Sekinan Data: Letter to Y, 2 June 2024.
: Letter to Y, 2 June 2024 Dear Y, The other day on TV, there was a documentary about a female cooking expert and beauty expert in their 8...
My current central theme is to express language using mathematical quanta, which is one of the fundamental concepts of physics, and can now be completely expressed using mathematical group theory, and to develop this by constructing language as energy.
The meaning of language is also constructed as energy.
Energy can now be expressed mathematically. It is very difficult, but it is the result of Perelman, who solved the Poincaré conjecture.
I can only understand the basics of mathematics at this time.
The rest is omitted.
SRFL News
Tuesday, 12 November 2024
Under the Zelkova Trees. Uploaded at the very same day of 2012
Under the Zelkova Trees. Uploaded at the very same day of 2012
https://sekinandata.blogspot.com/2024/11/under-zelkova-trees.html
Under the Zelkova Trees
TANAKA Akio
There are many fine zelkova trees in the National Institute of Neuroscience, Tokyo. There a relative of mine had ever worked as a researcher. I heard that he had studied on anti-psychotic agents as one of the typical researchers at the field in Japan. Several years later he went to Canada for the further studies aiming the top circumstance of the field.
Time passed by, and after returning home, in a short time, he contracted a disease. He had worked as the daily study fighting against the disease, but sadly he died as young as only 55 yeas old in the midst of his research.
The rest is omitted.
12 Novemeber 2024
Tokyo
Sekinan Hills
https://sekinandata.blogspot.com/2024/11/under-zelkova-trees.html
Under the Zelkova Trees
TANAKA Akio
There are many fine zelkova trees in the National Institute of Neuroscience, Tokyo. There a relative of mine had ever worked as a researcher. I heard that he had studied on anti-psychotic agents as one of the typical researchers at the field in Japan. Several years later he went to Canada for the further studies aiming the top circumstance of the field.
Time passed by, and after returning home, in a short time, he contracted a disease. He had worked as the daily study fighting against the disease, but sadly he died as young as only 55 yeas old in the midst of his research.
The rest is omitted.
12 Novemeber 2024
Tokyo
Sekinan Hills
Sunday, 10 November 2024
Letter to WPM. Maria Pires’ Schumann KINDERSZENEN 19 June 2020. P.S. added 9 August 2020 Generation Theorem Reprint 31 August 2020
Letter to WPM. Maria Pires’ Schumann KINDERSZENEN 19 June 2020. P.S. added 9 August 2020 Generation Theorem Reprint 31 August 2020
The next 5 papers are added this time, 9 November 2024.
On generation Theorem, please refer to the
https://sekinantable.blogspot.com/2022/12/letter-to-wpm-maria-pires-schumann.html
On von Neumann Algebra, please refer to the
https://sekinantable.blogspot.com/2018/07/the-days-of-von-neumann-algebra-2015.html
On Algebraic Linguistics, please refer to the
https://srflnews.blogspot.com/2015/01/linguistic-premise-premise-of-algebraic.html
Also refer to the next papers.
The days between von Neumann Algebra and Complex Manifold Deformation Theory
https://sekinan-library.sit 123.me/paper/the-days-between-von-neumann-algebra-and-complex-manifold-deformation-theory
Energy of Language, One of the most important for me today is written at the next paper.
https://sekinantable.blogspot.com/2017/09/stochastic-meaning-theory-4-energy-of.html
Letter to WPM
Dear WPM,
It rains gently all day in Tokyo. Now during the rainy season,
probably till July.
I listened to the CD of Maria Pires’ Schumann KINDERSZENEN, OP. 15.
Delicate and accurate.
Once in life, I should like to write such a fine paper, so delicate and accurate.
Kind regards,
T. A.
Tokyo
19 June 2020
Geometrization Language
Hydrangea is the June’s flower during the rainy season in Japan.
P.S.
I have never written a paper like Pires’ piano.
But several paper are very dear for me by various reasons.
One of the dearest papers is Generation Theorem written in 2008.
The paper has a memory of my age 20s, 1970s.
Those days I had a fresh dream, standing at the entrance of research as a youth, probably visiting to all the youth who hope to get a ticket to a respectable researcher.
Dream was making all the meanings of natural language from the one and only Empty set.
In those days I had devoted myself to Kurt Godel and his following researcher TAKEUCHI Gaishi.
Godel’s Incompleteness Theorem shows me the perfect meaning of Incompleteness of natural language.
So I started a very tiny one step to the grandeur to construct natural language generated from one and only empty set.
I learnt Bourbaki’s series bought at Kanda Tokyo, where the books seeking for maybe certainly got to you if you were roaming over shops till the narrow streets and remaining the power going up the rattling stairs.
But my ability towards the aim was very low and limited. And overlooking mathematics in those days, applied math using to the different fields probably was not enough arranged for the beginners like me.
Visiting the making a fresh start in my life to math was in 1990s end, age already nearly 50. Happily contemporary math level was fully spread and easy to enter for me. I read math books day after day, especially of algebraic geometry, which was the most familiar for me and seemed to be applied to my study.
And at last my dream had come true at a tiny paper entitled Generation Theorem in 2008.
Cordially again,
T.A. Tokyo
9 August 2020
Sekinan Geometry
von Neumann Algebra 2 Note Generation Theorem
von Neumann Algebra 2
Note
Generation Theorem
TANAKA Akio
[Main Theorem]
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 = ∫1-1 λdEλ(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
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
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 Set a, 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 of power 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 separation x, 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∈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 X Y
S ={A∩Y ; A∈T}
Subtopological space (Y, S)
Topological space is abbreviated to subspace.
Compact>
3-1
Set X
Subset of X Y
Family of X’s subset that is not empty set U =
U is covering of Y. ∪U = ∪i∈I ⊃Y
Subfamily of U V = (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 X a
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 a V(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 a U
Neighborhood of b V
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 K X
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
<1 Stone-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
<2 Norm algebra>
C* algebra A
Arbitrary element of A A
When A is normal, limn→∞||An||1/n = ||A||
limn→∞||An||1/n is called spectrum radius of A. Notation is r(A).
[Note for norm algebra]
<2-1>
Number field K = R or C
Linear space over K X
Arbitrary elements of X x, y
< x, y>∈K satisfies next 3 conditions is called inner product of x and y.
Arbitrary x, y, z∈X, λ∈K
(i) ≧0, = 0 ⇔x = 0
(ii) =
(iii) = λ +
Linear space that has inner product is called inner space.
<2-2>
||x|| =1/2
Schwarz’s inequality
Inner space X
||≦||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 X F, G
Open set of X U, 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.
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 V D
Element of D x
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 V D
sup{||x|| ; x∈D} < ∞
D is called bounded.
Linear operator from norm space V to norm space V1 T
D ( T ) = V
||Tx||≦γ (x∈V ) γ > 0
T is called bounded linear operator.
||T || := inf {γ : ||Tx||≦γ||x|| (x∈V)} = sup{||Tx|| ; x∈V, ||x||≦1} = sup{
; x∈V, x≠0}
||T || is called norm of T.
Hilbert space H ,K
Bounded linear operator from H to K B (H, K )
B ( H ) : = B ( H, H )
Subset K ⊂H
Arbitrary x, y∈K, 0≦λ≦1
λx + (1-λ)y ∈K
K is called vertex set.
<3-4 Homomorphism>
Algebra A that has involution* *algebra
Element of *algebra A∈A
When A = A*, A is called self-adjoint.
When A *A= AA*, A is called normal.
When A A*= 1, A is called unitary.
Subset of A B
B * := B*∈B
When B = B*, B is called self-adjoint set.
Subalgebra of A B
When B is adjoint set, B is called *subalgebra.
Algebra A, B
Linear map : A →B satisfies next condition, π is called homomorphism.
π(AB) = π(A)π(B) (∀A, B∈A )
*algebra A
When π(A*) = π(A)*, π is called *homomorphism.
When ker π := {A∈A ; π(A) =0} is {0},π is called faithful.
Faithful *homomorphism is called *isomorphism.
<3-5 Representation>
*homomorphism π from *algebra to B ( H ) is called representation over Hilbert space H of A . <3-6 Character> Homomorphism that is not always 0, from commutative algebra A to C, is called character.
All of characters in commutative Banach algebra A is called character space or spectrum space. Notation is Sp( A ).
<3-7 Gerfand representation>
Commutative Banach algebra A
Homomorphism ∧: A →C(Sp(A))
∧is called Gelfand representation of commutative Banach algebra A.
<4 Gelfand-Naimark Theorem>
When A is commutative C* algebra, A is equal distance *isomorphism to C(Sp(A)) by Gelfand representation.
[Note for Gelfand-Naimark Theorem]
<4-1 equal distance operator>
Operator A∈B ( H )
Equal distance operator A ||Ax|| = ||x|| (∀x∈H)
<4-2 Equal distance *isomorphism>
C* algebra A
Homomorphism π
π(AB) = π(A)π(B) (∀A, B∈A )
*homomorphism π(A*) = π(A)*
*isomorphism { π(A) =0} = {0}
<5 Banach-Alaoglu theorem>
When X is norm space, (X*)1 is weak * topology and compact.
[Note for Banach-Alaoglu theorem]
<5-1 Unit sphere>
Unit sphere X1 := {x∈X ; ||x||≦1}
<5-2 Linear functional>
Linear space V
Function that is valued by K f (x)
When f (x) satisfies next condition, f is linear functional over V.
(i) f (x+y) = f (x) +f (y) (x, y∈V)
(ii) f (αx) = αf (x) (α∈K, x∈V)
<5-3 weak * topology>
All of Linear functionals from linear space X to K L(X, K)
When X is norm space, X*⊂L(X, K).
Topology over X , σ(X, X*) is called weak topology over X.
Topology over X*, σ(X*, X) is called weak * topology over X*.
<6 *subalgebra of B ( H )>
When *subalgebra N of B ( H ) is identity operator I∈N , N ”= N is equivalent with τuw-compact.
[Note for *subalgebra of B ( H )]
<6-1 Identity operator>
Norm space V
Arbitrary x∈V
Ix = x
I is called identity operator.
<6-2 Commutant>
Subset of C*algebra B (H) A
Commutant of A A ’
A ’ := {A∈B (H) ; [A, B] := AB – BA = 0, ∀B∈A }
Bicommutant of A A ' ’’ := (A ’)’
A ⊂A ’’
<6-3 von Neumann algebra>
*subalgebra of C*algebra B (H) A
When A satisfies A ’’ = A , A is called von Neumann algebra.
<6-4 Ultra-weak topology>
Sequence of B ( H ) {Aα}
{Aα} is convergent to A∈B ( H )
Topology τ
When α→∞, Aα →τ A
Hilbert space H
Arbitrary {xn}, {yn}⊂H
∑n||xn||2 < ∞
∑n||yn||2 < ∞
|∑n| →0
A∈B ( H )
Notation is Aα →uτ A
[ 7 Distance theorem]
For von Neumann algebra N over separable Hilbert space, N1 can put distance on τs and τw topology.
[Note for distance theorem]
<7-1 Equipotent>
Sets A, B
Map f : A → B
All of B’s elements that are expressed by f(a) (a∈A) Image(f)
a , a’∈A
When f(a) = f(a’) →a = a’, f is injective.
When Image(f) = B, f is surjective.
When f is injective and surjective, f is bijective. When there exists bijective f from A to B, A and B are equipotent.
<7-2 Relation>
Sets A, B
x∈A, y∈B
All of pairs between x and y are set that is called product set between a and b.
Subset of product set A×B R
R is called relation.
x∈A, y∈B,∈R Expression is xRy.
When A =B, relation R is called binary relation over A.
<7-3 Ordinal number>
Set a
∀x∀y[x∈a∧y∈x→y∈a]
a is called transitive.
x, y∈a
x∈y is binary relation.
When relation < satisfies next condition, < is called total order in strict sense.
∀x∈A∀y∈A[x
When a satisfies next condition, a is called ordinal number.
(i) a is transitive.
(ii) Binary relation ∈ over a is total order in strict sense.
<7-4 Cardinal number>
Ordinal number α
α that is not equipotent to arbitrary β<α is called cardinal number.
<7-5 Cardinality>
Arbitrary set A is equipotent at least one ordinal number by well-ordering theorem and order isomorphism theorem.
The smallest ordinal number that is equipotent each other is cardinal number that is called cardinality over set A. Notation is |A|.
When |A| is infinite cardinal number, A is called infinite set.
<7-6 Countable set>
Set that is equipotent to N countable infinite set
Set of which cardinarity is natural number finite set
Addition of countable infinite set and finite set is called countable set.
<7-7 Separable>
Norm space V
When V has dense countable set, V is called separable.
