A

1 Language has meaning. At first, meaning was verified by ideogram.

Refer to the following papers.

2 For verification of ideogram, several concepts were presented.

Refer to the following papers.

3 From verification of ideogram, several regulations of language were led.

Refer to the following papers.

4 From regulations, automaton of language were presented.

Refer to the following papers.

5 Automaton of language led me to algebraic phase of language.

Refer to the following papers.

6 From algebraic verification, Quantum Linguistics was presented.

Refer to the following papers.

7 From Quantum Linguistics, new perspective is opened.

Refer to the following paper groups.

Especially the next papers are kernels.

8 As the result of verification, symmetrical and unsymmetrical structures emerged from topological consideration.

Refer to the following papers.

B

9 Now space is expressed by

**string**and**.***i*-string
Refer to the following paper’s items.

10 Here dimensional space that contains language is called

**world**and minus dimensional world that contains language is called anti-world, also called**.***i-*world
Refer to the following paper’s items.

Also refer to the following paper’s items.

Also refer to the following paper’s concept.

11 World’s dimensions are confirmed by string figure’s freedom but i-world’s confirmation is difficult by figure.

Refer to the following paper’s items.

12 In 4-dimensional space, separated two knotted strings are freely connected each other.

Refer to the following paper’s items.

13 In 4-dimensional world, problem that is difficult to solve in 3-dimensional world is solved by having free perspective and operation for solution. In other word, 4-dimensional world verifies and solves 3-dimensional world’s all occurrences. This operation in 4-dimensional world is now called

**true**.
Refer to the following early works.

Also refer to the following papers.

14 In Minus 4-dimensional world, problem that is difficult to solve in minus 3-dimensional world is solved by inductive analogy. This operation in minus 4-dimensional world is now called

**false**.
15 By minus 4-dimensional world’s false operation, i-world in which from minus 1-dimensional to minus 3-dimensional operations are exist, is classified.

16 Minus 3-dimensional world belongs to false phenomena that are not able to solve. For example, “His saying is not true.”

17 In minus 4-dimensional world, “his saying” is verified. When “his saying” is “not true”, “his saying” belongs to

**false**.
18 What belongs to

**true and false**is clearly classified by world’s dimension.
C

19

**World and i-world**that contain**true and false**are on cut-tube-ring that is generated from torus. Torus and plane are topologically same but not same at the point of continuity.
Refer to the following paper’s items.

20 Language that is expressed by torus and cut-tube-ring becomes discreteness for making dimension as space.

21

**Real world’s continuity**and**language’s world’s discreteness**is related to**substantiality of language**.
Refer to the following papers.

22

**Torus**,**tube-ring**,**string**and**group**is the kernel for substantiality of language.
23

**From Brouwer’s fixed point theorem, closed unitary sphere has fixed point. But torus has not fixed point.**
24

**Tube-ring also has not fixed point.****When solid tube-ring is cut at the maximum diameter, there emerges a new ring**that has inner and outer rings and a hollow ring at the center of cross section. Inner ring and outer ring are separated by hollow.**Now flow fluidities at inner and outer rings.**If**inner and outer flows have opposite directions**,**new ring has fixed point**somewhere at two fluidities come into contact.
25 If two directions of fluidities in the new ring are models of language’s essential elements, fixed point is seemed to be a kernel of language. Now I suppose that inner fluidity is

**frame**and outer is**transmission**. At the fixed point, there generates**language**that contains frame and transmission at the same time.
Refer to the following paper.

26 True- false, symmetry and continuity on language will be verified from fixed point theorem that should lead me to the new frontier of

**linguistic****universals**.**Tokyo July 25, 2006**

**Tokyo July 28, 2006 Added**

**Relevant to the theme <Freedom and String> at Oze July 17, 2006**

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