1 Sentence of language is expressed by plane or torus.

2 Torus is regarded topologically same as plane of Hilbert space.

3 Torus is a closed space.

4 On thinking about function space in torus space, infinite parallel translation can not be done for its closed space condition.

5

**From viewpoint of quantum mechanics, torus is limited to discrete parallel translation for periodic condition of wave function.**
6 Word of language is expressed by lineation of plane or torus.

7 Lineation consists of quanta that are entangled conditions.

8 Quantum and quanta carry semantic information on language.

9 What quantum becomes element of language is called

**quantum language**. The abbreviation is**QL**.
10

**Quantum language has discrete parallel translation on torus.**
11

**Quantum language breaks continuous symmetry.**
12

**Quantum language has discrete symmetry.**
13

**Quantum language clearly shows the spatial structure on language.**
14

**Language that consists of substantiality, abbreviated to SL, is topologically same between plane and torus, but is not symmetrically same between the two.**
15

**Breaking spatial symmetry on torus from plane indicates the existence of language’s classification.**
16

**Substantial language classifies two. One has continuous symmetry. The other has discrete symmetry.**
17

**Language has hierarchy that contains continuity at underlayer and discreteness at upperlayer.**
18

**Hierarchy of language is useful to semantic analysis. For instance, notion that contains truth-fault value is analyzed from hierarchy of language in which truth is treated to give continuity and discreteness but fault is treated to give only discreteness.**
19 One assumption is now adopted that natural language has no layer and super-language containing truth-fault value and so forth has layer.

20

**Natural language is finally contained to substantial language for the latter’s comprehensiveness.**
21 Quantum language that has be clearly recognized the spatial structure will advance the research of language one step profoundly.

**Tokyo June 11, 2006**

Sekinan Research Field of Language

www.sekinan.org

Sekinan Research Field of Language

www.sekinan.org

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