<7-8 N1>
von Neumann algebra N
A∈B ( H )
N1 := {A∈N; ||A||≦1}
<7-9 τs and τw topology>
<7-9-1τs topology>
Hilbert space H
A∈B ( H )
Sequence of B ( H ) {Aα}
{Aα} is convergent to A∈B ( H )
Topology τ
When α→∞, Aα →τ A
|| (Aα- A)x|| →0 ∀x∈H
Notation is Aα →s A
<7-9-2 τw topology>
Hilbert space H
A∈B ( H )
Sequence of B ( H ) {Aα}
{Aα} is convergent to A∈B ( H )
Topology τ
When α→∞, Aα →τ A
|| →0 ∀x, y∈H
Notation is Aα →w A
<8 Countable elements>
von Neumann algebra N over separable Hilbert space is generated by countable elements.
<9 Only one real function>
For compact Hausdorff space Ω,C(Ω) that is generated by countable idempotent elements is generated by only on real function.
<9-1>
Set that is defined arithmetic・ S
Element of S e
e satisfies a・e = e・a = a is called identity element.
Identity element on addition is called zero element.
Ring’s element that is not zero element and satisfies a2 = a is called idempotent element.
To be continued
Tokyo April 20, 2008
Sekinan Research Field of Language
www.sekinan.org
Read more: https://srfl-paper.webnode.com/news/von-neumann-algebra-2-note-generation-theorem/
P.S. and Generation Theorem end here.
31 August 2020
Generation Theorem all text reprint.
T.A.
The next 5 papers are added this time, 9 November 2024.
On generation Theorem, please refer to the
https://sekinantable.blogspot.com/2022/12/letter-to-wpm-maria-pires-schumann.html
On von Neumann Algebra, please refer to the
https://sekinantable.blogspot.com/2018/07/the-days-of-von-neumann-algebra-2015.html
On Algebraic Linguistics, please refer to the
https://srflnews.blogspot.com/2015/01/linguistic-premise-premise-of-algebraic.html
Also refer to the next papers.
The days between von Neumann Algebra and Complex Manifold Deformation Theory
https://sekinan-library.sit 123.me/paper/the-days-between-von-neumann-algebra-and-complex-manifold-deformation-theory
Energy of Language, One of the most important for me today is written at the next paper.
https://sekinantable.blogspot.com/2017/09/stochastic-meaning-theory-4-energy-of.html
Letter to WPM
Dear WPM,
It rains gently all day in Tokyo. Now during the rainy season,
probably till July.
I listened to the CD of Maria Pires’ Schumann KINDERSZENEN, OP. 15.
Delicate and accurate.
Once in life, I should like to write such a fine paper, so delicate and accurate.
Kind regards,
T. A.
Tokyo
19 June 2020
Geometrization Language
P.S.
I have never written a paper like Pires’ piano.
But several paper are very dear for me by various reasons.
One of the dearest papers is Generation Theorem written in 2008.
The paper has a memory of my age 20s, 1970s.
Those days I had a fresh dream, standing at the entrance of research as a youth, probably visiting to all the youth who hope to get a ticket to a respectable researcher.
Dream was making all the meanings of natural language from the one and only Empty set.
In those days I had devoted myself to Kurt Godel and his following researcher TAKEUCHI Gaishi.
Godel’s Incompleteness Theorem shows me the perfect meaning of Incompleteness of natural language.
So I started a very tiny one step to the grandeur to construct natural language generated from one and only empty set.
I learnt Bourbaki’s series bought at Kanda Tokyo, where the books seeking for maybe certainly got to you if you were roaming over shops till the narrow streets and remaining the power going up the rattling stairs.
But my ability towards the aim was very low and limited. And overlooking mathematics in those days, applied math using to the different fields probably was not enough arranged for the beginners like me.
Visiting the making a fresh start in my life to math was in 1990s end, age already nearly 50. Happily contemporary math level was fully spread and easy to enter for me. I read math books day after day, especially of algebraic geometry, which was the most familiar for me and seemed to be applied to my study.
And at last my dream had come true at a tiny paper entitled Generation Theorem in 2008.
Cordially again,
T.A. Tokyo
9 August 2020
Sekinan Geometry
von Neumann Algebra 2 Note Generation Theorem
von Neumann Algebra 2
Note
Generation Theorem
TANAKA Akio
[Main Theorem]
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 = ∫1-1 λdEλ(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
*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
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
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 Set a, 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 of power 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 separation x, 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
(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 X Y
S ={A∩Y ; A∈T}
Subtopological space (Y, S)
Topological space is abbreviated to subspace.
Compact>
3-1
Set X
Subset of X Y
Family of X’s subset that is not empty set U =
U is covering of Y. ∪U = ∪i∈I ⊃Y
Subfamily of U V =
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 X a
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 a V(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 a U
Neighborhood of b V
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 K X
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
<1 Stone-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
<2 Norm algebra>
C* algebra A
Arbitrary element of A A
When A is normal, limn→∞||An||1/n = ||A||
limn→∞||An||1/n is called spectrum radius of A. Notation is r(A).
[Note for norm algebra]
<2-1>
Number field K = R or C
Linear space over K X
Arbitrary elements of X x, y
< x, y>∈K satisfies next 3 conditions is called inner product of x and y.
Arbitrary x, y, z∈X, λ∈K
(i)
(ii)
(iii)
Linear space that has inner product is called inner space.
<2-2>
||x|| =
Schwarz’s inequality
Inner space X
|
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 X F, G
Open set of X U, 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.
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 V D
Element of D x
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 V D
sup{||x|| ; x∈D} < ∞
D is called bounded.
Linear operator from norm space V to norm space V1 T
D ( T ) = V
||Tx||≦γ (x∈V ) γ > 0
T is called bounded linear operator.
||T || := inf {γ : ||Tx||≦γ||x|| (x∈V)} = sup{||Tx|| ; x∈V, ||x||≦1} = sup{
; x∈V, x≠0}
||T || is called norm of T.
Hilbert space H ,K
Bounded linear operator from H to K B (H, K )
B ( H ) : = B ( H, H )
Subset K ⊂H
Arbitrary x, y∈K, 0≦λ≦1
λx + (1-λ)y ∈K
K is called vertex set.
<3-4 Homomorphism>
Algebra A that has involution* *algebra
Element of *algebra A∈A
When A = A*, A is called self-adjoint.
When A *A= AA*, A is called normal.
When A A*= 1, A is called unitary.
Subset of A B
B * := B*∈B
When B = B*, B is called self-adjoint set.
Subalgebra of A B
When B is adjoint set, B is called *subalgebra.
Algebra A, B
Linear map : A →B satisfies next condition, π is called homomorphism.
π(AB) = π(A)π(B) (∀A, B∈A )
*algebra A
When π(A*) = π(A)*, π is called *homomorphism.
When ker π := {A∈A ; π(A) =0} is {0},π is called faithful.
Faithful *homomorphism is called *isomorphism.
<3-5 Representation>
*homomorphism π from *algebra to B ( H ) is called representation over Hilbert space H of A . <3-6 Character> Homomorphism that is not always 0, from commutative algebra A to C, is called character.
All of characters in commutative Banach algebra A is called character space or spectrum space. Notation is Sp( A ).
<3-7 Gerfand representation>
Commutative Banach algebra A
Homomorphism ∧: A →C(Sp(A))
∧is called Gelfand representation of commutative Banach algebra A.
<4 Gelfand-Naimark Theorem>
When A is commutative C* algebra, A is equal distance *isomorphism to C(Sp(A)) by Gelfand representation.
[Note for Gelfand-Naimark Theorem]
<4-1 equal distance operator>
Operator A∈B ( H )
Equal distance operator A ||Ax|| = ||x|| (∀x∈H)
<4-2 Equal distance *isomorphism>
C* algebra A
Homomorphism π
π(AB) = π(A)π(B) (∀A, B∈A )
*homomorphism π(A*) = π(A)*
*isomorphism { π(A) =0} = {0}
<5 Banach-Alaoglu theorem>
When X is norm space, (X*)1 is weak * topology and compact.
[Note for Banach-Alaoglu theorem]
<5-1 Unit sphere>
Unit sphere X1 := {x∈X ; ||x||≦1}
<5-2 Linear functional>
Linear space V
Function that is valued by K f (x)
When f (x) satisfies next condition, f is linear functional over V.
(i) f (x+y) = f (x) +f (y) (x, y∈V)
(ii) f (αx) = αf (x) (α∈K, x∈V)
<5-3 weak * topology>
All of Linear functionals from linear space X to K L(X, K)
When X is norm space, X*⊂L(X, K).
Topology over X , σ(X, X*) is called weak topology over X.
Topology over X*, σ(X*, X) is called weak * topology over X*.
<6 *subalgebra of B ( H )>
When *subalgebra N of B ( H ) is identity operator I∈N , N ”= N is equivalent with τuw-compact.
[Note for *subalgebra of B ( H )]
<6-1 Identity operator>
Norm space V
Arbitrary x∈V
Ix = x
I is called identity operator.
<6-2 Commutant>
Subset of C*algebra B (H) A
Commutant of A A ’
A ’ := {A∈B (H) ; [A, B] := AB – BA = 0, ∀B∈A }
Bicommutant of A A ' ’’ := (A ’)’
A ⊂A ’’
<6-3 von Neumann algebra>
*subalgebra of C*algebra B (H) A
When A satisfies A ’’ = A , A is called von Neumann algebra.
<6-4 Ultra-weak topology>
Sequence of B ( H ) {Aα}
{Aα} is convergent to A∈B ( H )
Topology τ
When α→∞, Aα →τ A
Hilbert space H
Arbitrary {xn}, {yn}⊂H
∑n||xn||2 < ∞
∑n||yn||2 < ∞
|∑n
A∈B ( H )
Notation is Aα →uτ A
[ 7 Distance theorem]
For von Neumann algebra N over separable Hilbert space, N1 can put distance on τs and τw topology.
[Note for distance theorem]
<7-1 Equipotent>
Sets A, B
Map f : A → B
All of B’s elements that are expressed by f(a) (a∈A) Image(f)
a , a’∈A
When f(a) = f(a’) →a = a’, f is injective.
When Image(f) = B, f is surjective.
When f is injective and surjective, f is bijective. When there exists bijective f from A to B, A and B are equipotent.
<7-2 Relation>
Sets A, B
x∈A, y∈B
All of pairs
Subset of product set A×B R
R is called relation.
x∈A, y∈B,
When A =B, relation R is called binary relation over A.
<7-3 Ordinal number>
Set a
∀x∀y[x∈a∧y∈x→y∈a]
a is called transitive.
x, y∈a
x∈y is binary relation.
When relation < satisfies next condition, < is called total order in strict sense.
∀x∈A∀y∈A[x
(i) a is transitive.
(ii) Binary relation ∈ over a is total order in strict sense.
<7-4 Cardinal number>
Ordinal number α
α that is not equipotent to arbitrary β<α is called cardinal number.
<7-5 Cardinality>
Arbitrary set A is equipotent at least one ordinal number by well-ordering theorem and order isomorphism theorem.
The smallest ordinal number that is equipotent each other is cardinal number that is called cardinality over set A. Notation is |A|.
When |A| is infinite cardinal number, A is called infinite set.
<7-6 Countable set>
Set that is equipotent to N countable infinite set
Set of which cardinarity is natural number finite set
Addition of countable infinite set and finite set is called countable set.
<7-7 Separable>
Norm space V
When V has dense countable set, V is called separable.
<7-8 N1>
von Neumann algebra N
A∈B ( H )
N1 := {A∈N; ||A||≦1}
<7-9 τs and τw topology>
<7-9-1τs topology>
Hilbert space H
A∈B ( H )
Sequence of B ( H ) {Aα}
{Aα} is convergent to A∈B ( H )
Topology τ
When α→∞, Aα →τ A
|| (Aα- A)x|| →0 ∀x∈H
Notation is Aα →s A
<7-9-2 τw topology>
Hilbert space H
A∈B ( H )
Sequence of B ( H ) {Aα}
{Aα} is convergent to A∈B ( H )
Topology τ
When α→∞, Aα →τ A
|
Notation is Aα →w A
<8 Countable elements>
von Neumann algebra N over separable Hilbert space is generated by countable elements.
<9 Only one real function>
For compact Hausdorff space Ω,C(Ω) that is generated by countable idempotent elements is generated by only on real function.
<9-1>
Set that is defined arithmetic・ S
Element of S e
e satisfies a・e = e・a = a is called identity element.
Identity element on addition is called zero element.
Ring’s element that is not zero element and satisfies a2 = a is called idempotent element.
To be continued
Tokyo April 20, 2008
Sekinan Research Field of Language
www.sekinan.org
Read more: https://srfl-paper.webnode.com/news/von-neumann-algebra-2-note-generation-theorem/
P.S. and Generation Theorem end here.
31 August 2020
Generation Theorem all text reprint.
T.A.
Tuesday, 5 November 2024
Verse Recalled, Under the lamplight 2015
Saturday 14 March 2015
Verse Recalled, Under the lamplight
拾遺詩篇
里行
RI Kohr
灯下
帰るところは
清水のように澄んでいた
貧しさだけの自分
Under the lamplight
The place where I am back
is myself only indigent
clear like spring water
Verse Recalled, Under the lamplight
拾遺詩篇
里行
RI Kohr
灯下
帰るところは
清水のように澄んでいた
貧しさだけの自分
Under the lamplight
The place where I am back
is myself only indigent
clear like spring water
Monday, 4 November 2024
Verse Recalled Mountain Hut by RI Kohr. Translated by Google
Verse Recalled
Mountain Hut
by RI Kohr
Selected Poems
Village Journey
Hut
When was the last time I visited here?
