
What distinguishes language from apple? The answer is uncertain. So I make the language models parting from natural language.
Tokyo
22 August 2012
Sekinan Research Field of Language
.............................................................................................................................................
2.
Language&s substantiality has been considered since I returned to the mathematical approach for learn language universals from the utterly beginning. In 2005 I wrote a tiny trial paper on the substantiality of language for thinking the study course hereafter.
1 Substance of language is completion which possesses the distance from the real world.
2 The distance is sustained by the fixation for which meaning and time are abstracted.
3 If language has not distance, language appears and disappears following the real world proceeding.
4 Language is substantially unchangeable. Changeability occurs on surrounding.
5 The distance is measured by the longitude from the real world to the substantiality that meaning and time possess.
6 Substantiality is a frame of language.
7 Substantiality is free from the real world.
8 Substantiality is powered by outer energy.
9 Powered substantiality moves complied with possessed command, namely meaning and time.
10 Powered moving substantiality of language is called .
11 The idea of quantum is partially realized by in the supermarket or bookstore.
12 Substantiality is bar code of can or book. Outer energy is bar code reader. Quantum moves in a cash register. Language generates price addition in the real world.
13 Bar code is not language. Bar code is substantiality of language. Bar code does not move by itself. When bar code reader becomes energetic, bar code generates in a cash register. Language, namely, price-additional-work, starts at bookstore of station front in the bustling evening.
Tokyo February 27, 2005
For the Memory of Tanashi Station Front Street February 26, 2005
3.
In 2013, I again wrote on the substantiality of language at the new level containing the determinate essence of language, dimension and time. The title is Macro Time and Micro Time. In this paper I thought that dimension is the essential factor of meaning, especially containing Infinitive meaning.
24 July 2013 atbankofdam 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 #0 For WITTGENSTEIN Ludwig Position of Language / December 10, 2005 – August 3, 2012 / Sekinan Research Field of Language #1 Time of Word / Complex Manifold Deformation Theory / January 1, 2009 / sekinanlogos #2 PASCAL PENSÉES. Translated with an introduction by A.J. Krailsheimer. PENGUIN BOOKS 1966. #3 Escalator language and Time For SHINRAN’s Idea and BOHDISATTVA / Escalator Language Theory / December 16, 2006 / Sekinan Research Field of Language #4 From Finiteness to Infinity on Language / Topological Group Theory / February 1, 2009 / sekinanlogos #5 Understandability of Language / Complex Manifold Deformation Theory /January 9, 2009 / sekinanlogos
5.
Relation between boundary and synthesis in language is utterly unknown field for me. Study has just started from the entrance position. Recent results are the next.
Synthesis
1 Conjecture for synthesis of meaning in word
29/09/2013 19:25
For synthesis of meaning in word, Conjecture: Condition for synthesis of meaning in word i s proposed by cohomological expression.
2 Conjecture: Condition for synthesis of meaning in word
29/09/2013 18:38
On condition for synthesis of meaning in word, at conjecture is proposed by the next result of etale cohomology.
Result
——————————————————-
Canonical natural equivalence
The next two are left exact additional functors.
F : A -> A’
G : A’ -> A” A and A’ have enough many injective objects.
If F transfers A’ s injective object to G acyclic object, the next canonical natural equivalence is concluded.
R ( G O F ) =~ RG O RF .
——————————————————–
Conjecture
Preparation
Word is shown by R . This word is called old word .
Base meaning in word is shown by F .
Word that has base meaning is shown by RF .
Additional meaning to word is shown by G .
Word that has additional meaning is shown by RG . This word is called intermediate word .
Word that has base meaning and additional meaning is shown by R ( G O F ). This word is called new word .
Conjecture
For completion of new word, old word and intermediate word have the condition shown by the canonical natural equivalence of etale cohomology.
3 Canonical natural equivalence
29/09/2013 18:08
Canonical natural equivalence
The next two are left exact additional functors.
F : A -> A’
G : A’ -> A” A and A’ have enough many injective objects.
If F transfers A ‘s injective object to G acyclic object, the next canonical natural equivalence is concluded.
R ( G O F ) =~ RG O RF .
6.
Three Conjectures containing Synthesis Conjecture are shown at the next.These conjectures are the latest result of language universals at SRFL Sekinan Research Field of Language.
1.