It is now near the end of summer, and once it was the end of autumn.
A misty rain was falling in that small hut.
I held my hands over the stove to dry my shoes.
Young me, all those who were young.
Ah, I have always wished for a scene like that day.
A bright fire, hot tea, and a hard chair.
If only those things could last.
I have thought many times that most of my life would have been fulfilled.
Until today.
It is a lively place I visited for the first time in a long time.
People's voices are coming and going, and corn is being sold outside.
It is difficult to think of the dark, gloomy sky of a long time ago.
It is not that my heart is troubled now, but the dark scenery of the past may be me.
But the stove burning red in the center of it is infinitely nostalgic and dear.
My beloved, I walked from here.
Mountain Hut
by RI Kohr
Selected Poems
Village Journey
Hut
When was the last time I visited here?
It is now near the end of summer, and once it was the end of autumn.
A misty rain was falling in that small hut.
I held my hands over the stove to dry my shoes.
Young me, all those who were young.
Ah, I have always wished for a scene like that day.
A bright fire, hot tea, and a hard chair.
If only those things could last.
I have thought many times that most of my life would have been fulfilled.
Until today.
It is a lively place I visited for the first time in a long time.
People's voices are coming and going, and corn is being sold outside.
It is difficult to think of the dark, gloomy sky of a long time ago.
It is not that my heart is troubled now, but the dark scenery of the past may be me.
But the stove burning red in the center of it is infinitely nostalgic and dear.
My beloved, I walked from here.
Wednesday, 30 October 2024
Daily Thoughts from West Side of Sayama Hills, Tokyo
Daily Thoughts from West Side of Sayama Hills, Tokyo
4 May 2011
Yesterday, I took a stroll with my wife to Sayama Hills, that is the last sanctuary in mid-Tokyo. In the hills, two dams are glittering under the early summer sunshine. The dams are used for the waterworks of Tokyo citizens.
The hills and dams are the very fantastic in the light green leaves, azalea, remained cherry and white dogwood.
There I frequently come to ease my mind with my friends, family or lonely to reflect my life.
Sayama Hills are also the last sanctuary for all the animals and plants in Metropolis Tokyo.
Please come to the Hills that are the Arcadia of Tokyo.
Tokyo Sekinan Research Field of Language
4 May 2011
Yesterday, I took a stroll with my wife to Sayama Hills, that is the last sanctuary in mid-Tokyo. In the hills, two dams are glittering under the early summer sunshine. The dams are used for the waterworks of Tokyo citizens.
The hills and dams are the very fantastic in the light green leaves, azalea, remained cherry and white dogwood.
There I frequently come to ease my mind with my friends, family or lonely to reflect my life.
Sayama Hills are also the last sanctuary for all the animals and plants in Metropolis Tokyo.
Please come to the Hills that are the Arcadia of Tokyo.
Tokyo Sekinan Research Field of Language
At Bank of Dam Again
Sekinan Research Field of Language
At Bank of Dam Again
TANAKA Akio
At bank of dam we conversed with friends on many innocent themes in our youth days.
Long time ago the place was the sight of the fireworks, for which father took me and elder sister to see in the summer night.
When returning home you perfectly slept soundly at father's back, the sister said to me later.
After some thirty years after, we came again with the family to play in the fallen leaves at the bank of dam. Children were rolling down at the slope of the bank wearing golden leaves on the clothes.
And after half a century we have come again at the bank with wife protecting leg's slight pains each other.
Tokyo
16 July 2012
Sekinan Research Field of Language
At Bank of Dam Again
TANAKA Akio
At bank of dam we conversed with friends on many innocent themes in our youth days.
Long time ago the place was the sight of the fireworks, for which father took me and elder sister to see in the summer night.
When returning home you perfectly slept soundly at father's back, the sister said to me later.
After some thirty years after, we came again with the family to play in the fallen leaves at the bank of dam. Children were rolling down at the slope of the bank wearing golden leaves on the clothes.
And after half a century we have come again at the bank with wife protecting leg's slight pains each other.
Tokyo
16 July 2012
Sekinan Research Field of Language
Ars longa Seeing Masterpieces of French Landscape Paintings from the Pushkin State Museum of Fine Arts, Moscow
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 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 payed 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 drew in 1885, over 130 years ago. But all the landscapes were vivid like the present and probably in future.
Tokyo 27 May 2018
Sekinan Zoho
[Note]
6 June 2018
Time and Eternity
TANAKA Akio
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 originally written in Japanese, now show by the English Eddition by Google Translate.
Letter to Y. Of Broad language 4th Edition 5 February 2018
Translated by Google 2020.
Letter to Y. Of Broad Language 4th Edition 5 February 2018. Translated by Google translate 2020.
Letter to Y. Of Broad Language 4th Edition 5 February 2018
Letter to Y. Of Broad Language 4th Edition
Dear Y.,
1. From the definition of language to determining the direction of language research
1.1
I don’t use the word “research” in Japanese much, but here I think about language To briefly describe the above in terms of linguistic research, I think the question is the aim of linguistic research and the application of linguistic research.
When it comes to what language is, I think that language is generally a way for humans to communicate their state of mind with great precision . It is usually assumed that humans speak and hear. So-called natural language. However, I do not define such a so-called language in my own research on language. My research, of course, includes natural language, but it is more extensive . And in my opinion, defining a language in natural language only makes it ambiguous. This is the reason why superlanguages are advocated in basic mathematics.
1.2
So, I don’t call my research linguistics, and I don’t use terms like linguistics or philology in English. Because these terms are centred on natural language. In my case, it is more extensive, so I just write research on language. This broad language, in my term Broad Language , will be discussed later.
So, I’m wondering if such undefined things will cause confusion, but in my case, the written content (maybe) tells me the situation of the language I speak, so more ambiguous The definition is not used. Since I mainly use mathematics, it means that the world being built by the axioms and theorems is the language that I show.
Mathematics is often written as 5,000 years old since Greece, but it has refined results in a long history. In the field of probability and statistics, it is often said that this result has been verified 100 million times, so it is probably okay, but then, when verified at the 101st time, it is not guaranteed that there will be a failure.
1.3
Mathematics cannot exist without absolute guarantee. That is proof proof. But the word “perfect” is not commonly used. This is because Kruto Godel proved the incompleteness theorem Incompleteness theorem in 1928 that “it is not possible to prove the perfection of mathematics by using the method inherent in mathematics” . Iwanami Bunko now publishes the translation, but I still don’t fully understand it. I also read some proofs. From the outside, it looks anxious, but mathematics itself is firm even if there is such a theorem.
1.4
Next, for example, in a language, I use the word distance. It would be quite difficult to define the word distance itself exactly in natural language.
The term “language space” is also used, but it is quite difficult to define a space in natural language.
The word linguistic change is often used, but what changes from where to where and how it changes, if there is no substance, if there is no substance, the change itself is meaningless. In the first place, when we start to think about what changes are, we can no longer control them . One of Wittgenstein’s famous words is that “philosophy is a history of misunderstandings”, but it seems to have built something like a tower on the sand on the ambiguity of language.
Basically, trying to define a language by language presents difficulties. Details are omitted, but progress has been made especially in the field of basic mathematical theory since the 1970s. Last summer, a Japanese pioneer in the basic theory of mathematics called Takeuchi Gaishi died. I also learned a lot from him. He is featured in the February issue of the Mathematics Seminar this year. It was very interesting to me.
But I’m not denying philosophy. On the contrary, I also think that my core is derived from philosophy.
1.5} For this reason, I no longer write the basic language in the language. It’s easy to say, but in my case it took me in my 20s to 40s to get here.
At the end of the 1970s, maybe summer vacation in 1978 (because I was a faculty member), 31 years old, I’m still in Tokyo, but I’ve been working on a research application paper at T Research Institute. Not because I wanted to win an award, but because I wanted to confirm my own challenges based on that. The content was what a sentence in a language was, so I tried to put together a sort of preparatory stage for what I am currently thinking about. The method tried to use set theory and basic theory of mathematics. In conclusion, as soon as I started to write, I was convinced that I couldn’t write what I was aiming for in the collections of the time in me, and this plan was abandoned. By the way, in the West, basic mathematics is positioned as a division of logic rather than a division of mathematics. I also think that is better.
1.6
Why did you cancel at this time? It is natural that I have little knowledge of language and mathematics, and my ability is low, so I will list the others
. # 1 I mainly tried to use the set theory of mathematics, but the results of mathematics in the field at that time alone (maybe) cannot handle the situation of complicated languages.
# 2 The basic theory of mathematics follows the development of logic, and the root of the language itself cannot be approached (by the achievements at that time).
# 3 The whole language is vast, and it is uncertain where in the language I focus my discussion.
Was the main reason for the cancellation.
1.7
I returned to college at the age of 32 in 1979 and reunited with Eiichi Chino of Linguistics (I first met in 1969 as a teacher of Russian), where I mainly studied the situation of the Prague Linguistics Circle in the 1920s. I was taught in detail. Among themThe presence of Sergej Karcevskij has overwhelmed me. Chino, who he called the only genius in his last year’s book Open Door to Linguistics, pointed out the duality of language . The language is soft and flexible to absorb the outside world, but at the same time has a strong and robust structure . In this contradictory duality, the essence of language was said to be. This is a part of the semantics in a broad sense, but the most important thing in the language of this meaning is shelved as it was, and still is too difficult, and more precise phonology etc. I went to the building. For example, American structural linguistics from the 1950s onwards is a representative example. After that, I almost excluded the meaning of Chomsky’s generative grammar, and searched for the structure of grammar. Edward Sapir was one of the most prominent of these historical developments , but I suggested a lot. The concept is Drift . He reveals language and movement, the temporal element of language . This will later be linked to the existence of Perelman in me.
After all, I didn’t improve my Russian, but I still have a strong attachment to Russian, and I read a booklet on Russian grammar after a long time last year. Although the grammar in Hakusui’s Kuseju library was good, Brian Kemple’s book from Dover Publications was concise and detailed with great details, and it was wonderful. The author was also impressed by the statement on page 94:
“The definitions do not pretend to be complete, or to settle points of interpretation that grammarians have been disputing for the past several hundred years.”
1.8
Despite the fact that meaning is one of the most important things in the language, In the rest of linguistics it has always been excluded. After World War II, the field of general semantics expanded temporarily in the United States and other countries, but this is a macro, such as what role language plays in society, and eventually sociology and humankind. It will be absorbed in the school. The meaning itself was still an unexplored field. In my case, the philosophical ones are already based on Wittgenstein’s sharp philosophical criticism (verification), so with the addition of Karcevskij, I’m almost ready. Since I was already thinking of advancing the subject in Kanji and the extremely strict linguistics (elementary school ) of Chinese modernity centred on Kanji, the issue was how to refine mathematics as a writing method.
1.9
Fortunately, since the 1980s, the era of rapid development of mathematics and its application to a wide range of fields has come. Iwanami Shoten has been developing the mathematics series in the order of introduction, basics, and development for almost 30 years. Kyoritsu Shuppan has traditionally had a series, so we continue to publish various modern mathematics achievements and are still in progress. I am now a lover of the “Mathematics Shine” series.
It is symbolized by a mathematician who said in a dialogue, “Now math has finally accumulated problems describing various fields”, but I stopped in the 1970s This time, I can now write my own problems while freely choosing rich mathematical methods. Here in philosophy · Wittgenstein, elementary school, such as object-Wang Guowei, purpose · Karcevskij, method · Algebraic Geometry algebraic geometry was aligned, and everything. The mid-1980s.
1.10
In
1986, I completed my research career at a university, quit teaching, made a library, and was able to concentrate almost exclusively on language research. Of course, the biggest thing was understanding of the surroundings. My income has decreased sharply, but I am still at the present while securing a minimum income with Chinese professors, history courses, Buddhist courses, Japanese language teachers, etc. In 1985, there was a talk from Professor A to a lecturer at K University. At this time, the university was extremely thankful to me, but it was no longer the field of the main I am going.
1.11
While reading mainly Chinese and Buddhist literature since 1986 However, when I was admitted to O General Hospital with pneumonia in 2002, I was able to think intensively by chance, so based on the article by Kingdom Wei, language, in my case , Kanji, but what summarised the problem of time inherent in it was On Time Property Inherent in Characters, the nature of time inherent in language. At this time, I explored the direction of my language research from a Macro perspective, and it was later uploaded as the Manuscript of Quantum Theory for Language. In March 2003, we went to skiing in Hakuba, Nagano prefecture, and when everyone was skiing, we concentrated ourselves and put together the final summary. nostalgic.