When one first hear the existence of time in language, he may doubt its certainty. But I have intuitively believe it since I learned the ancient Chinese inscription on bone ad tortoise shell (in Chinese called Jiaguwen). In my early 20s, I met with the book of Chinese modern linguists, WANG Guowei, this belief changed the conviction. His lifework book Guantangjilin is hard to read till now. But some papers in it are always inspires me by his deep and vast insight to character, language and history of ancient China. He also wrote fine criticism on Chinese pre-modern poem Ci.The title is RenjianCihua. The book is one of my favourite books of Chinese literature. People sometimes say that he was the highest genius after Song Dynasty, 1,000 years.In 2003 I wrote a tiny paper hinted by WANG's paper. It was the first paper for me that I directly faced the time inherent in inscription using Jiaguwen's update linguistic results. The title is " On Time Property Inherent in Characters".
2.
In summer 2003, I stayed at Hakuba, Nagano for a while for writing over the paper that was intended to present a symposium at Nara in winter. The paper was taking up the structure of written language that was dealt with the relation between time and grammar. But I did not solve the question on with what shape language exists in the language world. What shape has language and at where space does language exist or float? The theme on space was hard to deal at that time. I only concentrated to the shape in space. At 28 August I was fatigued to think and went for a stroll outside the inn putting up. The place was at the mountain side of the Hakuba Range and there was only one convenience store, where I walked in the shop and saw one advertisement of electric pocket dictionary. I returned having this advert to the inn and read its sentences. At the very time I found the shape of language I sought was sphere that was inherited time in it, also having grammatical functions. The paper's title was named to " Quantum Theory for Language" by the shape of language. This was a really product of clear and fine atmosphere of Hakuba with a distant view of the North Alps of Japan.
3.
From 2004 to 2008 I wrote some papers on inscription and language. But I was not satisfied inwardly for the style of intuitive approach to language. I wanted to write more simple and clear expression. For being realised of my wish, I definitely needed to use mathematical tools. I returned to my 20s days' reading of Bourbaki that was desperately difficult for may ability. I again gradually read mathematical books and journals for seeking useful source of my hope to converting to language study. A certain results that came to my papers with satisfaction was appeared in 2008 by the papers titled Complex Manifold Deformation Theory.
4.
The definition of space in which language exists is one hard target for me to write satisfactory. A fixed results came to me at the papers group titles Symplectic Language Theory in 2009.
5.
Related with the shape of language, quantization and discreteness on language was the urgent themes for the further step of studying the total image of language I was pursuing. Floer Homology Language was the one milestone for me to overcome to the next stage.
6.
What situation does the time in language have? This question exists in my mind at the early days when I wrote the paper "On Time Property Inherent in Characters". The first step to solution was described at the paper " Prague Theory". The group of Prague Theory was written due to dedicate to Prague, The Linguistic Circle of Prague and Sergej Karcevskij with the memory of my teacher CHINO Eiichi.
In this paper, Chinese Character /kun/, that meaning is difficult in English, was used for the eternity of loop time. This loop time was also appeared in the paper " On Time Property Inherent in Characters". But Prague Theory shows more direct and compact by growing tree and its obstructive enclosing fence. This intuitive image was more clearly described at the paper " Word as Infinite Loop Time " at Infinite Loop Space Language in 2012.
In this paper, time in language is clearly connected with dimension of algebraic group saying as the next. Word has dimension that belongs to algebraic K group.
7.
The relation between time and dimension was entered on a new phase at the learning of algebraic geometry, especially of arithmetic geometry. Arithmetic Geometry Language, abbreviated to AGL, was the starting papers for me to arithmetic method.
At these conjectures, time inherent in language is in the basis of describing dimension, synthesis and reversion. The process of leading to the conjectures is over viewing the next.
8.
Acknowledgement
Time inherent in language is a fantastic but as hard to pursue for me still now. I would examine this theme further more and more, probably till the end of my research life. Now all the thanks are going to The Linguistic Circle of Prague and especially its member Sergej Karcevskij, with my teacher CHINO Eiichi who taught me their precise information from his long study at Prague in 1960s.
9.
For CHINO Eiichi
9.1 Golden Prague
C also died early, who had taught me Russian and linguistics. He loved
the old city that had the beautiful towers and bridges.
In C's many works there was the essay "The Moon of Carpathians". He wrote
that the conference was over, departed at Kiev, saw the moon and
churches over the Carpathian Mountains, impetuously went to the west,
passed Slovakia, Moravia, Bohemia, and at last reached "Golden Prague".
Prague, it was his youth itself.
Now I cannot hear his voice telling the various anecdotes on languages,
of which he freely had commanded. By the short heading, a newspaper
reported his death, naming as "the genius of linguistics".
- 9 October 2014 -
9.2 Coffee shop named California
If C live, he also may ask me, "What are you researching now?"
And I also will answer him as same as ever.
"I have pursued universals, never done facts, without repenting."
Oh C, if you live, will we also talk on language?
At the table facing each other under the low ceiling of the shop going up the steep stairs.
The name of the shop is California.
For the memory of our daily forgetful life,
its never miserable though poor all over,
I will write down our delight.
- 27 October 2014 -
10.
Ode to Kanda
"I need not more wander the book shop streets." / From Tale, Print, 2012
This tale was written by TANAKA Akio, pen-named LI Koh in autumn 2012 for remembering the poor but brilliant youth time of myself. This is one of my favourite phrases in this tale.
The book shop streets described in the tale is Kanda, Tokyo, which is located in the central Tokyo, where I frequently walked seeking the old Chinese classic books for the study from Oriental way of linguistics. In late 1960s, the streetcars were surely running in the old fashioned streets of Kanda, now perfectly changed to the subway streets.
From Print 2012, Chapter 10
もはや本屋街をさまようことはない。I need not more wander the book shop streets. 対象は私のうちにある。The object exists in my mind. 私はただこの運河をながめていればいい。I would better watch the canal. 遍歴は終わった。Wandering is over now. たぶん永遠にマイスターにはなれないだろうが、みずからの小さな仕事場で、日が落ちるまで作業をすればいい。Perhaps I would not become meister forever. In my narrow working place, I 'd better do my work till sunset. すると仕事場の窓辺を聖者が通って行く。 So out of the window by the working place, the saint passes by. かつてそんなロシアの民話を読んだ。I ever read the Russian folk tale like that.
秋の日ぐれは早い。The Autumn evening is fast. 路面電車のヘッドランプがまぶしいくらいだ。The headlight of streetcar is dazzling. 黄褐色の窓に少ない乗客が照らし出され、古本屋街の方へ消えて行った。In the yellow-lighten window the passengers are picked out by the light. The car disappeared to the book streets. 駅の売店がにぎやかな橙の光に包まれている。The station shop is also lighted up by the yard's busy orange light.
1.
True-false problem of the Crete gives us the infinite circulation of true-false value.
This fact indicates us the existence of deep structure or hierarchy in language.
The Crete's true-false is solved by the perspective from 2-dimension to 3-dimension on structure in language world.
2.
Language has long history as the system of etymology. Apparently language has gradually added the new meaning on the old established meaning in word. At this point new meaning is synthesised to the old meaning. At synthesis word mathematically reduces its dimension to the lower one. As the result time in word relatively occurred in the new word and inevitably connected with dimension.
3.
Where and how does word exists in the world?
The distance from a certain point is absolutely demanded for measuring or observing for knowing the word's place.Reversion is a result for measuring or observing from a point.
4.
For precise description of dimension, synthesis and reversion mathematical tools are definitely needed and for more simple describing algebraic method is the most useful to approach for me and in order to easy-seeing and clear intuition geometrical approach is always inevitable to searching. I am greatly thanks to relevant mathematicians researching against severe problems still now for contemporary times.
Here ends the preparatory work for What is signal?, that began from 16 October 2016. From now on this paper will be written at the viewpoint of quantum group for the relationship between quantum and signal-language, that has been the most important theme, quantum language since 2003, when I wrote a paper titled, manuscript of Quantum Theory for Language.
refer to the next.