Although 1.12
is skipped, it was around this time that I learned the depth of Buddhist literature. I read about it in the Taisho Shinshu Daizo Sutra, the Japanese Buddhist complete books, etc., but the literature on the end of Buddhism in India is particularly interesting, for example, the spiral structure of the world is clearly shown by the 4th and 5th century AD. I will. It is interesting to compare it with the situation of modern biology such as DNA, but easy analogy should be avoided. Although I have a deep attachment to the early days of molecular biology derived from physics. Saicho, Kukai in Japan I read mainly. The impression is that Saicho is hard to read and Kukai is easy to read. Professor K of Japanese literature, which I adore, was asked by an ex-Soviet scholar to send Kukai’s “Bunkyo Higaku Furon” and fulfills his promise. It was. This book is highly regarded as the phonological theory of the Tang dynasty, without any books of the same age, but it is also readable as modern phonological theory. However, it will be difficult to read if punctuation is not entered. Nowadays there are good books in China.
1.13
Unauthorized ・ I read the Buddhist theory of my family in the Taisho Shinshu Okura sutra, but as a high peak of philosophy in the Orient, there is something that unintentionally corrects the collar regardless of faith. I still want to read it again if I have time. I feel that my belief that I started walking from the Orient when I entered university has come to fruition here.
Last autumn 2017, at the Tokyo National Museum, there was a special exhibition of the Kamakura era sculptor Unkei, and after a long time, I reunited with an unwritten and worldly statue . It was in my thirties that I saw Kofukuji Temple in Nara. There, I also reunited with the statue of Shigen , who had promoted the reconstruction of Todaiji Temple . The first view of this statue was at the Kyoto National Museum, and when I visited, there was no one but me on the floor. The statue of the high priest at that time was a peaceful old monk who had finished recruiting, but when he met again last fall, the old teacher felt a much more youthful and fulfilling energy than I did. I felt the flow of my age and age.
In addition , I was reminded of the time when I was read with my two friends after being recommended by my teacher about the “Mikuni Buddhist Hodentsu Engi”, a school monk from Todaiji Temple in the Kamakura period . This is how I got to know the Chinese language.
I will omit about the modern Chinese elementary school.
2. Why is language research so attractive, and its development and applications?
2.1
Base is my theory lover. The thing that attracted me most in high school was theoretical physics. In my case, it wasn’t the direction of Hideki Yukawa’s discovery of mesons, but Shinichiro Tomonaga’s super-multi-hour theory . The whole picture is quite difficult, but if you have knowledge of calculus and differential equations, it will be great. I later organized it and put together a summary of the timeliness of the language. Suggested by Kingdom Wei and Sapir. Considering it now, it seems that the conversion from theoretical physics to language was quite necessary. During this time, it was a great harvest to notice the existence of a clear physicist called Dirac. About this British man, who won the Nobel Prize in Physics last year and died, Yoichiro Nanbu wrote in an essay.
2.2
I liked this theory, and I also liked the direction of philosophies that seek the fundamental. It was ambiguous in high school, but later in the 1970s, in my late twenties, Wittgenstein’s translations appeared one after another, and while reading them, I made a fundamental examination of the heritage of philosophy. In my consideration, I should avoid ambiguity in philosophy and seek a different direction. As a result, mathematics seemed to be the most effective. I have liked mathematics since high school, and when I was trying to find a solution to the movement of physics in the 3rd year, the most effective method was the differential equation, but I could not solve it at the level of high 3 calculus. I was impressed that I thought I would not be after college.
2.3
In my
twenties, I was studying mathematics little by little as a teacher. Here in Kanda, the French math group, BourbakiMeet you. This set the course for my math thereafter. Bourbaki meant that anyone could go from a clear and concise starting point to the apex of complex modern mathematics, but instead of precision, it was huge, and I studied it carefully while looking at its existence sideways. Continued.
2.4
As
mentioned in 1.7 , from 1986 to 2003, we have Wittgenstein, Kingdom Wei, Karcevskij, and Algebraic Geometry, so we can finally start moving. The appeal of this research is that a. First of all, no matter what you do , it is infinite, that is , infinite . I’m not very interested in finite things. In terms of content, b. Language is a great human tool, but it is both elaborate and often misleading . Liar’s paradox, or self-reference self-reference may be one example. Wittgenstein elaborately describes such a situation. Moreover, the meaning of the c. Language is an impenetrable lone castle that has been given up to attack for almost 100 years . In other words, if you have infinity, elaborateness, and impregnability, it would be almost the same as a mountaineer aiming for unexplored peaks . Someone said why you climb a mountain , because there is a mountain there,Is an eternal saying.
2.5
My position is as described above, but I hardly think about whether there is any development or application in the real world from it, but if I force it, one thing is considered now.
It has medical applications. I don’t do that much, but I still think that only the theoretical direction is mathematically possible, and I am not mainly aiming at application for preparation for that, but now in progress. My Site, Geometrization Language in, Preparatory genre is it that the (preliminary). Geometrization Language is a meaning like ” geometric language “.
2.6
First of all, it will be necessary to give a brief description of what geometry is. In 1980 Thurston submitted a conjecture conjecture that a three-dimensional closed manifold decomposes into eight different geometric structures . In the early 1980s Hamilton is this expected to be formulated as a kind of equation , Perelman from 2002 to 2003 was finally settled. To make it more concise, three-dimensional figures can be classified into eight types, and their formulation is also possible.
2.7
Here is my inference. In the medical field, nowadays various image analysis image analysis It is used to identify the disease and the stage of disease progression. Judgment of this analysis depends on the doctor’s visual observation, but now that images are diversified and the amount is enormous, it is now categorized by performing statistical processing and divided into several types, It seems that the decision has been made. If it is possible to classify this statistical collection by geometricalization , the iconography will be mathematically formalized, and the formulation will be converted into natural language, so that the iconography analysis is precise and accurate. Will be able to be shared with.
2.8
As
I’ve already said, I’m not doing linguistic research aiming at such applications. As shown in 2.4, I’m just one mountaineer who has a longing for unexplored peaks. I made a small Base Camp by myself, just below Takamine . There are countless climbers in the world. But all these comparisons and crufts disappear when you see the unexplored peaks of the blue sky. Because there is a mountain there.
2.9
Let’s hurry to the immediate conclusion. I am thinking of incorporating the images shown in 2.6, 2.7 etc. into the area of language. Emoji Emoji and LATEX are also included. I call this area of language a broad language, Broad Language . In thisAlso includes the Egyptian hieroglyph hieroglyph and the Chinese ancient hieroglyph Jaguwen . But my field isn’t semiotic semiotics that was once popular. I think Semiotics is a fertile Hirono, but the method is not clear. I will refrain from detailing it for now.
Thinking this way, one can imagine how important the ancient Chinese shell texts since BC 1400 are. Kanji is an existing character system that has inherited the ancient hieroglyphics without interruption and is an important field of language. I first targeted this kanji for research.
2.10
Will the development of my language research become more or less visible? The meaning of the language is clearly expressed in mathematics as a geometrical figure including temporal changes. But I have hardly thought about such development. I just start walking with less luggage to build my next Base Camp. It is better to have less luggage to reach higher places. For my baggage, all I need is kanji and mathematics . In order to prevent oxygen deficiency, Chinese elementary school and Chinese translation of Buddhist scriptures, Dan Judgment, Kingdom Wei, Shorin, Taisho Shinshu Daizo Sutra and Nihon Zakura Sutra are sometimes necessary. The 1920s Linguistic Circle of Prague remains a major source of energy replenishment . I don’t know how close I can go to the unexplored peaks. That’s not what I ask anymore.
This essay was written with a focus on memories, so there may be differences in memories, even in small years. I’m also not sure if it answers the question.
Please forgive me about that point . If I had written such a thing, then a Buddhist teacher in Kyoto remembered the words that were written in the book. When the teacher had a Buddhist discussion in the open air at night in Tibet, Buddhist monks voiced their sutras based on their memories, but the teacher did research based on the literature on the desk. I was told that I could not respond to it quickly because I was doing it. It also showed their sincere attitude towards Buddhism and was struck by the depth of faith and scholarship.
Please take good care of yourself.
Cordially
5 February 2018
TANAKA Akio
——————————————– ————————————————– ————————— References for Letter to Y. Of Broad language
TANAKA Akio
1. From definition of language to the decision of direction for research on language
1.1
1. Presupposition on Natural 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 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.
Reference
For WITTGENSTEIN Ludwig / Position of Language / 10 December 2005-3 August 2012
22 August 2012
Sekinan Research Field of Language
2. Sayama Assumption on Language
3. Description
1.2
1. Inspiration The Time of Quantum
In August 2003, I went toHakuba 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 wrotethe sketch-like paperof 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 sphericalsubstance 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.
September 29, 2008
Sekinan Research Field of Language
[January 23, 2012]
The title changed.The former title is “From Quantum to Manifold”.
[Postscript. January 25,2012]
On quantization of Language.Refer to the next.
Quantization of Language
1.3
Glitter of youth through philosophy and mathematics in 1970s
1.4
Distance Theory Algebraically supplemented Distance
1.5
Thanks to physics about which I ever dreamt in my future
1.6
Bourbaki’ ELEMENTS DE MATHEMATIUE THEORY OF THE ENSEMBLES F ascicule of resiltats Third edition 1964
1.7
1.Fortuitous Meeting
What CHINO Eiichi Taught Me in the Class of Linguistics
CHINO taught me the core of linguistics in the class of structural linguistics.The most remarkable thing is what he explained the paper of KARCEVSKIJ to us.The title is “Du dualisme asymétrique du signe linguistique”. It became a miracle of my life. I summarize the essence of the paper from one of CHINO’s most major book,Gengogaku eno hirakareta tobira, Janua linguarum reserata in Latin. Language has the dualism.One is firm structure. The other is flexible variability.This is a very revelation in the roaming of study.At first I selected the firmness of language for my research target.It overlapped with the research of Chinese characters.Thought of KARCEVSKIJ fructified the quantum of language.The theory I reached is Quantum Theory for Language.The starting point of the theory was given from CHINO.I deeply appreciate him for teaching me almost all the things on language. CHINO Eiich died March 19, 2002.At age 70.December 5, 2004July 16, 2014 Added 2. Linguistic Circle of Prague
3. Edward Sapir gave me a moment to study language universals together with Sergej Karcevskij
4. Note for KARCEVSKIJ Sergej’s “Du dualisme asymetrique du signe linguistique”
5. Karcevskij conjecture 1928 and Kawamata conjecture 2002
6. Brian Kemple. Essential Russian grammar. Dover Publications. 1993.
1.8
The Time of WANG Guowei
The Time of Wittgenstein
1.9
For WITTGENSTEIN Ludwig Revised Position of Language
Essay on WANG Guowei
The Complete Works of WANG Guowei Revised
For WANG Guowei A Letter Being led by Karcevskij’s conjecture
The Days of von Neumann Algebra
The days between von Neumann Algebra and Complex Manifold Deformation Theory
Bridge between mathematics and physics / Revised
1.10
Sekinan Library
The Days of Sekinan Library
1.11
On Time Property Inherent in Characters
Manuscript of Quantum Theory for Language
Quantum Theory for Language
Quantum Language between Quantum Theory for Language 2004 and Generation of Word 2008 adding their days and after A conclusion for the present on early papers of Sekinan Library
1.12
1. Max Delbluck From Physics to Biology Application to different Fields
1.13
1.Special Exhibition UNKEI The Great Master of Buddhist Sculpture 2017.Tokyo National Museum
2. Why is there attractive of language research, and how are there developments or applications in the future
2.1
Meaning minimum On Roman Jakobson, Sergej Karcevskij and CHINO Eiichi
1.
Meaning minimum is one of the kernel concepts for the model of language universals on my study. The concept was at first thought from Roman Jakobson’s semantic minimum on which I first read at his book, ESSAIS DE LINGUISTIGUE GENERALE, 1973. His concept was yet intuitive at the linguistic study history in the latter half of the 20th century.Comparison with his concept, my definition of meaning minimum was a certain basis prepared in the learning of mathematics, especially on algebraic geometry, that is the most fantastic approach to the construction of the language model. But the contents of meaning minimum is vacant. This concept shows the minimum unit of one big constructive meaning of word. meaning minimum seems to be correspondent with element of set theory, which theory and foundations of mathematics had been my favourite mathematical basis in 1970s, my youth time. Bourbaki was always echoed around us. Grothendieck was a highest star in this world.
2.
Time went fast from at that time. Set theory became one of the premise field of mathematics. But in my part, set theory’s agenda was put at a another point. Because language has a certain expanded world that seems to be continuous. Set theory’s atomic discreteness does not match in my primary learning level. So, in my age 30s, I had sank in the philosophically intuitive thinking often referring the tradition of 1920s, especially of the Linguistic Circle of Prague. On the circle my teacher CHINO Eiichi had taught me from time to time on the campus of university or coffee shop near the station we used. CHINO had gone to the Czechoslovakia Republic from 1959 to 1967. I first met him in 1969 at his Russian class at my third year of university student. I was the age 21 and he was 37.
3.