Manuscript of Quantum Theory for Language with Preface, Note and Note 2 2003-2018
以下に示す「言語の量子理論」は、英文で書かれたQuantum Theory for Language の草稿となるもので、２００３年３月に長野県白馬の白馬アルプスホテルで書かれたものである。発表するのは今回が初めてである。いままで発表しなかったのは、この草稿がまったく資料のないホテルの部屋できわめて短時間のうちに書かれたものであり、そのためその内容が非常に直感的で、通常の論考とは異なる、私にとってはかなり先鋭的なものであったためである。しかも論考は途中で終わり未完のままである。２００３年１２月に或るシンポジウムで発表するためにこの草稿をもとに書き上げたQuantum Theory for Languageでは、論考の趣旨はほぼ一貫しながらもその表現をより穏やかなものにした記憶がいまもはっきりと残っている。しかし現在この草稿を読み返してみると、私が２００３年当時気にした直感性や先鋭さは、やはり私の言語論の本質に深く根ざしたものであり、ほぼ十年におよぶ言語に関する数学的な記述を経て振り返ると、私が今なお書き残しているもっとも重要ないくつかの主題は、ほぼこの草稿に記されたものであることを私はあらためて確認するに至っている。言語の量子化、量子の出現と消滅、量子の接合と階層、量子集合体、量子群の進行と階層、陽性量子と陰性量子、量子の意味とエネルギー。いずれも私にとって、依然として未知であり魅惑的であり続ける。今後私はふたたびこの草稿の位置にもどり、あらためてみずからの思考を紡いてゆくことになるであろう。老年の今となっては、本質は形態に先行し、もっとも表現したいものを、私にとってそれにもっともふさわしい方法で記述してゆくこととなるであろう。いくばくかの時間がなお残されているのであればだが。二十歳のころ恩師が教えてくれた句は今もそのまま生きている。いざゆかん雪見にころぶところまで。 ２０１５年３月２３日、東京にて記す。
This manuscript was written at a hotel of Hakuba, Nagano, Japan in March 2003, where my family stayed for hot spring and ski. In autumn 2002, I thought of relationship between time and characters inspired by WANG Guowei's paper written on old Chinese character's studies, one of which he declared that character heng 亙 was imaged from a ship coming and going the banks. This character contained the notation of the continuous time of ship operation between the banks. But if character contain the time going, character seemed to have any existence of inherent energy in it.
Note 2
29 June 2018
Definition of quantum in this manuscript was intuitive while in my mind there was rather precise image that was not able to write by mathematical approach in the days of 2003.
Now the situation has been changed drastically through development of quantum group. Particularly from the Drinfeld's speech at the international mathematician conference in 1984.
I wrote the simple trial paper on quantum group in 2008. Kac-Moody Lie Algebra Note 2 Quantum Group2008
Papers related on the pre-thought on quantum group is seen at SRFL Lab. SRFL Lab's Preparatory paper
Inherent energy in language has been become a little updated after writing in 2003. Now arranged at the next.
αi ⊂h*
∈ Z
ij Ki - Ki-1 / qi – qi-1 ( i , j∈I )
p [1-aijp]qiEi1-aij-pEjEip = 0 ( i , j∈I , i ≠j )
is topological space.
is simplicial space.
is represented by geometric realization of 
as the next.
is topological space.
is singular simplex.
is free Abelian group generated by set 
.
.
is singular chain complex of 
and has strongly convergence spectral sequence
.
.
.
.
and 
*(Sn)
, 
.
[x1, x2, ..., xn]
Cn f (a1, a2, ..., an) = 0, 
a }
Rf
.
)-1U)
is surjection, t
.
p
is dominant.
satisfies next conditions is called algebraic variety.
I, intersection 
is open partial set of 
.
that defines surjective homomorphism is expressed by 
.
of closed embedding defined by 
is called glue of A and B by C.
Spm R, Spm T 
Spm S
, next is equivalent.
is generated by R and S.
is called R value point of X.
X(S)
is function from ring category over k to category of set.
over ring R {
}
satisfies the next conditions, 
.
,
is existent uniquely.
k, 
(k') is always bijection.
is functor to group's category is called algebraic group.
are commutative for 
.
for A.
{
}
.
is called closed map when 
is closed set image 
becomes closed set.
is closed map for arbitrary manifold Y.
is closed map.
generates 
)
) that quadrastic Lie bracket of 
generates.
) that Im η generates 
becomes isomorphic with holonoly Lie algebra completion 
.
of M's fundamental group.
and 
become dual space each other.
X } 
X } S ∞ ( X ) 
min{( x | z)x 0 , ( y | z ) x 0 }- δ 
, δ -hyperbolic space is abbreviatedly called hyperbolic. 
max{ d ( x, z ) + d ( y, w ), d ( x, w ) + d ( y, z ) } +2 δ 
[0, λ ] 
X is expressed by 
. 
xyz = 
is called geodesic triangle. 
X }. 