At the age 23’s 1971 spring, I graduated university and once became a high school’s teacher and again returned back to university in 1979 after 8 year job of the school. At that time I thought of characters’ distinctive features on Written Chinese classics. I mainly read WANG Guowei, ZHANG Binglin, DUAN Yucai, WANGYyinzhi being guided by Japanese modern scholar KANO Naoki. Expressly I had attracted to WANG Guowei and his book Guantangjilin. Besides reading these China’s Qing dynasty’s linguistic peaks, I had always thought on Ludwig Wittgenstein for his endless pursuit on language. So I resigned school and came back to the campus where I again met with CHINO. I was age 30s and he was 50s. He was already the big scholar at the linguistic field but I was a poor return student. But I dare to say we were colleagues for language study. He taught me the detailed and strict tradition of the linguistic Circle of Prague. He frequently talked on Sergej Karcevskij and his eminent discernment on language. In the later year’s masterpiece, Janua Linguisticae Reserata, 1994, he wrote only Karcevskij as genius in the great linguists.
4.
Being led by CHINO, I again started linguistic learning on meaning that I had been interested in from my 20s but too hard to approach by my talent. This time I had Karcevskij’s fine insight to meaning enough absorbing the fertile tradition of Prague, where also exist Jakobson and Mathesius. Through the learning I gradually lean to desire to write clear definitions on language. I again remembered the little learning of my 20s age’s mathematics. Bourbaki, Godel, TAKEUCHI and their set theory, foundations of mathematics and that Incompleteness theorem. I had learnt mathematics little by little, inch by inch.
5.
CHINO Died in 2002 at age 70 and I became 55. The next year 2003, I wrote a short paper titled “Quantum Theory for Language”. This paper was showed at a international symposium on Silk road for dealing with language from Chinese characters on linguistic viewpoint. I knew that Asian civilisation and history had great concern not only from Asia but also European continents. At the symposium some 400 researchers gathered in the various scholarly fields. It was a awesome encounter for my study, namely, East meet West. Probably Chinese character’s agenda will be written by Europe oriented mathematics. WANG Guowei will meet with karcevskij mediated through mathematics’ description. The target confronted at that time was time inherent in characters, or time in word. In Chinese, particularly in classical written Chinese, all the characters show enough independent meaning in one character probably including even time. It was my first conjecture taught from Karcevskij and CHINO. Meaning minimum is on the boat going across to the opposite shore. This metaphor was derived from WANG Guowei’s famous paper, “Yin- bu zhong suojian xiangong xianwang kao”
6.
The concept of time inevitably led to the concept of distance. In 2004, I wrote a paper titled “Distance Theory”. But the paper was yet intuitive and not clear for descriptive definition. So hereinafter I learnt algebra inch by inch being assisted with the rich heritage of geometry. In the centre of learning, always exist time that connotes finiteness and infinity. But infinity is not easily obtained without probably only loop space at the present. And again returns back to meaning minimum as the passenger of the boat named time property inherent. This time the passenger on the boat is called operad or algebraic language.
7.
After all I came back to the very dream that I had embraced since the high school days. It was a fundamental ask on language related with mathematics and physics. The root of language would be able to describe by mathematics and physics. In my mind language is always put at the centre of the pursuit that was what anyone can clearly understand. Description by mathematics, but physics why (Note 1)?. Physics treats with substance that constructs the world in which I had desire to let language enter. It started at Substantiality of language (References 2. 2). It was my dream and probably will be so, hereafter.
References
1.
Cell Theory Continuation of Quantum Theory for Language / From Cell to Manifold For LEIBNIZ and JAKOBSON / Tokyo June 2, 2007
The Time of Language Ode to The Early Bourbaki To Grothendieck / January 10, 2012
2.
Fortuitous Meeting What CHINO Eiichi Taught Me in the CLass of Linguistics / Tokyo December 5, 2004
Linguistic Circle of Prague / Tokyo 13 July 2012, 19 July 2012 Added
3.
The Complete Works of WANG Guowei / Tokyo 24 May 2012
The Time of Wittgenstein / Tokyo January 20, 2012
Notes for KARCEVSKIJ Sergej / Note for KARCEVSKIJ Sergej’s “Du dualisme asymetrique du signe linguistique” / Tokyo September 8, 2011
4.
Quantum Linguistics / Growth of Word Dedicated to TAKEUCHI Gaishi / Tokyo January 30, 2006
5.
Quantum Theory for Language Synopsis / Tokyo January 15, 2004
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 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 payed 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 drew in 1885, over 130 years ago. But all the landscapes were vivid like the present and probably in future.
Tokyo 27 May 2018
Sekinan Zoho
[Note]
6 June 2018
Time and Eternity
TANAKA Akio
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 originally written in Japanese, now show by the English Eddition by Google Translate.
Letter to Y. Of Broad language 4th Edition 5 February 2018
Translated by Google 2020.
Letter to Y. Of Broad Language 4th Edition 5 February 2018. Translated by Google translate 2020.
Letter to Y. Of Broad Language 4th Edition 5 February 2018
Letter to Y. Of Broad Language 4th Edition
Dear Y.,
1. From the definition of language to determining the direction of language research
1.1
I don’t use the word “research” in Japanese much, but here I think about language To briefly describe the above in terms of linguistic research, I think the question is the aim of linguistic research and the application of linguistic research.
When it comes to what language is, I think that language is generally a way for humans to communicate their state of mind with great precision . It is usually assumed that humans speak and hear. So-called natural language. However, I do not define such a so-called language in my own research on language. My research, of course, includes natural language, but it is more extensive . And in my opinion, defining a language in natural language only makes it ambiguous. This is the reason why superlanguages are advocated in basic mathematics.
1.2
So, I don’t call my research linguistics, and I don’t use terms like linguistics or philology in English. Because these terms are centred on natural language. In my case, it is more extensive, so I just write research on language. This broad language, in my term Broad Language , will be discussed later.
So, I’m wondering if such undefined things will cause confusion, but in my case, the written content (maybe) tells me the situation of the language I speak, so more ambiguous The definition is not used. Since I mainly use mathematics, it means that the world being built by the axioms and theorems is the language that I show.
Mathematics is often written as 5,000 years old since Greece, but it has refined results in a long history. In the field of probability and statistics, it is often said that this result has been verified 100 million times, so it is probably okay, but then, when verified at the 101st time, it is not guaranteed that there will be a failure.
1.3
Mathematics cannot exist without absolute guarantee. That is proof proof. But the word “perfect” is not commonly used. This is because Kruto Godel proved the incompleteness theorem Incompleteness theorem in 1928 that “it is not possible to prove the perfection of mathematics by using the method inherent in mathematics” . Iwanami Bunko now publishes the translation, but I still don’t fully understand it. I also read some proofs. From the outside, it looks anxious, but mathematics itself is firm even if there is such a theorem.
1.4
Next, for example, in a language, I use the word distance. It would be quite difficult to define the word distance itself exactly in natural language.
The term “language space” is also used, but it is quite difficult to define a space in natural language.
The word linguistic change is often used, but what changes from where to where and how it changes, if there is no substance, if there is no substance, the change itself is meaningless. In the first place, when we start to think about what changes are, we can no longer control them . One of Wittgenstein’s famous words is that “philosophy is a history of misunderstandings”, but it seems to have built something like a tower on the sand on the ambiguity of language.
Basically, trying to define a language by language presents difficulties. Details are omitted, but progress has been made especially in the field of basic mathematical theory since the 1970s. Last summer, a Japanese pioneer in the basic theory of mathematics called Takeuchi Gaishi died. I also learned a lot from him. He is featured in the February issue of the Mathematics Seminar this year. It was very interesting to me.
But I’m not denying philosophy. On the contrary, I also think that my core is derived from philosophy.
1.5} For this reason, I no longer write the basic language in the language. It’s easy to say, but in my case it took me in my 20s to 40s to get here.
At the end of the 1970s, maybe summer vacation in 1978 (because I was a faculty member), 31 years old, I’m still in Tokyo, but I’ve been working on a research application paper at T Research Institute. Not because I wanted to win an award, but because I wanted to confirm my own challenges based on that. The content was what a sentence in a language was, so I tried to put together a sort of preparatory stage for what I am currently thinking about. The method tried to use set theory and basic theory of mathematics. In conclusion, as soon as I started to write, I was convinced that I couldn’t write what I was aiming for in the collections of the time in me, and this plan was abandoned. By the way, in the West, basic mathematics is positioned as a division of logic rather than a division of mathematics. I also think that is better.
1.6
Why did you cancel at this time? It is natural that I have little knowledge of language and mathematics, and my ability is low, so I will list the others
. # 1 I mainly tried to use the set theory of mathematics, but the results of mathematics in the field at that time alone (maybe) cannot handle the situation of complicated languages.
# 2 The basic theory of mathematics follows the development of logic, and the root of the language itself cannot be approached (by the achievements at that time).
# 3 The whole language is vast, and it is uncertain where in the language I focus my discussion.
Was the main reason for the cancellation.
1.7
I returned to college at the age of 32 in 1979 and reunited with Eiichi Chino of Linguistics (I first met in 1969 as a teacher of Russian), where I mainly studied the situation of the Prague Linguistics Circle in the 1920s. I was taught in detail. Among themThe presence of Sergej Karcevskij has overwhelmed me. Chino, who he called the only genius in his last year’s book Open Door to Linguistics, pointed out the duality of language . The language is soft and flexible to absorb the outside world, but at the same time has a strong and robust structure . In this contradictory duality, the essence of language was said to be. This is a part of the semantics in a broad sense, but the most important thing in the language of this meaning is shelved as it was, and still is too difficult, and more precise phonology etc. I went to the building. For example, American structural linguistics from the 1950s onwards is a representative example. After that, I almost excluded the meaning of Chomsky’s generative grammar, and searched for the structure of grammar. Edward Sapir was one of the most prominent of these historical developments , but I suggested a lot. The concept is Drift . He reveals language and movement, the temporal element of language . This will later be linked to the existence of Perelman in me.
After all, I didn’t improve my Russian, but I still have a strong attachment to Russian, and I read a booklet on Russian grammar after a long time last year. Although the grammar in Hakusui’s Kuseju library was good, Brian Kemple’s book from Dover Publications was concise and detailed with great details, and it was wonderful. The author was also impressed by the statement on page 94:
“The definitions do not pretend to be complete, or to settle points of interpretation that grammarians have been disputing for the past several hundred years.”
1.8
Despite the fact that meaning is one of the most important things in the language, In the rest of linguistics it has always been excluded. After World War II, the field of general semantics expanded temporarily in the United States and other countries, but this is a macro, such as what role language plays in society, and eventually sociology and humankind. It will be absorbed in the school. The meaning itself was still an unexplored field. In my case, the philosophical ones are already based on Wittgenstein’s sharp philosophical criticism (verification), so with the addition of Karcevskij, I’m almost ready. Since I was already thinking of advancing the subject in Kanji and the extremely strict linguistics (elementary school ) of Chinese modernity centred on Kanji, the issue was how to refine mathematics as a writing method.
1.9
Fortunately, since the 1980s, the era of rapid development of mathematics and its application to a wide range of fields has come. Iwanami Shoten has been developing the mathematics series in the order of introduction, basics, and development for almost 30 years. Kyoritsu Shuppan has traditionally had a series, so we continue to publish various modern mathematics achievements and are still in progress. I am now a lover of the “Mathematics Shine” series.
It is symbolized by a mathematician who said in a dialogue, “Now math has finally accumulated problems describing various fields”, but I stopped in the 1970s This time, I can now write my own problems while freely choosing rich mathematical methods. Here in philosophy · Wittgenstein, elementary school, such as object-Wang Guowei, purpose · Karcevskij, method · Algebraic Geometry algebraic geometry was aligned, and everything. The mid-1980s.
1.10
In
1986, I completed my research career at a university, quit teaching, made a library, and was able to concentrate almost exclusively on language research. Of course, the biggest thing was understanding of the surroundings. My income has decreased sharply, but I am still at the present while securing a minimum income with Chinese professors, history courses, Buddhist courses, Japanese language teachers, etc. In 1985, there was a talk from Professor A to a lecturer at K University. At this time, the university was extremely thankful to me, but it was no longer the field of the main I am going.
1.11
While reading mainly Chinese and Buddhist literature since 1986 However, when I was admitted to O General Hospital with pneumonia in 2002, I was able to think intensively by chance, so based on the article by Kingdom Wei, language, in my case , Kanji, but what summarised the problem of time inherent in it was On Time Property Inherent in Characters, the nature of time inherent in language. At this time, I explored the direction of my language research from a Macro perspective, and it was later uploaded as the Manuscript of Quantum Theory for Language. In March 2003, we went to skiing in Hakuba, Nagano prefecture, and when everyone was skiing, we concentrated ourselves and put together the final summary. nostalgic.
Although 1.12
is skipped, it was around this time that I learned the depth of Buddhist literature. I read about it in the Taisho Shinshu Daizo Sutra, the Japanese Buddhist complete books, etc., but the literature on the end of Buddhism in India is particularly interesting, for example, the spiral structure of the world is clearly shown by the 4th and 5th century AD. I will. It is interesting to compare it with the situation of modern biology such as DNA, but easy analogy should be avoided. Although I have a deep attachment to the early days of molecular biology derived from physics. Saicho, Kukai in Japan I read mainly. The impression is that Saicho is hard to read and Kukai is easy to read. Professor K of Japanese literature, which I adore, was asked by an ex-Soviet scholar to send Kukai’s “Bunkyo Higaku Furon” and fulfills his promise. It was. This book is highly regarded as the phonological theory of the Tang dynasty, without any books of the same age, but it is also readable as modern phonological theory. However, it will be difficult to read if punctuation is not entered. Nowadays there are good books in China.
1.13
Unauthorized ・ I read the Buddhist theory of my family in the Taisho Shinshu Okura sutra, but as a high peak of philosophy in the Orient, there is something that unintentionally corrects the collar regardless of faith. I still want to read it again if I have time. I feel that my belief that I started walking from the Orient when I entered university has come to fruition here.
Last autumn 2017, at the Tokyo National Museum, there was a special exhibition of the Kamakura era sculptor Unkei, and after a long time, I reunited with an unwritten and worldly statue . It was in my thirties that I saw Kofukuji Temple in Nara. There, I also reunited with the statue of Shigen , who had promoted the reconstruction of Todaiji Temple . The first view of this statue was at the Kyoto National Museum, and when I visited, there was no one but me on the floor. The statue of the high priest at that time was a peaceful old monk who had finished recruiting, but when he met again last fall, the old teacher felt a much more youthful and fulfilling energy than I did. I felt the flow of my age and age.
In addition , I was reminded of the time when I was read with my two friends after being recommended by my teacher about the “Mikuni Buddhist Hodentsu Engi”, a school monk from Todaiji Temple in the Kamakura period . This is how I got to know the Chinese language.
I will omit about the modern Chinese elementary school.
2. Why is language research so attractive, and its development and applications?
2.1
Base is my theory lover. The thing that attracted me most in high school was theoretical physics. In my case, it wasn’t the direction of Hideki Yukawa’s discovery of mesons, but Shinichiro Tomonaga’s super-multi-hour theory . The whole picture is quite difficult, but if you have knowledge of calculus and differential equations, it will be great. I later organized it and put together a summary of the timeliness of the language. Suggested by Kingdom Wei and Sapir. Considering it now, it seems that the conversion from theoretical physics to language was quite necessary. During this time, it was a great harvest to notice the existence of a clear physicist called Dirac. About this British man, who won the Nobel Prize in Physics last year and died, Yoichiro Nanbu wrote in an essay.
2.2
I liked this theory, and I also liked the direction of philosophies that seek the fundamental. It was ambiguous in high school, but later in the 1970s, in my late twenties, Wittgenstein’s translations appeared one after another, and while reading them, I made a fundamental examination of the heritage of philosophy. In my consideration, I should avoid ambiguity in philosophy and seek a different direction. As a result, mathematics seemed to be the most effective. I have liked mathematics since high school, and when I was trying to find a solution to the movement of physics in the 3rd year, the most effective method was the differential equation, but I could not solve it at the level of high 3 calculus. I was impressed that I thought I would not be after college.
2.3
In my
twenties, I was studying mathematics little by little as a teacher. Here in Kanda, the French math group, BourbakiMeet you. This set the course for my math thereafter. Bourbaki meant that anyone could go from a clear and concise starting point to the apex of complex modern mathematics, but instead of precision, it was huge, and I studied it carefully while looking at its existence sideways. Continued.
2.4
As
mentioned in 1.7 , from 1986 to 2003, we have Wittgenstein, Kingdom Wei, Karcevskij, and Algebraic Geometry, so we can finally start moving. The appeal of this research is that a. First of all, no matter what you do , it is infinite, that is , infinite . I’m not very interested in finite things. In terms of content, b. Language is a great human tool, but it is both elaborate and often misleading . Liar’s paradox, or self-reference self-reference may be one example. Wittgenstein elaborately describes such a situation. Moreover, the meaning of the c. Language is an impenetrable lone castle that has been given up to attack for almost 100 years . In other words, if you have infinity, elaborateness, and impregnability, it would be almost the same as a mountaineer aiming for unexplored peaks . Someone said why you climb a mountain , because there is a mountain there,Is an eternal saying.
2.5
My position is as described above, but I hardly think about whether there is any development or application in the real world from it, but if I force it, one thing is considered now.
It has medical applications. I don’t do that much, but I still think that only the theoretical direction is mathematically possible, and I am not mainly aiming at application for preparation for that, but now in progress. My Site, Geometrization Language in, Preparatory genre is it that the (preliminary). Geometrization Language is a meaning like ” geometric language “.
2.6
First of all, it will be necessary to give a brief description of what geometry is. In 1980 Thurston submitted a conjecture conjecture that a three-dimensional closed manifold decomposes into eight different geometric structures . In the early 1980s Hamilton is this expected to be formulated as a kind of equation , Perelman from 2002 to 2003 was finally settled. To make it more concise, three-dimensional figures can be classified into eight types, and their formulation is also possible.
2.7
Here is my inference. In the medical field, nowadays various image analysis image analysis It is used to identify the disease and the stage of disease progression. Judgment of this analysis depends on the doctor’s visual observation, but now that images are diversified and the amount is enormous, it is now categorized by performing statistical processing and divided into several types, It seems that the decision has been made. If it is possible to classify this statistical collection by geometricalization , the iconography will be mathematically formalized, and the formulation will be converted into natural language, so that the iconography analysis is precise and accurate. Will be able to be shared with.
2.8
As
I’ve already said, I’m not doing linguistic research aiming at such applications. As shown in 2.4, I’m just one mountaineer who has a longing for unexplored peaks. I made a small Base Camp by myself, just below Takamine . There are countless climbers in the world. But all these comparisons and crufts disappear when you see the unexplored peaks of the blue sky. Because there is a mountain there.
2.9
Let’s hurry to the immediate conclusion. I am thinking of incorporating the images shown in 2.6, 2.7 etc. into the area of language. Emoji Emoji and LATEX are also included. I call this area of language a broad language, Broad Language . In thisAlso includes the Egyptian hieroglyph hieroglyph and the Chinese ancient hieroglyph Jaguwen . But my field isn’t semiotic semiotics that was once popular. I think Semiotics is a fertile Hirono, but the method is not clear. I will refrain from detailing it for now.
Thinking this way, one can imagine how important the ancient Chinese shell texts since BC 1400 are. Kanji is an existing character system that has inherited the ancient hieroglyphics without interruption and is an important field of language. I first targeted this kanji for research.
2.10
Will the development of my language research become more or less visible? The meaning of the language is clearly expressed in mathematics as a geometrical figure including temporal changes. But I have hardly thought about such development. I just start walking with less luggage to build my next Base Camp. It is better to have less luggage to reach higher places. For my baggage, all I need is kanji and mathematics . In order to prevent oxygen deficiency, Chinese elementary school and Chinese translation of Buddhist scriptures, Dan Judgment, Kingdom Wei, Shorin, Taisho Shinshu Daizo Sutra and Nihon Zakura Sutra are sometimes necessary. The 1920s Linguistic Circle of Prague remains a major source of energy replenishment . I don’t know how close I can go to the unexplored peaks. That’s not what I ask anymore.
This essay was written with a focus on memories, so there may be differences in memories, even in small years. I’m also not sure if it answers the question.
Please forgive me about that point . If I had written such a thing, then a Buddhist teacher in Kyoto remembered the words that were written in the book. When the teacher had a Buddhist discussion in the open air at night in Tibet, Buddhist monks voiced their sutras based on their memories, but the teacher did research based on the literature on the desk. I was told that I could not respond to it quickly because I was doing it. It also showed their sincere attitude towards Buddhism and was struck by the depth of faith and scholarship.
Please take good care of yourself.
Cordially
5 February 2018
TANAKA Akio
——————————————– ————————————————– ————————— References for Letter to Y. Of Broad language
TANAKA Akio
1. From definition of language to the decision of direction for research on language
1.1
1. Presupposition on Natural 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 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.
Reference
For WITTGENSTEIN Ludwig / Position of Language / 10 December 2005-3 August 2012
22 August 2012
Sekinan Research Field of Language
2. Sayama Assumption on Language
3. Description
1.2
1. Inspiration The Time of Quantum
In August 2003, I went toHakuba 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 wrotethe sketch-like paperof 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 sphericalsubstance 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.
September 29, 2008
Sekinan Research Field of Language
[January 23, 2012]
The title changed.The former title is “From Quantum to Manifold”.
[Postscript. January 25,2012]
On quantization of Language.Refer to the next.
Quantization of Language
1.3
Glitter of youth through philosophy and mathematics in 1970s
1.4
Distance Theory Algebraically supplemented Distance
1.5
Thanks to physics about which I ever dreamt in my future
1.6
Bourbaki’ ELEMENTS DE MATHEMATIUE THEORY OF THE ENSEMBLES F ascicule of resiltats Third edition 1964
1.7
1.Fortuitous Meeting
What CHINO Eiichi Taught Me in the Class of Linguistics
CHINO taught me the core of linguistics in the class of structural linguistics.The most remarkable thing is what he explained the paper of KARCEVSKIJ to us.The title is “Du dualisme asymétrique du signe linguistique”. It became a miracle of my life. I summarize the essence of the paper from one of CHINO’s most major book,Gengogaku eno hirakareta tobira, Janua linguarum reserata in Latin. Language has the dualism.One is firm structure. The other is flexible variability.This is a very revelation in the roaming of study.At first I selected the firmness of language for my research target.It overlapped with the research of Chinese characters.Thought of KARCEVSKIJ fructified the quantum of language.The theory I reached is Quantum Theory for Language.The starting point of the theory was given from CHINO.I deeply appreciate him for teaching me almost all the things on language. CHINO Eiich died March 19, 2002.At age 70.December 5, 2004July 16, 2014 Added 2. Linguistic Circle of Prague
3. Edward Sapir gave me a moment to study language universals together with Sergej Karcevskij
4. Note for KARCEVSKIJ Sergej’s “Du dualisme asymetrique du signe linguistique”
5. Karcevskij conjecture 1928 and Kawamata conjecture 2002
6. Brian Kemple. Essential Russian grammar. Dover Publications. 1993.
1.8
The Time of WANG Guowei
The Time of Wittgenstein
1.9
For WITTGENSTEIN Ludwig Revised Position of Language
Essay on WANG Guowei
The Complete Works of WANG Guowei Revised
For WANG Guowei A Letter Being led by Karcevskij’s conjecture
The Days of von Neumann Algebra
The days between von Neumann Algebra and Complex Manifold Deformation Theory
Bridge between mathematics and physics / Revised
1.10
Sekinan Library
The Days of Sekinan Library
1.11
On Time Property Inherent in Characters
Manuscript of Quantum Theory for Language
Quantum Theory for Language
Quantum Language between Quantum Theory for Language 2004 and Generation of Word 2008 adding their days and after A conclusion for the present on early papers of Sekinan Library
1.12
1. Max Delbluck From Physics to Biology Application to different Fields
1.13
1.Special Exhibition UNKEI The Great Master of Buddhist Sculpture 2017.Tokyo National Museum
2. Why is there attractive of language research, and how are there developments or applications in the future
2.1
Meaning minimum On Roman Jakobson, Sergej Karcevskij and CHINO Eiichi
1.
Meaning minimum is one of the kernel concepts for the model of language universals on my study. The concept was at first thought from Roman Jakobson’s semantic minimum on which I first read at his book, ESSAIS DE LINGUISTIGUE GENERALE, 1973. His concept was yet intuitive at the linguistic study history in the latter half of the 20th century.Comparison with his concept, my definition of meaning minimum was a certain basis prepared in the learning of mathematics, especially on algebraic geometry, that is the most fantastic approach to the construction of the language model. But the contents of meaning minimum is vacant. This concept shows the minimum unit of one big constructive meaning of word. meaning minimum seems to be correspondent with element of set theory, which theory and foundations of mathematics had been my favourite mathematical basis in 1970s, my youth time. Bourbaki was always echoed around us. Grothendieck was a highest star in this world.
2.
Time went fast from at that time. Set theory became one of the premise field of mathematics. But in my part, set theory’s agenda was put at a another point. Because language has a certain expanded world that seems to be continuous. Set theory’s atomic discreteness does not match in my primary learning level. So, in my age 30s, I had sank in the philosophically intuitive thinking often referring the tradition of 1920s, especially of the Linguistic Circle of Prague. On the circle my teacher CHINO Eiichi had taught me from time to time on the campus of university or coffee shop near the station we used. CHINO had gone to the Czechoslovakia Republic from 1959 to 1967. I first met him in 1969 at his Russian class at my third year of university student. I was the age 21 and he was 37.
3.
At the age 23’s 1971 spring, I graduated university and once became a high school’s teacher and again returned back to university in 1979 after 8 year job of the school. At that time I thought of characters’ distinctive features on Written Chinese classics. I mainly read WANG Guowei, ZHANG Binglin, DUAN Yucai, WANGYyinzhi being guided by Japanese modern scholar KANO Naoki. Expressly I had attracted to WANG Guowei and his book Guantangjilin. Besides reading these China’s Qing dynasty’s linguistic peaks, I had always thought on Ludwig Wittgenstein for his endless pursuit on language. So I resigned school and came back to the campus where I again met with CHINO. I was age 30s and he was 50s. He was already the big scholar at the linguistic field but I was a poor return student. But I dare to say we were colleagues for language study. He taught me the detailed and strict tradition of the linguistic Circle of Prague. He frequently talked on Sergej Karcevskij and his eminent discernment on language. In the later year’s masterpiece, Janua Linguisticae Reserata, 1994, he wrote only Karcevskij as genius in the great linguists.
4.
Being led by CHINO, I again started linguistic learning on meaning that I had been interested in from my 20s but too hard to approach by my talent. This time I had Karcevskij’s fine insight to meaning enough absorbing the fertile tradition of Prague, where also exist Jakobson and Mathesius. Through the learning I gradually lean to desire to write clear definitions on language. I again remembered the little learning of my 20s age’s mathematics. Bourbaki, Godel, TAKEUCHI and their set theory, foundations of mathematics and that Incompleteness theorem. I had learnt mathematics little by little, inch by inch.
5.
CHINO Died in 2002 at age 70 and I became 55. The next year 2003, I wrote a short paper titled “Quantum Theory for Language”. This paper was showed at a international symposium on Silk road for dealing with language from Chinese characters on linguistic viewpoint. I knew that Asian civilisation and history had great concern not only from Asia but also European continents. At the symposium some 400 researchers gathered in the various scholarly fields. It was a awesome encounter for my study, namely, East meet West. Probably Chinese character’s agenda will be written by Europe oriented mathematics. WANG Guowei will meet with karcevskij mediated through mathematics’ description. The target confronted at that time was time inherent in characters, or time in word. In Chinese, particularly in classical written Chinese, all the characters show enough independent meaning in one character probably including even time. It was my first conjecture taught from Karcevskij and CHINO. Meaning minimum is on the boat going across to the opposite shore. This metaphor was derived from WANG Guowei’s famous paper, “Yin- bu zhong suojian xiangong xianwang kao”
6.
The concept of time inevitably led to the concept of distance. In 2004, I wrote a paper titled “Distance Theory”. But the paper was yet intuitive and not clear for descriptive definition. So hereinafter I learnt algebra inch by inch being assisted with the rich heritage of geometry. In the centre of learning, always exist time that connotes finiteness and infinity. But infinity is not easily obtained without probably only loop space at the present. And again returns back to meaning minimum as the passenger of the boat named time property inherent. This time the passenger on the boat is called operad or algebraic language.
7.
After all I came back to the very dream that I had embraced since the high school days. It was a fundamental ask on language related with mathematics and physics. The root of language would be able to describe by mathematics and physics. In my mind language is always put at the centre of the pursuit that was what anyone can clearly understand. Description by mathematics, but physics why (Note 1)?. Physics treats with substance that constructs the world in which I had desire to let language enter. It started at Substantiality of language (References 2. 2). It was my dream and probably will be so, hereafter.
References
1.
Cell Theory Continuation of Quantum Theory for Language / From Cell to Manifold For LEIBNIZ and JAKOBSON / Tokyo June 2, 2007
The Time of Language Ode to The Early Bourbaki To Grothendieck / January 10, 2012
2.
Fortuitous Meeting What CHINO Eiichi Taught Me in the CLass of Linguistics / Tokyo December 5, 2004
3.
The Time of Wittgenstein / Tokyo January 20, 2012
Notes for KARCEVSKIJ Sergej / Note for KARCEVSKIJ Sergej’s “Du dualisme asymetrique du signe linguistique” / Tokyo September 8, 2011
4.
Quantum Linguistics / Growth of Word Dedicated to TAKEUCHI Gaishi / Tokyo January 30, 2006
5.
Quantum Theory for Language Synopsis / Tokyo January 15, 2004
Verse Recalled Mountain Hut by RI Kohr
Verse Recalled
Mountain Hut
by RI Kohr
拾遺詩篇
里行
小屋
ここを前におとずれたのはいつの日であったか
今は夏の終わりに近くかつては秋の終わりに
霧のような雨が降っていたその小さな小屋の
ストーブに手をかざし靴を乾かしていた
若かった私よ 若かったすべてのものたちよ
ああその日のような風景になりたいと
私はいつも希っていた
明るいほのおと温かいお茶と固いひとつの椅子と
それらがあれば それらが持続すれば
私の生のほとんどは多分満ちていたのだと
幾度となく考えていた
久しぶりにおとずれたここははなやかで
人々の声が行き交い外ではとうもろこしが売られ
遠い日の暗く沈んだ空もようを思うことは難かしい
私の心が今はなやいでいるという訳ではないが
かつての暗い風景はもしかしたら私自身なのかもしれず
しかしその中心にストーブが赤々ともえていたのが
限りなくなつかしい
愛する人よ
私はここから歩いて来たのです
Mountain Hut
by RI Kohr
拾遺詩篇
里行
小屋
ここを前におとずれたのはいつの日であったか
今は夏の終わりに近くかつては秋の終わりに
霧のような雨が降っていたその小さな小屋の
ストーブに手をかざし靴を乾かしていた
若かった私よ 若かったすべてのものたちよ
ああその日のような風景になりたいと
私はいつも希っていた
明るいほのおと温かいお茶と固いひとつの椅子と
それらがあれば それらが持続すれば
私の生のほとんどは多分満ちていたのだと
幾度となく考えていた
久しぶりにおとずれたここははなやかで
人々の声が行き交い外ではとうもろこしが売られ
遠い日の暗く沈んだ空もようを思うことは難かしい
私の心が今はなやいでいるという訳ではないが
かつての暗い風景はもしかしたら私自身なのかもしれず
しかしその中心にストーブが赤々ともえていたのが
限りなくなつかしい
愛する人よ
私はここから歩いて来たのです
Verse Recalled Mountain Hut by RI Kohr . Translated by Google
Verse Recalled
Mountain Hut
by RI Kohr
Selected Poems
Village Journey
Hut
When was the last time I visited here?
It is now near the end of summer, and once it was the end of autumn.
A misty rain was falling in that small hut.
I held my hands over the stove to dry my shoes.
Young me, all those who were young.
Ah, I have always wished for a scene like that day.
A bright fire, hot tea, and a hard chair.
If only those things could last.
I have thought many times that most of my life would have been fulfilled.
Until today.
It is a lively place I visited for the first time in a long time.
People's voices are coming and going, and corn is being sold outside.
It is difficult to think of the dark, gloomy sky of a long time ago.
It is not that my heart is troubled now, but the dark scenery of the past may be me.
But the stove burning red in the center of it is infinitely nostalgic and dear.
My beloved, I walked from here.
Mountain Hut
by RI Kohr
Selected Poems
Village Journey
Hut
When was the last time I visited here?
It is now near the end of summer, and once it was the end of autumn.
A misty rain was falling in that small hut.
I held my hands over the stove to dry my shoes.
Young me, all those who were young.
Ah, I have always wished for a scene like that day.
A bright fire, hot tea, and a hard chair.
If only those things could last.
I have thought many times that most of my life would have been fulfilled.
Until today.
It is a lively place I visited for the first time in a long time.
People's voices are coming and going, and corn is being sold outside.
It is difficult to think of the dark, gloomy sky of a long time ago.
It is not that my heart is troubled now, but the dark scenery of the past may be me.
But the stove burning red in the center of it is infinitely nostalgic and dear.
My beloved, I walked from here.
Tuesday, 29 October 2024
Sekinan Table: The eve of festival From Print 2012, Chapter 5
Sekinan Table: The eve of festival From Print 2012, Chapter 5
https://lnkd.in/g5bXcduM
As they entered the city centre, the lights of the cars were dazzling, the buildings were getting taller, and above them, small red and navy flags with gold trimmings were decorated along the sidewalk, stretching out into the distance.
-It feels like the eve of a festival.
-I'm not sure if it was the eve of something, but there were certainly days in the past when I felt like I was part of it.
-The night before?
-Yes, the night before.
-Like Christmas.
- It wasn't anything special. But I guess I was waiting for something, in my own way.
-What were you waiting for?
The light from the car shines on I's hair.
-I can't remember exactly, but I think I was just feeling at peace. That's a strange way to put it.
-No, that's not the case, but did it happen?
-Maybe it didn't come.
I thought to myself when I heard that the celebration had never come.
A light rain wets the shoulders of people passing by.
The eve of festival From Print 2012, Chapter 5. Translated by Google 2024
sekinantable.blogspot.com
https://lnkd.in/g5bXcduM
As they entered the city centre, the lights of the cars were dazzling, the buildings were getting taller, and above them, small red and navy flags with gold trimmings were decorated along the sidewalk, stretching out into the distance.
-It feels like the eve of a festival.
-I'm not sure if it was the eve of something, but there were certainly days in the past when I felt like I was part of it.
-The night before?
-Yes, the night before.
-Like Christmas.
- It wasn't anything special. But I guess I was waiting for something, in my own way.
-What were you waiting for?
The light from the car shines on I's hair.
-I can't remember exactly, but I think I was just feeling at peace. That's a strange way to put it.
-No, that's not the case, but did it happen?
-Maybe it didn't come.
I thought to myself when I heard that the celebration had never come.
A light rain wets the shoulders of people passing by.
The eve of festival From Print 2012, Chapter 5. Translated by Google 2024
sekinantable.blogspot.com
Saturday, 26 October 2024
Intuition and Mathematics through Chinese classic Yi-jing. 2012-2019
Intuition and Mathematics through Chinese classic Yi-jing. 2012-2019
Sep 21, 2021
Intuition and Mathematics
What NISHI Junzo remained for us 2
TANAKA Akio
Intuition and mathematics are deeply concerned with each other. In my stand, intuitive concept is first flowing up and the next mathematical description is arranged. According to this situation, intuition is very important and if there is no such flowing up thinking, the development is almost not so easy proceeding.
The time concept in language is the key concept of my language model that is at first found from the ancient Chinese characters’ construction and after writing a short intuitive paper, the more precise descriptions are taken up using mathematics especially of geometry.
But at the deepest basis of language, time is seemed to be infinitive but not spread with a strait line to the future, more likely going round as circle or circular situation.
This conjecture was firmed by Yi-jing that is one of the Five Great Classics of China. I received the lecture on Yi-jing from philosopher NISHI Junzo some five years at the university.
The world of Yi-jing consists from perfect infinitive circularity and this world is perfectly recognised by human for its closed situation of infinity.
It is very hard to recognise infinity as perfect whole image and Yi-jing is resolved this baffling problem through the shut-in world, that is “compact” concept of mathematics.
Tokyo 30 August 2012
8 September 2019 Text revised
SRFL Paper
Sep 21, 2021
Intuition and Mathematics
What NISHI Junzo remained for us 2
TANAKA Akio
Intuition and mathematics are deeply concerned with each other. In my stand, intuitive concept is first flowing up and the next mathematical description is arranged. According to this situation, intuition is very important and if there is no such flowing up thinking, the development is almost not so easy proceeding.
The time concept in language is the key concept of my language model that is at first found from the ancient Chinese characters’ construction and after writing a short intuitive paper, the more precise descriptions are taken up using mathematics especially of geometry.
But at the deepest basis of language, time is seemed to be infinitive but not spread with a strait line to the future, more likely going round as circle or circular situation.
This conjecture was firmed by Yi-jing that is one of the Five Great Classics of China. I received the lecture on Yi-jing from philosopher NISHI Junzo some five years at the university.
The world of Yi-jing consists from perfect infinitive circularity and this world is perfectly recognised by human for its closed situation of infinity.
It is very hard to recognise infinity as perfect whole image and Yi-jing is resolved this baffling problem through the shut-in world, that is “compact” concept of mathematics.
Tokyo 30 August 2012
8 September 2019 Text revised
SRFL Paper
Under the Dim Light 2012
Under the Dim Light
TANAKA Akio
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 the university professor but I was a poor research student. But he was always showed me the general tenderness.
The subject he gave me were 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.
Tokyo
1 August 2012
Sekinan Research Field of Language
The eve of festival. From Print 2012, Chapter 5. Translated by Google 2024
The eve of festival
From Print 2012, Chapter 5 The number of cars and people gradually increased.
Original text is Japanese. The translation has some anbiguous explession. So Sorry.
https://srflnews.blogspot.com/2014/06/the-eve-of-festival.html
As they entered the city center, the lights of the cars were dazzling, the buildings were getting taller, and above them, small red and navy flags with gold trimmings were decorated along the sidewalk, stretching out into the distance.
-It feels like the eve of a festival.
-I'm not sure if it was the eve of something, but there were certainly days in the past when I felt like I was part of it.
-The night before?
-Yes, the night before.
-Like Christmas.
- It wasn't anything special. But I guess I was waiting for something, in my own way.
-What were you waiting for?
The light from the car shines on I's hair.
--I can't remember exactly, but I think I was just feeling at peace. That's a strange way to put it.
-No, that's not the case, but did it happen?
-Maybe it didn't come.
I thought to myself when I heard that the celebration had never come.
A light rain wets the shoulders of people passing by.
- But I'm sure you managed to do something.
Because I am in this way.
At some point, the anticipation of the festival disappeared. Perhaps the festival and the eve passed without me even noticing. Source: Tale / Print by LI Koh / 27 January 2012
Posted by TANAKA Akio
From Print 2012, Chapter 5 The number of cars and people gradually increased.
Original text is Japanese. The translation has some anbiguous explession. So Sorry.
https://srflnews.blogspot.com/2014/06/the-eve-of-festival.html
As they entered the city center, the lights of the cars were dazzling, the buildings were getting taller, and above them, small red and navy flags with gold trimmings were decorated along the sidewalk, stretching out into the distance.
-It feels like the eve of a festival.
-I'm not sure if it was the eve of something, but there were certainly days in the past when I felt like I was part of it.
-The night before?
-Yes, the night before.
-Like Christmas.
- It wasn't anything special. But I guess I was waiting for something, in my own way.
-What were you waiting for?
The light from the car shines on I's hair.
--I can't remember exactly, but I think I was just feeling at peace. That's a strange way to put it.
-No, that's not the case, but did it happen?
-Maybe it didn't come.
I thought to myself when I heard that the celebration had never come.
A light rain wets the shoulders of people passing by.
- But I'm sure you managed to do something.
Because I am in this way.
At some point, the anticipation of the festival disappeared. Perhaps the festival and the eve passed without me even noticing. Source: Tale / Print by LI Koh / 27 January 2012
Posted by TANAKA Akio
Friday, 25 October 2024
Thursday, 24 October 2024
Thursday, 17 October 2024
Language-comprehension-from-past.html. 2004-2018
https://hillswest.blogspot.com/2023/09/language-comprehension-from-past.html
Language comprehension from the Past
TANAKA Akio
1955
Tableau of dialogue of Nagano district
When I was the second grade of elementary school, I visited Nagano district being taken by mother in summer vacation.
There I first heard Nagano dialect. I was interested in the dialog.
After returning home of Tokyo, I summarized the experience of Nagano to a tableau in which I wrote a comparison of dialect between Nagano and Tokyo.
This tableau was pinned up on the wall of the classroom in new autumn term.
It was a pleasant remembrance of my language comprehension.
1956
Question about a notation
When the third grade of elementary school, I asked a question about the notation of Japanese.
Having same pronunciation /o/ between the following two words, why < many > is written to ooi, while is written to otousan?
1957
First learning of foreign language
When the forth grade of elementary school, I began to learn English, the first foreign language, by myself reading texts of my elder sister.
1964
Symbolism of France
When the second school of high school, I learned French for reading the poems of symbolism in France.
1967
Memorization of Saying of Mao Zedong
When learning the composition of Chinese, we memorized and wrote the phrase of Saying of Mao Zedong once a week.
It is a peculiar time of my life on language learning.
1970
Learning of Russian I learned Russian from the daughter of Russian noblewoman.
Her pronunciation is clearly remembered at present in my heart.
She taught me the Russian poem for the festival of Russian class of the university.
1979
Pronunciation of Korean
When learning of pronunciation of Korean, the teacher was not satisfied with my pronunciation of imnida.
I recognized the difficulty of foreign language again there.
The teacher whom I respected died at age 47.
His name is CHO Shokichi.
One of his most important works is Watashino Chosengo sho-jiten, My little dictionary of Korean Language.
Tokyo November 14, 2004
March 11, 2007 Revised
October 10, 2018 Reprinted
SQGL
SQGL is Sekinan Library's specialised site for QGL Quantum Group for Language that has researched since 2017 being carried out the original invention in spring 2003 at Hakuba, Nagano. Manuscript of Quantum Theory for Language shows the intention's details. But at the time 2003, the invention did not have any actuality for the realization as a mathematical theory. What changed the state of my study resulted from the progress of quantum groups at mathematics and the development of particle physics. Speech and writing is the first phase of language and it is a distinct physical phenomena for human being. Here exists my clear point of departure.
Language comprehension from the Past
TANAKA Akio
1955
Tableau of dialogue of Nagano district
When I was the second grade of elementary school, I visited Nagano district being taken by mother in summer vacation.
There I first heard Nagano dialect. I was interested in the dialog.
After returning home of Tokyo, I summarized the experience of Nagano to a tableau in which I wrote a comparison of dialect between Nagano and Tokyo.
This tableau was pinned up on the wall of the classroom in new autumn term.
It was a pleasant remembrance of my language comprehension.
1956
Question about a notation
When the third grade of elementary school, I asked a question about the notation of Japanese.
Having same pronunciation /o/ between the following two words, why < many > is written to ooi, while
1957
First learning of foreign language
When the forth grade of elementary school, I began to learn English, the first foreign language, by myself reading texts of my elder sister.
1964
Symbolism of France
When the second school of high school, I learned French for reading the poems of symbolism in France.
1967
Memorization of Saying of Mao Zedong
When learning the composition of Chinese, we memorized and wrote the phrase of Saying of Mao Zedong once a week.
It is a peculiar time of my life on language learning.
1970
Learning of Russian I learned Russian from the daughter of Russian noblewoman.
Her pronunciation is clearly remembered at present in my heart.
She taught me the Russian poem for the festival of Russian class of the university.
1979
Pronunciation of Korean
When learning of pronunciation of Korean, the teacher was not satisfied with my pronunciation of imnida.
I recognized the difficulty of foreign language again there.
The teacher whom I respected died at age 47.
His name is CHO Shokichi.
One of his most important works is Watashino Chosengo sho-jiten, My little dictionary of Korean Language.
Tokyo November 14, 2004
March 11, 2007 Revised
October 10, 2018 Reprinted
SQGL
SQGL is Sekinan Library's specialised site for QGL Quantum Group for Language that has researched since 2017 being carried out the original invention in spring 2003 at Hakuba, Nagano. Manuscript of Quantum Theory for Language shows the intention's details. But at the time 2003, the invention did not have any actuality for the realization as a mathematical theory. What changed the state of my study resulted from the progress of quantum groups at mathematics and the development of particle physics. Speech and writing is the first phase of language and it is a distinct physical phenomena for human being. Here exists my clear point of departure.
Friday, 11 October 2024
Mt. Tateyama and campers, August 2009
Mt. Tateyama and campers, August 2009
Posted on July 30, 2013
Mt. Tateyama is the precipitous mountain that I love the most in the many mountains in Japan.
We went its foot and walked around afar seeing the severe mountain’s cliffs from here and there.
It was a really fantastic experience for us.
Seeing the mountain is my and wife’s long desire.
Many family, hikers, travellers and genuine climbers were gathering all over Japan and overseas. Their camping base is located below under the mountain bottom.
Looking down the scene gave us also very fine feeling for confirming the mountain's dignified appearance.
11 October 2024
Revised a little
Sekinan Hills
Posted on July 30, 2013
Mt. Tateyama is the precipitous mountain that I love the most in the many mountains in Japan.
We went its foot and walked around afar seeing the severe mountain’s cliffs from here and there.
It was a really fantastic experience for us.
Seeing the mountain is my and wife’s long desire.
Many family, hikers, travellers and genuine climbers were gathering all over Japan and overseas. Their camping base is located below under the mountain bottom.
Looking down the scene gave us also very fine feeling for confirming the mountain's dignified appearance.
11 October 2024
Revised a little
Sekinan Hills
Thursday, 10 October 2024
QNT News : Sekinan Data: Karcevskij conjecture 1928 and Kawam...
QNT News : Sekinan Data: Karcevskij conjecture 1928 and Kawam...: Sekinan Data: Karcevskij conjecture 1928 and Kawamata conjecture... : Karcevskij conjecture 1928 and Kawamata conjecture 2002 TANAKA Aki...
QNT News : Floer Homology Language Note4 Reversibility of Lan...
QNT News : Floer Homology Language Note4 Reversibility of Lan...: Sekinan Table: Floer Homology Language Note4 Reversibility of Lan... : Floer Homology Language TANAKA Akio Note4 Reversibility of ...
atbankofdam again: Intuition and Mathematics through Chinese classic ...
atbankofdam again: Intuition and Mathematics through Chinese classic ...: Sep 21, 2021 Intuition and Mathematics What NISHI Junzo remained for us 2 TANAKA Akio Intuition and ma...
atbankofdam again: Sekinan Table: Word as Infinite loop Space
atbankofdam again: Sekinan Table: Word as Infinite loop Space: Sekinan Table: Word as Infinite loop Space : Word as Infinite loop Space TANAKA Akio 1. Result of D. G. Quillen by Annals of Mathema...
atbankofdam again: Sekinan Table: Energy Distance Theory Conjecture 2...
atbankofdam again: Sekinan Table: Energy Distance Theory Conjecture 2...: Sekinan Table: Energy Distance Theory Conjecture 2 Geometry of ... : Energy Distance Theory Conjecture 2 Geometry of Word TANAKA Aki...
atbankofdam again: Sekinan Table: Deep Fissure between Word and Sentence
atbankofdam again: Sekinan Table: Deep Fissure between Word and Sentence: Sekinan Table: Deep Fissure between Word and Sentence : Tuesday, 26 February 2013 Deep Fissure between Word and Sentence Linguistic Re...
atbankofdam again: Meaning minimum / On Roman Jakobson, Sergej Karcev...
atbankofdam again: Meaning minimum / On Roman Jakobson, Sergej Karcev...: Meaning minimum On Roman Jakobson, Sergej Karcevskij and CHINO Eiichi TANAKA Akio ifbetrue 6 April 2013 1. Meaning minimum is one of the ...
SRFL News: Why I started Quantum-Nerve Theory? Note and Note ...
SRFL News: Why I started Quantum-Nerve Theory? Note and Note ...: Why I started Quantum-Nerve Theory? Note and Note 2 for The Time of Language The Time of Language Ode to The Early Bourbaki To Grothendie...
SRFL News: Inspiration The Time of Quantum
SRFL News: Inspiration The Time of Quantum: 31/08/2015 15:5 Inspiration The Time of Quantum TANAKA Akio In August 2003, I went to Hakuba in Nagano prefecture for the summer...
Sekinan Table: Quantum Group Language Word Indexed and Word Synth...
Sekinan Table: Quantum Group Language Word Indexed and Word Synth...: Quantum Group Language Word Indexed and Word Synthesized 14/07/2018 18:41 Quantum Group Language Word Indexed and Word Synthesized ...
atbankofdam again: Another pass way to mathematics
atbankofdam again: Another pass way to mathematics: Saturday, 27 July 2013 Another pass way to mathematics Another pass way to mathematics 02jan13 In some 40 years I had concerned with m...
Wednesday, 9 October 2024
Blogger atbankofdam 2013
Blogger atbankofdam May-July -2013
https://atbankofdamblg.blogspot.com/
Memory of Famuly and Sayama Hills, West Tokoy
atbankofdam
Skinan Library
Tokyo
9 October 2024
Copyed by Sekinan Hills
Memory of Famuly and Sayama Hills, West Tokoy
atbankofdam
Skinan Library
Tokyo
9 October 2024
Copyed by Sekinan Hills
At Bank of Dam Again
Sekinan Research Field of Language
At Bank of Dam Again
TANAKA Akio
At bank of dam we conversed with friends on many innocent themes in our youth days. Long time ago the place was the sight of the fireworks, for which father took me and elder sister to see in the summer night. When returning home you perfectly slept soundly at father's back, the sister said to me later.
After some thirty years after, we came again with the family to play in the fallen leaves at the bank of dam. Children were rolling down at the slope of the bank wearing golden leaves on the clothes.
And after half a century we have come again at the bank with wife protecting leg's slight pains each other.
Tokyo
16 July 2012
Sekinan Research Field of Language
At Bank of Dam Again
TANAKA Akio
At bank of dam we conversed with friends on many innocent themes in our youth days. Long time ago the place was the sight of the fireworks, for which father took me and elder sister to see in the summer night. When returning home you perfectly slept soundly at father's back, the sister said to me later.
After some thirty years after, we came again with the family to play in the fallen leaves at the bank of dam. Children were rolling down at the slope of the bank wearing golden leaves on the clothes.
And after half a century we have come again at the bank with wife protecting leg's slight pains each other.
Tokyo
16 July 2012
Sekinan Research Field of Language
EVERWENTLIBRARY Daily Thoughts from West Side of Sayama Hills, West Tokyo
atbankofdam: EVERWENTLIBRARY Daily Thoughts from West Side of S...:
everwentlibrary
Daily Thoughts from West Side of Sayama Hills, Tokyo 4 May 2011 Yesterday, I took a stroll with my wife to...
Daily Thoughts from West Side of Sayama Hills, Tokyo 4 May 2011 Yesterday, I took a stroll with my wife to...
Subscribe to:
Posts (Atom)